A PID control method based on optimal control strategy

Hong Niu; Zhijiang Feng; Qijin Xiao; Yajun Zhang

doi:10.3934/naco.2020019

Article Contents

2021, Volume 11, Issue 1: 117-126. Doi: 10.3934/naco.2020019

This issue Previous Article A density matrix approach to the convergence of the self-consistent field iteration Next Article Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control

A PID control method based on optimal control strategy

1.
College of Science, Liaoning Shihua University, Fushun Liaoning, 113001, China
2.
State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang Liaoning 110819, China

^* Corresponding author: Hong Niu
^* Corresponding author: Hong Niu

Received: May 2019

Revised: October 2019

Early access: March 2020

Published: March 2021

This paper is supported by the National Natural Science Foundation of China (61603168, 61773107, 61866021, 61890923) and CSC (201808210410)

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Abstract

A PID control method which combined optimal control strategy is proposed in this paper. The posterior unmodeled dynamics measurement data information are made full use to compensate the unknown nonlinearity of the system, and the unknown increment of the unmodeled dynamics is estimated. Then, a nonlinear PID controller with compensation of the posterior unmodeled dynamics measurement data and the estimation of the increment of the unmodeled dynamics is designed. Finally, through the numerical simulation, the effectiveness of the proposed method is vertified.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Performance of proposed PID control mehtod (Output $ y $, Reference Input $ w $)

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Figure 2. The controller $ u $

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Figure 3. The estimation of unmodelled dynamics

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Figure 4. The estimation error

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