Tension control algorithms used in electrical wire manufacturing processes: a systematic review

Abstract

Most manufactured electrical cables suffer from reductions in their physical, mechanical and electrical properties. These setbacks are mainly attributed to the improper control of wire tension during the cable manufacturing process. Hence, this paper systematically reviewed different control algorithms involved in controlling tension in moving webs, which include conventional control, advanced control, observer-based control, artificial intelligence-based control and hybrid control techniques. Thus, the review provided information about existing tension control techniques in moving webs, including their strengths and weaknesses. It was observed in this review that although a significant research effort has been made on web tension control systems, a thorough literature review is still lacking. It was concluded that controller optimisation using hybrid control algorithms is gaining popularity in web tension control due to their improved control response. Hence, its application in wire tension control can better help cable manufacturers improve the quality of manufactured cables.

Keywords:

• Cable manufacturing
• control algorithms
• motor drive
• parameter variations
• tension control

REVIEWING EDITOR:

• Qingsong Ai, Wuhan University of Technology, China

SUBJECTS:

• Mechanical Engineering
• Manufacturing Engineering
• Systems & Control Engineering
• Electrical & Electronic Engineering

1. Introduction

Electrical cables are produced worldwide due to their widespread utilization. They are made of materials that are fire and electric shock proof, resistant to thermal effects, oil, water and other factors. Essentially, a conductor is a broad term for a wire that is not separated by coating or insulation, whereas a wire is a single conductor that is typically made of copper or aluminum. Similar to wires, cables are collections of two or more conductors, either solid or stranded, that are twisted, wrapped or otherwise bound together with or without insulation and are utilized for the transmission of electrical or telecommunication signals (Ofosu et al., 2020). Electrical cables are important because they are the heart of the world; they are used to carry electrical signals and they provide the foundation on which electrical devices can execute any work. Access to electricity will be useless without electrical cables and life will be unpleasant for humans (Ofosu et al., 2020; Thue, 2012).

A variety of manufacturing techniques are necessary to produce electrical cables that are durable, efficient and high-quality. One of these crucial production steps is the drawing process, which involves pulling or drawing a copper or aluminum rod through a series of progressively smaller synthetic diamond or tungsten carbide dies housed in mild steel casing to give extra strength and toughness to the dies. Drawing is done to reduce the rod to a wire of the desired diameter that has an excellent surface finish, closely controlled dimensions and improved mechanical properties such as strength and hardness (Abdul-Kareem & Alyaa, 2015; Kasper, 2010; Sudhakar & Shweta, 2019; Tasevski & Petreski, 2016). The drawing process of a typical copper rod consists of four main stages. These include unwinding, drawing, annealing and rewinding. In the unwinding stage, the thick copper rod is unwound at the payoff drive to the diesing chamber. In the diesing chamber, the thick copper wire is passed through a series of progressively smaller dies under high pressure to produce the final wire diameter. In the diesing chamber, lubricant such as oil is circulated in order to reduce friction and tear of the wire. It also has rollers to guide the movement of the wire form the diesing chamber to the annealing chamber.

In the annealing chamber, the drawn copper wire is subjected to a specified heat treatment in order to soften the wire to improve upon its malleability because drawing copper wires increases the temper of the wire as the wire is drawn down to the required diameter (Larsson et al., 2018; Wright, 2010). Care should be taken to ensure that the heat from the annealing process is not above the specified as excessive heat can result is stretching of the wire hence further reducing its diameter.

During the wire drawing process, the diameter of wire at the pay-off roll decrease in size as the machines run. As a result, to keep the line speed steady, the pay-off drive accelerates when the radius gets smaller. In the same instance, the take-up roll spool radius increases, altering the speed and tension of the take-up drive. To overcome this problem a dancer system is used to detect and correct the undesirable tension deviation (Damour, 2013; Duong et al., 2015; Hyunkyoo & Kee-Hyun, 2018; Jorg & Brunner, 2008). With the assistance of the traverse, the drawn wire is uniformly coiled unto a bobbin at the take-up. Information on the length of wire coiled onto the bobbin is given by a counter mounted on the moving web near the dancer. A schematic diagram of the copper wire drawing process is shown in Figure 1.

Figure 1. Copper wire drawing process schematic diagram.

where, d₁ is original diameter of wire before drawing, d₂ is actual diameter of wire after drawing, V₀=V₁ is line speed of pay-off or capstan, V₂ is line speed of take up, T₀=T₁ is torque of payoff or capstan, T₂ is torque of take up, ω₂ is angular speed of take-up drive.

After the drawing stage, the wires are bundled together to form a cable, which is then extruded with insulating polymers like Cross-Linked Polyethylene, Polyethylene, and Polyvinyl Chloride (Mahto & Murmu, 2015). Extrusion is a crucial stage in the manufacturing process because it prevents copper losses in cables and guards the conductor against physical harm and environmental dangers. After extrusion, the final product after passing the quality assurance tests is prepared for the market for consumption.

In the cable manufacturing industry, one of the most crucial factors to consider is the final resistance or diameter of the wire whose value should not deviate significantly from the norm after production. That is, the tension of the wire should be kept constant during unwinding and winding stages of the cable production process so that there is minimal change in the wire’s diameter or cross-sectional area. This is because variation in the final resistance of the drawn wire as a result of an increase in length causes a commensurate reduction in the wire’s diameter or cross-sectional area as depicted in Equation (1)(1) $$R=\rho \frac{l}{A}$$(1) . This causes heat generation when rated current flows through the manufactured cable. The consequence of this phenomenon is insulation failure and subsequently fire outbreaks that occur at homes, market places and industries killing innocent lives and destroying properties running into millions of dollars (Hou et al., 2018; Kang & Kee-Hyun, 2018). (1) $$R=\rho \frac{l}{A}$$(1) where, R is resistance at 20 °C (Ω), ρ is the conductor’s bulk resistivity (Ωmm²/m), l is conductor’s length (m), A is cross-sectional area (mm²).

Research has shown that the major factor that causes variation in the final resistance during the drawing process of the cable manufacturing process is improper tension control as a result of torque or speed variation due to changes in roll diameter between the payoff drive and the take-up drive and changing line speed in the drawing stage of the cable production process (Duong et al., 2015; Jie-Shiou et al., 2018; Park & Lee, 2018).

This is due to the fact that most cable manufacturing companies use primitive means to control tension during the cable manufacturing process, such as mechanical spring-operated strap brakes or Programmable Logic Controllers (PLCs) with conventional controllers like Proportional Integral Derivative (PID), Proportional Derivative (PD) and Proportional Integral (PI). However, due to the oscillatory response, overshoots, large values in the rise and settling times and difficulties in the presence of non-linearities, these conventional controllers have difficulties in keeping the tension within acceptable limits. Once more, the PID gains must be adjusted whenever there is a change in tension response.

However, because the PID gains remain constant during the process, they are unable to achieve strong dynamic performance across a variety of web operating conditions (Mahto & Murmu, 2015). This consequently results in tension variation in the wire during the manufacturing process.

The phenomenon of improper tension control results in wire breakage and inconsistent thickness due to the stretching of wire above its tensile strength. This scenario causes frequent stoppage of the machines resulting in the production of scraps which is a major challenge for most electrical cable manufacturing industries because they lose huge quantity of money or profit as a result of material waste (Hou et al., 2018; Huang et al., 2021; Kang & Kee-Hyun, 2018; Prabhakar et al., 2007). As a result, to increase the quality of the manufactured cable, it is important to have a method in place to control tension.

To overcome this problem, a tension control loop with load cell or position control loop with dancer system is used to detect and correct the undesirable tension deviation by sending tension variations from the web of material to the tension controller,

which controls the output of the speed or torque drive, brake or clutch to maintain the required tension level, on a continuous basis. This guarantees that the tension is constant throughout the whole production process (Dwivedula et al., 2006; Hyunkyoo & Kee-Hyun, 2018; Jie-Shiou et al., 2018; Jorg & Brunner, 2008; Raul & Pagilla, 2015).

In practice, dancer control methods are frequently employed in cable manufacturing industries to regulate cable tension, particularly during the unwinding and winding phases of the cable drawing processes. A potentiometer is applied to the dancer to achieve a motor speed adjustment. The potentiometer measures the dancer’s displacement and compares it to the reference or setpoint tension. Consequently, constant dancer position and constant tension are maintained across variations in line speed, motor loading and roll diameter (Hanafi et al., 2015; Hyunkyoo & Kee-Hyun, 2018; Zheng, 2018).

Dancer systems can be broadly divided into active and passive dancers, which can be differentiated by an external actuator. While the passive dancer is made up of a dancer roll, spring and damper without an external actuator, the active dancer uses a potentiometer to determine the position of the dancer roll and an external actuator to force the roll in order to control tension disturbances. However, the hybrid dancer, which combines passive and active dancer elements, is also used to indirectly control tension disturbances. Its characteristics distinguish it from a passive or active dancer. The dancer rollers are free to oscillate in one direction regardless of the loading and they are divided into translational and rotational dancers based on their degree of freedom. Depending on the situation, a process or space restriction may be used to determine the type of dancer for a particular application (Jie-Shiou et al., 2018).

Contrarily, load cell tension measurement makes use of strain gauges to determine the pull force exerted on an idler roll as a result of tension, allowing for the implementation of corrective control measures (Damour, 2013; Raul & Pagilla, 2011).

Several factors may necessitate the choice for a particular type of dancer or load cell for tension measurement. Due to the dancer arm’s limited rotational range and ability to handle small magnitudes of variation, the passive dancer offers effective tension regulation for low-speed web lines. Active dancers, on the other hand, offer accurate tension control throughout a broad frequency range of disturbances. The dynamics of the actuator for the dancer’s roll, however, limit the performance of an active dancer. Active dancer systems typically function poorly in dynamic conditions due to the actuator’s delayed response. Additionally, it is more expensive and more challenging to deploy. Consequently, an active dancer is rarely used for tension measurement (Lee et al., 2009). Furthermore, the installation of load cells or dancers leads to increased economic costs in the design of the machine. Additionally, these tension sensors are sensitive to appropriate alignment and balancing, which reduces system reliability and increases the complexity of web systems. They also occupy space and require frequent maintenance and calibration (Lee et al., 2009). Moreover, for load cell, a large filter is required for smoothing the actual signal in order to eliminate the noise signal consequently resulting in a slow response of the sensor (Wolfermann, 1995). Again, the dancer control circuit also has a slow response because there is an inherent time delay in the position signal since the position control circuit can only respond after a movement of the dancer roll (Raul et al., 2015; Raul & Pagilla, 2015; Xie et al., 2017; Yuan-Yu, 2013).

As a result, a common technique for estimating the tension of the web is the deployment of observers or estimators, which depends on the system model (Cheng et al., 2005). A tension observer offers a reliable, non-contact way to measure tension. Since it depends on the dynamical model, it is essential to create a precise dynamic model in order to obtain good observer performance. The observer algorithms are commonly accomplished by control code, making them more dependable than sensors and easily adaptable to other web materials or web tension control systems (Li et al., 2021; Lynch et al., 2004; Valenzuela et al., 2006).

Ultimately, the main contribution of this study is the comprehensive review and comparison of the various control methods employed in tension control of moving webs. It was also observed in this review that although a significant research effort has been made on web tension control systems, a thorough literature review is still lacking. This paper, to the best of the authors’ knowledge, is the first to conduct a survey on the various control algorithms in electrical wire tension control. It was also evident from the related works that although many control methods have been applied for tension control applications, a novel control method using recent hybrid algorithms has not been employed in electrical cable manufacturing tension control. Hence, future work will employ these novel control approaches and compare their responses to that of the other controllers. It is anticipated that such a comprehensive review will be helpful to scholars researching on tension control of moving webs.

2. System model of the wire manufacturing process

The tension control system of the unwinding and the winding stages of a typical wire drawing process consists of the pay-off drive, dancer, take-up drive and gear arrangements coupled with a center drive mechanism (Kang et al., 2011; Liu et al., 2020). The conceptual diagram of the wire drawing process is depicted in Figure 2. The steady-state and dynamic behavior of the web in the longitudinal or machine direction is influenced by the physical properties of the wire and the dynamic characteristics of the mechanical parts. The gear transmission system is coupled to the payoff and take-up rollers, which serve as inputs. By properly controlling the take-up and payoff drive velocities, a stable wire tension is maintained. A dancer with a spring and damper setup coupled to a potentiometer that serves as the output is used to measure the wire tension. In essence, the web material, drive train and dancer are the three categories into which the mathematical model of the wire tension control system may be divided. The tangential velocities of the payoff and take-up rollers and the dancer are related via the web material or wire. Three laws control this interaction (Koc et al., 2002; Larsen & Jenson, 2007; Sakamoto & Fujino, 1995). These include Hooke’s law, which models the elasticity of the wire; Coulomb’s law, which gives the tension variation due to friction and the contact force between wire and rollers; and Mass Conservation law, which expresses the cross-coupling between wire velocity and strain or gives the dancer’s position and velocity variation due to the wire tension. In this paper, mathematical modeling of the payoff and take-up stages of the wire drawing process, including the dancer dynamics, is considered since in cable production lines, dancer control methods are often used to regulate wire tension (Hanafi et al., 2015).

