Multi-loop PI/PID Controller Design Based on Direct Synthesis for Multivariable Systems Abstract—In this paper, a new analytical method based on the direct synthesis approach is proposed for the design of a multi-loop proportional-integral-derivative (PID) controller. The proposed design method is aimed to achieve a desired closed-loop response for the multiple-input, multiple-output (MIMO) processes with multiple time delays. The ideal multi-loop controller is firstly designed in terms of relative gain and desired closed-loop transfer function. Then the standard multi-loop PID controller is obtained by approximating the ideal multi-loop controller by the Macraulin series expansion. Simulation study demonstrates the effectiveness of the proposed method the in multi-loop PID controller design. The multi-loop PID controller designed by the proposed method shows a fast, well-balanced, and robust response with the minimum integral absolute error (IAE). Index Terms—Multi-loop PI/PID controller, Direct synthesis, Multivariable system. IMC-PID tuning, Robust controller design. I. INTRODUCTION The multi-loop PI/PID controllers, sometimes called as decentralized PI/PID controllers, have been widely utilized for processes with modest interactions for many decades because of many practical advantages such as a simple control structure, fewer tuning parameters, robustness against sensor/actuator failure, and easy understanding. Hence, many multi-loop design methods have been reported in the process control literature. However, most of the existing design methods are based on the extension of single-input, single-output (SISO) PI/PID controller design methods. The modification of the Ziegler-Nichols (Z-N) method [1] with a detuning factor to meet the stability and performance of the multi-loop control system is a typical one of this class. In the family of the modified Ziegler-Nichols method [2]-[4], the desired critical point has to be determined by identifying the critical gain and frequency and then the multi-loop controllers are tuned by the Z-N tuning method with a weighting factor. However, a common disadvantage in these methods is that they try to cope with the interaction effect by detuning while neither dynamic nor static interactions is incorporated in the design stage. Another widely used approach is the extension of single-loop relay tuning to MIMO case [5],[6]. This approach is straightforward because it directly combines a single-loop relay auto-tuning and a sequential tuning, wherein the multi-loop control system is tuned sequentially loop by loop, closing the ith loop while it is tuned and the jth loop has to open [5]. However, the poor output responses can be obtained when the MIMO system has large multiple time delays which is one of main causes for the strong dynamic interactions. It is well known that the integral model control (IMC) method [7] is very effective to design the IMC-PID controller for taking into account time delays and closed-loop interactions. Recently, several methods [8], [9] which extend the IMC-PID method of the SISO case to the MIMO case, are reported. In this paper, a simple but efficient design method for multi-loop PI/PID controller is presented which exploits process interactions for the improvement of loop performance. The proposed method is based on the direct synthesis approach [10],[11] in which the multi-loop PI/PID controller is designed based on the desired closed-loop transfer function [8],[9],[12]. The resulting analytical design rule includes a frequency-dependent relative gain array [13], [14] that provides information of dynamic interactions useful for estimating the controller parameters. Manuscript received July 22 nd , 2008. This work was supported by Brain Korea (BK) 21. Truong Nguyen Luan Vu and Moonyong Lee are with the School of Display & Chemical Engineering, Yeungnam University, 214-1, Dae-dong, Gyeongsan , Gyeongbuk 712-749, Korea (corresponding author to provide phone: 082-53-810-3241; fax: 082-53-811-3262; e-mails: tnluanvu@yahoo.com, mynlee@yu.ac.kr ). Truong Nguyen Luan Vu and Moonyong Lee G cn (s) " G c2 (s) G c1 (s) G(s) Y 1 R 1 - Y 2 R 2 + + - Y n R n + - Fig.1 Multi-loop control system. Proceedings of the World Congress on Engineering and Computer Science 2008 WCECS 2008, October 22 - 24, 2008, San Francisco, USA ISBN: 978-988-98671-0-2 WCECS 2008