Dynamic Modeling and Control System Design for Shape Memory Alloy Actuators

Shape memory alloy (SMA) is a type of smart material which remembers its original state. It is light weight and small, and known to provide high contraction force with low noise. Its application has wide range from robotics to medical science. One of its potential applications in space is a supporting system of membrane structure that can be used as synthetic aperture radar (SAR) antenna to achieve high flatness. It exhibits nonlinear phenomena called hysteresis when it's electrically heated. Hysteresis is a nonlinear phenomenon that refers to the dependence of a physical system on the environment. Hysteresis in SMA causes a major difficulty in control system design. Un-modeled or poorly modeled hysteresis introduces inaccuracy in tracking and the performance of the system. Experimental test bench is constructed for one set of SMA actuators that resembles the membrane structure's supporting system. Hysteresis is obtained by running open loop test with the test bench. Dynamic model of the SMA wires is developed using classical Preisach model and modified Maxwell model. Then the inverse model is implemented in feed-forward loop to compensate for nonlinear hysteresis. Simple feedback controllers are added to correct the modeling errors. Experimental results reveal that the error is significantly reduced when comparing feedback controller with hybrid feedback and feed-forward controller

A Methodology Towards Comprehensive Evaluation of Shape Memory Alloy Actuators for Prosthetic Finger Design

Presently, DC motors are the actuator of choice within intelligent upper limb prostheses. However, the weight and dimensions associated with suitable DC motors are not always compatible with the geometric restrictions of a prosthetic hand; reducing available degrees of freedom and ultimately rendering the prosthesis uncomfortable for the end-user. As a result, the search is on-going to find a more appropriate actuation solution that is lightweight, noiseless, strong and cheap. Shape memory alloy (SMA) actuators offer the potential to meet these requirements. To date, no viable upper limb prosthesis using SMA actuators has been developed. The primary reasons lie in low force generation as a result of unsuitable actuator designs, and significant difficulties in control owing to the highly nonlinear response of SMAs when subjected to joule heating. This work presents a novel and comprehensive methodology to facilitate evaluation of SMA bundle actuators for prosthetic finger design. SMA bundle actuators feature multiple SMA wires in parallel. This allows for increased force generation without compromising on dynamic performance. The SMA bundle actuator is tasked with reproducing the typical forces and contractions associated with the human finger in a prosthetic finger design, whilst maintaining a high degree of energy efficiency. A novel approach to SMA control is employed, whereby an adaptive controller is developed and tuned using the underlying thermo-mechanical principles of operation of SMA wires. A mathematical simulation of the kinematics and dynamics of motion provides a platform for designing, optimizing and evaluating suitable SMA bundle actuators offline. This significantly reduces the time and cost involved in implementing an appropriate actuation solution. Experimental results show iii that the performance of SMA bundle actuators is favourable for prosthesis applications. Phalangeal tip forces are shown to improve significantly through bundling of SMA wire actuators, while dynamic performance is maintained owing to the design and implementation of the selected control strategy. The work is intended to serve as a roadmap for fellow researchers seeking to design, implement and control SMA bundle actuators in a prosthesis design. Furthermore, the methodology can also be adopted to serve as a guide in the evaluation of other non-conventional actuation technologies in alternative applications

Position control of a shape memory alloy actuator using a four-term bilinear PID controller

Shape memory alloy (SMA) actuators have a number of appealing features, such as their low weight or their high force-to-weight ratio, that make them a potential alternative to traditional actuation technologies in fields such as space applications, surgical devices or wearable robotics. In this paper, a type of bilinear controller consisting of a conventional PID controller cascaded with a bilinear compensator, known as BPID, is proposed. Bilinear controllers are a subset of nonlinear controllers, which is why the BPID may be a promising alternative to control the position of a SMA actuator. Nonlinear control techniques are commonly applied to control SMA actuators, because of their nonlinear behavior caused by thermal hysteresis. The BPID controller is simpler and easier to implement than other nonlinear control strategies, which makes it a very appealing candidate to control SMA actuators. The performance of the BPID controller has been compared with other two controllers, a conventional PID and a commuted feed-forward PIPD, controlling a real SMA actuator. To this end, a set of five tests has been defined, in which the controlled actuator must follow a series of position references. From these tests, the position and error of the actuator have been plotted, and a series of metrics has been computed to have quantitative measurements of the performance of the three controllers. It is shown that, in most of the experiments, the BPID has a better performance than the other two tested controllers, especially tracking step references. However, the power consumption is slightly higher when the actuator is controlled with this strategy, although-the difference is minimal. Also, the BPID imposes greater energy variations to the SMA actuator, which might affect its service life. Overall, the BPID controller has proved to be a viable alternative to control SMA actuators.The research leading to these results has received funding from the STAMAS (Smart technology for artificial muscle applications in space) project, funded by the European Union’s Seventh Framework Programme for Research (FP7) (grant number 312815), and from the RoboHealth (DPI2013-47944-C4-3-R) Spanish research project

