Fourier series neural network-based adaptive variable structure control for servo systems with friction

It is truism that friction is a natural phenomenon that is hard to model. Many control laws based on a friction model cannot accomplish an excellent control performance for the specific applications with high-precision positioning and low-velocity tracking. In the paper, a Fourier series neural network is introduced to approximate a nonlinear, complex and unknown function caused by the frictional phenomenon. The learning algorithm possesses a bounded gain which is increasing and has a negative derivative for a finite process time. A persistent excitation of neural network results from the combination of a bounded random signal with reference input or control input. Under these circumstances, the weighting parameters of a neural network are forced into the vicinity of their true values. Because of the advantages of variable structure control, a Fourier series neural network-based adaptive variable structure control is designed to enhance the control performances. The stability of the overall control system is verified by the Lyapunov stability criteria. Simulations are also given to confirm the usefulness of the proposed controller.