Design of a Nonlinear PID Controller and Tuning Rules for First-Order Plus Time Delay Models

This paper introduces a simple but effective nonlinear proportional-integral-derivative (PID) controller and three model-based tuning rules for first-order plus time delay (FOPTD) models. The proposed controller is based on a conventional PID control architecture, wherein a nonlinear gain is coupled in series with the integral action to scale the error. The optimal parameter sets of the proposed PID controller for step setpoint tracking are obtained based on the FOPTD model, dimensional analysis and a genetic algorithm. As for gauging the performance of the controller, three performance indices (ISE, IAE and ITAE) are adopted. Then, tuning rules are derived using the tuned parameter sets, potential rule models and the least squares method. The simulation results carried out on three processes demonstrate that the proposed method exhibits better performance than the conventional linear PID controllers.