# Neuroadaptive Robust Speed Control for PMSM Servo Drives with Rotor Failure
## 1 Introduction
In [16] an adaptive control structure with neural data processing was designed for two converter-fed DC machines coupled by a flexible connection. The controller is based on a recurrent neural network and is inspired by the Elman model. For the selection of constant coefficients of the controller, the particle swarm optimizer is applied. In the last twenty years, various control schemes based on B-Spline neural network (BSNN) have been designed because BNN can compute different control signals due to its adaptability nature through proper online training. The diverse shapes of BNN have been used to constitute the control schemes for mechatronics and electromechanical systems [17; 18; 19; 20; 21]. Recently, in [18] an adaptive PI controller is used to compute on-line the parameters of the regulator structure using a BNN for a CD motor. The procedure for the BNN online learning algorithm (OLA) is to calculate the weights and base functions of the neural network at each instant of time while the PI controller is working. Depending on the structure and size of the BNN, the algorithm computes the different weights of the network considering only the values of the inputs and the desired output, thus obtaining a faster result and at a lower computational cost, in relation to the ANN based on a backpropagation algorithm [20; 21]. Seeking to contribute to the diagnosis and control of PMSM subject to temporary degradation due to the effects of a load of use. In this work, we analyze the behavior of PMSM with the presence of fissure in the rotor shaft and unknown frictions; with the analysis and proposed theory. In the work, a detailed analysis of the PMSM modeling with the presence of a fracture in the rotor is carried out, and the procedure to obtain a precise, robust and stable control scheme under different operating conditions, contributing to obtain a more precise mathematical description of the dynamic behavior of the PMSM. Therefore, to solve the aforementioned problem, we design a neuroadaptive robust trajectory tracking controller to reduce speed ripples of PMSM servo drive based on traditional PI controllers with the ability to update their parameters through a BSNN. The principal contribution of the work are: (a) introduction of an adaptive robust neural trajectory tracking controller for a PMSM with the presence of fissure in the rotor shaft, abrupt changes of load torque disturbance, and unknown frictions; (b) a novel approach is used to simultaneously for adjust multiple parameters of a PMSM control scheme; (c) with the methodology used, the behavior of an adaptive controller with self-tuning capacity is obtained in a practical approach; and (d) with the most optimal search of the PIBSNN parameters, the algorithm learns online, avoiding the use of additional stages for its training. The shapes curve of the activation functions of the BSNN presents several advantages in relation to the radial functions, where the curve changes only in the neighborhood of some control points that have been modified. But the BSNN functions are limited in relation to the maximum and minimum values of the desired rotor speed that can be selected as input signals to the BSNN, then using the gradient descent rules the neuroadaptive controller weights are updated in line. Therefore, the neuroadaptive controller can reject internal and non-parametric disturbances that happen in the PMSM during its operation, warranting a globally stable system against limited disturbances. The controller takes advantage of BSNN to compensate for the abrupt changes of load torque disturbance and unknown frictions. The remainder of this paper is prepared as follows: In Section 2 an overview of the mathematical model of the PMSM in the \(dq\) reference frame with the presence of fissure in the rotor shaft, abrupt changes of load torque disturbance, and unknown frictions are presented. In Section 3, the proposed neuroadaptive controller based on BSNN is set out in detail.