Improved Continuous Cycling Method of Tuning PID Controllers for Unstable Systems

In the present work, an improved continuous cycling method is proposed for tuning proportional-integral-derivative (PID) controllers for unstable systems. The method involves the determination of the controller settings by solving the magnitude criterion and the phase angle criterion for the system. Subsequently, incorporating the transfer function of the PID controller, with unity proportional gain, with the system model and again solving the amplitude and the phase angle criteria to get the updated gain of the controller. The proposed method is applied by simulation on (i) a second-order system with one unstable pole and (ii) a nonlinear model of a bioreactor. The method is also extended for the relay tuning method to automate the improved continuous cycling method. The controller settings significantly enhance the performances (integral time absolute error) of both the servo and the regulatory problems and also give a robust performance. The present method is compared with the reported methods based on the ultimate cycle and with the method proposed by Jeng and Fu [“Closed Loop Tuning of Set Point Weighted Proportional-Integral-Derivative Controllers for Stable, Integrating and Unstable Processes: A Unified Data Based Method”, Ind. Eng. Chem. Res., 54, pp. 1041–1058 (2015)].