# American Institute of Mathematical Sciences

March  2021, 11(1): 117-126. doi: 10.3934/naco.2020019

## 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

Received  May 2019 Revised  October 2019 Published  March 2020

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

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.

Citation: Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019
##### References:

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##### References:
Performance of proposed PID control mehtod (Output $y$, Reference Input $w$)
The controller $u$
The estimation of unmodelled dynamics
The estimation error
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