Tuning of PID Controllers for Unstable Systems Using Direct Synthesis Method

Abstract

Tuning of proportional integral derivative (PID) controllers for unstable first-order plus time delay systems and unstable second-order plus time delay systems is proposed using the direct synthesis (DS) method. In this method, the mode of PID controller is selected and the characteristic equation of the unstable process with the PID controller is compared with the desired characteristic equation to derive PID controller parameters. The performance of the proposed controller is compared with the recently reported DS method, internal model control method and setpoint overshoot method (SOM) to demonstrate the efficiency of the controller. The performance comparison is made in terms of integral absolute error (IAE). The smooth functioning of controller is determined in terms of total variation (TV) (input usage). The controllers designed by the present method are applied to many transfer function models and the nonlinear model of isothermal continuous stirred tank reactor (CSTR) carrying out an enzymatic reaction with nonlinear kinetics and jacketed CSTR carrying out a first-order reaction. The robustness of the controller is given in terms of Ms (maximum magnitude of the sensitivity function), phase margin and gain margin.

Keywords:

• Unstable FOPTD system
• Unstable SOPTD system PID controller
• Direct synthesis method
• Time delay
• CSTR