A Novel Self-Tuning Control Design Approach for Industrial Applications Richard J. Eucker and Zhiqiang Gao Department of Electrical and Computer Engineering Cleveland State University, Cleveland, Ohio 44145 Abstract: A real time self-tuning control algorithm was developed to accommodate slow and sudden changes in the plant dynamics. Using a matrix interpolation technique, the controller coefficients are updated based on the changes in the frequency response of the plant so that a predetermined desired loop gain is maintained throughout the operation. The computer algorithms developed here can also be used as a computer aided design (CAD) tool for off-line control design. It replaces a tedious design process with a simple, easy to use, computer algorithm. The new algorithms were tested successfully in both software and hardware in the loop simulation. I. INTRODUCTION Most control systems in industry today are fixed simple PID control loops. These control loops do not take into account the dynamic variations that occur in many systems. Therefore, over time, as the dynamics of the process inevitably varies, they fall out of tune, which causes the performance and stability to degrade. The design techniques available to control engineers include PID (Proportional-Integral-Derivative), root-locus, state-space, and the frequency response based loop shaping technique, see [1,2,5] for more details. All these techniques require the engineer to know the actual transfer function of the plant. The identification of the transfer function of the plant can be quite a tedious procedure. Even when the transfer function of the plant is known, the controller design can still be a time consuming. Among the available classical control techniques, the loop shaping technique [5] is arguably the most powerful one because it addresses all design issues such as command following, disturbance rejection, uncertainty in the process, noises, and stability margins, etc. The main idea is to determine a controller based on constraints of the loop gain transfer function, which are determined based on closed loop specifications. Unfortunately, the design process is an iterative one where one uses Bode and Nyquist plots to come up with an appropriate compensator to match the loop gain constraints. Such design is often tedious requiring skills and experiences; furthermore, once the controller is determined, it can not be easily tuned, like a PID controller, to accommodate changes in the process dynamics. An algorithmic approach to loop shaping design was proposed in [3], which is based on the matrix interpolation method [7]. The objective for the current investigation is to address the implementation issues of the method in [3] and to develop a computer aided design (CAD) software package to allow an engineer to quickly and easily design compensators for general purpose control systems. To automatically determine the transfer function of the controller, the new design package only requires a set of dynamic I/O data taken from the plant and the closed loop system specifications. The transfer function model of the plant is not required, which makes the package much more practical and easy to use. Note that similar software algorithms based on [7] have already been developed for single input and single output (SISO) as well as multi-input and multi-output system identification [8,9]. The identification and the loop shaping control design problems are similar in that both are trying to obtain a transfer function from a given frequency response. Another objective of the current research is investigating the implementation of a real time self-tuning algorithm based on the interpolation method described above. Since the method only requires the I/O data and closed loop specifications, the design can be carried out in real time, where controller frequently adjusts itself to accommodate subtle changes in the process. Although this concept has been tested successfully in software simulation in a Web Tension Process [4], the actually implementation in hardware proves to be much more challenging [13]. II. A MATRIX INTERPOLATION APPROACH TO CONTROL DESIGN To begin to understand the theory behind the self-tuning algorithm based on matrix interpolation, first consider the linear and time invariant SISO control system in Figure 2.1. In the block diagram, G p (s) represents the transfer function of the plant, G c (s) represents the transfer function of the compensator to be determined. The variables r, u, y represent the reference commend (setpoint), plant input, and plant output, respectively. The loop gain transfer function is defined as L(s)=G p (s)G c (s). The design specifications are first translated into the loop gain frequency response constraints [5], L(jϖ)=G p (jϖ)G c (jϖ29, and then G c (s) is designed to meet these constraints. G c (s) r y + - G p (s) u Figure 2.1 A Feedback Control System Currently, G c (s) is determined iteratively so that the loop gain frequency response, L(jϖ), satisfies all constraints. With all the constraints the designer must meet, the process of finding the appropriate G c (s) requires human intuition and experience. A great deal of trial and error is required and compromises have to be made. Such compromises include