Identification for PID control

Abstract

In this study, we address issues arising in system identification-based plant modeling for the purpose of tuning PID controllers. We discuss some of the more celebrated tuning methods and make an attempt to anticipate future directions of identification procedures in the effort to provide reliable answers to more involved problems. The algorithmic progression of the different methods starts with easy-to-estimate, minimal information about the plant, in the form of a single frequency point in the Nyquist plot or a couple of parameters of the step response, aiming to produce the tuning parameters with back-of-the-envelope calculations. High order general models from either first-principles modeling or system identification were then used in a variety of off-line or on-line optimization problems to produce optimal PID tunings, and were often converted to the always elusive set of quick calculations that could tune a PID controller in the field. Highest in complexity, are the most recent methods which involve maximal information about the plant, in the form of one or more nominal models and a description of uncertainty, and aim for a tuning that combines high performance, adequate robustness, and high reliability. The latter appears to be the key qualitative difference between early and late identification and controller tuning procedures, that is, the ability to provide a reliable tuning with minimal trial-and-error. An alternative implementation of the same concepts can be performed as a direct optimization of the PID parameters, that can be readily converted to an attractive on-line tuning application. Finally, employing more complex, min–max identification methods can safeguard against performance deterioration problems due to disturbances or poorly designed excitation, albeit with a significant increase in computational load and identification time.