Design of an Optimal Digital Controller with Control Delay

A quadratic optimal design is proposed for a digital control system in which there exists control delay. The design consists of: i) deriving a discrete-time equivalent plant model which includes the control delays, ii) defining a quadratic performance index which penalizes the plant states and control input continuously in time, iii) finding an optimal control law which minimizes the quadratic performance as a function of the sample period, T, and control delay, ¿, and iv) comparing the performance of the resulting design as a fuction of T, and ¿.