Discretized PID control on an integer grid

This paper describes discretized PID control and robust stabilization for continuous plants on an integer grid. 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, a modified Nichols diagram and parameter specifications are applied. Numerical examples are provided to verify the validity of the designing method.