Figure 2. Schematic diagram of the wire drawing process with payoff, take-up and dancer mechanism.

where, M1 is drawing motor, M2 is take-up motor, C1-C5 are capstans, G1 is gear box, D1-D5 are drawing dies, R1, R2 are dancer rolls.

The dynamic modeling of the pay-off and the take-up of the wire drawing process during cable manufacturing is as discussed as follows. The transfer function of the dynamics of the web material which is the wire is as shown in Equation (2)(2) $$H_{\mathit{\text{wire}}}=\frac{T}{-V_1+V_2-2V_d}=\frac{\frac{\mathit{\text{EA}}}{L_N}+\frac{\mathit{\text{CAs}}}{L_N}}{s+\frac{V_1}{L_N}}$$(2) (Larsen & Jenson, 2007; Valenzuela et al., 2002). (2) $$H_{\mathit{\text{wire}}}=\frac{T}{-V_1+V_2-2V_d}=\frac{\frac{\mathit{\text{EA}}}{L_N}+\frac{\mathit{\text{CAs}}}{L_N}}{s+\frac{V_1}{L_N}}$$(2) where, T is wire tension (N), V₁ is velocity of pay-off roll (m/s), V₂ is velocity of take-up roll (m/s), V_d is velocity of dancer (m/s), E is Young’s modulus of wire (N/m), A is cross-sectional area of the web (m²), L_N is nominal length of wire (m), C is damping ratio of wire (Pa/s)

The motor and gear that convert the angular rotation of the motor rotor to the wire’s velocity make up the drive train model. It creates a link between the motor’s input torque and output angular velocity as shown in Equation (3)(3) $$\frac{{\omega }_m}{{\tau }_m-{\tau }_e}=\frac{1}{J_{m}s+B_m}$$(3) . (3) $$\frac{{\omega }_m}{{\tau }_m-{\tau }_e}=\frac{1}{J_{m}s+B_m}$$(3)

ω_m is motor angular velocity (rads/sec), τ_m is motor mechanical torque (Nm), τ_e is electromagnetic torque of the motor (Nm), J_m is moment of inertial of the motor (Nm²), B_m is viscous friction constant of motor (Nm.s/rad)

The tangential velocity of the roll or wire is created by the motor’s angular velocity depicted in Equation (4)(4) $$V_2=\frac{R{\omega }_m}{N_g}$$(4) The wire speed is influenced by the roll’s radius, the motor’s rotating speed and the gear ratio. (4) $$V_2=\frac{R{\omega }_m}{N_g}$$(4) where, R is radius of roll, N_g is gear ratio of motor.

Newton’s second law of motion is used to describe the mechanics of the dancer’s roll and the forces that are applied, such as friction and a connected spring that is modeled as an ideal spring running parallel to a viscous damper. The equation of motion of the dancer is as shown in Equation (5)(5) $$2T-F_w-F_L=(M_d{s}^2+B_{d}s+K_d)d$$(5) . (5) $$2T-F_w-F_L=(M_d{s}^2+B_{d}s+K_d)d$$(5) where, F_w is dancer exerting force, F_L is the dancer’s spring loading, M_d is dancer’s mass, B_d is dancer’s coefficient of friction, K_d is dancer’s spring constant, d is position of dancer.

The block representation of the dynamic modeling of the system using Equations (2)–(5) is shown in Figure 3. It should be noted that certain assumptions are made in the system modeling as reported in (Koc et al., 2000; Larsen & Jenson, 2007; Sakamoto & Fujino, 1995; Shin, 1991).

Figure 3. Complete system model of wire tension system with dancer dynamics.

3. Control techniques in tension control systems

With the need to increase productivity and performance in the cable manufacturing industry, an efficient controller design is needed to transmit the web at a specified speed while keeping its tension within tolerable limits under a wide range of dynamic situations such as variances in roll diameter, web properties and anomalies in speed (Benlatreche et al., 2006; Gassmann & Knittel, 2007; Wolfermann, 1995). In the literature, many different control algorithms for web tension control have been proposed. Basically, the control algorithm can be classified as open loop, closed loop or manual control. In most cases, closed loop control, though expensive, is the preferable method because it provides extremely accurate and precise tension control during both transient and steady-state operating conditions of the manufacturing process (Imamura et al., 2003; Ofosu et al., 2023).

As a result, web tension control design has gained a lot of interest from open loop control such as mechanical or manual control to closed loop control systems such as conventional PID control, advanced control, observer-based control, artificial intelligence control and hybrid control methods (Claveau et al., 2005; Gassmann et al., 2012; Haripriya et al., 2016; 2019; Jeetae, 2006; Knittel et al., 2003; Lin, 2003; Muthukumar et al., 2015; Ofosu et al., 2020; Prabhakar et al., 2007; Sakamoto & Izunihara, 1997; Tan et al., 2014; Wang et al., 2008; Xiong et al., 2012; Zhao & Ren, 2017) as shown in Figure 4. The implementation of each of these control algorithms is based on centralized, decentralized and overlapping control architecture (Shanhui et al., 2013; Koc et al., 2002). Typically, centralized control is used on web systems with three or fewer motors (Baumgart & Pao, 2007; Claveau et al., 2008; Koc et al., 2002; Valenzuela et al., 2012). However, because industrial web control systems frequently incorporate several drive rolls in reality, they are typically viewed as large-scale systems, for which centralized control is inconvenient. The decentralized method of control provides an easy approach to governing an entire system by creating a controller for each subsystem without requiring communication between them (Askari et al., 2009; Knittel et al., 2006; Prabhakar et al., 2007; Raul et al., 2015; Raul & Pagilla, 2015). However, disregarding subsystem interconnections reduces decentralized control’s capacity to reject disturbances produced by neighboring subsystems. As a result, overlapping control techniques are employed to improve system anti-interference capabilities by utilizing subsystem interconnections (Benlatreche et al., 2006; Doghmane et al., 2015; Dou & Wang, 2010).

Figure 4. Schematic diagram of the control algorithms applied in tension control systems.

3.1. Mechanical tension control

According to Perduková et al. (2019), Imamura et al. (2003), Shankam and Vivek (2005) and Xiao-Ming et al. (2018), a great majority of wires are tensioned by mechanical means such as mechanical spring-operated strap brake, magnetic particle brake and electro-magnetic brake. These devices mostly comprise of mechanical parts such as pulleys, rollers and disc with no active sensors to measure the tension but passive elements such as feelers and springs. Simple structure and ease of use characterize the mechanical tension control. However, the control precision is poor and the tension value cannot be automatically adjusted due to the fact that tension control with a mechanical system is based on the subjectivity of the operator. This results in a loss of production and inferior quality. It is also characterized by high maintenance costs, low speed and low efficiency (Mayr et al., 2021; Pan et al., 2011; Zhang, 1982).

3.2. Conventional PID control

To address the shortcomings associated with the mechanical or manual control method, linear control techniques such as conventional PID controllers have been extensively employed to regulate the tension of moving web due to their inherent benefits such as simplicity, reduced computation load, ease of implementation and cost effectiveness in tension control when compared to the manual method (Li et al., 2016; 2021; Mahto & Murmu, 2015; Ofosu et al., 2016). Generally, a cascade PID control loop is usually employed for web tension regulation, in which the inner loop is used for speed control and the outer loop is used for tension control as shown in Figure 5 (Hou, 2001).

Figure 5. Tension control with PI controller.

PID control essentially employs the system model as a feedback control method. It calculates the error, which is the deviation of the desired setpoint from the measured process variable and modifies the control signal in accordance with the magnitude of the error signal. The PID control algorithm employs three different control methods. These include the proportional term, which pertains to the current offset; the integral term, which depends on the accumulation of previous errors; and the derivative term, which forecasts future offsets based on the process’s current change rate. A control signal is generated based on the weighted aggregate of these three actions described by the control law as shown in Equation (6)(6) $$u(t)=k_{p}e(t)+k_i{\int }_{-\infty }^{t}e(\tau )d\tau +k_d\frac{\mathit{\text{de}}}{\mathit{\text{dx}}}(t)$$(6) . Despite numerous advancements in PID controller design methodologies, the conventional Ziegler-Nichols approaches are still widely used for the tension control of moving webs. (6) $$u(t)=k_{p}e(t)+k_i{\int }_{-\infty }^{t}e(\tau )d\tau +k_d\frac{\mathit{\text{de}}}{\mathit{\text{dx}}}(t)$$(6)

where, $u(t)$ is control signal, $e(t)$ is error signal and $k_p,$ $k_i,$ $k_d$ are the proportional, integral and derivative gains, respectively

PID control methods has been applied severally to control web tension. In view of this, Kang and Lee (2008) suggested a Multi-Input Multi-Output (MIMO) tension modeling and control system for a gravure printing machine. An improved gravure printing machine’s nonlinear MIMO web-tension model was created first, with the length of span varying over time rather than fixed. The web span length varied over time because of the turret movements of machines used for unwinding and rewinding and the displacement of the dancer. Then, using MATLAB/Simulink software, a feedback control system based on PI control was implemented and the performance of web-tension control was investigated at steady-state and transient conditions. According to simulation results, the control system had resonance at the given parameter setting at around 4 m/s. The simulation results, on the other hand, were not experimentally verified. Zhu, (2010) researched on precise tension control of fiber winding and placement machine using closed-loop tension control system built with PIC16F877A MCU, digital AC servo motor as actuator and tension sensor for feedback. MATLAB/Simulink simulations were used to evaluate the system’s effectiveness with PID control. The results revealed that the system’s static slip and instability under constant speed and constant tension conditions met the requirements for tension control. Hyun-Kyoo et al. (2011) suggested a hybrid pendulum dancer-based tension regulator for a roll-to-roll printing system. This novel hybrid pendulum dancer was implemented to overcome the challenges of the active and passive dancers. First, a model of the pendulum dancer was created. A potentiometer was used to measure the dancer’s arm angle, which was filtered with a first-order low-pass filter. Using a PI-controller to indirectly adjust the tension, the dancer’s arm position was controlled by adjusting the in-feeding roll’s speed. The reliability and stability of the suggested hybrid pendulum dancer in attenuating tension disruptions were demonstrated by simulation and experimental results.

Raul and Pagilla (2011) modeled and controlled the web tension with a pendulum dancer and compared its performance with that of a load cell. Time and frequency response analyses for two control schemes were used to test the developed model’s efficacy to determine resonant frequencies. The first was an outer-loop tension controller that was based on dancer position feedback, while the second was done using a roller-mounted loadcell with tension feedback. The frequency domain tests were carried out through the injection of disturbance, which is sinusoidal to the S-wrap roller, whereas the time domain analysis was performed using a ramp or step change in velocity. The load-cell and dancer feedback were controlled using normalizing gains developed from a PI tension controller. Simulation and experimental results showed that, due to the dancer’s ability to filter low-frequency disturbances, tension changes with the dancer were substantially smaller than with the load cell within a low frequency spectrum of 0 Hz to 3 Hz. Yang (2012) established a precise dynamical model to characterize tension and proposed a tension control strategy for a shaftless printing web press. A complete winding tension simulation model consisting of several sub-modules such as the servo motor module, winding tension module, taper tension reference value module and diameter real-time calculation module was simulated using MATLAB/Simulink software. A closed-loop PID double cascaded controller was used to control the tension. Simulated results were shown by modifying the slave control loop’s and master control loop’s parameters. The results indicated that the controller could track the speed and tension reference effectively. However, the control performance could be improved with an adaptive controller.

Tasevski et al. (2014) modeled in d-q reference frame and simulated an actuator consisting of AC induction motor with vector control in MATLAB/Simulink software environment for a wire drawing machine. The tension in the wire was measured using a dancer arm as a sensor. To keep the tension in the wire constant, a PID controller and a variable frequency controller were employed to control the actuator anytime the dancer signal error changed relative to the preset tension. Based on the simulation results, the system was able to precisely control the tension. Cazac and Nuca (Cazac & Nuca, 2015) developed a mathematical model for a wire drawing and winding mechanism employing an asynchronous motor drive system with vector control based on the linear velocity and moment of inertia of the wire. A pneumatic cylinder supplying pressurized airflow through a pressure regulator regulated the tension force of the wire drawing machine. A frequency converter using PID tuning was used for controlling the speed loop of the wire drawing machine. Results obtained revealed that the suggested strategy demonstrated optimum efficiency and stability in wire tension control over a wide range of operating speeds while avoiding mechanical shocks that could cause wire breaks.

