MINIMIZATION OF RESIDUAL VIBRATIONS IN LUMPED-PARAMETER POSITIONERS -A NON-TIME-OPTIMAL BANG-BANG CONTROL

Fast and accurate vibration free positioning requires sophisticated co ntrol techniques such as bang-bang switching for a satisfactory soluti on. While several workers have addressed this problem, it still remain s a fact that for controlling an n-degree-of-freedom degenerate system , 2n-1 accurate switches will have to be operated for a time-optimal c ontrol. This is at once complex and expensive, and shows high sensitiv ity to variation in system parameters and switching times. The present proposal is very pragmatic and eliminates the multi-point switching b y use of a simple mid-point strategy. The current study on a three-deg ree-of-freedom (degenerate) system with a three-term Fourier series fo rcing has documented great benefits, such as robustness to system para meter (mass, stiffness and damping) perturbations and errors in switch ing time and phase. The control is not time-optimal as it does not use full motor capacity throughout, but the same will be welcomed in most applications where cost-effectiveness, reliability and hardware simpl icity are prime considerations. (C) 1996 Academic Press Limited