An RBFNN-Based Direct Inverse Controller for PMSM with Disturbances

Table 1

Nomenclature.

Symbol	Description (unit)	Symbol	Description (unit)
	real matrix space		Trajectory of the matrix
	Real number set		Euclidean norm
	The minimum eigenvalue of matrix		Frobenius norm ( norm)
	The maximum eigenvalue of matrix		Input
	State vector of (1)		Output
	Unknown continuous functions including internal uncertainties	,	Bounded reference trajectory
	External disturbances		Arbitrarily nonnegative constant
	Approximated by estimated function with neural networks systems		Approximated by estimated function with neural networks or fuzzy systems
	Estimated weights		Input vector
	RBFNN controller output		Gaussian activation function of the hidden layer
	Weight		Central values of the hidden layer node
	Arbitrarily small positive number		Output of the neural network
	Number of the clusters		Estimation error
	Angular velocity		Torque constant (Nm/A)
	Viscous friction coefficient (Nms/rad)		Rotor position (rad)
	Current input		Inertia (kg·m^2)
	Reference position		Load torque (N·m)