Design of optimal PID controller with \(\epsilon\)-Routh stability for different processes
type: Item
instance of: scholarly article
title: Design of optimal PID controller with \(\epsilon\)-Routh stability for different processes
zbMATH Open document ID: 1299.93186
DOI: 10.1155/2013/582879
author: Xianhong Li
author: Mingzhe Yuan
author: Haibin Yu
published in: Mathematical Problems in Engineering
publication date: 2014-11-24T00:00:00Z
review text: Summary: This paper presents a design method of the optimal proportional-integral-derivative (PID) controller with \(\epsilon\)-Routh stability for different processes through Lyapunov approach. The optimal PID controller could be acquired by minimizing an augmented integral squared error (AISE) performance index which contains control error and at least first-order error derivative, or even may contain \(n\)th-order error derivative. The optimal control problem could be transformed into a nonlinear constraint optimization (NLCO) problem via Lyapunov theorems. Therefore, optimal PID controller could be obtained by solving NLCO problem through interior method or other optimization methods. The proposed method can be applied for different processes, and optimal PID controllers under various control weight matrices and \(\epsilon\)-Routh stability are presented for different processes. Control weight matrix and \(\epsilon\)-Routh stability's effects on system performances are studied, and different tuning methods' system performances are also discussed. \(\epsilon\)-Routh stability's effects on disturbance rejection ability are investigated, and different tuning methods' disturbances rejection ability is studied. To further illustrate the proposed method, experimental results of coupled water tank system (CWTS) under different set points are presented. Both simulation results and experiment results show the effectiveness and usefulness of the proposed method.
Mathematics Subject Classification ID: 93C85
Mathematics Subject Classification ID: 93C80
Mathematics Subject Classification ID: 93B50
zbMATH DE Number: 6372781
Wikidata QID: Q59026892
describes a project that uses: LIPSOL
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/582879
OpenAlex ID: W1980430598
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description: scientific article; zbMATH DE number 6372781