Generating self-excited oscillation in a class of mechanical systems by relay-feedback

Recently, a few research efforts are made to utilize artificially generated self-excited vibration in several mechanical and micromechanical applications. The present paper considers some important theoretical aspects in connection with the efficacy of the relay-feedback in generating and controlling self-excited oscillation in a class of mechanical systems. The force applied by the relay-feedback is essentially constant and acts in the direction of the measured quantity. Mathematically, an ideal relay-feedback is represented by the signum function of the measured variable. Detailed theoretical analyses, both analytic and numerical, are presented for single, two, and three degrees-of-freedom spring–mass–damper systems under relay-feedback with underactuated, collocated, and noncollocated control configurations. It is shown that relay-feedback, if used in a suitable way, can be effective in selectively generating a particular mode of oscillation in a multi degrees-of-freedom mechanical system. It is also possible to change the mode of oscillation and its amplitude by suitably selecting the control gains.