Robust stabilization and PID control for nonlinear discretized systems on a grid pattern

This paper describes robust stabilization and PID control for discrete-time and discrete-value (discretized/quantized) control systems. Although all control systems are currently realized using discretized signals, the analysis and design of such nonlinear discrete-time control systems has not been elucidated. In this paper, the robust stability analysis of discrete-time and discrete-value (digital) control systems with discretizing units at the input and output sides of a nonlinear continuous element (sensor/actuator) are examined in a frequency domain, and a method of designing PID control and robust stabilization for nonlinear discretized systems on a grid pattern in the time and control variables space is presented. A modified Nichols diagram and parameter specifications are used in this study. Numerical examples are provided to verify the validity of the designing method.