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A neural networks (NN) compensator is designed for systems with multi-segmentpiecewise-linear nonlinearities. The compensator uses the back steppingtechnique with NN for inverting the multi-segment piecewise-linearnonlinearities in the feedforward path. This scheme provides a generalprocedure for determining the dynamic pre-inversion of an invertible dynamicsystem using NN. A tuning algorithm is presented for the NN compensator whichyields a stable closed-loop system. In the case of nonlinear stability proofs,the tracking error is small. It is noted that PI controller without NNcompensation requires much higher gain to achieve same performance. It is alsodifficult to ensure the stability of such highly nonlinear systems using onlyPI controllers. Using NN compensation, stability of the system is proven, andtracking errors can be arbitrarily kept small by increasing the gain. The NNweight errors are basically bounded in terms of input weight and hidden weight.Simulation results show the effectiveness of the piecewise linear NNcompensator in the system. This scheme is applicable to xy table-like servosystem and shows neural network stability proofs. In addition, the NN piecewiselinear nonlinearity compensation can be further and applied to backlash,hysteresis, and another actuator nonlinear compensation.

Neural Networks Compensation of Systems with Multi-segment Piecewise Linear Nonlinearities