Identification And Speed Control Of Ultrasonic Motors Based On Fuzzy Neural Networks

The ultrasonic motor (USM) is a kind of new-type driver that wasdeveloped at the beginning of the 1980's. It has a lot of excellentcharacteristics such as high energy density, direct drive, no electromagneticinterference, high torque at low speeds, no noise, flexible structure and rapidresponse and many others. It has got extensive applications so far. Theidentification and control of the USM are important problems in theapplications of the USM. According to the conventional control theory, wemust set up an accurate mathematical model. But there are many factors thataffect the motor working states, such as material performance, friction,temperature and so on. Unfortunately, people have not made it clear on thefriction mechanism yet, so it is very hard to establish accurate mathematicalmodel. In this paper, a kind of fuzzy neural network is employed to identifyand control the USM, where the complex theoretical analysis of theoperational mechanism and the exact mathematical description of the USMare avoided.The efforts in this paper mainly include the following two contents:1. Speed identification of USM based on fuzzy neural networks.Both Neural network and fuzzy system can imitate the intelligentbehavior of human and they can solve the uncertain and complex problemswhich traditional technologies can not solve without using accuratemathematical models. The combination of neural network and fuzzy systemhas not only the advantage of neural networks, such as the parallel calculation,the ability of fault tolerance and strong learning ability etc, but also theadvantage of fuzzy system, such as some good experiences of the experts, theinference way similar to the thoughts of person etc.In FNN system, the most important thing is to select fuzzy membershipfunction and the weight correction algorithm, which directly influences theefficiency of FNN system.(1) Propose a new Non-Symmetric Sinusoidal Mountain-shapeMembership Function (NSSMMF)Per experience, the selection of the shape of membership functionaffects fuzzy system. Triangle type and ladder type of membership functionhave simple structure and easy to realized, but they are not smootheverywhere, therefore it will have strong negative effect on fuzzy systematicin convergence and precision. Gauss type of membership function is notflexible, hard to change its shape or reach given shape and no zero point etc.And it needs to carry out the complex calculation. Sigmoid type ofmembership function may guarantee smooth and asymmetric, but it also doesnot exist the zero point. And it also needs the complexity calculation, so it isnecessary to propose an improved membership function. We propose a new Non-Symmetric Sinusoidal Mountain-shapeMembership in order to avoid the above shortcomings of the commonmembership function. NSSMMF has the flexible form, adaptive parameter, zero point, smoothand its calculation is comparatively small. In particular, NSSMMF has the characteristic of the mountain shapefunctions: the value of membership: left points and central point, centralpoint and right points, is 0.5 that may well guarantee the value ofmembership not too high or too low. (2) Present a new learning algorithm of FNN based on NSSMMF We propose a learning algorithm based on NSSMMF respectivelyconsidering the influence to its parameter of a, b, c and network's weight w. (3) Given the adaptive learning rate Too small learning rate can make the learning of network too slow, andtoo big learning rate can make the learning of network instable. The givenadaptive learning rate considers the influence of the error and the error gradson the object function. Identification of USM is applied based on the NSSMMF method and thetriangle type method. The error based on the triangle type Membershipfunction is bigger than the error based on the NSSMMF. Under equal experiment condition, comparing the FNN based onNSSMMF that proposed in this paper with usual neural network , from thebeginning stage ,disturb stage, final stage and stabilize stage of motor,Identification error of FNN based on the method in this paper is superior toneural network , while the calculation time of them are equal approximately. 2.Speed control of ultrasonic motors based on the FNN We propose a method based on the NSSMMF and the FNN to control...