Design and tuning method of PID controller for a class of inverse response processes

Inverse response processes are difficult to be controlled due to presence of right half plant (RHP) zeros. In this paper, firstly the RHP zeros are approximated to the form of dead time in terms of Pade approximation theory. Thus, the controlled processes can be regarded as general stable processes plus dead time without RHP zeros. Then based on the internal model control (IMC) structure, an analytical PID controller design procedure is developed for the transformed inverse response processes. The resulting controller includes a single adjustable control parameter. Through stability analysis for the proposed control system, the stable range of the control parameter is derived according to a simple method called dual-locus diagram, and meanwhile, the sufficient and necessary condition for holding the proposed closed-loop system robust stability is provided. By monotonously tuning the single controller parameter, the good compromise between the nominal performance and robust stability of the closed loop system can be realized. The simulation example demonstrates the superiority of the proposed control scheme.