Multi-objective Optimal Antiwindup Compensation of Discrete-Time Nonlinear Systems Under Input Saturation

This paper deals with the discrete-time antiwindup compensator (AWC) synthesis for nonlinear discrete-time systems under input saturation. The proposed method considers the objective of an optimal AWC design for fast convergence and for improved performance against the saturation nonlinearity. A discrete-time full-order AWC architecture is presented for nonlinear discrete-time systems to achieve an improved performance against the saturation nonlinearity. Additionally, an equivalent decoupled AWC architecture for nonlinear discrete-time system is derived through algebraic analysis and transformation of saturation to dead-zone function. To achieve fast convergence, a more generic Lyapunov function has been applied for the AWC design by incorporating an exponential term in the Lyapunov function. Then, new conditions for the AWC synthesis are revealed by application of the resultant decoupled discrete-time architecture, nonlinearity condition, a modified quadratic-exponential Lyapunov function, optimally exponential L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{2}$$\end{document} approach, and input saturation properties. The design conditions are provided for both global and local design scenarios, which can be applied to both stable and unstable plants. Compared with the conventional methods, the proposed approach deals with nonlinear systems, can be more practical due to discrete-time scenario, provides an optimal design for both fast convergence and performance, and applicable to both stable and unstable plants. A simulation example has been provided to demonstrate the efficacy of the proposed nonlinear AWC design.