High-precision adaptive fractional order sliding mode tracking control for piezoelectric platform

To realize the high-precision command tracking control of the piezoelectric platform，an adaptive fractional order sliding mode tracking control method was proposed in this paper to address the serious hysteresis problems. At first，the fractional order operator and adaptive law based on the Duhem model were introduced into the design of the sliding mode surface. It increased the degree of freedom variability of the sliding mode surface and achieved the adaptive adjustment of parameters. Next，an uncertainty and disturbance estimation technique was proposed to replace the traditional switching term of the sliding mode controller，which solved the chattering problem of the sliding mode controller and improved its robustness. Finally，the experimental results of the command tracking control of the piezoelectric platform show that compared with traditional PID and sliding mode control method，the tracking error of the adaptive fractional order sliding mode controller has decreased by more than 80%，and the root mean square tracking error of the piezoelectric platform based on adaptive fractional order sliding mode controller is reduced to 0.41 μm under the reference command signal at 50 Hz. Therefore，the adaptive fractional order sliding mode controller has more superior tracking performance. © 2024 Chinese Academy of Sciences. All rights reserved.