Combining a multirate repetitive learning controller with command shaping for improved flexible manipulator control

Comand shaping, a feedforward approach used to control flexible manipulator s, 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 le arning controller (MRLC) is used in conjunction with a command shaping meth od known as the optimal arbitrary time-delay filter (OATF) for discrete-tim e joint control of a single flexible link manipulator containing nonlineari ties. With very little a priori knowledge of the given system, a MRLC is ab le to cancel the repetitive tracking errors caused by nonlinearities at sel ect frequencies and thereby achieve near-perfect tracking of a periodic ref erence trajectory. By doing this, a MRLC controls the joint of the flexible link manipulator to follow a given shaped command more closely, thus allow ing the OATF to more effectively attenuate residual manipulator tip vibrati ons. It is shown both analytically and experimentally that this combined co ntrol strategy is more effective than a conventional PID and OATF controlle r at attenuating residual tip vibrations.