Robust Discrete-Time Quasi-Sliding Mode Based Nonlinear PI Controller Design for Control of Plants with Input Saturation

Abstract

This paper proposes a new design of discrete-time nonlinear PI (DNPI) controller, which is based on the sliding mode (SM) control principle with disturbance observation via integral of the switching function. To enhance robustness to uncertainties and external disturbances, sign element is inserted between the switching function and the controller’s integrator. Thus, high integral-gain is obtained for low-level signals, whereas the output signal has limited amplitude. Such structure looks like as discretized variant of continuous-time super twisting algorithm (STA) structure, in which the square root element is replaced by a linear one. Furthermore, the standard STA structure is here additionally modified in order to adjust the quasi-sliding domain reaching speed and to suppress large overshoots. Tuning of the proposed DNPI controller is very simple. Since control system with DNPI controller produces steady-state oscillations due to digital implementation, oscillation parameters are determined for nominal system. Additionally, in case of a system with unmodeled inertial dynamics, a simple procedure is developed for determining parameters or the consequential oscillations, using describing function approach. Theoretical explanations are illustrated by simulation results.