Asymptotic tracking and disturbance rejection of time-varying signals with a discontinuous PID controller. (March 2020) - Moreno, Jaime A.
Highlights: A novel Discontinuous PID Controller is presented, which is able to track in finite time a large class of time-varying references while rejecting time-varying perturbations for uncertain SISO nonlinear systems having relative degree two and Bounded-Input-Bounded-State zero dynamics. This is a simple solution to the classical asymptotic tracking and disturbance rejection problem is achieved thanks to the use of the discontinuous integral term, which acts as a universal internal model for the class of references and perturbations which are Lipschitz continuous, i.e. with a bounded time derivative. This is in contrast to the known solutions to this problem, which require a rather complex internal model of high dimension, that not only makes the realization of the controller more difficult, but also deteriorates the transient behavior in closed loop. The advantages of our proposal is illustrated by a comparison in simulation with a nice solution to the problem given in the literature. The Discontinuous PID controller proposed is driven by the output of the system, and this is achieved by using a continuous observer, which plays the role of the D-term of the PID control. Abstract: A novel non linear PID controller is introduced in this paper, which has a discontinuous integral term. It is able to robustly asymptotically track any time-varying reference while rejecting perturbations with bounded derivatives for uncertain SISO nonlinear plants of well-defined relative degree two and with bounded zero dynamics. This is achieved because the discontinuous integral term takes the role of a universal internal model for this class of references and perturbations. The proposed controller is compared with a well established solution for this problem in the literature to illustrate its advantages. The main benefit is possibly the simplicity of the controller structure and its universality, since it applies to a large class of plants, references and perturbations without modifications.