# Neuroadaptive Robust Speed Control for PMSM Servo Drives with Rotor Failure
## 1 Introduction  
The Permanent Magnet Synchronous Motors (PMSM), have extraordinary efficiency, excellent performance, wide speed range, fast response, great accuracy compact construction, and higher torque per volume ratio. This motor plays an important protagonist in industrial applications such as chip mount machines, scraper conveyors, marine propulsion, aerospace, hard disk drives, and semiconductor production machines [1, 2, 3]. The linear control scheme such as vector control with proportional-integral (PI) loops is the industrial standard control of the PMSM due to its simplicity, excellent performance, and efficiency [2, 4]. Nevertheless, the large trouble of the traditional PI controllers is its sensitivity to the parametric variations of the plant (PMSM) [5]. Another issue that is getting interested is faults in electric motors due to vibration problems produced by an imbalance that is caused by degradation in the rotor shaft, which last will origin a fissure in the rotor shaft by the fatigue phenomena [6]. A topic of great interest in the field of engineering is to know and determine the dynamic behavior of a crack in solid materials to contribute to the preservation of the life of mechanical devices [7]. However, designing a precise control scheme for a PMSM is a challenging task due to the complexity of the system caused by nonlinearities, unpredictable parameter variations, external load disturbances and unmolded nonlinear dynamics of the motor. The set of differential equations that describe the dynamic response of electromechanical systems with the presence of a fissure in the rotor depict a non-linear behavior, causing that traditional tuning techniques for PI controllers present a poor performance, for whichit is necessary to use techniques of tuning based on heuristic algorithms or artificial intelligence techniques [8; 9]. Rotor failures have been studied by different groups of researchers. Classical control has been applied to deal with the presence of degradation problems, fault, and broken rotors in electromechanical systems, such as optimal linear quadratic regulator [9; 10], sliding mode control [11], feedback linearization controller [12], and fuzzy logic control [13]. In [9] an optimal linear state feedback control scheme was designed using the optimal linear quadratic regulator technique, for a PMSM with rotor failure. A sliding mode control (SMC) for a quad-rotor with a rotor failure has been presented in [11]. The controller has a good performance to a total rotor failure, uncertainties and different weather conditions caused by wind speed. However, by its nature, the SMC has some inherent problems in its operation such as the chattering phenomenon due to the discontinuity in the switching strategy of the control law. In [12] a feedback linearization controller was made to offer better precision control for induction motor drive subject to short circuit faults in the stator winding and some broken bars in the rotor. An observer based on the feedback of states with the capability to compensate for some failures was designed for two coupling PMSM systems [14]. The controller is based on a robust adaptive observer to estimate the PMSM faults. The controller compensates for the faults and allows the motors to track the reference. In [13] a fuzzy adaptive controller was designed to reject the effects caused by electrical faults for PMSM based on dynamic surface technology. Fuzzy logic control (FLC) has been used because it is simple to implement and this controller does not require an accurate mathematical model of uncertain nonlinear systems [15]. However, the gains of an FLC are fixed, require knowledge or experience into membership functions, fuzzy rules, or fuzzy inference system databases. These issues are the main disadvantages of FLC systems design. Some groups of investigators try to overcome this drawback using hybrid PI controllers or novel tuning rules to improve their performance against faults and parameter variations.