Robust Proportional-Integral-Derivative Controller Design for Stable/Integrating Processes with Inverse Response and Time Delay

Processes that exhibit dynamic behaviors of inverse response and time delay increase the difficulty of control system design. This paper presents the design concepts that lead to robust tuning of a proportional-integral-derivative (PID) controller for stable/integrating processes with inverse response and time delay. The proposed control system design is based on a Smith-type compensator for nonminimum phase dynamics, which aims to remove these elements from the feedback loop. In this control scheme, it is necessary to factorize the process model into minimum phase and nonminimum phase parts. By investigating and comparing different factorization methods, this study shows that a system based on the direct factorization method can achieve better trade-off between control performance and system robustness. Furthermore, this study approximates the equivalent feedback controller for the proposed control configuration as a classical PID controller based on Maclaurin-series approach. Analytical tuning rules for the PID controller are developed, and the analysis of robust stability is provided. Adjusting a tuning parameter can achieve a superior trade-off between nominal performance and robust stability of the closed-loop system. Simulation results confirm the superiority of the proposed control design method.