Robust Stabilization and Discretized PID Control

Abstract

At present, almost all feedback control systems are realized using discretized (discrete-time and discrete-value, i.e., digital) signals. However, the analysis and design of discretized/quantized control systems has not been entirely elucidated. The first attempt to elucidate the problem was described in a paper by Kalman (1) in 1956. Since then, many researchers have studied this problem, particularly the aspect of understanding and mitigating the quantization effects in quantized feedback control, e.g.,(2–4). However, few results have been obtained for the stability analysis of the nonlinear discrete-time feedback system. This article describes the robust stability analysis of discrete-time and discrete-value control systems and presents a method for designing (stabilizing) PID control for nonlinear discretized systems. The PID control scheme has been widely used in practice and theory thus far irrespective of whether it is continuous or discrete in time (5; 6) since it is a basic feedback control technique. In the previous study (7–9), a robust stability condition for nonlinear discretized control systems that accompany discretizing units (quantizers) at equal spaces was examined in a frequency domain. It was assumed that the discretization is executed at the input and output sides of a nonlinear continuous elemet (sensor/actuator) and that the sampling period is chosen such that the size is suitable for discretization in the space. This paper presents a designing problem for discretized control systems on a grid pattern in the time and controller variables space. In this study, the concept of modified Nyquist and Nichols diagrams for nonlinear control systems given in (10; 11) is applied to the designing procedure in the frequency domain.