Designing and tuning MIMO feedforward controllers using iterated LMI restriction

Saeedreza Tofighi; Farshad Merrikh-Bayat; Farhad Bayat; Saeedreza Tofighi; Farshad Merrikh-Bayat; Farhad Bayat

doi:10.3934/era.2022126

Electronic Research Archive

2022, Volume 30, Issue 7: 2465-2486. doi: 10.3934/era.2022126

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Research article

Designing and tuning MIMO feedforward controllers using iterated LMI restriction

Department of Electrical and Computer Engineering, University of Zanjan, University Blvd., Zanjan 45371-38791, Iran

Academic Editor: Predrag Stanimirovic

Received: 29 December 2021 Revised: 18 April 2022 Accepted: 25 April 2022 Published: 29 April 2022

In this paper, a multi-input multi-output (MIMO) feedforward control structure is proposed and designed based on the linear matrix inequality (LMI) approach to improve disturbance rejection and reference tracking of the given feedback system. The proposed architecture consists of two MIMO feedforward controllers, where each controller can be designed independently using the proposed method. The unknown variables of the feedforward controllers are calculated using LMI restrictions such that the H_∞-norm of the transfer function matrix from disturbance (set-point) to output (error) is minimized. By taking advantage of the frequency sampling techniques and using some iterative algorithms, convergence of the solution to a local optimal point is guaranteed. For solving this optimization problem the CVX optimization tool is used and the numerical results are presented. The proposed method can be considered as a new tractable approach for tuning the parameters of MIMO feedforward controllers.
- MIMO feedforward controller,
- disturbance rejection,
- set-point tracking,
- linear matrix inequality (LMI),
- semidefinite program (SDP) optimization
Citation: Saeedreza Tofighi, Farshad Merrikh-Bayat, Farhad Bayat. Designing and tuning MIMO feedforward controllers using iterated LMI restriction[J]. Electronic Research Archive, 2022, 30(7): 2465-2486. doi: 10.3934/era.2022126

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Abstract

In this paper, a multi-input multi-output (MIMO) feedforward control structure is proposed and designed based on the linear matrix inequality (LMI) approach to improve disturbance rejection and reference tracking of the given feedback system. The proposed architecture consists of two MIMO feedforward controllers, where each controller can be designed independently using the proposed method. The unknown variables of the feedforward controllers are calculated using LMI restrictions such that the H_∞-norm of the transfer function matrix from disturbance (set-point) to output (error) is minimized. By taking advantage of the frequency sampling techniques and using some iterative algorithms, convergence of the solution to a local optimal point is guaranteed. For solving this optimization problem the CVX optimization tool is used and the numerical results are presented. The proposed method can be considered as a new tractable approach for tuning the parameters of MIMO feedforward controllers.

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