Practical design of PID-type controllers with constraints

Abstract

The proportional-integral-derivative (PID) controller has extensively been used in the process industries and is taught in most undergraduate engineering and engineering technology programs. Various PID design/tuning methods have been proposed over the years such as the famous Ziegler-Nichols method, the Internal Model Control (IMC) method, and the many variations of it. Given a process model, these methods estimate values for the PID tuning parameters: proportional gain, integral time, and derivative time. Many of the tuning methods include a tunable parameter, for instance the filter time constant in the case of the IMC method that the user must "tune". Furthermore, none of these techniques considers process constraints in the PID design. However, from a practical viewpoint, process and final control element constraints must be accounted for. Recently, a methodology based on has been developed to design PID controllers subject to controlled variable as well as manipulated variable (size and rate) constraints while a performance criterion is optimized. This paper extends this methodology to determine the "tunable" parameters of other PID design methods while process and equipment constraints are satisfied. Estimation of the IMC filter time constant is considered. Simulation and experimental results demonstrate the practicality of the new PID design method.