Motion Control of Smart Material Based Actuators: Modeling, Controller Design and Experimental Evaluation

Smart material based actuators, such as piezoelectric, magnetostrictive, and shape memory alloy actuators, are known to exhibit hysteresis effects. When the smart actuators are preceded with plants, such non-smooth nonlinearities usually lead to poor tracking performance, undesired oscillation, or even potential instability in the control systems. The development of control strategies to control the plants preceded with hysteresis actuators has become to an important research topic and imposed a great challenge in the control society. In order to mitigate the hysteresis effects, the most popular approach is to construct the inverse to compensate such effects. In such a case, the mathematical descriptions are generally required. In the literature, several mathematical hysteresis models have been proposed. The most popular hysteresis models perhaps are Preisach model, Prandtl-Ishlinskii model, and Bouc-Wen model. Among the above mentioned models, the Prandtl-Ishlinskii model has an unique property, i.e., the inverse Prandtl-Ishlinskii model can be analytically obtained, which can be used as a feedforward compensator to mitigate the hysteresis effect in the control systems. However, the shortcoming of the Prandtl-Ishlinskii model is also obvious because it can only describe a certain class of hysteresis shapes. Comparing to the Prandtl-Ishlinskii model, a generalized Prandtl-Ishlinskii model has been reported in the literature to describe a more general class of hysteresis shapes in the smart actuators. However, the inverse for the generalized Prandtl-Ishlinskii model has only been given without the strict proof due to the difficulty of the initial loading curve construction though the analytic inverse of the Prandtl-Ishlinskii model is well documented in the literature. Therefore, as a further development, the generalized Prandtl-Ishlinskii model is re-defined and a modified generalized Prandtl-Ishlinskii model is proposed in this dissertation which can still describe similar general class of hysteresis shapes. The benefit is that the concept of initial loading curve can be utilized and a strict analytical inverse model can be derived for the purpose of compensation. The effectiveness of the obtained inverse modified generalized Prandtl-Ishlinskii model has been validated in the both simulations and in experiments on a piezoelectric micropositioning stage. It is also affirmed that the proposed modified generalized Prandtl-Ishlinskii model fulfills two crucial properties for the operator based hysteresis models, the wiping out property and the congruency property. Usually the hysteresis nonlinearities in smart actuators are unknown, the direct open-loop feedforward inverse compensation will introduce notably inverse compensation error with an estimated inverse construction. A closed-loop adaptive controller is therefore required. The challenge in fusing the inverse compensation and the robust adaptive control is that the strict stability proof of the closed loop control system is difficult to obtain due to the fact that an error expression of the inverse compensation has not been established when the hysteresis is unknown. In this dissertation research, by developing the error expression of the inverse compensation for modified generalized Prandtl-Ishlinskii model, two types of inverse based robust adaptive controllers are designed for a class of uncertain systems preceded by a smart material based actuator with hysteresis nonlinearities. When the system states are available, an inverse based adaptive variable structure control approach is designed. The strict stability proof is established thereafter. Comparing with other works in the literature, the benefit for such a design is that the proposed inverse based scheme can achieve the tracking without necessarily adapting the uncertain parameters (the number could be large) in the hysteresis model, which leads to the computational efficiency. Furthermore, an inverse based adaptive output-feedback control scheme is developed when the exactly knowledge of most of the states is unavailable and the only accessible state is the output of the system. An observer is therefore constructed to estimate the unavailable states from the measurements of a single output. By taking consideration of the analytical expression of the inverse compensation error, the global stability of the close-loop control system as well as the required tracking accuracy are achieved. The effectiveness of the proposed output-feedback controller is validated in both simulations and experiments

On the adaptive controls of nonlinear systems with different hysteresis model representations

The hysteresis phenomenon occurs in diverse disciplines ranging from physics to biology, from material science to mechanics, and from electronics to economics. When the hysteresis nonlinearity precedes a controlled system, the nonlinearity usually causes the overall closed-loop system to exhibit inaccuracies or oscillations, even leading to instability. Control techniques to mitigate the unwanted effects of hysteresis have been studied for decades and have recently once again attracted significant attention. In this thesis, several adaptive control strategies are developed for systems with different hysteresis model representations to guarantee the basic stability requirement of the closed-loop systems and to track a desired trajectory with a certain precision. These proposed strategies to mitigate the effects of hysteresis are as follows: i). With the classical Duhem model, an observer-based adaptive control scheme for a piezoelectric actuator system is proposed. Due to the unavailability of the hysteresis output, an observer-based adaptive controller incorporating a pre-inversion neural network compensator is developed for the purpose of mitigating the hysteretic effects; ii). With the Prandtl-Ishlinskii model, an adaptive tracking control approach is developed for a class of nonlinear systems in p-normal form by using the technique of adding a power integrator to address the challenge of how to fuse this hysteresis model with the control techniques to mitigate hysteresis, without necessarily constructing a hysteresis inverse; iii). With a newly proposed hysteresis model using play-like operators, two control strategies are proposed for a class of nonlinear systems: one with sliding mode control and the other with backstepping technique

