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

In this 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. Due to 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