Communications in Information and Systems

Volume 21 (2021)

Number 3

Control of nonlinear uncertain systems by extended PID with differential trackers

Pages: 415 – 440



Lei Guo (Key Laboratory of Systems and Control, ISS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

Cheng Zhao (Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Shandong, China)


It is well-known that the classical proportional-integral-derivative (PID) controller plays a dominating role in practical control systems, and that most of the existing studies on PID are focused on linear systems. Recently, we have established global stability and convergence of the PID controller for a class of nonlinear uncertain systems with relative degree two and, at the same time, provided some necessary and sufficient conditions for the choice of the PID parameters. We will in this paper consider a class of affine-nonlinear uncertain systems with a general relative degree n, and investigate the capability of the extended PID with differential trackers together with the choice of the controller parameters. We will show that under suitable conditions on the uncertain system nonlinearities, an $(n + 1)$-dimensional parameter set can be constructed explicitly, such that whenever the extended PID parameters are chosen from this parameter set, the regulation error will converge to $0$ globally and exponentially.

This work was supported by the National Natural Science Foundation of China under Grant No. 11688101.

Received 16 May 2020

Published 4 June 2021