A mechanical model of a longitudinal oscillation ultrasonic motor and a method of analyzing its frequency–temperature characteristics are presented. The sticking and slipping between the stator and the rotor in the intermittent contact region are analyzed theoretically. An analytical expression for the motor’s driving force that undergoes continuous changes is given. The behaviors of the ultrasonic motor (USM), including the revolving speed of the rotor, the output kinetic energy from the rotor to the other object, the input kinetic energy from the beam tip, and the efficiency of the energy transformation, are discussed. The effects of the initial compressive force, driving frequency, load, and the moment of inertia of the motor on the behavior of the motor are examined. In the study of the temperature effect, the course of the vibration of the piezoelectric element inside the USM is expounded, the main factors affecting the frequency–temperature characteristics are analyzed, and the analytical expression for the change of the resonance frequency with respect to the temperature is given. Numerical simulations show that the results obtained in this paper agree with reported experimental results.

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An ultrasonic motor (USM) is a newly developed motor that has many excellent performances, useful features and extensive applications. The operational characteristics of the USM are affected by many factors. Strongly nonlinear characteristics could be caused by the increase of temperature, the changes of load, driving frequency and voltage and many other factors. Therefore, it is difficult to perform effective control on USMs using traditional control methods based on mathematical models of systems. Recently, artificial intelligent methods based on neural networks have become the main approaches to perform USM control. However, the existing neural-network-based methods for USM control have some shortcomings, such as complex network structures, slower convergent speeds and lower convergent precision, as well as no theoretical guarantee on the convergence of control. Furthermore, it is difficult to obtain accurate control input for the USM by using a speed controller with a single control variable. In this paper, a bimodal controller is designed where both the driving frequency and amplitude of the applied voltage are used as control inputs. A novel input–output recurrent neural network (IORNN) identifier is constructed to dynamically identify the input–output relation of the ultrasonic motors. To guarantee convergence and for faster learning, the adaptive learning rates are derived using discrete-type Lyapunov stability analysis. Numerical results show that the proposed IORNN identifier can approximate the nonlinear input–output mapping of ultrasonic motors quite well. Compared with the existing method, the control precision can be increased by about three times and the convergence time can be decreased by about two times when the proposed method is employed. Good effectiveness of the proposed control scheme is also obtained for various reference speeds.

The temperature system of the Continuous Stirred Tank Reactor (CSTR) has the characteristics of strong nonlinearity and uncertain parameters. The linear PID controller makes it difficult to meet CSTR’s control requirements. Nonlinear PID (NPID) can improve the control effect of nonlinear controlled objects, but due to the influence of nonlinear function selection and manual parameter setting, when parameters are uncertain or subject to external interference, the control performance of the system will decrease. To improve the adaptive capability of the NPID controller, the RBF-NPID control algorithm is proposed. The learning ability of RBF neural network is used to adjust NPID parameters online to improve the control performance of the system. In order to verify the effectiveness of the proposed algorithm, a CSTR model was established in MATLAB and algorithm comparison research was carried out. Simulation results show the effectiveness and superiority of the proposed algorithm.

A neural-network-based iterative controller is presented focusing on the speed control of ultrasonic motors. Suitable ranges of the adaptive learning rates are presented through the theoretical analysis on the proposed model, which could guarantee the fastest convergence of the neural network controller. Numerical results show that the neural-netwoikbased controller is effective for various kinds of reference speeds of ultrasonic motors. Comparisons with the existing method show that the precision of control could be increased using the proposed method. Simulations also show that the proposed scheme is fairly robust against random disturbance to the control variables. Keywords:ultrasonic motor; speed control. IntroductionElman neural network; recurrent hack-propagation;An ultrasonic motor (USM) has excellent performances and many useful features such as low speed and high-torque density, quick response, wide velocity m g e , excellent controllability, fine position resolution, high poweriweight ratio and high efficiency, compact size and light weight, and many others. Owing to these advantages the USM has been used in many practical applications and has attracted many researchers in the study on USM modeling and control [I-81.The USM is a peculiar motor whose driving principle is different from that of other electromagnetic-type motor, and its characteristics have not been elucidated in detail. Furthermore the USM has strongly nonlinear speed characteristics that vary with driving conditions. The operational characteristics of the USM depend on many factors, including the mode shape, resonant frequency, contact stiffness, frictional characteristics, working temperature and many others. The study on the model relates to electronics, mechanics, piezoelectricity, materials science, mechanical design, precision machining and many other subjects. It is therefore difficult to construct a precise model of the USM. In recent years, some models of the USM have been proposed, hut most models are too complex for applying to practical applications. Therefore, it is of significance in theory and applications to construct practical models and adjust input parameters properly to realize the quick and precise speed control.Neural networks have good potential for identification and control applications because they can approximate nonlinear input-output mappings of systems. Accordingly, neural networks have been applied widely in the field of identification and control. More recently, they have been applied successfully to the model reduction of microelectromechanical systems (MEMS) [9-1 I]. In this paper, focusing on the USM, a newly developed neuralnetwork-based iterative controller (NNBIC) is constructed.The NNBIC divides the controlling procedure into two parts. If the system error is large, a neural network controller [NNC) is used to control the USM running. Otherwise, if the system error is smaller than a threshold defined, an iterative controller (IC) is employed to perform the control. Numerical results show that the pro...