Nonlinear Constraint Optimization Based Robust Decentralized PID Controller for a Benchmark CSTR System Using Kharitonov-Hurwitz Stability Analysis

This paper exploits the design of a decentralized proportional integral derivative (PID) controller based on nonlinear optimization for a continuously stirred tank reactor system. The basic objective is to attain the design specifications by maintaining both the temperature and concentration. The continuously stirred tank reactor is modeled to a first-order plus dead time system by designing a decoupler. The proposed PID controller is designed on the basis of fundamentals of nonlinear optimization. Further, the overshoot is bounded with constraints on the maximum closed-loop amplitude ratio. The control algorithm is designed for decoupled systems to reduce the loop interactions and attain the servo response. The robust stability is analyzed by considering multiplicative input as well as output uncertainties, while stability is verified with the Kharitonov-Hurwitz theorem. A concise comparison is made between the proposed technique with existing methods. It is envisaged that the proposed control algorithm exhibits better servo and regulatory responses compared to the existing techniques. Furthermore, the efficacious nature of the proposed control scheme is validated by considering a wide range of closed-loop amplitude ratios.