This paper proposes an iterative linear matrix inequality (LMI) method for tuning the parameters of multi-input multi-output (MIMO) proportional–integral–derivative (PID) controllers. The proposed method calculates the parameters of controller such that the singular values (SVs) of the sensitivity function are shaped according to the given weight function. For this purpose, first using bounded real lemma (BRL), this problem is represented as a bilinear matrix inequality (BMI) where one of the matrix variables is the variable of Lyapunov equation and the other is structured and contains the matrices of the state-space representation of the controller. This BMI is solved approximately using a novel iterative procedure which linearizes the BMI around an initial solution to arrive at an LMI. The point around which the BMI is linearized is updated automatically at each iteration and the linearized BMI has the nice property that it is obtained by minimizing the amplitude of nonconvex terms.
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November 2018
Research-Article
Multivariable Proportional-Integral-Derivative Controller Tuning Via Linear Matrix Inequalities Based on Minimizing the Nonconvexity of Linearized Bilinear Matrix Inequalities
Farshad Merrikh-Bayat
Farshad Merrikh-Bayat
Department of Electrical and
Computer Engineering,
University of Zanjan,
Zanjan 4537138791, Iran
e-mail: f.bayat@znu.ac.ir
Computer Engineering,
University of Zanjan,
Zanjan 4537138791, Iran
e-mail: f.bayat@znu.ac.ir
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Farshad Merrikh-Bayat
Department of Electrical and
Computer Engineering,
University of Zanjan,
Zanjan 4537138791, Iran
e-mail: f.bayat@znu.ac.ir
Computer Engineering,
University of Zanjan,
Zanjan 4537138791, Iran
e-mail: f.bayat@znu.ac.ir
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received October 11, 2017; final manuscript received May 19, 2018; published online June 18, 2018. Assoc. Editor: Yunjun Xu.
J. Dyn. Sys., Meas., Control. Nov 2018, 140(11): 111012 (9 pages)
Published Online: June 18, 2018
Article history
Received:
October 11, 2017
Revised:
May 19, 2018
Citation
Merrikh-Bayat, F. (June 18, 2018). "Multivariable Proportional-Integral-Derivative Controller Tuning Via Linear Matrix Inequalities Based on Minimizing the Nonconvexity of Linearized Bilinear Matrix Inequalities." ASME. J. Dyn. Sys., Meas., Control. November 2018; 140(11): 111012. https://doi.org/10.1115/1.4040420
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