Giannoccaro et al. (2016) improved a web processing system’s control response by automatically adjusting the PI parameter values in each span. Using an overlapping decomposition, the whole control system was formulated as a decentralized system made up of four drive systems. The experimental results showed that by adopting a setpoint ramp profile, the proposed technique ensured effective web velocity control from a standstill to a high speed of 2 m/s. It also ensured that the tension forces were well controlled and that dangerous tension values were never produced.

The error dynamic model and reference control input was used by Hailiang et al. (2016) to provide a resilient decentralized control technique for web-handling systems. The necessary condition for the decentralized controller’s existence was formulated using Linear Matrix Inequalities (LMIs). The control technique was then applied to a web-winding system with three-motors. The controller was shown to be effective at suppressing tension variations in simulation and experimental tests using a PID controller. The controller, however, was unable to adequately limit the disturbances triggered by reference value changes. Li et al. (2016) created a mechanism for controlling wire tension for a High Speed-Wire Electrical Discharge Machine (HS-WEDM). The control system was mathematically modeled using a tension sensor, linear motion platform and a DC servo motor. The PID parameters were then calculated using a simulation model that included the transfer function of the system. The effectiveness of the wire tension control system was tested using simulation-based validation and experiments. The results showed that the variation in wire tension value was reduced by nearly half. Furthermore, the workpiece surface roughness with the wire tension control system was 0.6 μm lower than the workpiece without any control.

Zhewei et al. (2020) used a microcontroller unit with a PID control algorithm for ultrafine enameled wire winding tension control. The Ziegler and Nichols method were used to calculate the PID gains. The angular sensor used was an incremental photoelectric encoder and the actuator was an AC servo motor. To translate changes in tension to variations in rod swing angle, a rod-spring mechanism was utilized as a dancer. The system’s viability was tested via simulation using MATLAB/Simulink software. A prototype was also made and tested on enameled wires, which were ultra-fine and had a diameter of 0.08 mm. The findings revealed that the controller performed effectively in both the transient and steady states, as well as having good anti-interference capacity. However, the PID controller gains had to be set manually, which was a huge issue.

Although conventional PID controllers have been widely used to regulate the tension of moving webs, their main disadvantage is that they are unsuitable for complex, nonlinear, multivariable coupled systems, uncertain and time-varying systems such as the dynamic nature of wire tension control. This is because the PID gains remain constant throughout the process, making it unable to achieve strong dynamic performance under a variety of web operating situations. They are also sluggish, with significant overshoots and extended settling times. Moreover, the conventional PID controller adopts a Single-Input Single-Output (SISO) system, resulting in undesirable deviations when used in Multiple-Input Multiple-Output systems such as the wire tension control (Abjadi et al., 2009; Mahto & Murmu, 2015; Mirinejad et al., 2012; Nishida et al., 2013; Ofosu et al., 2016).

Therefore, recent research is focusing on modern control strategies such as advanced control, observer-based control, artificial intelligence control and hybrid control to enhance the performance of PID controllers or provide a better alternative to the web tension control. Some of these modern control strategies include Genetic Algorithm (GA), Artificial Neural Network (ANN), fuzzy logic, PI-based Particle Swarm Optimisation (PI-PSO), Sliding Mode Control (SMC), H-Infinity Control, Adaptive Backstepping Algorithm (ABA), Active Disturbance Rejection Controller (ADRC) with state estimators and observers (Chu et al., 2020; Sanz et al., 2017; Xiao-Ming et al., 2018). These control systems have demonstrated superior control response in the regulation of tension on moving webs, including greater responsiveness, decreased computational load and improved performance in the time-varying and nonlinear nature of the web during transient and steady-state operations. Hence, maintaining the stability of the system under different reference tensions and transport speeds (Duc et al., 2020; Zhang et al., 2017). As indicated, there are several modern control algorithms employed for the regulation of web tension. However, the most commonly employed techniques are reviewed in this section.

3.3. Advanced control techniques

Advanced control techniques have been used extensively in the tension control of webs and have achieved the desired control response to ensure that the product quality meets the required quality assurance test, unlike the conventional PID control. Nonlinear advanced control techniques typically employ the system’s dynamical model to provide an effective control action. The most commonly used advanced control techniques in web tension control systems are model predictive control, adaptive control, optimal control and robust control (Perera et al., 2014).

3.3.1. Model predictive control

Model Predictive Control (MPC) is a multivariable control technique mostly used in web tension control. It makes predictions about the system’s future output using both past data and future inputs. MPC ensures that the tension values are kept at the desired limits by creating an appropriate control vector using the system’s model to minimize a defined cost function across the prediction horizon under constraints and disturbances (Candanedo & Athienitis, 2011; Ma et al., 2011; Prívara et al., 2011; Rehrl & Horn, 2011). While solving the optimization problem online, only the first value of the computed control sequence is used. This predictive control process is repeated with updated states at the subsequent time step. This controller can therefore adjust the tension within the specified bounds and is resilient to both time-varying systems and disturbances. There are no strict limitations on the model structure and model identification is the process’s bottleneck. The MPC could be designed using any form of model, including white box, black box and grey box models (Prívara et al., 2011). But for the nonlinear time varying nature of the wire tension control, grey-box and other data-driven models are employed. However, it requires quality measured data for the model to be accurate which increases the complexity of the model. Data driven models can be created utilizing support vector machines, fuzzy logic, artificial neural networks and other statistical models such as Autoregressive Moving Average (ARMA). Because the MPC makes it easy to establish a control strategy in the event of uncertainty, its implementation in tension control systems is advantageous. Additionally, it offers enhanced performance in terms of resistance to disturbances, consistency of performance under varying situations and improved transient response. However, MPC involves online optimization, which necessitates reasonably powerful processing devices for real-time applications. This raises financial issues and MPC suffers from model error-related performance degradation (Pourseif & Mohajeri, 2020; Široký et al., 2011).

Figure 6 illustrates an MPC circuit’s basic design. The desired progression of the plant output y[k] is defined by a reference trajectory, r[k]. A plant model is used to estimate the process behavior based on the control variable u[k]'s future values. The functional relationship between u[k] and y[k] in the future is revealed by the plant output forecast. A state estimator calculates the states $\widehat{x}[k]$ at each time step and gives an estimated output $\widehat{y}[k]$ (Camacho & Bordons, 2007).

Figure 6. Model predictive controller basic circuit design.

Model predictive control is described by the control law shown in Equation (7)(7) $$J(\Delta u[k])={\sum _{J=N_1}^{N_2}\left[r[k+j]-\widehat{y}[k+j]\right]}^2+\lambda \cdot \sum _{j=0}^{N_u}\Delta u^2[k+j]$$(7) (Gerngrob et al., 2020). (7) $$J(\Delta u[k])={\sum _{J=N_1}^{N_2}\left[r[k+j]-\widehat{y}[k+j]\right]}^2+\lambda \cdot \sum _{j=0}^{N_u}\Delta u^2[k+j]$$(7) where, $J(\Delta u[k])$ are the estimated variances between the reference value r[k] and the estimated plant output $\widehat{y}[k]$ within the forecasting horizon j = N₁ … N₁ and adjustments to the control variable $\Delta u[k]$ in the horizon of control j = 0…N_u, the control variable $u[k]$ is determined by adding together the differences $\Delta u[k],$ the relevance of the changes $u[k]$ is weighed by $\lambda .$

The application of MPC was employed by Gerngrob et al. (2020) for nozzle exit wire tension control in a needle winding process. Wire tension at the nozzle outlet was regulated with an MPC approach to prevent loose windings, with the wire tension calculated by an Extended-Kalman-Filter (EKF). Dynamically altering the reference wire tensions while winding serves to validate the controller. To enable a real-time calculation, a strategy based on the linearization of the individual nonlinearities was chosen. The MPC when compared with PID control provided an improved tension regulation when uncertainties and disturbances are present. However, model predictive control relies on process models for an accurate tension regulation which are challenging to fulfill in a web system.

Active dancers were utilized by Yuet (2002) to provide a periodic attenuation of tension disturbances in web process lines. An active dancer with a hydraulic actuator was first mathematically modeled. The active dancer’s Self-Tuning Controller (STC) was developed and tested against an Internal Model Controller (IMC) and a PI controller. Finally, the active dancer was tested. In terms of decreasing tension disturbances, the PI controller and IMC outperformed the STC. Kuppuswamy (2004) looked at passive and active dancers for intermittent tension fluctuation suppression in web processing. Using web dynamic equations and the concept of gas-springs for passive dancers, a mathematical model for active and passive dancers was initially established. Extensive experiments were undertaken to assess the performance of both active and passive dancers on disturbance attenuation. According to experimental results, the active dancer outperformed the passive dancer when subjected to high-frequency periodic disturbances utilizing an internal model controller.

Muthukumar et al. (2016) presented an Adaptive Model Predictive Controller (AMPC) for the paper industry’s web transport system, taking into account the variations of the web radius with the passage of time. An online optimization technique, a prediction model and a parameter estimation block made up the controller design. With an estimation error of 0.4%, the parameter estimation block used the variables from the web transport system to estimate the changes in web radius. At each time epoch, the prediction model was updated to account for the parametric variations using the estimated web radius. With regard to the physical and operational constraints, an online optimization method was used to provide the best possible control input. The performance of AMPC was compared to that of traditional MPC to confirm the performance improvement it had achieved. The findings demonstrated that AMPC could efficiently manage dynamic changes with a 6% improvement in integrity of the material and a 50.5% boost in quality of material. Additionally, the AMPC controller’s performance in controlling web tension outperformed traditional MPC by up to 4.2%.

3.3.2. Optimal control method

Optimal control techniques a class on nonlinear control are widely used in the area of wire or web tension regulation. In optimal control, control signals are formed to fulfill certain physical limitations and to extremize a selected performance criterion simultaneously (Becerra, 2008; Rui & Lingfeng, 2012). Generally, to employ an optimal controller for web tension regulation, the system’s mathematical model is required. Although optimal control is characterized by its rapid response, simple design and ease of implementation, its implementation is characterized by inherent complexity due to the lack of an effective analytical solution and poor robustness (Behrooz et al., 2018; Zulu & John, 2014). The most frequently used optical controller in web tension control is a Linear Quadratic Regulator (LQR) (Huang et al., 2022).

3.3.2.1. Linear quadradic regulator

Linear Quadradic Regulators (LQRs) are still employed in the regulation of web tension because they can govern dynamic systems that are complex. Although the LQR is only applicable to linear control systems, the linearization of nonlinear system dynamics has demonstrated that the application of LQR can improve control response (Huang et al., 2022; Xie et al., 2016). The LQR controller employs a series of mathematical techniques to provide an efficient controller that can accommodate external perturbations (Xie et al., 2016). In order for the controller to work at its best, the control input must be changed based on the condition of the system. This is accomplished by examining the modifications to the feedback signal that will impact the overall cost function J as indicated by Equation (8)(8) $$J=\underset{0}{\overset{\infty }{\int }}(x^T(t)\mathit{\text{Qx}}(t)+u^T(t)\mathit{\text{Ru}}(t))\mathit{\text{dt}}$$(8) . Hence, stability can be attained by controlling the control input and system states to minimize the cost function J. (8) $$J=\underset{0}{\overset{\infty }{\int }}(x^T(t)\mathit{\text{Qx}}(t)+u^T(t)\mathit{\text{Ru}}(t))\mathit{\text{dt}}$$(8) where $x\in {\mathbb{R}}^n$ and $u\in {\mathbb{R}}^m$ express the input vector and state variations, $Q\in {\mathbb{R}}^{n\times n}$ represents the state matrix of the system and $R\in {\mathbb{R}}^{m\times m}$ symbolizes the control signal matrix

In a tension control system, the desired state can be achieved by increasing the control input. Therefore, it is crucial to carefully choose the parameters for this controller to avoid having the system overshoot due to the control input (Saeed et al., 2015; Zulu & John, 2014).

Due to the robust stability of LQR, Park et al. (2001) employed LQR and a gain-scheduling technique to build an adaptive tension velocity controller for a winding process that compensates for the system’s time-varying parameters. The LQR theory was used because it was a good way to produce the system’s control variable with a number of control goals that contradict each other, such as tension and velocity. The controller was then utilized on an experimental winding machine. The closed loop system’s performance was validated by simulations and experiments, which revealed that at reasonably fast web speed, both speed and tension could be controlled under a narrow margin of error. Zheng (2018) presented an observer-based control system that uses a Linear Quadratic Regulator (LQR) to reduce registration error in roll-to-roll electronic fabrication. To create a full observer-based centralized Multiple Input Multiple Output (MIMO) controller, three observers were modeled and simulated: reduced order, extended Kalman filter, and unknown input disturbance observer. In comparison to the decentralized method, the MIMO centralized controller employing an unknown input observer displayed much better speed and tension reference tracking and lower registration error. However, the time lag aspect of the registration error model was not considered and centralized control suffers from huge computational costs for high-order systems.

