Study On Fractional Modeling For Permanent Magnet Synchronous Motor

This paper presents the fractional order modeling for the permanent magnet synchronousmotor (PMSM). Study on the existence of fractional model for PMSM and fractional-ordermodeling for PMSM from time and frequency responses. The performance of step response isalso studied based on a fractional proportion integration controller which is designed by theproposed fractional model of PMSM.The existence of PMSM fractional model is primarily studied. Considering there is norelated research and report that whether the fractional-order for PMSM is exist or not, what ismore, there is no unified understanding of the physical interpretation for the fractionalcalculus, so it is difficult on the mechanism to validate the existence of fractional-order modelfor PMSM. This paper assumes that if the fractional order model of PMSM is exist, it ismeans fractional-order model is more precise to describe the PMSM than the integer model,in that way, using the same controller which is designed by the fractional-order to control thePMSM should have better performance than the integer model. Based on the results ofsimulations and real-time experiments, the existence of PMSM fractional model is validated.Time domain modeling of fractional-order system for PMSM is presented by adoptingthe combination of mechanism and data. A fractional model for the PMSM is proposed, thepseudo-random signals is designed to obtain real-time experiment data and numerical fittingto get the fractional order, then data modeling is realized by using the output-erroridentification algorithm of fractional-order system. In model validation, two proportionalintegral (PI) controllers are designed with the same scheme according tothe identifiedfractional order model and the traditional integer order one, and real-time experimental resultsare presented to demonstrate the advantage of the proposed fractional order model.Frequency domain modeling of fractional-order system for PMSM is presented byadopting the combination of mechanism and data.A fractional model for the PMSM isproposed, in order to identify the parameters of the proposed fractional order model, anenhancement of the classic Levy identification method with weights is applied. In a real-timePMSM velocity servo plant, the fractional order model is identified according to theexperimental tests using the presented algorithm. Two proportional integral (PI) controllersare designed for velocity servo using a simple scheme according to the identified fractionalorder model and the traditional integer order one, respectively. The experimental testperformance using these two designed PI controllers is compared to demonstrate theadvantage of the proposed fractional order model of the PMSM velocity system. Discuss and compare the results with two methods of fractional-order moding for PMSMin time domain and frequency domain. Experimental data is used for demonstration that thefractional order model fits much better for the system identification frequency data over theinteger order model. This may be explained by the nature of the distributed parameter systemof the electromagnetism coupling thus may not be captured by integer finite order modelingwhile a fractional order modeling can offer potential to perform a better fitting. With the samefractional controller design rules, two simple PIλcontrollers aredesigned using the phasemargin and gain crossover frequency specifications according to the identified fractional orderand integer order models, the performance of the step response is compared.