The maximum-gain, minimum-integral principle applied to materials testing

The maximum-gain, minimum-integral principle is a method of tuning PID controllers proposed by E.C. Hind (1978, 1980) who first expressed this approach in terms of frequency response and then later (1981) in the time domain using set-point changes. This paper describes the application of the time-domain method for tuning PID controllers for servo-hydraulic and electromechanical materials-testing machines. Good tuning is essential to ensure that applied loads and strains are faithfully replicated. The tuning method is simple to use and an automated version of it is now commercially available for materials-testing machines. Two improvements to Hind´s method have been proposed: first, a better final response is obtained if the undershoot is monitored during the maximum-gain phase rather than overshoot. Second, the minimum-integral phase is easier to apply if the servo error is monitored with the demand set to a triangular waveform shape. For systems which have a lightly damped resonance, derivative compensation reduces the stability margin. For such systems, it is better to augment PID with a series lag filter and use lag instead of derivative compensation