A stop operator-based Prandtl-Ishlinskii model for compensation of smart actuator hysteresis effects

The positioning and tracking performance of smart materials actuators is strongly limited due to the presence of hysteresis nonlinearity. The hysteresis of smart actuators, employed in micro-positioning tasks, is known to cause oscillations in the open-loop system's responses, and poor tracking performance and potential instabilities of the close-loop system. Considerable efforts are thus being made continuously to seek effective compensation of hysteresis effects in real-time applications. In this dissertation research, a stop operator-based-Prandtl-Ishlinskii model (SOPI) is proposed as a feedforward compensator for the hysteresis nonlinearities in smart actuators. The complementary properties of the proposed stop operator-based model in relation to the most widely used play operator-based Prandtl-Ishlinskii model are illustrated and applied to realize the desired compensation. It is shown that the stop operator-based model yields hysteresis loops in the clockwise direction, opposite to that of the piezoceramic micro-positioning actuators. It is further proven that the stop operator-based model exhibits concave initial loading behavior, while the play operator-based model, used to characterize the hysteresis behavior, follows a convex initial loading relation between the output and the input. On the basis of these complementary properties, it is hypothesized that a stop operator-based Prandtl-Ishlinskii model may serve as an effective compensator for known hysteresis nonlinearity that is described 'by a play operator-based model. The proposed stop operator-based model is subsequently implemented as a feedforward compensator in conjunction with the play operator-based model describing a known hysteresis nonlinearity. The effectiveness of the proposed compensator is demonstrated through simulation and experimental results attained with a piezoceramic micro-positioning stage. Both the simulation and the experimental results show that the proposed stop operator-based model can serve as an effective feedforward hysteresis compensator. A methodology for identifying the stop operator-based model parameters is proposed using those of a known play operator hysteresis model. Relations between the stop and play operator based-model parameters are also derived in the order to facilitate parameter identification. Furthermore, the relation between the stop operator based Prandtl-Ishlinskii model and the inverse Prandtl-Ishlinskii model, which has been proven effective hysteresis compensator, is demonstrated

Modeling and Compensation of Rate-Dependent Asymmetric Hysteresis Nonlinearities of Magnetostrictive Actuators

Smart material actuators are increasingly being explored for various micropositioning applications. Magnetostrictive actuators, in particular, are considered attractive for micro/nano positioning and high speed precision machining due to their high energy density, resolution and force capacity. The magnetostrictive actuators, similar to other smart material actuators, however, exhibit considerable hysteresis and output saturation nonlinearities that tend to become far more significant under high rates of input. Such nonlinearities cause response oscillations and errors in the positioning tasks. Reliable compensation of such nonlinearities is thus highly desirable to enhance micro/nano positioning performance of the actuator over a wide range of operating conditions. This dissertation research is concerned with characterization of output-input nonlinearities of a magnetostrictive actuator and control of hysteresis nonlinearities under a wide range of inputs. A comprehensive experimental study was performed to characterize output-input characteristics of a magnetostrictive actuator under a wide range of excitation conditions include amplitude, frequency, and bias of the input and the mechanical loading of the actuator. The measured data were analyzed to characterize output-input properties and to formulate a hysteresis model, to describe the hysteresis properties of these actuators. A Prandtl-Ishlinskii model was considered due to its continuous nature and thereby the invertability to seek hysteresis compensation. A rate-dependent threshold function was proposed to describe hysteresis properties of the actuator over a wide range of input frequencies. The inverse of the proposed rate-dependent hysteresis model was subsequently formulated for compensation of rate-dependent symmetric hysteresis nonlinearities. The effectiveness of the inverse model was investigated through simulations and hardware-in-the-loop test methods considering a 100 μm magnetostrictive actuator acquired from Etrema Inc. The results clearly illustrated effective compensation of symmetric hysteresis nonlinearities under low magnitude excitation currents over the entire frequency range. The method, however, revealed substantial errors under medium to high amplitude excitation, which was attributed to output saturation and asymmetry. The concept of a stop-operator based Prandtl-Ishlinskii model was proposed to achieve compensation of hysteresis nonlinearities described by the play-operator based hysteresis model on the basis of the initial loading curve, it was shown that the complementary properties of stop operators can be effectively applied for compensation of actuator hysteresis described by the Prandtl-Ishlinskii model. The inverse rate-dependent Prandtl-Ishlinskii model and the stop-operator based Prandtl-Ishlinskii model, however, are applicable only for compensation rate-dependent symmetric hysteresis and rate-independent hysteresis nonlinearities, respectively. The proposed rate-Prandtl-Ishlinskii model was refined to describe the rate-dependent asymmetric hysteresis nonlinearities together with output saturation by integrating a memoryless function to the rate-dependent Prandtl-Ishlinskii model. The resulting integrated model could accurately describe the asymmetric hysteresis nonlinearities and output saturation of the magnetostrictive actuator. The inverse of the integrated model was obtained by integrating the inverse of the rate-dependent Prandtl-Ishlinskii model with that of the memoryless function. The effectiveness of the integrated inverse model in compensating for hysteresis nonlinearities was investigated through simulations and experimentally using hardware-in-the-loop test method. The results suggested that the proposed integrated model and its inverse could effectively characterize and compensate for rate-dependent asymmetric hysteresis nonlinearities of magnetostrictive actuator. Both the experimental and simulation results showed that the peak hysteresis observed under high magnitude excitation could be reduced from 49.1 % to 3.7 % in the 1-250 Hz range when the integrated model inverse is applied

Modeling and Compensation of Rate-Dependent Asymmetric Hysteresis Nonlinearities of Magnetostrictive Actuators

