A Design of Multivariable, Self-Tuning PID Controllers with an Internal Model Structure YOSHIHIRO OHNISHI, 1 TORU YAMAMOTO, 2 and SIGERU OMATU 3 1 Kure National College of Technology, Japan 2 Hiroshima University, Japan 3 Osaka Prefecture University, Japan SUMMARY Self-tuning control schemes (STC) are useful for systems with unknown or slowly time-varying parameters. Some single-input/single-output PID control schemes based on STCs have been proposed for such systems. However, there are a lot of multivariable systems in real process industries. And these systems often have relatively large time delays. In this paper, a design scheme of self-tun- ing PID control system is proposed for multivariable sys- tems with unknown parameters and time delays. The controlled object is equipped with an internal model in order to compensate the time delay and also unstable zeros. Subsequently, a multivariable PID controller is designed for the augmented or compensated system. The PID parameters are calculated recursively based on the relationship between the minimum variance control law and the PID control law. A simulation example is presented to demonstrate the ef- fectiveness of the proposed scheme. © 2004 Wiley Peri- odicals, Inc. Electr Eng Jpn, 146(4): 58–64, 2004; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/eej.10241 Key words: self-tuning control; PID control; pole- assignment control; time-delay compensator; minimum variance control; recursive least squares method. 1. Introduction PID control schemes based on the classical control theory have been widely used for various process control systems for a long time [2, 3]. This is mainly because PID controllers have simple control structures. Furthermore, in the industrial control system, many PID controllers are unified by the Distributed Control System (DCS). Thus, it is desired to use the existing control loop. However, since such processes have relatively large time delays and uncer- tainties caused by modeling errors and process fluctuation, it is difficult to choose “optimal” PID parameters. Some intelligent PID control methods using neural networks [4] and self-tuning PID control methods have been proposed for such a problem. On the other hand, although there are many uncertain MIMO systems in real process control systems, there are not many proposed MIMO PID control methods compared with SISO method. Reference 9 has proposed a design method of p 2 PID controllers for the system with p inputs and p outputs. It is difficult to employ for the real system because of its com- plex structure. Furthermore, Ref. 10 has proposed a design method of p PID controllers by decoupling. These PID parameters are calculated based on the relation between the generalized minimum variance control method. This calcu- lation requires replacement of the coefficient polynomials to the static gain. These polynomials compensate time delay. Therefore, in the systems with large time delay, there is a possibility that the transient property may become bad. In this paper, a design scheme of self-tuning PID control system is proposed for a system with unknown parameters and time delays [11]. First, we consider the design of an internal model in order to compensate for the time delay and also unstable zeros. Next, a PID control system is designed for the augmented or compensated system. The PID parameters are determined recursively based on the relationship between the minimum variance control law (MVC) and PID control laws, because MVC which have simple control structures can be designed eas- ily. By the proposed method, since the PID parameters can be calculated without approximating static gain for the time delay, good control performance for the systems with large time delay is expected. Finally, a simulated example is presented to demonstrate the effectiveness of the proposed scheme. © 2004 Wiley Periodicals, Inc. Electrical Engineering in Japan, Vol. 146, No. 4, 2004 Translated from Denki Gakkai Ronbunshi, Vol. 122-C, No. 11, November 2002, pp. 1947–1953 58