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Inconsistent frequency and mode coupling are primary concerns of ultrasonic motors. These modal properties are influenced by motor features, including piezoelectric ceramics, stator teeth, or other supports attached on a stator. While this influence is understood intuitively and has been studied numerically, they have not been clarified analytically. This work develops the analytical model of the example cylindrical stator and uses it to study the influence of the features on the modal properties. In this model, the stator is considered as a thin ring with equally spaced features. The analytical solution of the model is obtained by using the direct perturbation analysis, which connects the feature number and the wave number with the modal properties, and naturally provides an effective means to achieve the coincident frequency and suppress or even eliminate the predominant mode coupling only by optimizing the combination of the two numbers. Simulation results are well consistent with the analytical conclusions. The main feature of this work is that a quick and quantitative understanding of the effects of deviation from the perfect cylindrical stator is obtained. In addition, the derived analytical results contribute to the applications of common ultrasonic motor design choices. Furthermore, while the terminology of a cylindrical stator is used in this work, the analysis method applies for other stators, such as the disc-like or linear stator.

This work investigates the influence of the pole/slot combination on the elastic wave deformation of permanent magnetic motors. To this aim, the local wave superposition and distributed wave interaction methods are used during investigation. The methods borrow ideas from other fields such as the planetary gears, the turbines, and so on because of the inherent mechanical and magnetic symmetry of the motor. More precisely, the symmetry naturally presents some interesting and useful results without specifying the magnetic pulls/waves or even their magnitudes. The analysis results explicitly show that the elastic wave deformations only depend on whether particular algebraic relations are satisfied by the combination of pole number, slot number, magnetic pull order, and wave number. The predicted relationship and the wave suppression effectiveness are verified by the finite element method and a comparison with an existing literature. The relationship naturally provides simple guidelines for the elastic wave deformation suppression only by using the proper pole/slot combination.

The phasing effect of the slot/magnet combination on rigid-elastic vibration is addressed by incorporating the cyclic symmetry of permanent magnet (PM) motors. Expanding research is also carried out to achieve more general findings in rotary power-transmission systems widely available in practical engineering. To these aims, model-free analysis is used to deal with the effect via superposition treatment. The results imply that the vibration induced by temporal-spatial excitation can be classified into rotational, translational, and balanced modes, all of which have rigid and elastic vibrations having specific base and/or contaminated deflections, and the elastic vibration can be of the standing, forward traveling, and backward traveling waves. These modes can be suppressed or excited depending on whether particular algebraic relationships are satisfied by slot/magnet combination, excitation order, and base and contaminated wave numbers. Since the analysis is independent of any models, specified magnetic force, and rigid-elastic vibration, analytical results regarding the expected relationships can be naturally created due to the structural and force symmetries of the PM motors. Because of this, similar results can be found for other rotary systems basically consisting of a rotary rotor and a stationary stator both having equally-spaced features, apart from the PM motors, typically including the turbine machines having fluid field and planetary gears with a mechanical contact. As an engineering application, the proposed method can serve as a fundamental tool when predicting or even suppressing the possible excitations associated with particular vibration modes in the mechanical and electrical designs of the symmetric systems. The superposition effect and analytical predictions are verified by the finite element method and strict comparisons against those from disk-shaped structures in an existing study.

Abstract. The inherent nonlinear of switched reluctance motor (SRM) makes it hard to get a good performance by using the conventional PID controller to the speed control of SRM. This paper develops a radial basis function (RBF) artificial neural network (ANN) nonlinear prediction model based adaptive PID controller for SRM. ANN, under certain condition, can approximate any nonlinear function with arbitrary precision. It also has a strong ability of adaptive, selflearning and self-organization. So, combining it with the conventional PID controller, a neural network based adaptive PID controller can be developed. Appling it to the speed control of SRM, a good control performance can be gotten. At the same time, the nonlinear mapping property and high parallel operation ability of ANN make it suitable to be applied to establish nonlinear prediction model performing parameter prediction. In this paper, two ANN -NNC and NNI are employed. The former is a back propagation (BP) ANN with sigmoid activation function. The later is an ANN using RBF as activation function. The former is used to adaptively adjust the parameters of the PID controller on line. The later is used to establish nonlinear prediction model performing parameter prediction. Compared with BP ANN with sigmoid activation function, the RBF ANN has a more fast convergence speed and can avoid getting stuck in a local optimum. Through parameter prediction, response speed of the system can be improved. To increase the convergence speed of ANN, an adaptive learning algorithm is adopted in this paper that is to adjust the learning rate according to the error. This can increase the convergence speed of ANN and make the system response quick. The experimental results demonstrate that a high control performance is achieved. The system responds quickly with little overshoot. The steady state error is zero. The system shows robust performance to the load torque disturbance.

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