Iterative and Feedback Control for Hysteresis Compensation in SMA

In this paper, we investigate the design of an iteration-based control algorithm combined with feedback control to address the positioning error caused by hysteresis effect in a shape memory alloy (SMA) actuator. SMA actuators offer relatively large strain (up to 8%) and high strength-to-weight ratio, and as a result, they are being exploited in minimally invasive surgery tools and microrobotics. But unfortunately, SMA actuators exhibit significant hysteresis effect which can lead to loss in positioning precision; it can cause as much as 50% error in positioning. To address the prohibitive effect of hysteresis, we study the application of an iterative-feedforward algorithm specifically designed to account for this behavior. We show that one of the major challenges with iterative- feedforward inputs for SMA actuators is the slope of the hysteresis curve at the phase transition zones (from martensite to austenite and vice versa) can be significantly large, and thus the output response can be highly sensitive to small changes in the input. As a result, iterative-feedforward input provides limited performance because at the transition zones, small changes in the input (due to noise, for example) cause the output to change significantly, thus inducing tracking error. To alleviate this problem, and to help improve the performance of the feedforward method, we consider the addition of a feedback input to add robustness. We show: (1) experimental results that demonstrate the efficacy of the method and (2) the tracking precision can be reduced by over ten times compared to just using iterative-feedforward input. In particular, the ultimate tracking error was reduced to 0.15% of the total displacement range - approximately the sensor noise level.

Shape memory alloy (SMA) actuators’ unique features like compact design and high force to weight ratio attracts numerous position control applications. Due to the nonlinear behaviour and control difficulties SMA actuators are not widely employed in position control applications. In this work, a simple and easy to construct closing mode SMA wire actuated gripper is presented. The mechanical structure of the gripper includes a pair of jaws - one movable and other fixed, an SMA wire employed to close the jaw upon actuation and a torsion spring bias for the strain recovery in SMA wire. An experimental setup of the SMA gripper is established to perform the study. The SMA actuator is heated by an electric current. A non-contact laser displacement sensor is engaged to measure the position of the movable jaw. In order to control the position of the devised gripper, a model of the gripper is estimated from open loop experimental data using system identification technique. Experimental evaluation of manually tuned PI controller for SMA actuated closing mode gripper is compiled to track various stationary and variable (dynamic) trajectories to suit applications that can manipulate objects of varied dimensions. Control results demonstrate that the gripper is able to track the position rapidly and precisely.

The parameters of the bias spring have great impacts on the output performances of the shape memory alloy( SMA) actuator. To investigate the rules of influences,the output stroke and response rate of a SMA actuator with different bias spring stiffness and precompression load were studied. The output degradation due to cyclic actuation was also investigated. Experimental results show that the strokes and response rates decrease with the increase of preloads or stiffness. The performance of the actuator degrades significantly in the first few cycles and stabilizes eventually with the increase of the number of cycles. The test results also indicate that less cycling is needed to stabilize the actuator when the preload is increased,and the stiffness seems to affect the cyclic performance of the actuator slightly.

This paper describes the development of fuzzy systems for modeling the hysteresis behavior of shape memory alloy (SMA) actuators. Due to their simplicity and ease of actuation, SMA actuators are very attractive for applications such as miniature robots for micro manufacturing. However, SMAs have not been widely used for motion control applications due to their nonlinear behavior and control difficulties. One approach to design a position controller for SMA systems is to employ an inverse-model of the system in the control loop to compensate the hysteresis properties of the material. Fuzzy systems, due to their nonlinear learning and adaptation abilities, are good candidates for obtaining inverse-models. In this paper two fuzzy modeling approaches are employed and compared to develop a model for a SMA wire actuator. A set of experiments are conducted to generate the training data. The test stand includes a Nickel-Titanium (TiNi) SMA wire, a position sensor, a bias spring and a current amplifier. By comparing the performance of the two employed fuzzy modeling techniques, it is revealed that the approach based on fuzzy Gustafson-Kessel (GK) clustering shows a better performance in the modeling of the hysteresis in the SMA wire. Thus, GK clustering algorithm is employed to develop the inverse-model for the SMA. The reported results demonstrate the ability of the employed fuzzy algorithm for modeling the hysteresis in the system, and the merits of the introduced inverse-model in the control of the position of the SMA.

