Digital controller design for absolute value function constrained nonlinear systems via scalar sign function approach

Abstract

In this paper, a scalar sign function-based digital design methodology is developed for modeling and control of a class of analog nonlinear systems that are restricted by the absolute value function constraints. As is found to be not uncommon, many real systems are subject to the constraints which are described by the non-smooth functions such as absolute value function. The non-smooth and nonlinear nature poses significant challenges to the modeling and control work. To overcome these difficulties, a novel idea proposed in this work is to use a scalar sign function approach to effectively transform the original nonlinear and non-smooth model into a smooth nonlinear rational function model. Upon the resulting smooth model, a systematic digital controller design procedure is established, in which an optimal linearization method, LQR design and digital implementation through an advanced digital redesign technique are sequentially applied. The example of tracking control of a piezoelectric actuator system is utilized throughout the paper for illustrating the proposed methodology.