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 transfer 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 uncertainty. To reduce the effects of measurement noise a Kalman filter is incorporated in the measurement of amplitude and phase of the sinusoidal response. It is also 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. This is especially useful in multivariable applications