Abstract

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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