Optimal disturbance rejection controller design for integrating processes with dead time based on algebraic theory

In this paper, an H₂ optimal input-load disturbance rejection (ILDR) controller for integrating processes with dead time is proposed based on the internal model control principle. The main contribution of this work is that the optimal solution under ILDR criterion for integrating processes with dead time and input constant disturbances has been derived based on algebraic theory. To further improve the performance for both set-point tracking and input disturbance rejection, a two-degree-of-freedom (TDOF) control design method has also been developed. Compared with previous advanced control methods, the proposed design method has three main advantages. First, the optimal ILDR controller is derived systematically on the basis of algebraic theory. The designed controller is given in an analytical form. Second, a simple tune principle is developed. The set-point tracking performance specification and robustness stability specification can be quantitatively achieved by monotonously tuning the performance degree in the designed controller. Finally, both optimal set-point tracking performance and input disturbance rejection can be achieved by the proposed TDOF control structure. Numerical simulations are given to illustrate the effectiveness of the proposed method.