Robust time-delay control of multimode systems

This paper presents a procedure for the design of open loop controllers for flexible structures using multiple step inputs delayed in time. The controller attenuates the residual vibration by cancelling the complex poles of the system. Robustness is achieved by locating additional zeros at the cancelled poles of the system. The paper begins by addressing the control of a single mode and examines the effect of user selected time-delays on robustness and the reference input. Next, a procedure for the design of robust time-delay controllers for multiple modes with user selected time-delays is considered. This is followed by a design of a minimum time-delay controller, such that the step input magnitudes are constrained to values between 0 and 1. Two examples, a spring-mass system and a single-link flexible-arm robot are used to illustrate the effectiveness of the proposed controller.