Hysteresis Nonlinearity Identification Using New Preisach Model-Based Artificial Neural Network Approach

Preisach model is a well-known hysteresis identification method in which the hysteresis is modeled by linear combination of hysteresis operators. Although Preisach model describes the main features of system with hysteresis behavior, due to its rigorous numerical nature, it is not convenient to use in real-time control applications. Here a novel neural network approach based on the Preisach model is addressed, provides accurate hysteresis nonlinearity modeling in comparison with the classical Preisach model and can be used for many applications such as hysteresis nonlinearity control and identification in SMA and Piezo actuators and performance evaluation in some physical systems such as magnetic materials. To evaluate the proposed approach, an experimental apparatus consisting one-dimensional flexible aluminum beam actuated with an SMA wire is used. It is shown that the proposed ANN-based Preisach model can identify hysteresis nonlinearity more accurately than the classical one. It also has powerful ability to precisely predict the higher-order hysteresis minor loops behavior even though only the first-order reversal data are in use. It is also shown that to get the same precise results in the classical Preisach model, many more data should be used, and this directly increases the experimental cost

Design, Fabrication, Modeling and Control of Artificial Muscle Actuated Wrist Joint System

This research dissertation presents the design, fabrication, modeling and control of an artificial muscle (AM) actuated wrist joint system, i.e., a thermoelectric (TEM) antagonistically driven shape memory alloy (SMA) actuator, to mimic the muscle behavior of human beings. In the developed AM based wrist joint system, the SMA, exhibiting contraction and relaxation corresponding to its temperature, is utilized as the actuator in the AM. Similar to the nerve stimulation, TEM is introduced to provide heat stimulation to the SMA, which involves heating and cooling of the SMA. SMA possesses superelastic behavior that provides a large force over its weight and effective strain in practical applications. However, such superior material has been underutilized due to its high nonlinear hysteresis behavior, strongly affected by the loading stress. Using the data obtained from the experiments, based on the Prandtl-Ishlinskii (PI) model, a Stress-Dependent Generalized Prandtl-Ishlinskii (SD-GPI) model is proposed, which can describe the hysteresis behavior of the SMA under the influence of various stresses. The parameters of the SD-GPI models at various stresses are obtained using a fitting function from the Matlab. The simulation results of the SD-GPI showed that prediction error is achieved at mean values of ±2% and a standard deviation of less than 7%. Meanwhile, the TEM model is also developed based on the heat balance theory. The model parameters are identified via experimental data using Range-Kutta fourth order integration equation and Matlab curve fitting function. The TEM model has shown a satisfactory temperature prediction. Then, by combining the obtained two models, an integrated model is developed to describe the whole dynamics of the wrist joint system. To control the SMA actuated wrist system, the SD-GPI inverse hysteresis compensator is developed to mitigate the hysteresis effect. However, such a compensator shows errors in compensating the hysteresis effect. Therefore, the inverse hysteresis compensator error and the system tracking error are analyzed, and the adaptive back-stepping based control approach is adopted to develop the inverse based adaptive control for the antagonistic AM wrist joint. Subsequently, a corresponding control law is developed for the TEM system to generate the required temperature obtained from the adaptive controller. Simulations verified the developed approach. Finally, experiments are conducted to verify the proposed system. Input sinusoidal signal with frequency 0.1rad/s and amplitude of ±0.524rad (±30°) is applied to the wrist joint system. Experimental results verified that the TEMs antagonistically driven SMA actuators for artificial muscle resembling wrist joint has been successfully achieved

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

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

From model-driven to data-driven : a review of hysteresis modeling in structural and mechanical systems

Hysteresis is a natural phenomenon that widely exists in structural and mechanical systems. The characteristics of structural hysteretic behaviors are complicated. Therefore, numerous methods have been developed to describe hysteresis. In this paper, a review of the available hysteretic modeling methods is carried out. Such methods are divided into: a) model-driven and b) datadriven methods. The model-driven method uses parameter identification to determine parameters. Three types of parametric models are introduced including polynomial models, differential based models, and operator based models. Four algorithms as least mean square error algorithm, Kalman filter algorithm, metaheuristic algorithms, and Bayesian estimation are presented to realize parameter identification. The data-driven method utilizes universal mathematical models to describe hysteretic behavior. Regression model, artificial neural network, least square support vector machine, and deep learning are introduced in turn as the classical data-driven methods. Model-data driven hybrid methods are also discussed to make up for the shortcomings of the two methods. Based on a multi-dimensional evaluation, the existing problems and open challenges of different hysteresis modeling methods are discussed. Some possible research directions about hysteresis description are given in the final section

