An Amplitude‐ and Rate‐Saturated Controller for Linear Plants

Abstract

This paper proposes a new nonlinear controller applicable to single-input linear systems under bounded disturbance. The controller provides control signals satisfying specified amplitude and rate-of-change limitations. This feature is realized by its sliding mode-like structure comprising a set-valued function. The controller also employs a state-dependent parameter to broaden the region of attraction and to shrink the terminal attractor. In addition, this paper provides a discrete-time implementation of the proposed controller based on a model-based implicit discretization scheme. Numerical examples show the validity of the proposed controller.

Digital implementation of sliding‐mode control via the implicit method: A tutorial

“…which is obtained by inverting the set-valued signum function as in (1). From (10), and using (2), one obtains equivalently to (10):…”

“…• Variational Inequalities: Starting from (10) and (12) and using the normal cone definition, one finds:…”

“…These are introduced in [11,10], to control linear invariant systems with matched perturbations, as in (21). The input is defined through a differential inclusion as:…”

“…We should also mention the analysis of the implicit Euler method for linear complementarity systems and relay systems, with main applications in circuits with nonsmooth components [21,70,22]. In slidingmode control and observation, the implicit approach has been initiated and deeply analysed by two main research groups, in France [2,3,4,7,19,48,50,51,47,83,85,87,101,36,119,49,20], and in Japan [9,64,11,79,56,65,55,125,126,59,62,10,60,123,124]. We may also mention [66,67,121] (who apply a kind of semi-implicit discretization method based on pseudo linear representations), as well as the pioneering work in [30] where the implicit Euler discretization was advocated for the first time in Automatic Control for a scalar system with known perturbation (see Remark 1 below), and with a short analysis of its finite-time convergence properties.…”

Continuous and discrete-time stability of a robust set-valued nested controller

“…Also related to our work is [24], where the problem of control with amplitude-and rate-saturation constraints is addressed with a nested sigmoidal controller.…”