Optimization Based Approach for Industrial PI Controller Design for Optimal Servo Control of Integrating Process with Constraints

Abstract

Constrained optimal control using an industrial three term controller is remarkably challenging to achieve, even for processes with simple dynamics. In this paper, an optimization based practical approach for the design of an industrial PI controller is developed for optimal servo control of integrating processes with operational constraints. The constrained optimal servo problem is formulated and converted into a simple analytical form, which allows for graphical analysis to be used to find the global optimum, by using a clever parameterization. The Lagrangian multiplier method is then applied to analytically find the optimal PI parameters by solving the equivalent unconstrained optimization problem. The developed method minimizes the optimal performance measure and also explicitly deals with the important control constraints, such as the maximum allowable limits in the controlled variable, the manipulated variable, and the rate of change of the manipulated variable. The proposed method is demonstrated through the example of a CSTR level control system.