Model‐based synthesis of nonlinear PI and PID controllers

Abstract PI and PID controllers continue to be popular methods in industrial applications. It is well known that linear PI and PID controllers result from the application of model‐based controller design methods to linear first‐ and second‐order systems. It is shown that nonlinear PI and PID controllers result from the application of nonlinear controller design methods to nonlinear first‐ and second‐order systems. As a result, the controllers resulting from nonlinear model‐based control theory are put in a convenient form, more amenable to industrial implementation. Additionally, the quantities used in the controller are useful for monitoring the process and quantifying modeling error. Chemical engineering examples are used to illustrate the resulting control laws. A simulation example further demonstrates the performance of the nonlinear controllers, as well as their useful process monitoring quantities.