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| Design of Fractional Order MRAC Based on the Hyper Stability Theory |
| Xue Changsen, Qi Zhidong, Shan Liang, Tang Pengliang |
| School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China |
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Abstract Introducing the fractional order theory to control law is one of the effective ways to improve the performance of the traditional controller. A Model Reference Adaptive Controller (MRAC), widely used in engineering practice, is taken as the object of investigation in this paperand a new design method based on Popov hyper stability theory is proposed to determine the parameters of the controller in order to overcome the shortcoming of the present fractional order MRAC design method. Compared with the local optimal parameter based method (MIT) and Lyapunov second method, under the premise of ensuring the stability of the system, the new design method in this paper is better than the former two in the flexibility of the control law and the standardization of the design process. Fractional order MRAC is used in the speed control of two-phase ultrasonic motor, and the simulation results show that, compared with the integer order MRAC, the fractional order MRAC can improve the convergence speed of the system output, reduce the overshoot, and present better robustness by selecting the appropriate order of fractional order integration.
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Received: 12 October 2017
Published: 25 December 2017
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2018, Vol. 1 
