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