A method for nonlinear function identification and its application to learning control are presented. The control objective is to identify and compensate for a nonlinear disturbance function. The nonlinear disturbance function is represented as an integral of a predefined kernel function multiplied by an unknown influence function. Sufficient conditions for the existence of such a representation are provided. The learning rule indirectly estimates the unknown function by updating an influence function estimate. It is shown that the controller achieves the disturbance cancellation asymptotically. The method is extended to the repetitive control of robot manipulators. Simulation and actual real-time implementation results using the Berkeley/NSK robot arm show that the proposed learning is more robust and converges at a faster rate than conventional repetitive controllers.>

The digital implementation of two repetitive control schemes on a SCARA-type two-axes manipulator is described. The controllers consist of a linear proportional and derivative feedback term and a feedforward repetitive term. The repetitive feedforward is adjusted periodically by using a linear combination of the position and velocity tracking errors of the current and/or previous cycles. Explicit knowledge of the structure of the manipulator model is not required. Two different learning algorithms for updating the feedforward repetitive control action are investigated. A simulation is first conducted to evaluate the performance of the repetitive controllers. The implementation of the controllers on the Berkeley/NSK SCARA robot arm is then discussed. Simulation and implementation results are in agreement and show that the use of the repetitive feedforward action in the control scheme significantly improves the tracking performance of the robot.>