Theory and Design of PID Controller for Nonlinear Uncertain Systems
- 7 May 2019
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Control Systems Letters
- Vol. 3 (3), 643-648
- https://doi.org/10.1109/lcsys.2019.2915306
Abstract
It is well-known that the classical proportional-integral-derivative (PID) controller plays a fundamental role in various engineering systems. However, up to now a theory that can explain the rationale why the linear PID can effectively deal with nonlinear uncertain dynamical systems and a method that can provide explicit design formula for the PID parameters are still lacking. This motivates our recent study on the theoretical foundation of the PID control (see Zhao2017PID,zhao2017capability). The main purpose of the current paper is to extend the one-dimensional results of Zhao2017PID to higher dimensional nonlinear uncertain systems and to improve the results of zhao2017capability significantly by a refined method. We will also consider a class of multi-agent uncertain nonlinear systems where each agent is controlled by a PID controller using its own regulation error. We will show that a parameter manifold can be constructed explicitly so that when the PID parameters are chosen from this manifold, the multi-agent systems will be globally stable and the tracking error of each agent will coverage to zero exponentially fast.Keywords
Funding Information
- National Natural Science Foundation of China (11688101, 61227902)
This publication has 11 references indexed in Scilit:
- Performance analysis of 2‐DOF tracking control for a class of nonlinear uncertain systems with discontinuous disturbancesInternational Journal of Robust and Nonlinear Control, 2017
- On the Capability of PID Control for Nonlinear Uncertain SystemsIFAC-PapersOnLine, 2017
- On the applicability of PID control to nonlinear second-order systemsNational Science Review, 2017
- A Survey on Industry Impact and Challenges Thereof [Technical Activities]IEEE Control Systems, 2017
- PID controller design for second order nonlinear uncertain systemsScience China Information Sciences, 2017
- PID tuning using extremum seeking: online, model-free performance optimizationIEEE Control Systems, 2006
- PID Controllers for Time-Delay SystemsPublished by Springer Science and Business Media LLC ,2005
- PID controller design for robust performanceIEEE Transactions on Automatic Control, 2003
- How much uncertainty can be dealt with by feedback?IEEE Transactions on Automatic Control, 2000
- Refinements of the Ziegler–Nichols tuning formulaIEE Proceedings D Control Theory and Applications, 1991