A Review of Modeling and Control of Piezoelectric Stick-Slip Actuators

Piezoelectric stick-slip actuators with high precision, large actuating force, and high displacement resolution are currently widely used in the field of high-precision micro-nano processing and manufacturing. However, the non-negligible, non-linear factors and complexity of their characteristics make its modeling and control quite difficult and affect the positioning accuracy and stability of the system. To obtain higher positioning accuracy and efficiency, modeling and control of piezoelectric stick-slip actuators are meaningful and necessary. Firstly, according to the working principle of stick-slip drive, this paper introduces the sub-models with different characteristics, such as hysteresis, dynamics, and friction, and presents the comprehensive modeling representative piezoelectric stick-slip actuators. Next, the control approaches suggested by different scholars are also summarized. Appropriate control strategies are adopted to reduce its tracking error and position error in response to the influence of various factors. Lastly, future research and application prospects in modeling and control are pointed out

Design of a shape memory alloy actuator for soft wearable robots

Soft robotics represents a paradigm shift in the design of conventional robots; while the latter are designed as monolithic structures, made of rigid materials and normally composed of several stiff joints, the design of soft robots is based on the use of deformable materials such as polymers, fluids or gels, resulting in a biomimetic design that replicates the behavior of organic tissues. The introduction of this design philosophy into the field of wearable robots has transformed them from rigid and cumbersome devices into something we could call exo-suits or exo-musculatures: motorized, lightweight and comfortable clothing-like devices. If one thinks of the ideal soft wearable robot (exoskeleton) as a piece of clothing in which the actuation system is fully integrated into its fabrics, we consider that that existing technologies currently used in the design of these devices do not fully satisfy this premise. Ultimately, these actuation systems are based on conventional technologies such as DC motors or pneumatic actuators, which due to their volume and weight, prevent a seamless integration into the structure of the soft exoskeleton. The aim of this thesis is, therefore, to design of an actuator that represents an alternative to the technologies currently used in the field of soft wearable robotics, after having determined the need for an actuator for soft exoskeletons that is compact, flexible and lightweight, while also being able to produce the force required to move the limbs of a human user. Since conventional actuation technologies do not allow the design of an actuator with the required characteristics, the proposed actuator design has been based on so-called emerging actuation technologies, more specifically, on shape memory alloys (SMA). The mechanical design of the actuator is based on the Bowden transmission system. The SMA wire used as the transducer of the actuator has been routed into a flexible sheath, which, in addition to being easily adaptable to the user's body, increases the actuation bandwidth by reducing the cooling time of the SMA element by 30 %. At its nominal operating regime, the actuator provides an output displacement of 24 mm and generates a force of 64 N. Along with the actuator, a thermomechanical model of its SMA transducer has been developed to simulate its complex behavior. The developed model is a useful tool in the design process of future SMA-based applications, accelerating development ix time and reducing costs. The model shows very few discrepancies with respect to the behavior of a real wire. In addition, the model simulates characteristic phenomena of these alloys such as thermal hysteresis, including internal hysteresis loops and returnpoint memory, the dependence between transformation temperatures and applied force, or the effects of latent heat of transformation on the wire heating and cooling processes. To control the actuator, the use of a non-linear control technique called four-term bilinear proportional-integral-derivative controller (BPID) is proposed. The BPID controller compensates the non-linear behavior of the actuator caused by the thermal hysteresis of the SMA. Compared to the operation of two other implemented controllers, the BPID controller offers a very stable and robust performance, minimizing steady-state errors and without the appearance of limit cycles or other effects associated with the control of these alloys. To demonstrate that the proposed actuator together with the BPID controller are a valid solution for implementing the actuation system of a soft exoskeleton, both developments have been integrated into a real soft hand exoskeleton, designed to provide force assistance to astronauts. In this case, in addition to using the BPID controller to control the position of the actuators, it has been applied to the control of the assistive force provided by the exoskeleton. Through a simple mechanical multiplication mechanism, the actuator generates a linear displacement of 54 mm