Other optimal controllers were developed by Zinelabidine and Madjid (2018) where overlapping decomposition approach was used to enhance the reliability of a decentralized controller used in a longitudinal mechanism for winding webs. The system’s mathematical model was built using the inclusion or contraction concept. Furthermore, optimality constraints were added to address the larger-scale system’s optimal control challenge. A feedback decentralized controller was built with and without the proposed decomposition technique for a three-motor web machinery. Furthermore, simulation findings were provided with various input signals so as to generalize the utility of the suggested approach. The findings revealed the developed controller’s resilience in achieving the appropriate reference tension and velocity signals for the web winding motor system. However, a fuzzy state-feedback control system could increase the system’s performance. Chu et al. (2020) developed an efficient control technique for web winding mechanism to lessen tension surges during the acceleration phase. First, the inputs and equilibrium states for web winding mechanism powered by four motors were derived using Taylor expansion. The web winding system’s time-varying or unknown parameters were then used to create an interval matrix-based stable tension controller. The closed-loop system’s asymptotic stability was investigated using Lyapunov theory. Using MATLAB/Simulink software, simulations were run to test the efficiency of the designed controller. According to simulation results, the proposed controller surpassed the classical PID controller in relation to precision and robustness to system uncertainties.

3.3.3. Robust control

Robust control methods are designed to handle model uncertainty and system nonlinearity. It has been successfully used to cancel the disturbances in set point tracking because of the appealing characteristics of the robust control regarding external disturbances and model parameter uncertainty. Due to its weak tracking capacity, this method, while favorable in set point tracking and disturbance rejection, is not a good fit for tension regulation with significant fluctuations (Behrooz et al., 2018; Naidu & Rieger, 2014; Zulu & John, 2014). The most commonly used robust controllers in tension control are active disturbance rejection control, sliding mode, backstepping and $H\infty$ control.

3.3.3.1. Active disturbance rejection control

In the Active Disturbance Rejection Control (ADRC) method, any unknown dynamics and disturbances that are omitted by the usual plant characterization are included in a new state variable that is added to the system’s model. Using a state observer known as the Extended State Observer (ESO), the online measurement of this new state is carried out. Due to the fact that this control technique includes all uncertainties as an extended state variable, any modeling errors will not have an impact on the control mechanism. When the full knowledge of the system is not available, this method presents an intriguing solution due to its robustness against parameter changes, better adaptability and ability to reduce uncertainty (Han, 1998; Tan & Fu, 2015; Zhiqiang et al., 2018). Although ADRC has achieved much progress in control applications such as the web tension control, it is not suitable for systems with large time delay (Hongliang et al., 2016).

Figure 7 depicts the conceptual design of the ADRC (Tan & Fu, 2015). To obtain the desired response for the reference, the Tracking Differentiator (TD) is used. The Extended State Observer (ESO) is used to approximate the generalized disturbance and the plant output. The Nonlinear State Error Feedback (NLSEF), on the other hand, uses the error and its derivatives of various orders in a nonlinear manner to achieve good control performance. For the control signal u to be able to reject the disturbance, the estimated disturbance $\widehat{f}$ is integrated with the nonlinear state error feedback, which is a key feature of ADRC.

Figure 7. Schematic diagram of ADRC.

It is imperative to highlight that the ADRC only requires the relative order p of the controlled plant and its gain b, and not the disturbance and complete model of the controlled plant as described by the model shown in Equation (9)(9) $$y^{(p)}(t)=\mathit{\text{bu}}(t)+f(y(t),u(t),d(t))$$(9) (Madoński & Herman, 2015; Patelski & Dutkiewicz, 2020). (9) $$y^{(p)}(t)=\mathit{\text{bu}}(t)+f(y(t),u(t),d(t))$$(9) where f(u, y, d) is a mixture of the unknown dynamics and the external disturbance of the plant and u(t), y(t), and d(t) represent the system’s input, output and disturbance, respectively.

The application of ADRC has received significant attention in web tension control. In this regard, Hou (2001) developed a new ADRC technique for tension control in a web mechanism that actively compensates for nonlinear changes and unforeseen external disturbances. The synthetic control function for the second-order discrete time system was obtained using the isochronic region technique. A novel nonlinear PD controller was formulated based on this function and was utilized in conjunction with the ADRC to achieve web tension regulation. Realism was achieved by simulating a real-world industrial application. The results demonstrated that the proposed tension controller is capable of handling large dynamic variations that are frequent in web tension applications. Nagarkatti et al. (2000) designed a distributed parameter model of an axially moving material with integrated tension and speed controllers. Lyapunov techniques were utilized to build a model-based boundary control scheme that regulates longitudinal oscillation and subsequently maintains speed and tension of the material at predetermined setpoints. Load cells and roller encoders were used as feedback in the system. Actuation was provided by two roller motors at each end of the regulated span. When compared to the PI speed control and P tension control, experimental results demonstrated that the suggested full-order controller improved the regulation of tension and speed setpoints to axial disturbances.

Sicar and Hazzab (2011) developed a distributed control scheme utilizing ADRC and a Nonlinear-PI (NPI) controller for web transport systems. By treating every unidentified coupled interaction as a generic term and compensating them in real time with an extended state observer, the ADRC decoupled the control action, eliminating the need for an explicit unknown dynamic and disturbance model. The NPI controller modifies its gains in real time based on the tension variation pattern and tension error. According to simulation results, the proposed NPI and ADRC controllers surpassed a well-tuned conventional PI controller in tension control and exhibited significant stability to changes in elasticity modulus and inertia. However, no experimental setup was used and optimization algorithms could improve the results. Shanhui et al. (2013) introduced a novel ADRC for tension regulation in the unwinding system of the gravure printing machine. First, a nonlinear mathematical model based on the unwinding system’s operating principle was developed. A decoupling model was also built to determine the order of the plant. An ADRC system was designed to improve the tension stability during unwinding based on the order of the plant. Since the ADRC algorithm was less sensitive to disturbances, simulation and experimental findings showed that the suggested control technique could provide superior stability and robustness against variations in the unwinding system than the classic PID controller.

3.3.3.2. Sliding mode control

A variable structure control method called Sliding Mode Control (SMC) has now become a dominant controller in handling modeling and parametric uncertainties of nonlinear systems such as web tension and velocity control due to its robustness. The SMC operates by forcing the system to slide along a surface known as the sliding surface by sending a discontinuous control signal to the system. The dynamics is then kept at this surface for all consecutive times, regardless of nonlinearities (Armghan et al., 2020; Iqbal et al., 2017). Figure 8 (Gang, 2020) conceptualizes this concept.

Figure 8. Conceptual diagram of sliding mode control.

SMC’s design can be accomplished in two sequential steps:

The definition of the sliding surface $S(t)$ is the initial step given by Equation (10)(10) $$S(t)={\left(\lambda +\frac{d}{\mathit{\text{dt}}}\right)}^{r-1}\left(x_{\mathit{\text{ref}}}-x\right)$$(10) (Amimeur et al., 2012; Layadi et al., 2017; Pourseif & Mohajeri, 2020). (10) $$S(t)={\left(\lambda +\frac{d}{\mathit{\text{dt}}}\right)}^{r-1}\left(x_{\mathit{\text{ref}}}-x\right)$$(10) where r is the sliding mode’s degree, $\lambda$ denotes the weighting factor, x represents the state vector and x_ref is the reference state vector

The creation of the control law is the next step which is governed by Equation (11)(11) $$u(t)=u_{\mathit{\text{eq}}}(t)+u_N(t)$$(11) . (11) $$u(t)=u_{\mathit{\text{eq}}}(t)+u_N(t)$$(11) where $u(t)$ is the control signal, $u_{\mathit{\text{eq}}}(t)$ represents the decoupling control at $\dot{s}(t)=0$ that is used to keep the system on the sliding surface defined by $s(t)=0,$ $u_N$ denotes the switching control that guarantees that the system state trajectory converges towards the sliding surface. The reaching condition based on the Lyapunov stability theory is satisfied when $\dot{s}s<0.$

Sliding mode control theory can be used to develop efficient controllers for high-order nonlinear plants working under varying uncertainty circumstances. Its key benefits are great resilience, quick dynamic response, good tracking, insensitivity to parameter fluctuation and speedy convergence. The main drawback of SMC, however, is the chattering issue brought on by discrete switching to keep the system on the sliding surface. Frequently, these chattering phenomenon lead to inaccurate control, excessive wear on moving mechanical elements or even the collapse of the controlled structure (Huang et al., 2022; Zulu & John, 2014).

Sliding mode control been applied severally in web tension control. Hence, in a web machinery, Chieh-Li et al. (2004) described the modeling and control of the speed and tension of a film. A new control approach based on adaptation of the sliding mode control’s invariance property was used to maintain the speed and tension of the film. A recurrent neural network estimator was used to estimate the system uncertainties, which made the operating range more adaptable and enhanced the system’s efficiency. As demonstrated by numerical simulations, a recurrent neural network-based online estimator for sliding mode control is effective on a web handling system Abjadi et al. (2009) designed a number of motors for winding webs and a feedback linearization control system based on Sliding-Mode (SM). The tension and velocity of the web-winding mechanism were initially decoupled using an ideal feedback linearization control scheme. A single SM feedback linearization control system, comprising of two tension controllers and a speed controller, was then utilized to enhance the performance of the control system in the presence of uncertainty. The suggested controller is decentralized. Two tension observers were also designed to replace load cells. Lastly, simulations on a computer were utilized to test the efficacy and capability of the suggested control strategy, indicating that even when uncertainties exist, the tension and speed quickly match the reference values.

To fulfill web speed and tension control objectives in the event of unknown system uncertainties, Kuo-Ming and Yen-Yeu (2013) proposed a robust sliding mode control system on the basis of an extended state observer for roll-to-roll machines. Based on simulation findings, it was concluded that the developed control system could be implemented without prior knowledge of system uncertainties and could satisfactorily fulfill the control target under unknown system uncertainties. However, the proposed controller’s control performance was not tested in a laboratory setting. Lu and Pagilla (2014) developed an Adaptive Sliding Mode Controller (ASMC) for governing the tension in a web machine’s heating and cooling area. A nonlinear thermal transfer model for composite webs was developed to determine the temperature profile within the web. An equation that controls web tension was established based on the notion that the web is elastic and considering how temperature affects elastic modulus. By studying the governing equations for web tension and velocity, an ASMC was designed to regulate tension in a tension zone. An embossed part of an industrial web manufacturing line was utilized in a simulation analysis to evaluate the adaptive tension controller’s performance. The adaptive controller outperformed the conventional PID controller in terms of following the tension reference. The experimental validation, on the other hand, was not carried out.

Zhao et al. (2017) used lateral dynamics analysis and mathematical modeling to improve the winding accuracy of a composite tape winding system. A new Adaptive Sliding Mode Controller (ASMC) technique on the basis of fuzzy approximation of unknown nonlinear functions and fuzzy regulation of feedback and switching gains was given to account for nonlinearities and disturbances in the composite winding process. The Lyapunov theory and the Barbalat Lemma ensured the control system’s stability and convergence. In comparison to the PID controller and the standard sliding mode controller, both experiments and simulation findings demonstrated that the developed controller had more precise control and reduced chattering input. Jie-Shiou et al. (2018) investigated the regulation of enameled wire tension for automatically rewinding motors to resolve the lag time of passive sensors and maintain consistent wire tension. The proposed unwind roll motion control technique uses a multi-loop structure, with an inner loop feedforward speed controller and a PI feedback controller. To minimize external disturbances, the outer tension loop used the Iterative Learning Sliding Mode Control (ILSMC) and a Disturbance Observer (DO). The DO's estimated tension measurement was then compared to the load cell’s. Experiments with sensor and sensorless active wire tension regulation confirmed the efficiency of the suggested method. The sensorless technique, on the other hand, estimates external disturbance with more noise and greater phase delay than the sensor-based approach.

3.3.3.3. Backstepping control

The backstepping control approach is a recursive technique that divides the system’s control scheme into subsections. A virtual control rule is established in backstepping control by first considering the physical control input in a small subsystem. The design is then broken down into additional steps until the system can be fully controlled. The Lyapunov theorem, which deals with the stability of solutions utilizing differential equations, also forms the basis of the development process (Idrissi et al., 2022; Maxime et al., 2015). The system’s mathematical model serves as the foundation for the backstepping control. The benefit of the backstepping approach is that it can achieve the goals of tracking and stabilization better than the linearization approach, avoiding cancellations of valuable nonlinearities emerging in the system. Additionally, it quickly converges, using up fewer computer resources and is ideally suited to handling uncertainty and disturbances. The virtual controller’s repeated differential calculation is too complicated, though. Additionally, this technique has issues with parameter setting and item explosion (Fadhel S & Noaman, 2017; Huang et al., 2022; Shukla et al., 2018).

The backstepping control algorithm can be described by considering a generalized nth order dynamical system shown in Equation (12)(12) $${\dot{x}}_n=f_n(x_1,x_2,\dots x_n)+u_n$$(12) (Harkegard, 2011; Pourseif & Mohajeri, 2020). (12) $${\dot{x}}_n=f_n(x_1,x_2,\dots x_n)+u_n$$(12) where, $x(t)\in {\mathbb{R}}^n$ represents the system’s state vector, $f_{i,}i=1,2,\dots ,n$ are function either linear or nonlinear and $u_{i,}i=1,2,\dots ,n$ are the controller input.