Smart material actuators are increasingly being explored for various micropositioning applications. Magnetostrictive actuators, in particular, are considered attractive for micro/nano positioning and high speed precision machining due to their high energy density, resolution and force capacity. The magnetostrictive actuators, similar to other smart material actuators, however, exhibit considerable hysteresis and output saturation nonlinearities that tend to become far more significant under high rates of input. Such nonlinearities cause response oscillations and errors in the positioning tasks. Reliable compensation of such nonlinearities is thus highly desirable to enhance micro/nano positioning performance of the actuator over a wide range of operating conditions. This dissertation research is concerned with characterization of output-input nonlinearities of a magnetostrictive actuator and control of hysteresis nonlinearities under a wide range of inputs. A comprehensive experimental study was performed to characterize output-input characteristics of a magnetostrictive actuator under a wide range of excitation conditions include amplitude, frequency, and bias of the input and the mechanical loading of the actuator. The measured data were analyzed to characterize output-input properties and to formulate a hysteresis model, to describe the hysteresis properties of these actuators. A Prandtl-Ishlinskii model was considered due to its continuous nature and thereby the invertability to seek hysteresis compensation. A rate-dependent threshold function was proposed to describe hysteresis properties of the actuator over a wide range of input frequencies. The inverse of the proposed rate-dependent hysteresis model was subsequently formulated for compensation of rate-dependent symmetric hysteresis nonlinearities. The effectiveness of the inverse model was investigated through simulations and hardware-in-the-loop test methods considering a 100 μm magnetostrictive actuator acquired from Etrema Inc. The results clearly illustrated effective compensation of symmetric hysteresis nonlinearities under low magnitude excitation currents over the entire frequency range. The method, however, revealed substantial errors under medium to high amplitude excitation, which was attributed to output saturation and asymmetry. The concept of a stop-operator based Prandtl-Ishlinskii model was proposed to achieve compensation of hysteresis nonlinearities described by the play-operator based hysteresis model on the basis of the initial loading curve, it was shown that the complementary properties of stop operators can be effectively applied for compensation of actuator hysteresis described by the Prandtl-Ishlinskii model. The inverse rate-dependent Prandtl-Ishlinskii model and the stop-operator based Prandtl-Ishlinskii model, however, are applicable only for compensation rate-dependent symmetric hysteresis and rate-independent hysteresis nonlinearities, respectively. The proposed rate-Prandtl-Ishlinskii model was refined to describe the rate-dependent asymmetric hysteresis nonlinearities together with output saturation by integrating a memoryless function to the rate-dependent Prandtl-Ishlinskii model. The resulting integrated model could accurately describe the asymmetric hysteresis nonlinearities and output saturation of the magnetostrictive actuator. The inverse of the integrated model was obtained by integrating the inverse of the rate-dependent Prandtl-Ishlinskii model with that of the memoryless function. The effectiveness of the integrated inverse model in compensating for hysteresis nonlinearities was investigated through simulations and experimentally using hardware-in-the-loop test method. The results suggested that the proposed integrated model and its inverse could effectively characterize and compensate for rate-dependent asymmetric hysteresis nonlinearities of magnetostrictive actuator. Both the experimental and simulation results showed that the peak hysteresis observed under high magnitude excitation could be reduced from 49.1 % to 3.7 % in the 1-250 Hz range when the integrated model inverse is applied

Observer and robust H-inf control of a 2-DOF piezoelectric actuator equiped with self-measurement

International audienceThis paper introduces a dynamic observer in order to estimate the displacement in a 2-DOF piezoelectric actuator (piezoactuator) devoted to precise positioning and equipped with static self-measurement circuit. Then, the estimated displacement derived by the suggested observer is used as feedback for a robust H-inf controller. The 2-DOF piezoactuator is characterized by strong cross-couplings which are accounted for in the observer and in the feedback controller. Experimental results demonstrate the efficiency of the observer as well as the H-inf controller. The approach is very interesting for piezoelectric systems where it is difficult to implement sensors for feedback, such as in precise positioning applications at the small scale where measurement technology is still challenging

Further Results on Hysteresis Compensation of Smart Micro-Positioning Systems with the Inverse Prandtl-Ishlinskii Compensator.

International audienceA formula that characterizes the output of the in-verse compensation is derived when the inverse Prandtl-Ishlinskiihysteresis model is applied as a feedforward compensator. Forthat the composition property as well as the initial loading curveof the Prandtl-Ishlinskii model are used to obtain this formula.We demonstrate therefore that the output of the feedforwardcontrolled system is linear versus the input reference with anadditional nonlinear and bounded term. To illustrate the interestof this theoretical result, we propose an experimental applicationwith a piezoelectric actuator. First, we apply the Prandtl-Ishlinskii feedforward technique to control the piezoelectricactuator. Then, the formula of the previous theoretical result isused to construct an H ∞ feedback control from the feedforwardcontrolled actuator. The experimental results demonstrate theefficiency of the calculated controller and therefore the benefitsof the formula concerning the output of the inverse compensation

Enhancement of Micro-positioning Accuracy of a Piezoelectric Positioner by Suppressing the Rate-Dependant Hysteresis Nonlinearities

Abstract-Compensation of rate-dependent hysteresis nonlinearities of a Piezoelectric positioner is carried out by integrating the inverse of the ratedependent Prandtl-Ishlinskii model as a feedforward compensator. The proposed compensator was subsequently implemented to the positioner hardware in the laboratory to study its potential for ratedependent hysteresis compensation on a real-time basis. The experimental results obtained under different excitation frequencies revealed that the integrated inverse compensator can substantially suppress the hysteresis nonlinearities in the entire frequency range considered in the study. The proposed inverse model compensates for the rate-dependent hysteresis nonlinearities without using the feedback control techniques