Optimal Vibration Suppression Using On-line Pole/Zero Identification

Abstract

Vehicles and mechanisms which must perform very precise tasks or maneuvers require controllers to compensate for their inherent structural flexibility. Many of these applications involve structures that have time-varying dynamics, or have dynamics that are not considered in the traditional off-line controller design. These types of structures necessitate the use of adaptive control algorithms which can redesign themselves on-line in response to changes in the structural dynamics.

This work describes an on-line control algorithm that uses the pole-zero spacings of the collocated control-to-output transfer function to design the optimum Positive Position Feedback (PPF) control law. The PPF control law uses second-order filters to add closed-loop damping to resonant structural modes. An on-line PPF design algorithm was developed based on the theoretical model of the collocated control-to-output transfer function. The optimal PPF filter parameters are shown to be a function of the pole-zero spacing in the collocated transfer function. These parameters were found by solving the pole placement problem using a theoretical model for various pole-zero spacings. The parameters are then stored in a lookup table in the realtime controller, and a frequency sweep algorithm identifies the pole-zero spacing on-line and designs the PPF filters using the parameters in the lookup table.

A Phase-Locked Loop (PLL) was also studied as a means for adaptively tuning the PPF filters on-line. The PLL behavior in the presence of random and deterministic signals was characterized. The PLL was used experimentally to tune a PPF filter to a changing modal frequency.

Analysis of the theoretical model indicated the amount of closed-loop damping a PPF filter can add monotonically increases with the amount of frequency spacing of the pole/zero pair. Experimental results with the on-line optimal PPF control algorithm proved it to be effective at adding damping to structures and suppressing vibration. The poles and zeros of the control-to-output transfer function were accurately identified by the pole/zero identification routine. However, the closed-loop performance was shown to be very dependent on the correct placement of sensor and actuator pairs. Tests with pointing control problems showed the algorithm to be better suited to vibration suppression rather than vibration isolation. Simulations and experiments with the phase-locked loop showed it to be unable to track a modal frequency of a structure excited by broadband noise. Bandpass prefilters would be necessary to eliminate the frequency content of the other modes, limiting the usefulness of the PLL.