Performance limitations in the feedback control of a class of resonant systems

There has been a large literature on the feedback control of flexible and resonant systems. Such systems arise naturally when system weight and or response speed issues push designers toward lighter, faster structures for a range of mechanical systems. Feedback control of such systems is often proposed to ameliorate the effects of the resonance. We investigate the extent to which the dynamic structure of a simple class of resonant systems limits the achievable feedback control performance for such systems. It turns out that in the class of systems considered, there is a trade off between three common control objectives, namely: (i) good initial transient response (that is the absence of large overshoot or undershoot in the initial rise time), (ii) fast response, (iii) good settling behaviour (that is, the absence of very slow modes in the step response).