The development and result of applying a multirate repetitive learning controller (MRLC) to the problem of non-colocated control of a flexible manipulator is described. The flexible manipulator considered consists of a driven "base" mass coupled to a "tip" mass by a flexible link. The objective is to have the tip accurately track a periodic reference trajectory. The output of the MRLC, which is progressively updated according to a learning rule which seeks to eliminate tip tracking error, is added to the nominal trajectory the base mass follows. The resulting sum is a re-shaped trajectory which commands the base mass to move in such a way as to achieve the stated tip mass tracking objective. The control force to the base mass is computed based on a standard PD feedback controller. Experiments show that use of the MRLC results in a reduction of tip tracking error by about a factor of five when following a fairly aggressive (high-acceleration) periodic reference trajectory.
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