Tuning Proportional−Integral−Derivative Controllers for Integrator/Deadtime Processes

Abstract

Chien and Fruehauf proposed the use of a simple integrator/deadtime transfer function to model many chemical processes, particularly those with large time constants. Tyreus and Luyben presented tuning rules that give the optimal reset time and controller gain for proportional−integral (PI) control of this type of process. This paper extends the previous work with PI control to proportional−integral−derivative (PID) controllers. Tighter control is possible with PID control, provided signals are not noisy. Frequency domain methods are used to show that the derivative tuning constant should be set equal to the reciprocal of the ultimate frequency. The controller gain is then set equal to 0.46 times the ultimate gain. This process has unusual dynamic behavior when PID control is used, which makes controller tuning nontrivial. The system exhibits conditional stability: at low controller gains the loop is unstable, and at high controller gains the loop is again unstable. Contrary to conventional tuning, a decrease in gain results in an unexpected decrease in closed-loop damping coefficient over a certain range of controller gains.