Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

Abstract

Summary This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous L2 bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and L2 gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.

A note on a performance recovery method for a class of nonaffine‐in‐control nonlinear systems with input saturation

“…Theorem 1. Consider the nonaffine-in-control nonlinear system with input saturation in (1). 16) has unique solutions x ∈ S x and z ∈ S z , for t ∈ [t 0 , t 1 ], where S x and S z are compact subsets of D x and D z .…”

“…Actuator saturation is acquiesced to be considered for a number of systems since almost all physical control devices may have this kind of limitation. 1,2 The existence of input saturation may destroy the stability or degrade the transient performance of the predesigned control systems. Therefore, performance recovery of systems with input saturation is one of the most important issues in the control system design.…”

A Novel Distributed Consensus-Based Approach to Solve the Economic Dispatch Problem Incorporating the Valve-Point Effect and Solar Energy Sources

“…We took support from Lyapunov stability theory, and considered the following Lyapunov function [56,57]:…”

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

“…[20][21][22][23] In the case of saturating actuators it is advantageous to design an antiwindup structure to mitigate the consequence of saturating actuators. 24,25 The stability analysis and the synthesis of parameter varying dynamical controller for LPV systems with delayed states and saturating actuators lead to a challenging task that requires a local stability approach and a more involved way to characterize the region of attraction for the initial conditions. Delay-dependent conditions for the design of a robust observer-based output feedback controller are derived in Reference 26 to locally stabilize the uncertain continuous-time systems with delayed states, saturating actuators, and subjected to amplitude bounded disturbance inputs, where the uncertainties are time-varying and norm-bounded.…”

“…In the case of parameter varying dynamic output controllers for discrete‐time (quasi‐)LPV systems, one can find different results based on the Lyapunov approach 20‐23 . In the case of saturating actuators it is advantageous to design an antiwindup structure to mitigate the consequence of saturating actuators 24,25 …”