Analytical design for open loop unstable processes with time delay

This paper presents an efficient method for designing the controller for open loop unstable processes with time delay. Based on the optimal control theory and robust control theory, the stabilizing controller of the closed loop system is parametrized, an optimal design index is introduced for controller design, and explicit formulas are derived analytically. The optimal controller can be equivalent to the Smith predictor. It is found that the classical Smith predictor can not be used for the control of open loop unstable processes. By using the rational interpolation technique to cancel the right half plane zero of the controller, an approximate method is developed to implement the new controller in the unity feedback control loop. Examples are given to illustrate the new method