In this work, an analytical study has been performed on the Brushless Doubly Fed Machine's (BDFM) vibration due to the interaction of its fundamental magnetic fields, exerting bending forces in the back iron. The effects of rotor eccentricity on exacerbating the machine's vibration have been considered by assessing the stator back iron displacement function in the presence of rotor eccentricity. Finite element analysis is carried out for a 250 kW BDFM built in frame size D400 to validate the analytical methods. The stator back iron displacement is determined for an ideally-constructed machine as well as when the rotor has static and dynamic eccentricity. In addition, the prototype BDFM was tested at different operating conditions in order to examine its noise and vibration levels. A set of measurements was conducted to assess the main vibration component frequencies developed by the machine at different rotor speeds. It is shown that the main vibration components are created by bending setup in the back iron, rotor eccentricity, and the components with time and space harmonic natures. The results obtained from finite element analysis and experimentally agree with the analytical theory of BDFM vibration.
In this paper, a novel approach is proposed for adjusting the position of a magnetic levitation system using projection recurrent neural network-based adaptive backstepping control (PRNN-ABC). The principles of designing magnetic levitation systems have widespread applications in the industry, including in the production of magnetic bearings and in maglev trains. Levitating a ball in space is carried out via the surrounding attracting or repelling magnetic forces. In such systems, the permissible range of the actuator is significant, especially in practical applications. In the proposed scheme, the procedure of designing the backstepping control laws based on the nonlinear state-space model is carried out first. Then, a constrained optimization problem is formed by defining a performance index and taking into account the control limits. To formulate the recurrent neural network (RNN), the optimization problem is first converted into a constrained quadratic programming (QP). Then, the dynamic model of the RNN is derived based on the Karush-Kuhn-Tucker (KKT) optimization conditions and the variational inequality theory. The convergence analysis of the neural network and the stability analysis of the closed-loop system are performed using the Lyapunov stability theory. The performance of the closed-loop system is assessed with respect to tracking error and control feasibility.
In this paper, a robust and chattering-free sliding-mode control strategy using recurrent neural networks (RNNs) and H∞ approach for a class of nonlinear systems with uncertainties is proposed. The dynamic and algebraic models of the RNN are extracted based on the nominal model of the system and formulation of a quadratic programming problem. For tuning the parameters of the sliding surface, the performance index and the switching coefficient, a robust approach based on the H∞ method is developed. To this end, the control law is divided into two parts: (1) the main term, which includes the feedback error and (2) other terms, which include the network states, the reference input and its derivatives and the effects of the uncertainties. The feedback error gain is tuned by solving a linear matrix inequality. The neural optimizer determines the sliding-mode control law without being directly affected by the uncertainties. By applying the proposed method to the continuous-stirred reactor tank and the inverted pendulum problems, the performance of the proposed controller has been evaluated in terms of the tracking accuracy, elimination of the chattering, robustness against the uncertainties and feasibility of the control signals. Moreover, the results are compared with the conventional and twisting sliding-mode control methods.
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