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Ultrasonic motors (USMs) are commonly used in aerospace, robotics, andmedical devices, where fast and precise motion is needed. Remarkably, slidingmode controller (SMC) is an effective controller to achieve precision motioncontrol of the USMs. To improve the tracking accuracy and lower the chatteringin the SMC, the fractional-order calculus is introduced in the design of anadaptive SMC in this paper, namely, adaptive fractional-order SMC (AFOSMC), inwhich the bound of the uncertainty existing in the USMs is estimated by adesigned adaptive law. Additionally, a short memory principle is employed toovercome the difficulty of implementing the fractional-order calculus on apractical system in real-time. Here, the short memory principle may increasethe tracking errors because some information is lost during its operation.Thus, a compensator according to the framework of Bellman's optimal controltheory is proposed so that the residual errors caused by the short memoryprinciple can be attenuated. Lastly, experiments on a USM are conducted, whichcomparative results verify the performance of the designed controller.

Adaptive Fractional-Order Sliding Mode Controller with Neural Network Compensator for an Ultrasonic Motor