Simplified Adaptive Backstepping Neural Controller for Magnetic Bearing System

To relax the dependence of the adjustable parameter size on the sie of hidden neurons of the FNNs existing in the ABNC, a simplified ABNC (Simpl \(\_\) ABNC) with less parameters to be adjusted online is proposed to improve the control performance. In the Simpl \(\_\) ABNC, the adaption of the linking weights between the hidden neurons and output neurons is transformed into the adaption of norm bound of these weights. This results in a scalar optimization issue without relation with the hidden neuron quantity and reduces the controller design complexity. The simulation results demonstrate that the proposed ABNC and Simpl \(\_\) ABNC achieve better tracking performance comparing with other controllers including PID controller, conventional Backstepping controller and adaptive Backstepping sliding mode controller. Also, the results show that the Simpl \(\_\) ABNC has much less computation complexity and also better tracking performance than the ABNC.