Robust PID control of a tuned mass damper system and its stability analysis validation by Kharitonov and Edge theorems

ABSTRACT

A robust control and stability analysis of a tuned mass damper attached to benchmark the model of mass-spring-damper system via different Kharitonov-related approaches, including the post-Kharitonov Edge Theorem, is presented in this paper. The control of uncertain parameters of the given system is demonstrated via robust Proportional-Integral-Derivative (PID) system tuning techniques in MATLAB. Usually, the Kharitonov theorem is sufficient to check the stability analysis of a controlled interval system. A detailed stability analysis of the given system by forming the Kharitonov rectangular parameter boxes and testing the positivity of Hurwitz determinants of the enclosed segments connecting opposite corners of the box is explained here. Stability checking is validated by the analysis based on the Hurwitz matrices of two Kharitonov polynomials. The multi-linear affine system model in the overall system plant is controlled and analysed via Edge theorem.

KEYWORDS:

• Kharitonov rectangle
• Hurwitz
• mass-spring-damper
• Edge theorem

Acknowledgments

The author thanks Dr. S. Dasgupta for his valuable inputs. This work is supported by the Kerala University Post Doctoral Fellowship vide UO. No. Ac.EVII/Bud.Sp.I.8/2019 dt 22/11/2019.

Disclosure statement

The author finds no potential conflict of interest with the journal policy.

Data availability statement

The author declares that the data supporting the findings of the present research work are available in the reference which is publicly available https://engineering.purdue.edu/~ce573/Documents/Intro%20to%20Structural%20Motion%20Control_Chapter4.pdf

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Johnson Y

Johnson Y is Teacher in Electrical Engineering with research passion in control systems studies. Presently Postdoctoral Fellow in Technology Management in the University of Kerala, India. Received PhD from the University of Kerala in 2019 in aerospace and control system. More than 18 years of experience in teaching, research, industry and administration levels. Hold various positions in government and private engineering colleges as department heads/PG coordinators/Lecturers; in public and private industrial sectors as engineer and in government department as system administrator. Recipient of the prestigious Aerospace Engineering Division Prize international award in 2014 from the Institution of Engineers (India). Founder of the academic start-up M/s Future Tech Solution, registered under Industries Department, Govt of Kerala. Two patent application publications and more than 20 research articles are published in various international journals and conference proceedings. Worked as resource person and speaker in many conferences and webinars, attended in more than 100 workshops/seminars. Received many funded projects from Govt of India and Kerala. Member of many professional organizations like IE(I), KAS, ECS etc.