Command 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 nonlinearities at select frequencies and achieve near-perfect tracking of a periodic desired trajectory. By doing this, a MRLC controls the joint to follow a given shaped command more closely, thus allowing the OATF to more effectively attenuate residual tip vibrations. It is shown both analytically and experimentally that this controller is more effective than a conventional PID and OATF controller at attenuating residual tip vibrations.

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