Nonlinear Modeling of the Flux Linkage in 2-D Plane for the Planar Switched Reluctance Motor

This paper proposes a nonlinear flux linkage model in 2-D plane for the planar switched reluctance motor (PSRM). The inputs of the proposed model are the 2-D positions and the current, and the output is the flux linkage. The proposed model is established via a cascade-forward backpropagation neural network (CFNN). The designed CFNN consists of four layers: one input layer, two hidden layers, and one output layer. The first hidden layer has 20 neurons with a tan-sigmoid transfer function, and the second hidden layer has 20 neurons with a log-sigmoid transfer function. The output layer is a pure linear layer. The sample set with 179 755 samples is obtained experimentally in a dSPACE-based PSRM system by applying the dc excitation method. The sample set is divided into three sets. 35% and 30% of the samples are randomly chosen as the training sample set and validation sample set, respectively, and the remaining samples are utilized as the test sample set to assess the generalization performance of the CFNN-based model. According to the results of the test sample set, the maximum relative error is 11.05% and the mean relative error is 0.42% when the current ranges from 1 to 9 A. The CFNN has the capability to build a multi-input nonlinear model. The CFNN-based model is capable of reflecting the variations of flux linkage in 2-D plane caused by manufacturing tolerances. The effectiveness of the CFNN-based model is finally verified.