The recursive backstepping control design of Equation (12)(12) $${\dot{x}}_n=f_n(x_1,x_2,\dots x_n)+u_n$$(12) ensures the system will operate with global asymptotic stability. In addition to the development of a control input function $u_{i,}i=1,2,\dots ,n$ and a virtual control $a_{i,}i=1,2,\dots ,n$ that causes the system in Equation (12)(12) $${\dot{x}}_n=f_n(x_1,x_2,\dots x_n)+u_n$$(12) to converge to zero as time progresses, the i^th subsystem may be stabilized with respect to a specific Lyapunov function $V_{i,}i=1,2,\dots ,n$ by employing the backstepping control design at the i^th step.

With the application of backstepping control in web tension regulation, Kyung-Hyun et al. (2011) computed the optimal gains of a back-stepping controller by employing a genetic algorithm to build a novel precision control method to manage the speed and tension of a nonlinear single-span web system. A back-stepping controller with a mathematical formula was developed. MATLAB/Simulink tool was used to simulate the system, which was then compared to experimental results. When compared to existing techniques, simulation and experimental findings showed that the suggested method attained the performance characteristics of high stability and precision even when the unwinder and rewinder’s inertia changed. Tran and Kyung-Hyun (2014) developed a backstepping-based control approach for the nonlinear three-multiple-span electronics fabrication sector. A nonlinear mathematical model was created for the system and a backstepping controller was designed for it. The gains of the backstepping controller were best estimated using the modified genetic algorithm. Using the MATLAB/Simulink tool, the proposed controller’s outputs were demonstrated to be reliable in both simulation and experimental results.

A Double-Rope Winding Hoisting System’s (DRWHS) wire rope tension controller was built by Zhen-Cai et al. (2017). The DRWHS was investigated using a dynamic model with parameter uncertainty and external perturbations. The performance of the DRWHS' wire rope tension coordination control was improved by developing a Robust Nonlinear Adaptive Backstepping Controller (RNABC) with a Nonlinear Disturbance Observer (NDO). Experimental investigations on the DRWHS regulated by an xPC microfabrication system were performed to demonstrate the viability and robustness of the suggested controller. When compared to a standard PI controller and an adaptive backstepping controller, the suggested controller displayed exceptional ability to manage the tension of a wire rope.

3.3.3.4. H∞ control

The H∞ control has also received a wide application in web tension control. It uses a novel approach to consider control as a problem of mathematical optimization. Identifying the class of controllers for a particular system that maintains the closed loop system stability and limits the input-output H∞-norm to a set limit is the focus of the design problem. The general control scheme of the H∞ control is shown in Figure 9 (Doyle et al., 1989; Jafar et al., 2016). The controller is block K, while block P is the general plant. All input variables, such as uncertain disturbances, usual commands and external signals are handled through the input signal w. The system states are held by the output z, the measured variable is provided by the output y, and the control input u is used to enhance the plant P’s performance. The primary objective of this design is to reduce the inaccuracy of the output signal z by modifying the control input variable u using the measured variable y in K. The effective implementation of such a controller has demonstrated that external perturbations are rejected and that the controller is capable of successfully coping with system variations.

Figure 9. H∞ Control schematics.

Hence the objective of the H∞ control law is to design an internally stabilizing dynamic feedback controller, K(s), that minimize H∞ norm described by the transfer function, Tzw, of the closed-loop system shown in Figure 9. The Tzw is described by Equation (13)(13) $$T_{\mathit{\text{ZW}}}=F_t(P,K)=P_{11}+P_{12}K{(I-P_{22}K)}^{-1}{P}_{21}$$(13) (Vasičkaninová & Bakošová, 2016). (13) $$T_{\mathit{\text{ZW}}}=F_t(P,K)=P_{11}+P_{12}K{(I-P_{22}K)}^{-1}{P}_{21}$$(13) where $F_t(P,K)$ is lower fractional linear transformation of P and K.

H∞ control has the advantage that it can be used to solve problems involving multivariable systems with cross-coupling effects. It also ensures robust stability and satisfactory reference point tracking performance. However, its disadvantages are that the H∞ techniques require a significant degree of mathematical proficiency for their efficient use and a passable model of the system to be managed is required (Safonov et al., 1981; Xie et al., 2016).

Hence, Gassmann et al. (2009) offered an enhanced control alternative to PI controllers for pendulum dancers in web processing based on H∞ synthesis. The dancer’s subsystem was first modelled using nonlinear and linearized models. The dancer’s position controller was then created utilizing the conventional H∞ architecture and mixed sensitivity technique. Experiments on a sizable web testing platform featuring a pendulum dancer and four powered rollers in the unwind zone demonstrated the performance of the suggested approach. The dancer remained in a band of less than 0.1 degree during steady-state operations, according to the findings. Furthermore, despite the fact that speed reference adjustments generated disturbances, their impacts on dancer position were minor. However, the controller synthesis did not study the interplay of the other subsystems on the unwinding portion housing the pendulum dancer. Jinbao et al. (2009) proposed a self-optimizing algorithm-based mixed-sensitivity robust H∞ control to address the problem that the H∞ control method with parameter fuzzification fails to achieve good control response for fast speed and real-time needs of tension systems. The tension system’s modeling was first shown. Secondly, a mixed-sensitivity robust H∞ control was created and compared to a PID controller, which decreases the coupling between tension and velocity. The processing time of the H∞ controller was lowered attributable to the Hyper Generation Genetic Algorithm (HGGA). In addition, to compensate for the time delay, the error and the change in the error were tuned. Finally, a platform for experimentation was used to test the proposed methods. When compared to a classical PID controller, the results showed that the H∞ robust controller performed well in terms of robustness to radius fluctuation and the decoupling of speed from tension.

When the multistage printing system was subjected to disturbances, variations in speed and other operational variables, Dou and Wang (2010) presented a robust H∞ control technique to reduce tension fluctuations. The Linear Fractional Transformation (LFT) framework was used to create a state-space model for the system. The main sources of disturbances were variations in speed and tension from neighboring spans. Simulation and experimental testing were used to verify the efficiency of the proposed H∞ control approach. The PI control, LQR and H∞ control were compared in terms of control performance and robustness. According to the findings, the proposed H∞ controller outperformed both the LQR and the PI controllers in terms of rise time and disturbance rejection over most of the frequency bandwidth. Rotation non-synchronization errors were also effectively reduced by the proposed controller.

In order to optimize H₂ performance on a large web processing system, Benlatreche et al. (2005) developed a state feedback control, either with or without an integrator synthesized by Bilinear Matrix Inequality (BMI) optimization. Different controller topologies were investigated, including centralized and overlapping or non-overlapping semi-decentralized controllers. On an experimental bench, results of simulations using a nonlinear model for a web system were reported. The findings revealed that the control approach had better reference tracking than the H∞ control, with a vanishing static error. Gassmann et al. (2012) used a pendulum dancer to create a unique tension controller employing fixed-order H∞ control in the unwinding part of the web processing machinery. To compute the Single-Input Single-Output (SISO) position controller to indirectly control web tension, a pendulum dancer’s unwinding segment represented by a linear state-space model was developed. The mixed sensitivity technique was used for the synthesis. On a large experimental platform, tests were successfully implemented. When compared to a standard PI controller, the findings showed that the proposed control technique significantly enhanced the system’s performance in terms of speed and accuracy.

For an Automated Fiber Placement Machine (AFPM), Liu et al. (2020) presented a tension control technique using a passive dancer roll. A passive dancer roll was developed conceptually as an apparatus for the reduction of tension interruption to enable real-time adjustment variations in lower speed. The effect of dancer roll parameters on disturbance reduction capability was investigated utilizing a tension control system nonlinear model that included the rolling motions of the passive dancer. The H∞ mixed sensitivity approach was used to build the controller. Results of experiments on an AFPM device demonstrated the stability of the developed passive dancer automatic control having a steady-state error of 2%. Furthermore, under the disturbance of a 4 m/s² velocity variation, the highest fluctuation of tension did not surpass 1 N.

3.3.3.5. Adaptive control algorithm

Because the tension control system is complex, nonlinear and time-varying in moving webs in particular the roll’s inertia and radius keep changing with time has triggered researchers to use adaptive control techniques to improve robustness and stability in web tension control. The adaptive control strategy is an advanced control method that offers a structured framework for automatically updating the controller’s parameters in real time to govern a system with changing dynamics under normal conditions of operation but susceptible to unpredictable disturbances. As a result, adaptive control can alter its parameters in real time to meet the environment and unknown dynamics and produce the required control response. According to the parameter adaptation approach, adaptive systems are often classified as model reference adaptive and self-tuning systems (Behrooz et al., 2018; Naidu & Rieger, 2014).

In principle, the adaptive control system measures the Performance Index (PI) of the control system by utilizing the states, inputs, outputs and known disturbances. The adaptation mechanism updates the parameters of the adjustable controller after comparing the measured performance index with the reference PI to keep the control system’s performance index stable as shown in Figure 10. Consequently, the adaptive control system can be thought of as a feedback system, with the performance index serving as the controlled variable (Liu et al., 2020). The control is adaptive as a result of the primary feedback handling process signal fluctuations and the secondary feedback handling changes in the process parameters. Different adaptive control approaches have successfully been used to control the tension of moving webs. For instance, genetic-fuzzy and neuro-fuzzy techniques and PID controller optimized with other hybrid algorithms (Behrooz et al., 2018; Zulu & John, 2014; Nebos’ko et al., 2010; Ofosu et al., 2022).

Figure 10. Illustration of the adaptive control system.

To address the problem of actuator saturation of the conventional Model-Free Adaptive Control (MFAC) algorithm in the multi motor winding system, Xiong et al. (2018) proposed a modified Partial Form Dynamic Linearization-Model-Free Adaptive Control (PFDL-MFAC) approach. To minimize the complexity of the pseudo-Jacobian parameter matrix, the MFAC approach with adaptive observer was utilized. With the varying constraint of the control quantity in mind, an anti-saturation compensator was developed to limit the size and minimize the control variable input rate. Computer simulations were then used to evaluate the modified MFAC's performance compared to that of the traditional MFAC. The results indicated that, compared to the traditional MFAC, the challenge associated with saturation of the actuator can be resolved via the modified control technique, leading to quicker tracking and stability management of speed and tension. With the use of a PID controller, Zhi et al. (2018) designed a precise wire tension control mechanism to enhance the surface finish and geometric precision of wire winding systems. The control system’s transfer function was identified using the least square approach to system identification. To update the PID controller’s parameters, three intelligence schemes were used: Simulated Annealing (SA), Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). According to simulation and experimental results, the PSO-PID outperformed the other intelligent algorithms in terms of control precision, reaction time and interference-preventing abilities.

Zhiqiang et al. (2018) used the PI gains of an adaptive speed controller to build a sensorless tension control system. To eliminate the time delay caused by the sensor, an observer was built to replace it, and the observed tension value was used as feedback. The motors’ inertias during rewind and unwind were calculated using the Landau discrete-time recursive technique. This was done to address the flaws in the traditional method, which needed familiarity with the material’s thickness, density and other properties in order to estimate inertia. In addition, the calculated inertias were used to update the speed controllers’ PI gains online. The tension control system was able to retain a better control response even when the inertia changed significantly. The controller’s feasibility was demonstrated through experiments. Yan (2004) presented a wire feed and tension controller for a Wire Electrical Discharge Machine (WEDM) that assures consistent tension and seamless wire flow. The wire transport system’s equation of motion and system identification were examined and formulated. The dynamic behavior of the closed-loop wire tension controller design was examined using a one-step-ahead adaptive controller. Experimental findings show that the suggested adaptive controller performs better than a PI controller in terms of transient response time and steady state error.

Xiao-Ming et al. (2018) built a new tension control system to monitor the process of winding filaments, including its speed and tension. By considering the inertia and radius of the rollers’ time-varying characteristics, the dynamic models of the driven and idle rollers were developed. The incremental model was also used to explore the effect of parameters and speed variations on fiber tension. Following that, an adaptive fuzzy controller was developed for online PID parameter adjustments to control the master speed roller based on the driven roller characteristics and the effect of variation. According to simulations and laboratory investigations with carbon fiber at various reference speeds and tensions, the fuzzy-PID controller reduces steady-state error and settles more quickly than a traditional PID controller. However, in both the traditional and proposed ways, the tension varied around the reference values.

