MULTILOOP PID CONTROLLERS TUNING FOR DESIRED CLOSED LOOP RESPONSES Dong-Yup Lee 1 , Moonyong Lee 2 , Yongho Lee 3 and Sunwon Park 1* 1 Dept. Chem. Eng., KAIST, Taejon 305-701, Korea (*Email: swpark@mail.kaist.ac.kr) 2 School of Chem. Eng. & Tech., Yeungnam Univ., Kyongsan 712-749, Korea 3 Samsung Engineering Co., Ltd., Seoul, Korea Abstract: A tuning method of multiloop PID controllers is developed based on the gen- eralized IMC PID tuning rule by Lee et al. (1998a). To extend the SISO PID tuning method to MIMO systems, a new tuning criterion is proposed. The criterion is based on the closed loop frequency response method to meet desired performance and robustness as close as possible. Examples for 2 × 2, 3 × 3 and 4 × 4 systems are used to illustrate the proposed method. The results show that the proposed method is superior to the conven- tional methods such as the BLT tuning method. Keywords: Multiloop PID controllers tuning, frequency response, Mp. 1. INTRODUCTION Most chemical processes are basically MIMO sys- tems. MIMO systems show special characteristics, namely, process interactions: each manipulated vari- able can affect all the controlled variables. The mul- tiloop diagonal controller structure has been widely used for the multivariable processes because it usu- ally provides quite adequate performance for process control applications while the structure is most sim- ple, failure tolerant, and easy to understand (Gros- didier and Morri, 1987). In order to solve the mult i- loop control problem, the best pairings of controlled and manipulated variables should be firstly deter- mined by interaction analysis (Zhu and Jutan, 1996). Once the control structure is fixed, the control per- formance is then mainly determined by the tuning of each multiloop PID controller. Most multiloop PID controller tuning methods (Luy- ben, 1986; Grosdidier and Morari, 1987; Skogestad and Morari, 1989, Basualdo and Marchetti, 1990) currently available are similar in that they use the single loop tuning rules to obtain starting values for the individual controllers and then detune the indi- vidual loops to reserve stability of the overall system. For example, in the biggest log modulus tuning (BLT) method (Luyben, 1986), Zielgler-Nichols set- ting is used for initial settings for the individual con- trollers, then the controllers are detuned in such a way to satisfy the log modulus criterion. Economou and Morari (1986) developed the Internal Model Control (IMC) multiloop design method with the sufficient conditions for the stable filter to guarantee stability. However, it is known that the conditions are often too conservative and the resulting controllers give poor load disturbance response in certain situa- tion (Ho et al ., 1995). In this paper, a new tuning method for the multiloop PID controllers is presented. The proposed method extends the SISO PID tuning method by Lee et al . (1998a) to the multiloop PID controllers. In order to consider the interaction effects by off-diagonal terms in an optimal sense, a criterion based on the closed loop frequency responses is presented to select a set of l which corresponds to the closed loop time con- stant of the decentralized system. With this tuning criterion, the multiloop PID controllers can be des- igned to meet desired performance and robustness as close as possible. The contents of the paper are arranged as follows: The extension of the generalized IMC-PID tuning method to MIMO system is given first. Next the Mp (peak magnitude ratio) tuning criterion to select a set of tuning parameters l is presented. Simulation re- sults using three representative examples for 2× 2, 3× 3 and 4× 4 systems from the literature are given.