Ind. Eng. Chem. Res. 2006, 45, 4075-4080
4075
Relay Autotuning: An Overview and Alternative Approach Derek P. Atherton Department of Engineering and Design, UniVersity of Sussex, Falmer, Brighton, BN1 9QT, England
This paper discusses the use of relay-produced limit cycles for selecting the parameters of fixed controllers, with particular reference to the proportional-integral-derivative (PID) controller. This work shows how the current ideas relate to the early work of Ziegler and Nichols, particularly their loop cycling test. The evaluation of limit cycles in relay feedback systems is discussed, and details of their possibilities for determining parameters of an assumed plant transfer function or the value of the plant critical point are given. To conclude, it is shown how the approximate value of points on the plant frequency response locus can be determined from using the relay in parallel with the controller, which can be done without opening the control loop. 1. Introduction The primary objective of this paper is to give an overview of the use of relay-produced limit cycles for finding controller parameters and to do so by emphasizing principles rather than theoretical details. Given the current use of microprocessor controllers, high-powered computations such as fast Fourier transform (FFT) analysis of waveforms may be used, but these are not considered here. Although the paper is concerned with proportional-integral-derivative (PID) controllers, the procedures can be used for other controllers with adjustable parameters. Most of the ideas relate back to the pioneering work of Ziegler and Nichols;1 therefore, in the next section, some historical background is presented from that time. In the next section, again with some historical aspects, the determination of limit cycles in relay feedback systems, using both an exact method and the approximate describing function method, is first discussed. This is followed by a discussion of how the results may be used either to obtain the parameters of a plant transfer function model or the plant critical point. The concept of relay autotuning was initially introduced2 for the latter purpose, and, therefore, some aspects of how to use critical point information for determining the required controller parameters are then covered. Although relay autotuning has been widely accepted, one criticism is that the loop must be opened and the process must be disturbed to conduct the relay test. The penultimate section therefore presents some new results on autotuning, which can be performed in situ by placing the relay in parallel, which, of course, puts a small limit cycle on the operating condition. The idea of placing the relay in parallel seems to have been first suggested by Tan et al.,3 where it was used in a different identification procedure. Finally, some conclusions are presented. 2. Historical Background Control theory is typically taught from the starting point of having a mathematical model of a plant (most often, linear) and a controller must be designed to provide a specified performance. Techniques usually regarded as classical control consider simple forms of a controller, such as phase lead or PID, and the problem then becomes, once the specific form of controller has been chosen, to try and find parameters for the controller so that the system performance meets the specifications. When working with a mathematical model of the plant, many methods of classical control can be used to find the * To whom correspondence should be addressed. Tel.: +44 1273 678046.Fax: +441273678399.E-mailaddress:
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controller parameters. Depending on the specifications, there may be no solution, a unique solution, or many solutions to the problem. The latter, for example, could be the case if the only specification was on the response to a step input and required an overshoot of
