Study On Model-Free Adaptive Control Of Ultrasonic Motors

Ultrasonic motors(USMs),driven by the inverse piezoelectric effect and ultrasonic vibration,are widely used in high-precision positioning related fields such as biomedicine and aerospace due to its small size,fast response,and high precision.Thanks to the improved manufacturing techniques and structure,USMs are involving in more common applications like home robots.In light of this situation,user-friendly control methods are studied to meet the demands.Therefore,this study introduce the model-free adaptive control method and adapt it for the ultrasonic motor system.The research is as follow.1.A speed-frequency-time model of USM is established based on the operating data to verify the feasibility of the proposed methods.The analysis of the data shows that the USM system is nonlinear and time-varying,and should operate under special constraints.2.The model-free adaptive control(MFAC)method is applied on the USM system.The MFAC abstracts the state from the the I/O data instead of the mechanism of the USM,and estimates the inputs based on the predicted state of the system.Besides,a state correction criterion is attached to ensure the negative correlation between the output and input of the USM.Furtherore,a limit is imposed on the input to prevent the motor from damage caused by an exceeding frequency.Then,the tuning rules of parameter are summarized based on the simulation and obtain a set of optimal parameters.3.The Lagrange multiplier is introduced based punishedment(LMP)method to design the LMP-MFAC strategy.The one-step-forward-least-square estimation is replaced with LMP algorithm to restrict the value of input during the optimization for control.The simulation presents a smaller overshoot compared with that of the MFAC.However,LMP-MFAC realizes a more stable system at the cost of response speed due to an additional parameter.4.The active set(AS)method is introduced to construct the AS-MFAC strategy.In order to simplify the LMP-MFAC method,the optimization of inputs is replaced by the AS method.Simulation shows that the AS-MFAC strategy is equivalent to the LMP-MFAC method in terms of the average error,overshoot,rise time,control time and static time.Furthermore,with less parameters,the ASMFAC is easier for non-professionals to handle.5.The MFAC,LMP-MFAC and AS-MFAC are compared in terms of the average error,overshoot,rise time,control time and static time.Then,the AS-MFAC is selected as the best strategy of the MFAC series and compared with PID in terms of the five indexes.While the parameters of ASMFAC remain the same during the tests,the values of PID are tuned once the target changes.The comparison shows that AS-MFAC presents lower average stability error,shorter rise time,and stronger robustness to load changes than that of PID.