Control of a flexible manipulator tip using a multirate repetitive learning controller based on filtered tip reference input

The non-minimum phase dynamic characteristic of a flexible manipulator makes tracking control of its tip difficult. With the actuator located at the manipulator joint, tip tracking control results in a non-collocated control problem. The level of tip tracking performance is dependent on the characteristics of the tip reference trajectory, as well as on the characteristics of the flexible manipulator system. The current paper addresses the question of how to best specify a reference trajectory for the tip of a flexible manipulator to follow in order to achieve the objectives of reducing: tip tracking error, residual tip vibration, and the required actuation effort at the manipulator joint. Using a tip controller based on multirate repetitive learning control (MRLC), a command shaping filter is used to reshape the reference trajectory. For a typical trajectory, the MRLC-based tip controller has been shown to be capable of significantly reduction tip vibrations and requiring an accompanying larger actuation effort. A tip reference trajectory reshaped by a properly designed command shaping filter smoothes the trajectory's acceleration profile and avoids excitation of the system resonance. Numerical simulations demonstrate that the result is a drastic reduction in residual tip vibrations and the required actuation effort of the MRLC-based tip controller.