Sensorless control for hysteresis compensation of AFM scanner by modified Rayleigh model

A novel modified Rayleigh model was developed for compensating hysteresis problem of an atomic force microscope(AFM) scanner.In high driving fields,piezoelectric actuators that integrated a scanner have severe hysteresis,which can cause serious displacement errors.Piezoelectric hysteresis is from various origins including movement of defects,grain boundary effects,and displacement of interfaces.Furthermore,because its characteristic is stochastic,it is almost impossible to predict the piezoelectric hysteresis analytically.Therefore,it was predicted phenomenologically,which means that the relationship between inputs and outputs is formulated.The typical phenomenological approach is the Rayleigh model.However,the model has the discrepancy with experiment result as the fields increase.To overcome the demerit of the Rayleigh model,a modified Rayleigh model was proposed.In the modified Rayleigh model,each coefficient should be defined differently according to the field direction due to the increase of the asymmetry in the high fields.By applying an inverse form of this modified Rayleigh model to an AFM scanner,it is proved that hysteresis can be compensated to a position error of less than 5%.This model has the merits of reducing complicated fitting procedures and saving computation time compared with the Preisach model.

PI-funnel and inverse hysteresis compensation cascade control of smart soft dielectric elastomer actuator

Smart soft dielectric elastomer actuators(SSDEAs)possess wide applications in soft robotics due to their properties similar to natural muscles,including large deformation ratio,high energy density,and fast response speed.However,the complicated asymmetric and rate-dependent hysteresis property,creep property and quadratic input property of the SSDEA pose enormous challenges to its dynamic modeling and motion control.In this paper,first,we construct the dynamic model of the SSDEA by connecting a square module,a one-sided Prandtl–Ishlinskii(OSPI)model and a linear system in series to describe the above properties.The key and innovative aspect of the dynamic modeling lies in cascading the square module in series with the OSPI model to construct the asymmetric hysteresis model.Subsequently,a PI-funnel and inverse hysteresis compensation(PIFIHC)cascade control method of the SSDEA is proposed to actualize its tracking control objective.By performing the inversion operation on the asymmetric hysteresis model,the inverse hysteresis compensation controller(IHCC)is designed to compensate the asymmetric hysteresis property and quadratic input property of the SSDEA.In addition,a PI-funnel controller is designed to cascade with the IHCC to construct the PIFIHC cascade controller to obtain a good tracking performance.Then,the stability analysis of the PIFIHC cascade control system of the SSDEA is performed to theoretically prove that the tracking error can be controlled within the performance funnel and the steady-state error converges to zero.Finally,several practical tracking control experiments of the SSDEA are conducted,and RRMSEs are less than 2.30%for all experiments.These experimental results indicate the effectiveness and feasibility of the proposed PIFIHC cascade control method of the SSDEA.

Parameter Tuning Method for Dither Compensation of a Pneumatic Proportional Valve with Friction

In the practical application of pneumatic control devices, the nonlinearity of a pneumatic control valve become the main factor affecting the control effect, which comes mainly from the dynamic friction force. The dynamic friction inside the valve may cause hysteresis and a dead zone. In this paper, a dither compensation mechanism is proposed to reduce negative effects on the basis of analyzing the mechanism of friction force. The specific dither signal（using a sinusoidal signal） was superimposed on the control signal of the valve. Based on the relationship between the parameters of the dither signal and the inherent characteristics of the proportional servo valve, a parameter tuning method was proposed, which uses a displacement sensor to measure the maximum static friction inside the valve. According to the experimental results, the proper amplitude ranges are determined for different pressures. In order to get the optimal parameters of the dither signal, some dither compensation experiments have been carried out on different signal amplitude and gas pressure conditions. Optimal parameters are determined under two kinds of pressure conditions. Using tuning parameters the valve spool displacement experiment has been taken. From the experiment results, hysteresis of the proportional servo valve is significantly reduced. And through simulation and experiments, the cut-off frequency of the proportional valve has also been widened. Therefore after adding the dither signal, the static and dynamic characteristics of the proportional valve are both improved to a certain degree. This research proposes a parameter tuning method of dither signal, and the validity of the method is verified experimentally.

Sliding Mode Control with Perturbation Estimation and Hysteresis Compensator Based on Bouc-Wen Model in Tackling Fast-Varying Sinusoidal Position Control of a Piezoelectric Actuator

In this paper,a sliding mode control with perturbation estimation(SMCPE) coupled with an inverse hysteresis compensator is proposed for the motion tracking control of a microposition system with piezoelectric actuation.The inverse hysteresis compensator is employed to cancel the hysteresis nonlinearity,thus reducing the nonlinear system to a linear system with an inversion error.Then,a SMCPE controller is adopted to deal with all the unmodeled dynamics and disturbances,aiming at improving the dynamic performance and the robustness of system.An experiment of a piezoelectric actuator is presented to demonstrate the feasibility and effectiveness of the proposed control scheme.The result shows that for a fast-rate control input,the proposed method is capable of leading to a good performance of system behavior.

An improved Prandtl-Ishlinskii model for compensating rate-dependent hysteresis in fast steering mirror system

To solve the rate-dependent hysteresis compensation problem in fast steering mirror(FSM) systems, an improved Prandtl-Ishlinskii(P-I) model is proposed in this paper. The proposed model is formulated by employing a linear density function into the STOP operator. By this way, the proposed model has a relatively simple mathematic format, which can be applied to compensate the rate-dependent hysteresis directly. Adaptive differential evolution algorithm is utilized to obtain the accurate parameters of the proposed model. A fast steering mirror control system is established to demonstrate the validity and feasibility of the improved P-I model. Comparative experiments with different input signals are performed and analyzed, and the results show that the proposed model not only suppresses the rate-dependent hysteresis effectively, but also obtains high tracking precision.

Hysteretic Nonlinearity Observer Design Based on Kalman Filter for Piezo-actuated Flexible Beams with Control Applications

Piezoelectric actuators fundamentally possess hysteresis behavior. Estimation of the hysteresis is usually demanded for enhancing the performance of piezo-actuated systems. This paper presents an observer-based scheme to estimate the hysteresis in piezo—actuated flexible beams. The observer is based on a nonlinearity observer method. The discrete-time Kalman-filter algorithm is adopted for determination of the observer gains. The major advantages of the presented scheme include ease of implementation and robustness to uncertainty of hysteresis parameters. Simulation results demonstrate that the observer is able to estimate the hysteresis efficiently and has better robustness compared to the previous scheme existing in the literature. The present scheme was also successfully applied to a real-life system. Moreover, a control application example is included to demonstrate the effectiveness of the scheme.