Abstract
This chapter uses the general friction model. It is not required for the model to be linear in the unknown parameters. The chapter shows the way to design the friction compensator, and provides a rigorous closed-loop system stability proof that guarantees small tracking error and bounded neural network (NN) weights. The chapter presents a new NN structure for approximating piecewise continuous functions. A standard NN with continuous activation functions is augmented with an additional set of nodes with piecewise continuous activation functions. It is proved that such an NN can approximate any piecewise continuous function arbitrarily well, provided that the points of discontinuity are known. Because this is the case in much nonlinearity in industrial motion systems, such an NN is a powerful tool for compensation of systems with such nonlinearities. An NN controller with friction compensation is designed based on the new augmented NN. Based on the feedback linearization method, the NN controller approximates unmodeled dynamics including the unknown friction.
Published Version
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