Wave analysis and control of complex flexible systems

This paper first presents two wave models of non-uniform, lumped, chain-like systems, one shunt and one series. They consist of interlinked wave transfer functions, which turn out to be somewhat arbitrary. The series and shunt wave models are mutually consistent and can be combined into a single, composite wave model. Control strategies based on these wave ideas are then presented. They use wave models to resolve the actuator-system interface motion into outgoing and returning component motions. The controller sets the actuator to launch a wave that moves the flexible system half way to the target displacement, while adding the measured return wave which absorbs vibration and lands the system on target. This strategy achieves precise and rapid position control combined with active vibration damping. Explanations are offered for the effectiveness of the resulting control strategies and for their robustness to implementation errors, actuator limitations, and to large system changes. A refinement uses "cross-over wave transfer functions" which relate wave motion and wave force at a point, and vice-versa. This allows collocation of wave measurement exactly at the actuator-system interface, enabling the control strategy to achieve zero steady-state error even when the system is non-linear, or laterally flexing while simultaneously translating and rotating. Also considered is the extension of the work to control flexible systems with multiple actuators in series and to very complex 2-D and 3-D flexible systems.