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

Fuzzy PID Feedback Control of Piezoelectric Actuator with Feedforward Compensation

Piezoelectric actuator is widely used in the field of micro/nanopositioning. However, piezoelectric hysteresis introduces nonlinearity to the system, which is the major obstacle to achieve a precise positioning. In this paper, the Preisach model is employed to describe the hysteresis characteristic of piezoelectric actuator and an inverse Preisach model is developed to construct a feedforward controller. Considering that the analytical expression of inverse Preisach model is difficult to derive and not suitable for practical application, a digital inverse model is established based on the input and output data of a piezoelectric actuator. Moreover, to mitigate the compensation error of the feedforward control, a feedback control scheme is implemented using different types of control algorithms in terms of PID control, fuzzy control, and fuzzy PID control. Extensive simulation studies are carried out using the three kinds of control systems. Comparative investigation reveals that the fuzzy PID control system with feedforward compensation is capable of providing quicker response and better control accuracy than the other two ones. It provides a promising way of precision control for piezoelectric actuator

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

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

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

Hammerstein model for hysteresis characteristics of pneumatic muscle actuators

As a kind of novel compliant actuators, pneumatic muscle actuators (PMAs) have been recently used in wearable devices for rehabilitation, industrial manufacturing and other fields due to their excellent actuation characteristics such as high power/weight ratio, safety and inherent compliance. However, the strong nonlinearity and asymmetrical hysteresis cause difficulties in the accurate control of robots actuated by PMAs. In this paper, a method for hysteresis modeling of PMA based on Hammerstein model is proposed, which introduces the BP neural network into the hysteretic system. In order to overcome the limitation of BP neural network’s single-valued mapping, an extended space input method is adapted while the Modified Prandtl–Ishlinskii model is applied to characterize the hysteretic phenomenon. A conventional PID control is implemented to track the trajectory of PMA with and without the feed-forward hysteresis compensation based on Hammerstein model, and experimental results validate the effectiveness of the designed model which has the advantages of high precision and easy identification

Hysteresis Characterization andCompensation of Smart Material-BasedActuators via a New Modified Bouc-WenModel

芝浦工業大学2016年

The design, hysteresis modeling and control of a novel SMA-fishing-line actuator

Fishing line can be combined with shape memory alloy (SMA) to form novel artificial muscle actuators which have low cost, are lightweight and soft. They can be applied in bionic, wearable and rehabilitation robots, and can reduce system weight and cost, increase power-to-weight ratio and offer safer physical human-robot interaction. However, these actuators possess several disadvantages, for example fishing line based actuators possess low strength and are complex to drive, and SMA possesses a low percentage contraction and has high hysteresis. This paper presents a novel artificial actuator (known as an SMA-fishing-line) made of fishing line and SMA twisted then coiled together, which can be driven directly by an electrical voltage. Its output force can reach 2.65N at 7.4V drive voltage, and the percentage contraction at 4V driven voltage with a 3N load is 7.53%. An antagonistic bionic joint driven by the novel SMA-fishing-line actuators is presented, and based on an extended unparallel Prandtl-Ishlinskii (EUPI) model, its hysteresis behavior is established, and the error ratio of the EUPI model is determined to be 6.3%. A Joule heat model of the SMA-fishing-line is also presented, and the maximum error of the established model is 0.510mm. Based on this accurate hysteresis model, a composite PID controller consisting of PID and an integral inverse (I-I) compensator is proposed and its performance is compared with a traditional PID controller through simulations and experimentation. These results show that the composite PID controller possesses higher control precision than basic PID, and is feasible for implementation in an SMA-fishing-line driven antagonistic bionic joint

Frequency domain approach for dynamics identification of the actuator with asymmetric hysteresis

postprin