An empirical method for tuning a discrete PID controller to achieve near time-optimal response of a first order plus integrator plant

A method to choose controller gains for a PID controller to produce a fast response with no overshoot for step set point changes was developed for a First Order Lag plus Integrator System. By choosing controller gains such that the output remains saturated during most of the set point change, an approximately time-optimal response could be achieved. To tune the controller, a fixed value for the proportional gain was chosen to achieve saturation and a fixed value for the integral gain was chosen to eliminate steady-state errors due to disturbances. Using a simulation of the closed-loop system, a single-dimensional search algorithm to determine an optimal value of the derivative gain was used to generate a set of data relating this optimal gain to the time constant, plant gain, and set point system parameters. Using symbolic regression, a function to generate Kd based on these parameters was obtained. Simulation results showed that this tuning method resulted in the generation of a bang-bang type control actions, resulting in fast settling times and no overshoot while maintaining reasonable disturbance rejection. Similar results were obtained when the controller was implemented on a microcontroller controlling a DC motor