Discretized PID control and robust stabilization for continuous plants on an integer-grid pattern

This paper describes discretized PID control and robust stabilization for continuous plants on a grid pattern that is composed of integers. Although all control systems are currently realized using discretized signals, the analysis and design of discrete-time and discrete-value (digital) control systems has not been elucidated. In this paper, a designing problem of such nonlinear discrete-time control systems based on the PID algorithm is presented in a frequency domain. In the design procedure, the concept of a modified Nyquist and Hall diagram (off-axis M-circles) for nonlinear control systems is applied. Numerical examples for continuous plants with time delay are provided to verify the design method.