Study on an Adaptive Control System Based on the Ultimate Sensitivity Method

Abstract

An adaptive process control system is developed making the ultimate sensitivity method, due to J.G. Ziegler and N.B. Nichols, on-line. The essential point for making it on-line is to keep the amplitude of the ultimate oscillation so small that the oscillation gives no appreciable disturbance at the controlled process output. The ultimate oscillation gives the required information about the controlled process dynamic characteristics, that is, the ultimate sensitivity and the ultimate period, according to which the parameters of the PID process controller can be adjusted. The ultimate sensitivity is the reciprocal of the process gain at the frequency where the phase-lag is 180°. The ultimate period is the reciprocal of the frequency. Ziegler and Nichols gave appropriate formulae relating the process controller parameters, i.e., the proportional gain, the integral time and the derivative time to the ultimate sensitivity and the ultimate period. The adaptive control consists of the ultimate oscillation amplitude control, the ultimate period measurement, and the controller parameter adjustment.
Simulation studies are carried out on an analog computer, giving satisfactory results. The ultimate oscillation is generated and the amplitude of which is controlled stably at a sufficiently low level. The proportional gain, the integral time and the derivative time of the PID controller are adjusted proportionally to the ultimate sensitivity and the ultimate period measured, according to the formulae. The step response of the control system approaches a response curve with very short rise-time and with a suitable damping factor.
The dynamics of the ultimate oscillation amplitude control are analysed in the appendix, for the design of stable amplitude control. Also in the appendix, the dynamic behaviour in the adjustment of the integral time and the derivative time is explained, giving the stability condition for the system.