This paper presents the classical Preisach hysteresis modeling and tracking control of a curved pre-stressed piezoceramic patch actuator system with severe hysteresis The actuator is also flexible with very small inherent damping It has potential applications in active antennas A series of tests are conducted to study the hysteresis properties of the piezoceramic actuator system The numerical expressions of the classical Preisach model for different input variations are presented The classical Preisach model is applied to simulate the static hysteresis behavior of the system Higher order hysteresis reversal curves predicted by the classical Preisach model are verified experimentally The good agreement found between the measured and predicted curves showed that the classical Preisach model is an effective mean for modeling the hysteresis of the piezoceramic actuator system Subsequently, the inverse classical Preisach model is established and applied to cancel the hysteresis the piezoceramic actuator system for the real-time microposition tracking control In order to improve the control accuracy and to increase damping of the actuator system, a cascaded PD/lead-lag feedback controller is designed with consideration of the dynamics of the actuator In the experiments, two cases are considered, control with major loop hysteresis compensation, and control with minor loop hysteresis compensation Experimental results show that RMS tracking errors are reduced by 50% to 70% if the hysteresis compensation is added in the feedforward path in both cases Therefore, hysteresis compensation with the feedback controller greatly improves the tracking control accuracy of the piezoceramic actuator

Tracking control of a piezoceramic actuator with hysteresis compensation using inverse Preisach model

Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.

Modeling and Control of Piezo-Actuated Nanopositioning Stages: A Survey

A survey on hysteresis modeling, identification and control

Smart actuators employed in micropositioning are known to exhibit strong hysteresis nonlinearities, which may be asymmetric and could adversely affect the positioning accuracy. In this paper, the analytical inverse of a generalized Prandtl-Ishlinskii model is formulated to compensate for hysteresis nonlinearities of smart actuators. The generalized model was modified to ensure its continuity, and its validity in characterizing different hysteresis properties is briefly demonstrated by comparing the model responses with the measured data for the magnetostrictive, shape memory alloys (SMA), and piezo micropositioning actuators. Since the proposed generalized model is a mere extension of the analytically invertible classical Prandtl-Ishlinskii model, an inverse of the generalized model is formulated using the inverse of the classical model together with those of the envelope functions of the generalized play operator. The effectiveness of the inverse of the generalized model in compensating for the symmetric and asymmetric saturated hysteresis effects is subsequently investigated through simulations for a magnetostrictive and a SMA actuators, and through preliminary experiments performed on a piezo micropositioning stage. The simulation results suggest that the inverse of the generalized Prandtl-Ishlinskii model can be conveniently applied as a feedforward compensator to effectively mitigate the effects of the asymmetric and saturated hysteresis in magnetostrictive and SMA actuators. The experimental results further revealed that the proposed generalized analytical inverse model can be conveniently implemented as a real-time feedforward compensator to compensate for hysteresis nonlinearities of a piezo micropositioining stage.

An Analytical Generalized Prandtl–Ishlinskii Model Inversion for Hysteresis Compensation in Micropositioning Control

This paper proposes an improved sliding mode control with perturbation estimation (SMCPE) featuring a PID-type sliding surface and adaptive gains for the motion tracking control of a micromanipulator system with piezoelectric actuation One advantage of the proposed controller lies in that its implementation only requires the online estimation of perturbation and control gains without acquiring the knowledge of bounds on system uncertainties The dynamic model of the system with Bouc-Wen hysteresis is established and identified through particle swarm optimization (PSO) approach, and the controller is designed based on Lyapunov stability analysis A high-gain observer is adopted to estimate the full state from the only measurable position information Experimental results demonstrate that the performance of proposed controller is superior to that of conventional SMCPE in both set-point regulation and motion tracking control Moreover, a submicron accuracy tracking and contouring is achieved by the micromanipulator with dominant hysteresis compensated for a low magnitude level, which validates the feasibility of the proposed controller in the field of micro/nano scale manipulation as well

Adaptive Sliding Mode Control With Perturbation Estimation and PID Sliding Surface for Motion Tracking of a Piezo-Driven Micromanipulator

This paper presents the classical Preisach modeling of the hysteresis and tracking control of a Thunder actuator system. The numerical expressions of the classical Preisach model were presented in details for different input variations. It was found that the saturation output values in these numerical expressions could be cancelled out. A series of tests were conducted to study the hysteresis properties of the Thunder actuator system. The classical Preisach model was then applied to simulate the static hysteresis behavior of the system. Higher-order hysteresis reversal curves predicted by the classical Preisach model were verified experimentally. The good agreement found between the measured and predicted curves showed that the classical Preisach model is an effective mean for modeling the hysteresis of the Thunder actuator system. Subsequently, the inverse classical Preisach model was established and applied to the real time microposition tracking control of the Thunder actuator system. Real time tracking control was achieved by combining a lead-lag feedback controller and the inverse model. On a moving range of 0-0.1mm, the tracking error with hysteresis compensation was less than 2.5%, compared to an error of up to 10% without hysteresis compensation. Experimental results showed that control accuracy with hysteresis compensation is greatly improved compared to that without hysteresis compensation.

Preisach modeling of hysteresis and tracking control of a Thunder actuator system

Maintaining surface shape of precision structures such as spacecraft antenna reflectors has been a challenging task. The surface errors are often introduced by thermal distortions due to temperature differences. This paper presents numerical and experimental results of active compensation of thermal deformation of a composite beam using piezoelectric ceramic actuators. To generate thermal distortion to the composite beam, two film heaters are bonded to only one-side of the beam using thermally conductive materials. To correct thermal deformation caused by the film heaters, PZT (Lead Zirconate Titanate), a type of a piezoelectric ceramic material, is used in the form of patches as actuators. These PZT patches are bonded on the other side of the beam. First, finite element analyses are conducted with the consideration of the coupled effects of structural, electric, and thermal fields on the composite beam. These analyses include static coupled field modeling of the beam deformation with PZT actuation, transient modeling of the beam under thermal loading, and static coupled field modeling of the composite beam with thermal distortion and simultaneous PZT actuation to correct this distortion. Then, experiments are conducted to study thermal effect, PZT actuation effect and active thermal distortion compensation using PZT actuators with a Proportional, Integral, and Derivative (PID) feedback controller. FEM and experimental results agree well and demonstrate the proposed method can actively perform structural shape control in the presence of thermal distortion.

Xiaoqin Zhou

Papers

Tracking control of a piezoceramic actuator with hysteresis compensation using inverse Preisach model

Preisach modeling of hysteresis and tracking control of a Thunder actuator system

Thermal deformation compensation of a composite beam using piezoelectric actuators