On-line measurement of relative stability in feedback control systems

An online relative stability measurement technique based on measuring the size of appropriate closed-loop transfers functions at a series of frequencies is proposed. The idea is to excite the system with pure sinusoids until a resonance is measured. The resonance measures give information about relative stability in terms of the tolerable unstructured uncertainty. An algorithm to reduce and in some cases eliminate the transients which occur when the frequency of the input sinusoid is suddenly changed is also proposed. This allows steady-state operation to be quickly achieved, resulting in fast measurement of the relative stability. To reduce the effects of measurement noise, a Kalman filter is incorporated in the measurement of the amplitude and phase of the sinusoidal response. It is shown that if the system is simultaneously excited with many sinusoids, a Kalman filter can be designed to extract the amplitude and phase associated with each frequency component