Adaptive neural control of nonlinear systems with hysteresis

Ph.DDOCTOR OF PHILOSOPH

Modeling and Control of Magnetostrictive-actuated Dynamic Systems

Magnetostrictive actuators featuring high energy densities, large strokes and fast responses appear poised to play an increasingly important role in the field of nano/micro positioning applications. However, the performance of the actuator, in terms of precision, is mainly limited by 1) inherent hysteretic behaviors resulting from the irreversible rotation of magnetic domains within the magnetostrictive material; and 2) dynamic responses caused by the inertia and flexibility of the magnetostrictive actuator and the applied external mechanical loads. Due to the presence of the above limitations, it will prevent the magnetostrictive actuator from providing the desired performance and cause the system inaccuracy. This dissertation aims to develop a modeling and control methodology to improve the control performance of the magnetostrictive-actuated dynamic systems. Through thorough experimental investigations, a dynamic model based on the physical principle of the magnetostrictive actuator is proposed, in which the nonlinear hysteresis effect and the dynamic behaviors can both be represented. Furthermore, the hysteresis effect of the magnetostrictive actuator presents asymmetric characteristics. To capture these characteristics, an asymmetric shifted Prandtl-Ishlinskii (ASPI) model is proposed, being composed by three components: a Prandtl-Ishlinskii (PI) operator, a shift operator and an auxiliary function. The advantages of the proposed model are: 1) it is able to represent the asymmetric hysteresis behavior; 2) it facilitates the construction of the analytical inverse; 3) the analytical expression of the inverse compensation error can also be derived. The validity of the proposed ASPI model and the entire dynamic model was demonstrated through experimental tests on the magnetostrictive-actuated dynamic system. According to the proposed hysteresis model, the inverse compensation approach is applied for the purpose of mitigating the hysteresis effect. However, in real systems, there always exists a modeling error between the hysteresis model and the true hysteresis. The use of an estimated hysteresis model in deriving the inverse compensator will yield some degree of hysteresis compensation error. This error will cause tracking error in the closed-loop control system. To accommodate such a compensation error, an analytical expression of the inverse compensation error is derived first. Then, a prescribed adaptive control method is developed to suppress the compensation error and simultaneously guaranteeing global stability of the closed loop system with a prescribed transient and steady-state performance of the tracking error. The effectiveness of the proposed control scheme is validated on the magnetostrictive-actuated experimental platform. The experimental results illustrate an excellent tracking performance by using the developed control scheme

Retrospective-Cost Adaptive Control of Uncertain Hammerstein-Wiener Systems with Memoryless and Hysteretic Nonlinearities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97108/1/AIAA2012-4449.pd

Generalized Prandtl-Ishlinskii hysteresis model and its analytical inverse for compensation of hysteresis in smart actuators

Smart actuators such as piezoceramics, magnetostrictive and shape memory alloy actuators, invariably, exhibit hysteresis, which has been associated with oscillations in the open-loop system's responses, and poor tracking performance and potential instabilities of the close-loop system. A number of phenomological operator-based hysteresis models such as the Preisach model, Krasnosel'skii-Pokrovskii model and Prandtl-Ishlinskii model, have been formulated to describe the hysteresis nonlinearities and to seek compensation of the hysteresis effects. Among these, the Prandtl-Ishlinskii model offers greater flexibility and unique property that its inverse can be attained analytically. The Prandtl-Ishlinskii model, however, is limited to rate-independent and symmetric hysteresis nonlinearities. In this dissertation research, the unique flexibility of the Prandtl-Ishlinskii model is explored for describing the symmetric as well as nonlinear hysteresis and output saturation properties of smart actuators, and for deriving an analytical inverse for effective compensation. A generalized play operator with dissimilar envelope functions is proposed to describe asymmetric hysteresis and output saturation nonlinearities of different smart actuators, when applied in conjunction with the classical Prandtl-Ishlinskii model. Dynamic density and dynamic threshold functions of time rate of the input are further proposed and integrated in the classical model to describe rate-dependent symmetric and asymmetric hysteresis properties of smart actuators. A fundamental relationship between the thresholds of the classical and the resulting generalized models is also formulated to facilitate parameters identification. The validity of the resulting generalized Prandtl-Ishlinskii models is demonstrated using the laboratory-measured data for piezoceramic, magnetostrictive and SMA actuators under different inputs over a broad range of frequencies. The results suggest that the proposed generalized models can effectively characterize the rate-dependent as well as rate-independent hysteresis properties of a broad class of smart actuators with output saturation. The properties of the proposed generalized models are subsequently explored to derive its inverse to seek an effective compensator for the asymmetric as well as rate-dependent hysteresis effects. The resulting inverse is applied as a feedforward compensator and simulation results are obtained to demonstrate its effectiveness in compensating the symmetric as well as asymmetric hysteresis of different smart actuators. The effectiveness of the proposed analytical inverse model-based real-time compensator is further demonstrated through its implementation in the laboratory for a piezoceramic actuator. Considering that the generalized Prandtl-Ishlinskii model provides an estimate of the hysteresis properties and the analytical inverse is a hysteresis model, the output of the inverse compensation is expected to yield hysteresis, although of a considerably lower magnitude. The expected compensation error, attributed to possible errors in hysteresis characterization, is analytically derived on the basis of the generalized model and its inverse. The design of a robust controller is presented for a system preceded by the hysteresis effects of an actuator using the proposed error model. The primary purpose is to fuse the analytical inverse compensation error model with an adaptive controller to achieve to enhance tracking precision. The global stability of the chosen control law and the entire closed-loop system is also analytically established. The results demonstrated significantly enhanced tracking performance, when the inverse of the estimated Prandtl-Ishlinskii model is considered in the closed-loop control system