3.4. Observer-based control

State variables are required as feedback in the majority of design methodologies for web tension regulation. Utilizing sensors like the load cell or dancer, one may measure these variables directly. However, complicated systems with several states or missing states will necessitate a large number of sensors, which makes the control system cumbersome and costly. Likewise, measurement in numerous systems using sensors is problematic or often imprecise due to challenges such as sensor mounting, calibrating, harsh environmental conditions and noise making it unreliable during the process of measuring web tension. In order to estimate the missing variables and limit the utilization of expensive sensors, observers are utilized to reconstruct the state vector (Kravaris et al., 2012; Mohd Ali et al., 2015).

An observer basically functions as a system’s feedback model, estimating system states $\widehat{x}$ via the system’s online inputs and outputs that are well observable. The system’s error $(y-\widehat{y})$ and model feeds the feedback. The generic equation of an observer in state space is as shown in Equation (14)(14) $$\begin{array}{c}\dot{\widehat{x}}=A\widehat{x}+\mathit{\text{Bu}}+H(y-\widehat{y})\\ \widehat{y}=C\widehat{x}\end{array}$$(14) . There are several categories of observers each with its own merits and demerits. Luenberger-based observers, Kalman filters, unknown input observers, AI-based observers, hybrid observers, finite-dimensional system observers and Bayesian estimators are among them (Chu et al., 2018; Kumar et al., 2013; Mohd Ali et al., 2015). (14) $$\begin{array}{c}\dot{\widehat{x}}=A\widehat{x}+\mathit{\text{Bu}}+H(y-\widehat{y})\\ \widehat{y}=C\widehat{x}\end{array}$$(14)

Observer-based control was applied by Carrasco and Valenzuela (2006) where the development of two new estimators for paper tension based on sensorless control centered on the unwinding and rewinding parameters of a two-drum electric-braking-generator industrial winder was considered. The estimators took into consideration all of the significant inertial variation effects and dynamic friction. A two-drum winder dynamic model and braking generator was used to evaluate the tension-estimation effectiveness compared to an operational winder. Multiple sensitivity tests showed that the suggested estimators were resistant to parameter fluctuations and could regulate paper tension with consistency and accuracy without the use of load cell tension loops. Gassmann and Knittel (2007) investigated a cost-effective way of controlling tension in web systems using observer theory to reduce the quantity of dancers and load sensors in the line. Two distinct techniques for designing tension observers were given after a review of the basic laws used in modeling the system. The first method used a linearized system model with a Kalman filter, while the second method used a nonlinear model that also used extended Kalman filter theory. With adjustments to the nominal set points of the web speed and tension as well as friction torques, both approaches were assessed and contrasted. The simulation results revealed that the first strategy was extremely effective and reliable from an operational perspective in the model, particularly in web speed. The biggest issue was being speed-sensitive. The results of the second technique showed that the extended Kalman filter performs well in web tension estimation and is unaffected by major changes in friction conditions. Idler’s roll effects, on the other hand, were overlooked.

Prabhakar et al. (2007) designed and built a decentralized web processing line controller. The unwind and rewind rolls in a web process line were first modeled by precisely accounting for the roll inertia and radius being time-variable. Second, a method for splitting the web processing line into tension zones was presented. Based on the reference web tension of each zone and the master speed roller’s reference velocity, the desired web speed for the process line was established. Using an innovative approach, a fully decentralized state feedback controller was developed. According to findings from experiments on a massive web machinery, the suggested decentralized approach with the novel dynamic model achieved far better tension regulation than the earlier PI decentralized controller. The proposed controller’s stability and robustness under uncertainty and a variety of disturbances, however, were not evaluated. A powerful decentralized controller for a system with three motors for winding webs without a tension sensor was developed by Hailiang et al. (2015). The entire system was first divided into three subsystems. Then, a decentralized state feedback control method having two tension controllers and a web speed controller was introduced. Linear Matrix Inequalities (LMIs) were used to generate sufficient criteria for the existence of robust decentralized controllers. In order to do away with the expensive load cells, two nonlinear tension observers were employed to calculate the tension of the web. Finally, simulation tests were used to evaluate the effectiveness of the suggested control scheme, which revealed that the proposed controller performed well for reference tracking even when parameter uncertainties were present. The addition of observers did not, however, remove steady-state error.

To counteract interferences like variations in the film’s radius while being wound, Eum et al. (2016) proposed an effective tension control approach in accordance with a disturbance observer for a web processing machine. To begin, there were four parts to robust tension control: observer-based sensor signal processing, disturbance observer, vibration controller and tension controller. The web system’s dynamic model for tension control was then examined. The results of experimental testing involving disturbance observer performance, sensor signal processing and vibration control were then reported. When compared to a traditional tension control scheme, the suggested tension control improves the efficiency of the web winding equipment while reducing tracking error. To circumvent the high cost of load cells and boost system performance, Hou et al. (2018) proposed a Decentralized Coordinated Control (DCC) method using tension observers for a three-motor web machine. First, two nonlinear tension observers based on the dynamic model were presented to predict the tension of the unwinding and winding systems. The predicted tensions were then used as feedback signals in a state-space based DCC to minimise subsystem interference. The Lyapunov stability theory was used to illustrate the necessary requirements for asymptotic stability of a closed-loop web processing system. The observer and control gain matrices were also computed using Linear Matrix Inequalities (LMI). Finally, simulated and practical testing were used to assess the effectiveness of the tension observer and the suggested observer-based DCC, confirming that the proposed observer had high estimation capability in the midst of set-point and tension fluctuations. The proposed DCC observer, on the other hand, was responsive to changes in system parameters.

For roll-to-roll printing systems, Kang and Kee-Hyun (2018) developed a revolutionary accurate tension control scheme using a reduced-order observer. The principle of mass conservation and the torque equation were used to create the dancer’s mathematical model. The dynamic characterization of the suggested dancer model was investigated using Bode plots to explore the dancer’s roll and tension motion. According to numerical simulations, the dancer rod’s angle at a specific frequency was not closely related to the tension disturbance. The dancer’s tension control capability was then improved by estimation and tension control with a reduced order observer. In the entire frequency range considered by the simulation studies, the proposed observer for the dancer enhanced the tension control capability relative to the dancer without the observer. The proposed controller, on the other hand, requires high-precision tension regulation. Hwang et al. (2019) presented a Disturbance Observer (DOB) and a PI controller for roll-to-roll processes to improve stability against model fluctuations in inertia and parameter variations. The small-gain theorem was used to verify the closed loop control system’s robust stability. In addition, a feedforward controller was used to reduce tracking error in the transient condition of tension fluctuations. Finally, the Kalman filter approach was proposed for signal processing to lower the cost, measurement noise and mitigate the phase delay problem of a high-priced load cell. The DOB with a PI controller proved to be successful in compensating for disturbances and model uncertainties in experiments.

Perduková et al. (2019) created a new reliable control system for a continuous strip processing machine with many motor drives by integrating a new state variable into the system. By employing the Lyapunov second method, a novel tension controller based on a decentralized approach was devised to assure asymptotic stability of the expanded system by treating the speed and tension subsystems independently and the connection between them as a disturbance. When compared to the PI/PID control, experiment results on a continuous line proved the novel control structure’s robustness against parameter changes and disruptions. However, no observer was designed to acquire data on all of the controlled system’s state variables. Huang et al. (2021) presented a modified sensorless tension estimate approach based on a disturbance compensation system to solve the challenges with web systems’ tension and speed control. The tension feedback was provided via a Modified Tension Observer (MTOB). Furthermore, the H∞-controller control was used in the disturbance correction system’s design to increase the ability of disturbance rejection and thus the effectiveness of roll-to-roll manufacturing. To evaluate the efficacy of the suggested system, several tests were done using an MTOB-based disturbance compensator, as well as force sensor-based tension feedback and MTOBS. In tests, the modified tension observer-based web tension control system surpassed the actual tension sensor-based system. Furthermore, of the three control systems examined, the suggested control strategy effectively rejected disturbances.

Li et al. (2021) employed an Electro-Hydraulic Servo System (EHSS) to effectively regulate two wire rope tensions in the Double-Rope Winding Hoisting System (DWHS). The hoisting system and the EHSS were built as state space models. The Flatness-Based Controller (FBC) was developed for the hoisting system. A Disturbance Observer based on Integral Backstepping Controller (DO-IBC) was utilized to deal with external disturbances and unmodeled EHSS features. The Lyapunov function was employed to check the stability of the complete control system. According to simulation and experimental results, the hybrid control system was more effective than the PI controller at lowering the tension disparity between the two wire ropes.

3.5. Artificial intelligence control

Artificial Intelligence (AI) is the study and development of computer algorithms that have human-like perception, reasoning and behavior. The main goal of AI is the creation of machines that can address problems that can only be resolved by the ability of human thinking because of their capacity to learn and make good judgement. Intelligent control techniques use a variety of artificial intelligence techniques, of which some are inspired by biological principles, to control a system. These comprise Genetic Algorithm (GA), Adaptive Neuro Fuzzy Inference System (ANFIS), Artificial Neural Network (ANN), Fuzzy Logic (FL) and other evolutionary algorithms (Wright, 2010). Finding a suitable mathematical model for tension control systems may be difficult due to their nonlinearity, complexity and MIMO nature. The employment of intelligent control approaches has advantages since it does not require a model of the system. As a result, tension control systems frequently employ intelligent control techniques (Baumgart & Pao, 2007). The major challenge with the use of intelligent control algorithm is the complexity and abundant computational resources required for it operation (Duarte-Galvan et al., 2012; Mirinejad et al., 2012; Zulu & John, 2014).

3.5.1. Fuzzy logic control

Based on fuzzy set theory, Fuzzy Logic Control (FLC) is a form of real-world control approach that mimics human reasoning and decision-making processes in complex, nonlinear, time-varying systems by using simple mathematical techniques. The fundamental idea behind FLCs is to incorporate human expertise into the control of a system whose input-output relation is characterized as a set of fuzzy control rules involving linguistic variables as opposed to a sophisticated mathematical model of the system. Though fuzzy logic control does not require a mathematical model of the system, good physical knowledge of the process is required. Fuzzy logic control is well suited for controlling the tension of moving webs as a result of its ability to make decisions despite system uncertainty. Additionally, it efficiently handles the intricate and nonlinear nature of the web tension and line speed (Duarte-Galvan et al., 2012; Ofosu et al., 2022).

The fuzzy control algorithm is very simple in concept. It consists of fuzzification, inference system and defuzzification as shown in Figure 11. The fuzzification phase assigns the proper membership functions and truth values to the sensors and other inputs. The if-then decision-making structure of the inference system establishes the link between the input and output variables depending on the operator directives. Defuzzification transforms the output from the fuzzified phase into a crisp output that is supplied back to the plant for control (Duarte-Galvan et al., 2012; Ofosu et al., 2022). The main issue with fuzzy logic is the lack of established criteria for determining an optimal FLC. Typically, the best solution should be found through trial and error, which is incapable of learning and adapting to changing situations. In most cases, to adjust PID gains online, fuzzy logic is applied in the tension control system making it have a faster response, higher accuracy, stronger robustness and better stability (Huang et al., 2020; Ofosu et al., 2022; Pan et al., 2011).

Figure 11. Schematic diagram of fuzzy logic controller.

In the area of fuzzy logic control, Ganeshthangaraj et al. (2012) designed an active dancer system that controls web tension using a fuzzy control technique. A suitable fuzzy logic-based precise position control system was built after transforming the problem into a position control problem. A simple proportional control formula was then constructed and employed to provide tension control depending on the relationship between the movement of the dancer and the tension of the web. According to the research findings, the suggested controller was able to handle the web tension with tension fluctuations never surpassing 1.25 N. Yang and Zhang (2014) investigated a Fuzzy Adaptive PID Controller-based tension control system for web presses. Unwinding tension was studied using a dynamical model with several perturbation parameters. MATLAB/Simulink software was used to create a fuzzy adaptive PID controller whose output was used as an actuator to control the torque of a magnetic powder brake to keep the paper tension constant. Through experimentation, the developed controller was compared to a typical PID control. According to simulation results, the unwinding tension control system using an adaptive fuzzy PID controller can enhance anti-jamming capabilities and efficiently decrease overshoot in system response while accelerating to attain a steady-state in 5 seconds compared to 8 seconds for PID control.

To boost the effectiveness of a brushless DC coil winding machine, Duong et al. (2015) developed a system that uses active tension rather than passive tension. To examine and develop the proposed active tension system, an analysis of the cross-section winding processes with circular and non-circular cross-sections was made. A wire accumulator with a spring, servo valve and pneumatic cylinder was used to reduce wire tension variation during the winding operation. The system was then controlled by utilizing a fuzzy logic controller having two outputs and three inputs. Finally, when compared to a winding machine without an active tension system, experimental findings suggested that the winding machine with an active tension mechanism could work at a maximum speed and create a thinner coil of wire than a passive tension system. Cazac et al. (2016) developed a fuzzy controller to regulate the straining force in a wire drawing machine’s winding mechanism. The wire winding mechanism’s mathematical model was designed first. The straining force was then controlled with a fuzzy controller that was simulated using MATLAB/Simulink software and compared to a PI controller. The simulation results revealed that the fuzzy logic controller demonstrated optimal performance with a working speed spanning from 0 to 1200 m/min when the winding machine is moving quickly and slowly while processing wires with a diameter of 1.3 mm devoid of mechanical stresses that could damage the manufactured wire.

