Optimal adaptive state feedback control for a three degree-of-freedom series-type double inverted pendulum system by using particle swarm optimisation

ABSTRACT

This research tries to stabilise a three degree-of-freedom series-type double inverted pendulum system by employing an adaptive state feedback control approach optimised by a particle swarm optimisation (PSO) algorithm. To this end, the dynamical equations are derived via Lagrangian method and linearised by utilising approximation approaches. Then, the state feedback scheme is implemented to control the system states, that is, the angle and angular velocity of the first and second poles as well as the position and velocity of the cart. In order to timely regulate the control gains, the adaptation rules based on the gradient descent method and sliding surface relations are applied. The particle swarm optimisation algorithm is implemented to optimally tune the design parameters of the controller based on a proper objective function defined as summation of integrals of absolute values of the system errors. The time responses of the angles of the poles and the position of the cart clearly depict the feasibility and efficiency of the introduced control strategy to stabilise the system from different initial conditions to the final desired values.

KEYWORDS:

• Series-type double inverted pendulum
• Under-actuated dynamical system
• state feedback control
• adaptive control
• optimal control
• particle swarm optimisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

M.J. Mahmoodabadi

M. J. Mahmoodabadi received his BS and MS degrees in Mechanical Engineering from Shahid Bahonar University of Kerman, Iran in 2005 and 2007, respectively. He received his Ph.D. degree in Mechanical Engineering from the University of Guilan, Rasht, Iran in 2012. During his research, he was a scholar visitor with Robotics and Mechatronics Group, University of Twente, Enchede, the Netherlands for 6 months. Now, he is an Associate Professor of Mechanical Engineering at the Sirjan University of Technology, Sirjan, Iran. His research interests include optimization algorithms, nonlinear and robust control and computational methods.

N. Nejadkourki

N. Nejadkourki was born in Sirjan, Kerman, Iran in 1994. She received her BS degree in Robotic Engineering from Sirjan University of Technology, Sirjan, Iran in 2019. Now, she is an MS student in Mechanical Engineering at the Sirjan University of Technology, Sirjan, Iran. Her research interests include robotics and control theory.