PLC Implementation of Piecewise Affine PI Controller Applied to Industrial Systems with Constraints

Abstract

In this paper, the design of a piecewise affine proportional integral (PWA-PI) controller algorithm based on invariant set and multiparametric programming for constrained systems is proposed. We implemented the algorithm in a programmable logic controller (PLC) to control an industrial constrained level plant and analyze its behavior. Structured text routines were programmed and validated while controlling two systems with PLC. The results show that the constraints on the error, integral of the error, system output and control action are respected because PWA-PI controllers are tuned from the solution of an optimization problem. The evaluated performance indexes (such as mean square error, Goodhart, overshoot and settling time) show that PWA-PI can be adjusted for better performance than proportional integral (PI) controller tuned by Ziegler–Nichols (Z–N) rules. In the analyzed cases, a settling time of 108 s was obtained, whereas PI controller with Z–N rules presented a 179 s settling time. All of the analyzed performance indexes that we used to evaluate both controllers show PWA-PI as a better controller for constrained systems.