He et al. (2018) investigated a fuzzy adaptive PID control approach for controlling winding tension to lessen the vibration in tension. The sources of tension vibration were first investigated using a dual-motor powered winding control system model. After that, a fuzzy adaptive PID control model was implemented and compared to a PID controller’s fixed parameters. MATLAB/Simulink software was used to create a simulation model of the winding tension control system. The fuzzy adaptive control approach had a better inhibitory effect on tension vibration in comparison to PID control, according to the simulation results. However, various optimization techniques could increase the efficacy of the control strategy in order to reduce tension vibration.

3.5.2. Artificial neural network

An algorithm for machine learning called an Artificial Neural Network (ANN) imitates how the human brain processes data (Ross, 2010). By adjusting the weights and neuron activation function, it is utilized to correlate the input data set with the output data set as shown in Figure 12a (Tseng et al., 2021). The neuron’s output, y, is given as in Equation (15)(15) $$y=f\left(\sum _{i=1}^n(x_i{w}_i)+b_i\right)=f(X{W}_j^T+b_j)$$(15) (Tseng et al., 2021). (15) $$y=f\left(\sum _{i=1}^n(x_i{w}_i)+b_i\right)=f(X{W}_j^T+b_j)$$(15) where X is the input vector with the input data set $\left\{x_1,x_2,x_3,\dots .,x_n\right\}$ as its elements, $W_j^T$ is the weighting vector’s $W_j^{}$ transposition in the j-th layer and has weighted numbers $\left\{w_{1j},w_{2j},w_{3j},\dots .,w_{\mathit{\text{nj}}}\right\}$ as its elements, $b_j$ is the bias which is the neuron’s initial state and $f(x)$ represents the activation function

Figure 12. Artificial neural network architecture. (a) Neuron, (b) Artificial neural network.

Each input value is multiplied by a weighted number by the neuron and their sum is then determined. The activation function is then used to convert the summation that was added with a bias into an output. An input layer, an output layer and one or more hidden layers make up the ANN as shown in Figure 12b. Several neurons may be found in each hidden layer and there may be one or more inputs and outputs in the input and output layer. The different types of neural-network structures include Feed-Forward Networks (FFN), Multilayer Perceptron (MLP), Convolutional Neural Network (CNN), Recurrent Neural Network (RNN) and Radial Basis Function Neural Network (RBFNN) (Song, 2014; Tseng et al., 2021).

This technique’s main benefit is that a system model is not necessary. The ANN approach is frequently used to control the nonlinearities and time-varying dynamics of web tension due to its versatility, resilience, capacity to map arbitrary nonlinear functions and nonlinear recognition ability. It takes a long time to process a large neural network and requires training, which reduces the efficiency and performance of the neural network (Duarte-Galvan et al., 2012; Perera et al., 2014; Razmi & Afshinfar, 2019; Tseng et al., 2021).

Hence, Jian et al. (2011) developed a PID controller based on Backpropagation Neural Network (BPNN) to minimize periodic tension caused by the unwinding portion of the printing process due to the nonlinearity and time fluctuation of the unwinding system. In order to boost adaptive capacity and overcome the typical PID controller’s incapacity to provide optimal control performance, the BPNN was employed to self-adjust PID settings online. Simulation findings reveal that the suggested control strategy is effective in reducing systematic tension. To keep the wire tension constant, Zhang et al. (2017) integrated the Proportional Integral Neural Network (PINN) with a reduced actuator model for tension regulation of Stranded Wire Helical Springs (SWHSs) CNC machines. The PINN was enhanced by including a modifying element which was an error variance ratio in the second hidden layer, that accounts for wire interaction. The reduced model converted the improved PINN's output value into a control voltage value. The network parameters were adjusted using the gradient-based back-propagation algorithm to improve control performance. Experiments were used to verify the modified PINN's validity and consistency. The control strategy based on the enhanced PINN had improved performance in time-varying and nonlinear systems with less computational effort and faster response times compared to other techniques such as PI-based particle swarm optimization, multiple PIDNN and incremental PI.

Manh et al. (2019) used neural network to compute the varying inertia of unwind and rewind rolls due to the motion of the web material. A Radial Basis Function (RBF) network was used to create the neural network. A backstepping-sliding mode controller was fed the computed inertia data to ensure that the system’s velocity and tension were tracked. According to the simulation results, the control system was successful in tracking and adaptation. In addition, by utilizing RBF neural, the controller did not need a specific model of the plant, making the suggested controller extremely versatile for usage in a variety of industrial applications. Chunxiang et al. (2004) applied Back Propagation Neural Network (BPNN) algorithm to control the speed and tension of a filament winding machine to efficiently lessen the interaction between the speed and tension of the tension control system and overcome the drawbacks of the conventional PID control approach. Simulation results showed the effectiveness of the proposed control algorithm.

In the drying portion of an e-printing system, Chang et al. (2008) developed a feed-forward tension control system. First, a mathematical model was created that considered the drying section’s temperature effect. To tackle the issues of the conventional draw control scheme, a unique control scheme with a velocity compensator was proposed in order to mitigate thermal effects owing to temperature change in the dry region. Experimental and numerical studies were carried out to evaluate the effectiveness of the recommended control strategy. The results showed that the recommended control technique could successfully prevent temperature-related tension fluctuations in the e-printing system’s heating and cooling area. Due to roller eccentricity, the tension signals and dancer position both exhibited very minor fluctuations around their respective reference values.

Dinh et al. (2020) created a neural network on the basis of Radial Basis Function (RBF) network for the prediction of the roll inertia uncertainty in order to mitigate the effects of a web handling system’s improper roll arrangement. A backstepping sliding mode controller that ensured tension and velocity tracking received the data on estimated inertia as input. According to simulation results, the control system was able to track and adapt. Zubair et al. (2014) suggested a self-adapting neural network combined with active dancer and load cells to control the web tension of a multispan printed electronics system so as to minimise register errors while maintaining the printed devices’ density and roughness within acceptable limits. The control algorithm employed back propagation neural networks simulated using LabVIEW software. The effectiveness of the suggested technique was then compared to the PID control. The results obtained showed that the proposed algorithm was efficient in maintaining the web tension within the acceptable limits and had a rise time of 150 ms and settling time of 0.5 s when compared to the classical PID control.

3.5.3. Genetic algorithm

Genetic Algorithm (GA) is a population-based stochastic algorithm that mimics the process of natural evolution to generate solutions to optimize problems using techniques such as inheritance, mutation, selection and crossover as shown in Figure 13 (Albadr et al., 2020; Höschel & Lakshminarayanan, 2019). This algorithm is able to solve optimisation problems without the mathematical model of the system. Generally, the genetic algorithm is used to tune or optimised the performance of other controllers such as PID and fuzzy logic controller so as to enhance their control performance. GA still has various flaws notwithstanding its proven ability to solve several search and optimization challenges. These include the failure to create exploration in the solution search space due to involvement of random variables in the solution initialization. Additionally, the mutation and crossover operations might not ensure an optimal outcome (Albadr et al., 2020; Bi, 2010; Höschel & Lakshminarayanan, 2019).

Figure 13. Flow chart of genetic algorithm.

In relation to the application of genetic algorithm to web tension control, Vedrines and Knitte (Vedrines & Knitte, 2007) designed an optimized controller using a genetic algorithm for the position control of a pendulum dancer, since the pendulum dancer has rarely been studied in literature. In the MATLAB/Simulink software, a nonlinear model of the plant with a pendulum dancer was simulated. The speed and web tension references were tracked and decoupled using a PI controller. The dancer’s mechanical design was then optimized using a genetic algorithm. The obtained results showed the efficiency of the designed pendulum dancer in damping tension variations. However, experimental validation was not presented. Tran et al. (2011) designed a two-span web system for device fabrication incorporating web speed and tension control. A generalized mathematical model was given for the nonlinear two-span web control system and a modified backstepping control techniquewas implemented. The modified genetic algorithm was used to select the best design parameters. Simulations in the MATLAB/Simulink software environment and real-time experimental testing were used to validate the suggested algorithm’s reliability. The findings showed that the suggested method has high accuracy and robustness, with no overshoot and a settling time of 0.2 seconds.

Yanjun et al. (2022) designed a tension control scheme for a loom warp using a more advanced genetic algorithm optimized PID control to address the weak control responsiveness of the conventional PID control. The warp tension model was developed through the loom’s motion mechanism’s decoupling assessment. Simulation and experimental tests with the integral separation PID, conventional PID and the genetic PID on rapier loom model 910 showed that the proposed genetic PID controller ensured stable and dependable warp tension management under various weaving scenarios as opposed to the current fixed parameter controller. However, there was no proof that the algorithm worked on all loom types. Giannoccaro et al. (2018) developed a genetic algorithm to tune a PI controller that is decentralized on a web system that has several spans. The system was accurately modeled using the Transfer Matrix Model. A nonlinear approximation of the pattern of a sample dataset of values was created by a genetic algorithm in order to make the PI controller adaptive by predicting optimal PI parameters under particular scenarios. The usefulness and simplicity of the suggested control algorithm were demonstrated by simulations and experimental findings.

3.5.4. Adaptive neuro fuzzy inference system

The Adaptive Neuro Fuzzy Inference System (ANFIS), which combines fuzzy logic and neural network techniques, addresses the shortcomings of fuzzy logic to provide the optimum fuzzy rules and identify the membership functions for a more effective control operation (Dzib et al., 2016; Şahin & Erol, 2017). There are five layers in the ANFIS architecture. The node function defines the number of nodes for each layer. To express input-output relationships, ANFIS employs if-then rules of the Takagi-Sugeno type. The parameters in ANFIS are updated using a hybrid learning technique that combines the least squares and gradient descent algorithms. Using a least square estimate during the forward pass, the layer 4 parameters are determined. By employing the gradient descent approach to minimize the error signals, the membership function parameters are set during back propagation (Dzib et al., 2016; Li, 2015; Şahin & Erol, 2017). The ANFIS's architecture is illustrated in Figure 14 (Şahin & Erol, 2017).

Where x, y are the inputs, A_i and B_i are the node-specific membership function, ${\omega }_i$ is firing strength, f_i consequent parameters’ algebraic function and f is the output

Figure 14. ANFIS architecture.

The output node, which adds the contributions from all the layers, makes up the final layer as expressed in Equation (16)(16) $$f=\sum _i{\varpi }_i{f}_i=\frac{{\sum }_i{\omega }_i{f}_i}{{\sum }_i{\omega }_i}$$(16) (Dzib et al., 2016). (16) $$f=\sum _i{\varpi }_i{f}_i=\frac{{\sum }_i{\omega }_i{f}_i}{{\sum }_i{\omega }_i}$$(16)

Hence, Li (2015) devised a tension controller for the filament winding mechanism using a fuzzy neural network. Fuzzy neural networks with excellent predictive models were created using the BP method to train the controller for the tension control of filament winding systems. Simulation and tests were used to analyze the performance characteristics of the classical PID controller and the fuzzy neural controller. The outcomes demonstrated that the suggested controller displayed the expected performance characteristics, including high control accuracy, quick convergence, robustness, rapid dynamic response, good stability and less overshoot and was able to respond to a broad range of speed and tension force variations without any response delay when compared to the conventional PID controller.

3.6. Hybrid control

A hybrid controller is developed by the combination of two or more control techniques, which can be intelligent techniques, classical or advanced techniques as shown in Figure 15. Hybrid controllers are beneficial as a better control performance can be obtained compared to employing only one of the control approaches. However, the intelligent control part’s design necessitates user experience and a vast amount of data for training, while the classical or advanced controller is difficult to tune (Behrooz et al., 2018; Gruber & Balemi, 2010; Ofosu et al., 2019).

Figure 15. Schematic diagram of the hybrid control algorithm.

Current research trends on web tension control are focusing on using hybrid control algorithms to achieve good tracking performance, robustness and stability. In this regard, Nishida et al. (2013) built a self-tuning PI controller centered on Generalized Minimum Variance Control (GMVC) with an estimator based on Adaptive Particle Swarm Optimization (APSO) to control a web system. The efficiency of the proposed control strategy, as well as its resilience to the nonlinear characteristics of the system and measurement noise, were verified using simulations. However, because the dynamics and measurement noise of real-world web transport systems are difficult to replicate in simulations, real-machine verification has remained a barrier. Muthukumar et al. (2015) proposed a cascaded control scheme that included a Generalized Predictive Controller (GPC) in the outer loop and an offline evolutionary optimization-based PI controller in the inner loop to regulate the tension of a web. The mathematical model of the web transportation system was first presented. Two techniques, Real-Coded Genetic Algorithm (RGA) and Bacterial Foraging Particle Swarm Optimization (BF-PSO), were chosen to adjust the inner PI controller because they can solve nonlinear optimization issues and converge to a global optimum. When compared to the GPC–RGA cascaded control system, the GPC–BF-PSO cascaded control design performed well at controlling tension without breaking physical limits in the presence of process and external perturbations. The cascaded architecture improved performance by 39% to 60%. However, the performance of the controllers was not experimentally verified.

