Combining a Multirate Repetitive Learning Controller With Command Shaping for Improved Flexible Manipulator Control

Abstract

Comand shaping, a feedforward approach used to control flexible manipulators, performs most effectively when applied to a linear system. In practice, various nonlinearities are present in a given system that will deteriorate the performance of command shaping. In this work, a multirate repetitive learning controller (MRLC) is used in conjunction with a command shaping method known as the optimal arbitrary time-delay filter (OATF) for discrete-time joint control of a single flexible link manipulator containing nonlinearities. With very little a priori knowledge of the given system, a MRLC is able to cancel the repetitive tracking errors caused by nonlinearities at select frequencies and thereby achieve near-perfect tracking of a periodic reference trajectory. By doing this, a MRLC controls the joint of the flexible link manipulator to follow a given shaped command more closely, thus allowing the OATF to more effectively attenuate residual manipulator tip vibrations. It is shown both analytically and experimentally that this combined control strategy is more effective than a conventional PID and OATF controller at attenuating residual tip vibrations.