Integer discretized pid control for continuous plants with time delay

The state as well as time of discretized (digital) PID controller for continuous plants can be considered as an integer number. This paper describes a designing problem of such nonlinear discrete-time control systems on an integer-grid pattern. 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.