Robust stabilization for discretized PID control systems with transmission delay

This paper deals with a designing problem of nonlinear discrete-time and discrete-value (discretized) control systems on an integer grid. Especially, in this study, robust stabilization based on the discretized PID control accompanied with transmission delay is discussed. The transmission delay is assumed to be uncertain and varying within prescribed bounds. The robust stabilization is examined in a frequency domain with respect to the worst case. In this study, the concept of a modified Nyquist and Hall diagram (off-axis M-circles) for nonlinear control systems is applied to the design procedure. Numerical examples for continuous plants are provided to verify the design method.