Inverse Compensation of Hysteresis using Modified Generalized Prandtl-Ishlinskii Hysteresis Model

Smart material based actuators, due to their properties of high precision, fast response, high power density, and small sizes, have become ideal actuators in many industrial applications, i.e. micro positioning, atomic force microscopy, and so forth. However, these smart actuators exhibit hysteresis nonlinear effects, which may worsen tracking performances, lead oscillations or even instabilities. Therefore, the existence of the hysteresis nonlinearities limits the utilization of smart material based actuators, and became the bottleneck of the control strategies development for systems with the smart actuators. In order to overcome the effects of the hysteresis, a number of hysteresis models have been proposed in the literatures. Among them, the Prandtl-Ishlinskii (PI) model, thanks to its significant analytical invertible property, has become one of the most popular hysteresis models. Nevertheless, the PI model can only describe a kind of symmetric, rate-independent, and non-saturated hysteresis, which restricts the use of PI model. Therefore, it requires to generalize the PI model, making it able to represent more complicated hysteresis phenomena, while keeping analytically invertible property. In this thesis, based on the PI model and the Generalized Prandtl-Ishlinskii (GPI) model available in the literature, a modified Generalized Prandtl-Ishlinskii (mGPI) model is proposed, which aims to redefine the play operator in the GPI so as to describe a kind of asymmetric and saturated hysteresis nonlinearities. According to the proposed mGPI model, an analytical inverse model is also derived, which can be used as an inverse compensator of the hysteresis nonlinearities. To validated the proposed inverse model, simulation results are provided confirming the proposed analytical inverse of the mGPI model

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

Fabrication, Characterization and Modeling of Magnetorheological Elastomers

Magnetorheological elastomers (MREs) are a novel class of magneto-active materials comprised of an elastomeric matrix impregnated by micron-sized ferromagnetic particles, which exhibit adjustable mechanical properties such as stiffness and damping coefficient in a reversible manner under the application of an external magnetic field. MREs are solid state of magnetorheological (MR) materials. In contrast to MR fluids, which provide field-dependent apparent viscosity, MREs, being a smart viscoelastic material, are capable of providing controlled field dependent moduli. Yet having a solid grasp of highly complex behavior of this active composite is a fundamental necessity to design any adaptive structure based on the MRE. This study is concerned with investigation of the static and dynamic behavior of the magnetorheological elastomers. To this end, six different types of MREs with varying contents of the rubber matrix as well as ferromagnetic particles are fabricated and characterized statically in the shear mode as a function of the magnetic field intensity. The MRE containing the highest percentage of iron particles (40% volume fraction) exhibited a notable relative MR effect of 555% with 181.54 KPa increase in the MRE shear modulus. This particular MRE was then chosen for subsequent dynamic characterization. The dynamic responses of magnetorheological elastomers revealed strong dependence on the strain and strain rate as well as the applied magnetic field intensity. Dynamic characterization is performed in shear mode under harmonic excitations under the broad ranges of shear strain amplitude (2.5-20%), frequency (0.1-50 Hz) and magnetic field intensity (0-450 mT). The strain softening, strain stiffening, strain rate stiffening and the magnetic field stiffening phenomena are identified as the nonlinear properties of MRE stress-strain hysteresis loops. Subsequently, an operator-based Prandtl-Ishlinskii (PI) phenomenological model is developed to predict the nonlinear hysteresis behavior of the MREs as functions of strain, strain rate and field intensity. The stop-operator-based classical PI model using only 10 hysteresis operators provided very accurate predictions, and it involved identification of only four parameters, which were dependent on the loading conditions. The validity of the developed Classical Prandtl-Ishlinskii model is assessed using the laboratory-measured data for MRE over a wide range of inputs. The proposed model is further generalized to predict the dynamic behavior of MRE independent of the loading conditions, which could be beneficial for controlling the MRE-based adaptive devices in real time. The results demonstrated that the proposed generalized model could accurately characterize the nonlinear hysteresis properties of MRE under a wide range of loading conditions and applied magnetic fields