Multivariable PID controller design for chemical processes by frequency response approximation

In this paper we propose a systematic approach to designing low order controllers for chemical processes using frequency response approximation. The method consists of four major steps: (i) the desired behavior for the closed-loop system in the time domain is specified. The achievable performance of the closed loop is determined to ensure internal stability because of process inherent characteristics, i.e., non-minimum phase elements; (ii) the frequency response of the “ideal” controller, which is usually high order and too complex to be realized, is algebraically determined; (iii) this response is approximated in the frequency domain through a structured low order controller with PID parameters; and finally (iv) a closed loop simulation provides design evaluation. This novel design procedure is demonstrated through two case studies. These successful applications demonstrate its efficiency and applicability to the design of low order multivariable controllers for complex industrial processes.

► We developed an approach to design structured low order controllers using optimization in frequency domain.
► The attainable closed loop performance is derived in order to keep internal stability from the desirable performance.
► The problem is solved coupling the solution of two convex problems with analytical solution.
► The results show how to design low order controllers for complex processes.