and a force of 31 N, thus fulfilling the design requirements imposed by the application of the exoskeleton. Regarding the control of the device, the BPID controller is a valid control technique to control both the position and the force of a soft exoskeleton using an actuation system based on the actuator proposed in this thesis.La robótica flexible (soft robotics) ha supuesto un cambio de paradigma en el diseño de robots convencionales; mientras que estos consisten en estructuras monolíticas, hechas de materiales duros y normalmente compuestas de varias articulaciones rígidas, el diseño de los robots flexibles se basa en el uso de materiales deformables como polímeros, fluidos o geles, resultando en un diseño biomimético que replica el comportamiento de los tejidos orgánicos. La introducción de esta filosofía de diseño en el campo de los robots vestibles (wearable robots) ha hecho que estos pasen de ser dispositivos rígidos y pesados a ser algo que podríamos llamar exo-trajes o exo-musculaturas: prendas de vestir motorizadas, ligeras y cómodas. Si se piensa en el robot vestible (exoesqueleto) flexible ideal como una prenda de vestir en la que el sistema de actuación está totalmente integrado en sus tejidos, consideramos que las tecnologías existentes que se utilizan actualmente en el diseño de estos dispositivos no satisfacen plenamente esta premisa. En última instancia, estos sistemas de actuaci on se basan en tecnologías convencionales como los motores de corriente continua o los actuadores neumáticos, que debido a su volumen y peso, hacen imposible una integraci on completa en la estructura del exoesqueleto flexible. El objetivo de esta tesis es, por tanto, el diseño de un actuador que suponga una alternativa a las tecnologias actualmente utilizadas en el campo de los exoesqueletos flexibles, tras haber determinado la necesidad de un actuador para estos dispositivos que sea compacto, flexible y ligero, y que al mismo tiempo sea capaz de producir la fuerza necesaria para mover las extremidades de un usuario humano. Dado que las tecnologías de actuación convencionales no permiten diseñar un actuador de las características necesarias, se ha optado por basar el diseño del actuador propuesto en las llamadas tecnologías de actuación emergentes, en concreto, en las aleaciones con memoria de forma (SMA). El diseño mecánico del actuador está basado en el sistema de transmisión Bowden. El hilo de SMA usado como transductor del actuador se ha introducido en una funda flexible que, además de adaptarse facilmente al cuerpo del usuario, aumenta el ancho de banda de actuación al reducir un 30 % el tiempo de enfriamiento del elemento SMA. En su régimen nominal de operaci on, el actuador proporciona un desplazamiento de salida de 24 mm y genera una fuerza de 64 N. Además del actuador, se ha desarrollado un modelo termomecánico de su transductor SMA que permite simular su complejo comportamiento. El modelo desarrollado es una herramienta útil en el proceso de diseño de futuras aplicaciones basadas en SMA, acelerando el tiempo de desarrollo y reduciendo costes. El modelo muestra muy pocas discrepancias con respecto al comportamiento de un hilo real. Además, es capaz de simular fenómenos característicos de estas aleaciones como la histéresis térmica, incluyendo los bucles internos de histéresis y la memoria de puntos de retorno (return-point memory), la dependencia entre las temperaturas de transformacion y la fuerza aplicada, o los efectos del calor latente de transformación en el calentamiento y el enfriamiento del hilo. Para controlar el actuador, se propone el uso de una t ecnica de control no lineal llamada controlador proporcional-integral-derivativo bilineal de cuatro términos (BPID). El controlador BPID compensa el comportamiento no lineal del actuador causado por la histéresis térmica del SMA. Comparado con el funcionamiento de otros dos controladores implementados, el controlador BPID ofrece un rendimiento muy estable y robusto, minimizando el error de estado estacionario y sin la aparición de ciclos límite u otros efectos asociados al control de estas aleaciones. Para demostrar que el actuador propuesto junto con el controlador BPID son una soluci on válida para implementar el sistema de actuación de un exoesqueleto flexible, se han integrado ambos desarrollos en un exoesqueleto flexible de mano real, diseñado para proporcionar asistencia de fuerza a astronautas. En este caso, además de utilizar el controlador BPID para controlar la posición de los actuadores, se ha aplicado al control de la fuerza proporcionada por el exoesqueleto. Mediante un simple mecanismo de multiplicación mecánica, el actuador genera un desplazamiento lineal de 54 mm y una fuerza de 31 N, cumpliendo así con los requisitos de diseño impuestos por la aplicación del exoesqueleto. Respecto al control del dispositivo, el controlador BPID es una técnica de control válida para controlar tanto la posición como la fuerza de un exoesqueleto flexible que use un sistema de actuación basado en el actuador propuesto en esta tesis.Programa de Doctorado en Ingeniería Eléctrica, Electrónica y Automática por la Universidad Carlos III de MadridPresidente: Fabio Bonsignorio.- Secretario: Concepción Alicia Monje Micharet.- Vocal: Elena García Armad