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Design proportional‐integral‐derivative/proportional‐derivative controls for second‐order time‐varying switched nonlinear systems
Author(s) -
She Zhikun,
Zhang Aijing,
Lu Junjie,
Hu Ruiqi,
Sam Ge Shuzhi
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4857
Subject(s) - pid controller , control theory (sociology) , dwell time , nonlinear system , derivative (finance) , controller (irrigation) , mathematics , tracking (education) , proportional control , computer science , control system , control (management) , control engineering , engineering , physics , temperature control , medicine , clinical psychology , agronomy , pedagogy , psychology , electrical engineering , quantum mechanics , artificial intelligence , financial economics , economics , biology
Summary Based on proportional‐integral‐derivative (PID)/PD controls, we in the article investigate the tracking problem of a class of second‐order time‐varying switched nonlinear systems. To start with, for tracking a given point under arbitrary switching signals, we propose a sufficient condition about PID controller parameters, which can be implicitly described as semialgebraic sets. Successively, we consider the tracking problem under average dwell time (ADT)‐based switching signals and propose an alternative sufficient condition about PID controller parameters. Especially, for tracking an equilibrium point of the system without controls, we can further simply utilize the proportional‐derivative control and similarly construct corresponding semialgebraic conditions about proportional‐derivative controller parameters under arbitrary switching signals and ADT‐based switching signals. Finally, two examples are given to show the applicability of our theoretical results.