Using the Nonlinear Dynamic Matrix Control (NDMC) algorithm based on the polynomial Autoregressive Moving Average (ARMA) model, Xie et al. (2017) developed a new tension control approach for unwinding web systems. The unwinding system’s dynamic model was first proposed. Then, using MALTAB/Simulink software, an NDMC controller and a traditional PID controller were simulated. At various roll speeds and diameters, the performance of these controllers was compared. The results revealed that the new NDMC controller outperforms the traditional PID controller in terms of overshoots and settling time. Haripriya et al. (2019) improved the performance of the Fractional Order Controller (FOC) in the paper industry’s Web Transport System (WTS). The FOC variables were updated utilizing the Bacterial Foraging Optimization (BFO) algorithm to minimize the Integral Absolute Error (IAE) under the physical and operational restraints of the WTS. For a reference web tension of 168 N, the effectiveness of the BFO-FOC was verified by comparing its step response to that of the PID controller, Particle Swarm Optimization-Proportional Integral (PSO-PI), BFO-PI, and PSO-FOC. According to the findings, the BFO-FOC outperformed the PSO-FOC and conventional controllers in WTS, with material quality improvement of up to 91.5% and material savings of up to 73.1%. Furthermore, the BFO-FOC outperformed the PSO-FOC and conventional controllers in terms of transient response by 8.7% and steady state response by 7.1%.

Backstepping Sliding Mode Control (BSMC) combined with a Radial Basis Function Neural Network (RBFNN) was developed by Nguyen et al. (2020) for improper roll arrangement correction in web handling systems. BSMC for web speed and tension control was designed using system equations of motion. The RBFNN was developed to quantify the roll inertia uncertainty. The estimated inertia was input into a BSMC that tracked tension and velocity. The performance of the adaptive RBFNN-BSMC controller was compared to that of the BSMC controller in MATLAB/Simulink. The adaptive RBFNN-BSMC outperformed the BSMC in terms of reference tracking and adaptability. However, the system was not tested experimentally.

Moreover, recent research conducted on tension control on web materials in manufacturing industries revealed that optimizing fuzzy logic controller’s membership functions can improve its control performance by employing stochastic optimization techniques, such as Particle Swarm Optimization (PSO), Genetic Algorithms (GA) and Bacterial Foraging Algorithm (BFA), and others. This is attributable to their capability to solve non-linear objectives and the ease with which they can obtain a global optimum quicker compared to the traditional optimization techniques. This is important since the boundaries of the membership functions in traditional fuzzy control techniques are tuned based on expert observations, which can be trial and error and do not ensure system performance. Thus, by modifying the position and shape of the designed controller’s membership functions using these hybrid optimization algorithms, the controller becomes adapted to dynamic conditions, resulting in improved control response such as increased robustness, anti-interference and improved tracking compared to other control schemes. However, the challenge with the use of hybrid optimization algorithm results in huge computational load (Haripriya et al., 2019; Hongji et al., 2018; Siddique & Tokhi, 2006). Therefore, Zhang et al. (2018) developed an online self-tuning fuzzy-PID control system based on the Robust Extended Kalman Filter (REKF) for precise tension regulation of composite fiber tape winding molding. To lower the control system’s error function, the REKF method was utilized to adjust the shape of the membership function and the position of the fuzzy-PID controller in real time. Simulation and experimental designs were used to validate the mathematical model of the fiber tape winding tension control system. The REKF-based fuzzy-PID controller exhibited strong learning ability, robustness and anti-interference performance, according to the findings. The winding tension control precision improved by 40%–42% when compared to traditional fuzzy-PID control.

3.7. Advantages and disadvantages of the various controllers

As indicated in the previous sections, many control algorithms have been employed for the regulation of web tension such as the conventional control method, advanced control method, observer-based control, intelligent control method and hybrid control method. The use of this control methods comes with its own advantages and limitation. The advantages and limitations of this controllers are presented and summarized in Table 1 (Behrooz et al., 2018, Idrissi et al., 2022; Gruber & Balemi, 2010; Mohd Ali et al., 2015; Ofosu et al., 2019).

Table 1. Advantages and limitation of the various control algorithms.

Control method	Advantages	Limitations
Manual/ mechanical control	It is simple to implement. Low initial cost. Simple structure.	Low control precision. Unable to reach steady state. High maintenance cost. Low speed and low efficiency. Not accurate in setpoint tracking.
Conventional PID control	Dominant control technique in web tension control. Simple in construction and easy to design. Reduced computational load. Cost effective and easy to implement. Steady state error reduction can be attained by increasing parameter gains.	Use of mathematical model of the system for effective control. Produces oscillations and takes a longer time to settle at steady state. Not suitable for nonlinear, complex, uncertain and time varying systems. Instability of the system when PID gains are not tuned properly. Noise has a negative impact on performance.
Active disturbance rejection control	Simple control structure. Robustness against plant uncertainties and external disturbances. Characterised by fast response speed, high accuracy and minimum overshoot. Capability to estimate and compensate the overall effects of uncertainties. Control design does not depend on the model of the plant.	Unsuitable for systems with large time delay. Proper tuning of the ESO is key to its performance. Unproven convergence and stability criterion. Exact correlation between the tuning parameters of the control system and the performance requirements is difficult to ascertain.
Sliding mode control	Rapid convergence. Simple algorithm and strong robustness to parameter uncertainties. Applicable on wide range of nonlinear and higher order systems. External disturbance rejection capability. It can handle sudden and large changes in the system dynamics. Simplification of system dynamics in terms of linearization is not a requirement.	Control algorithm is affected by high switching chattering effects. Characterised by discontinuous control law. Controller design is complex and improper design of the sliding surface can lead to unacceptable performance.
Backstepping control	Able to cope well with model uncertainty. System dimension can be extended using the recursive method. Capable of avoiding the cancellation of useful nonlinearities. Robustness against external disturbances.	Nonlinear observer is necessary when all state variables are unmeasurable. Identification of Lyapunov function is complicated. Sensitive to parameter variations. Item explosion problem is the weakness of this algorithm. Difficult to implement.
H∞ control	Effective control performance under system uncertainties. Stability and performance provide solutions to complex control issues.	Complex mathematical algorithm. Implementation is complicated. A strong system model is necessary.
Model predictive control	Control technique is cost effective. Resilience to changes in disturbances and parameters. Ability to predict future disturbances. Capable of handling slow moving process with time delay. Suitable for large systems composed of several sub-systems.	A good system’s model is necessary. High implementation cost. Application area is limited by its online computing time.
Linear quadratic regulator	Simple and easy to implement. Minimal energy use and strong stability. Mathematically effective. Addition of the Kalman filter to the system boosts performance.	Controller design is limited by the use of linearized system’s model. Full access to system’s states is a requirement. Speed of response is not guaranteed. Unsatisfactory for applications that demand a constant minimal steady state error.
Adaptive control	Appropriate for nonlinear systems with time varying or uncertain parameters. Good stability. Control variables can be modified swiftly in reaction to changes in system dynamics. Ease of use and a fast reaction time. Suitable for systems with unpredictable parameter variation and disturbances.	Requirement of good system’s model. Tedious to implement the controller. Adequate excitation is required. Adaptive loop needs to be slow than the control loop to fulfil requirement. Prove of stability is difficult in situation of changing system dynamics.
Observer-based control	Simple computational method. Simple formulation and ease of implementation. Estimation is fast.	A perfect knowledge of the system is required for its design. For proper state estimation, an exact model of the system is required. Observer coefficients should be chosen critically for effective response. Operating conditions have a big impact on convergence.
Fuzzy logic	Design is intuitive. Control is not dependent on the exact system’s model. Expert experiences are used to formulate the control rules. Capable of managing uncertainty and imprecision. Able to model reasoning mechanisms and human decision-making. The control action greatly depends on the rules given.	Difficulty in implementing operator’s knowledge. Optimisation is based on trial and error. Finding the membership function parameters and developing the optimal number of fuzzy rules are challenging. Limit cycles could occur as a result of nonlinear operation. No precise guidelines for its design. Frequent tuning is required for critical system.
Artificial neural network	Exact mathematical model is not a requirement. Capable of controlling several data and input variables. Accurate and reliable predictions. Capable of resisting unknown disturbances. Offers adaptive control parameters to models with uncertainty. One can train the control system.	Training a huge neural network takes time. Large data set is needed for quality predictions. Problem of overlearning. Absence of a methodical approach to determining the optimal network topology and the number of neurons to be added to the hidden layers. Challenge in selecting the input data of the network weights and choosing the training step, which has a significant impact on the rate of convergence. Consumes more computer power.
Adaptive neuro fuzzy inference system	Combined effect can establish membership function parameters and produce the best fuzzy rules. Swift convergence and effective dynamic reaction. High control precision, robustness and reliability. No need for a precise mathematical model of the controlled object. Control principles and membership functions are independent of expertise.	Can only use a limited number of input variables. Characterised by computational complexity. Efficient training is required. Lack of unified design tools and well-known solutions for step-by-step learning algorithms.
Genetic algorithm	Global non-derivative based optimisation. Good optimisation tool and independent of mathematical model of the system. Fast convergence speed. Algorithm is easy to understand. Parallelism, efficiency, easily modified for different problems. Large and wide solution space searching ability.	Mostly inappropriate for real-time applications. Possibility to fall into premature convergence. Tuning can be challenging. Consumes more computer power. Low accuracy.
Hybrid control	Combine the benefits of multiple control philosophies to address issues that may not be handled by a single controller. Robust, high performance and accuracy.	Intelligent control needs a lot of training data and user experience. The traditional and advanced controllers are challenging to tune. Complicated architecture.

3.8. Summary of findings

It is worth noting that, literature reviewed so far has revealed that considerable research has been done on the area of tension regulation in the Wire Electrical Discharge Machine (WEDM), printing, textile, paper, polymer, films, strip or metal foils, thin film, fabric and flexible electronic fabrication. However, tension control in the drawing stage of the electrical cable production process has received very little attention (Zhang et al., 2017). Further, even though conventional, intelligent and advanced control techniques have been developed to control web tension, with their advantages and limitations summarized in this review, their performance in terms of maximum reduction in settling time and overshoots can still be improved by the use of hybrid optimization algorithms (Li et al., 2021; Padmavathi & Sri, 2015). Although a number of hybrid control algorithms has been considered in web tension control, there is still the need to explore other recent hybrid control techniques to better enhance the control response of web tension regulation under varying tension and speed variations. Hence future work will consider the design of a novel controller optimised by other intelligent optimisation algorithms to enhance the control response of electrical wire tension control. Other novel contribution of this paper is that it is the first to conduct a survey of the various control algorithms in electrical wire tension control.

4. Conclusions

Numerous studies have been carried out on tension control of web materials in recent times. This paper gave an overview of the electrical cable manufacturing process and reviewed current control algorithms used to address the challenges of tension control of moving web. The review clearly shows that no single control strategy is able to provide a good control response in the web tension control. Hence, hybrid control algorithms are now gaining popularity in web tension control due to their improved control response such as fast response and disturbance rejection, robustness, simplicity, tracking ability and adaptability. Therefore, future research will propose a novel hybrid control technique for the industrial electrical cable tension control to better enhance the control performance of the existing control method since research on cable manufacturing tension control is rarely reported in literature. It is therefore expected that electrical cable manufacturers shall achieve increased productivity by a cutdown on production cost, minimize material wastage and improve the quality of manufactured cable upon implementation of findings.

Acknowledgement

The authors thank Jiangsu University, China for providing the resources needed to finish this research work.

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Disclosure statement

The authors affirm that they have no apparent conflicts of interest that would have affected the research presented in this study.

Additional information

Notes on contributors

Robert Agyare Ofosu

Robert Agyare Ofosu holds the degrees of BSc Electrical and Electronic Engineering from University of Mines and Technology (UMaT), Ghana and MSc Electrical and Electronic Engineering (Control Engineering Option) from Jomo Kenyatta University of Agriculture and Technology (JKUAT), Kenya. He is currently a PhD candidate in Control Science and Engineering at Jiangsu University, China. He is a member of IEEE. His research interests include control engineering, artificial intelligence and electric drives.

Huangqiu Zhu

Huangqiu Zhu received the B.S. degree in automation from the School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, China, in 1987, the M.S. degree in management from Jiangsu University in 1993, and the Ph.D. degree from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2000. From 2002 to 2003, he was a Visiting Scholar with the Swiss Federal Institute of Technology, Zurich, Switzerland. He is currently a Professor with the Department of Electrical Engineering, Jiangsu University. His research interests include magnetic bearings, magnetic suspension (bearingless) motors, and motors and movement control.