This paper describes the development of a neural network control for shape memory alloy (SMA) actuators as well as the control tests. Precise control of SMA actuators that are integrated in the composite structure is difficult because of the hysteretic behaviour of SMA and time delays in the control system. The weakness of the static model of SMA is that it does not take into account the actuator dynamics. The NARMA-L2 neural network model enables us to solve the inverse dynamic model of the nonlinear discrete-time dynamical system. In this study the NARMA-L2 model of the airfoil (a cross section of wind turbine blade) was created using Matlab Simulink software and neural networks. Data for network training was measured from the specimen. The performance of the constituted NARMA-L2 controller was tested in control tests. According to the control tests the NARMA-L2 controller is well suited for controlling embedded SMA actuators. The constituted controller enabled fast and stable actuation in step responses and it was also able to compensate for changes in cooling conditions.

A new approach of designing and controlling a multi-axis actuator system using segmented binary control (SBC) is presented. In SBC, Shape Memory Alloy (SMA) actuator wire is divided into multiple segments and their thermal states are controlled in a binary manner using thermoelectric modules. Two-dimensional array architecture for multi-axis SMA actuators is created using SBC. Similar to the biological muscle network, multi-axis SMA actuator wires can be combined flexibly with a two-dimensional segmentation method in order to activate multiple links of a skeletal robot structure in a coordinated manner. Ten-axis actuator is built using this method. Thermoelectric modules are laid on a substrate made of PCB board and SMA actuators are placed in between two substrate layers with a gap to allow the movement of the actuators. The actuator creates coordinated gross motion as well as independent fine movements with reduced number of control loops. The new actuator architecture will provide a novel actuator system forming a network of array actuators connected to a vast number of bone-like linkages.

Position control of shape memory alloy actuator based on the generalized Prandtl–Ishlinskii inverse model

Wind turbine rotor upscaling has entered a range of rotor diameters where the blade structure cannot sustain the increased aerodynamic loads without novel load alleviation concepts. Research on load alleviation using morphing blade sections is presented. Antagonistic shape memory alloy (SMA) actuators are implemented to deflect the section trailing edge (TE) to target shapes and target time-series relating TE movement with changes in lift coefficient. Challenges encountered by the complex thermomechanical response of morphing section and the enhancement of SMA transient response to achieve frequencies meaningful for aerodynamic load alleviation are addressed. Using a recently developed finite element for SMA actuators [1], actuator configurations are considered for fast cooling and heating cycles. Numerical results quantify the attained ranges of TE angle movement, the moving time period and the developed stresses. Estimations of the attained variations of lift coefficient vs. time are also presented to assess the performance of the morphing section.

In most shape memory alloy (SMA) actuator systems presented in the literature, some form of PID or pulse-width modulating controller is typically used. Unfortunately, due to the hysteresis inherent in any SMA actuator system, the theoretical stability of these systems has been largely ignored. This paper employs a model developed by the author and a general form of the passivity theorem of Vidyasagar (1993) to prove the L/sub 2/-stability of an SMA actuator system employing a form of proportional control. The complex nonlinear behaviour of the SMA actuator is taken into account, along with nonlinear effects such as saturation. Due to the flexibility of the model in specifying the shape and position of the hysteresis, the stability result may be applicable to other hysteretic systems. >

Shape memory alloy (SMA) actuators have recently been developed in the form of torsional tubes that can undergo large twisting deformations. Wing twisting has been investigated as a means to reduce induced drag in cruise conditions in small aircraft, but the actuation hardware required to generate wing twist at larger scales is prohibitively cumbersome. Replacing conventional actuators with SMA torque tubes provides a way to minimize weight of the twisting system but wing structural design then becomes more challenging. This analysis-driven design study examines an SMA torque tube as applied to the twisting wing design problem. A composite skin is considered to maximize wing performance under combined twist and aerodynamic loads. The SMA has been analyzed using a 3-D thermo-mechanical constitutive model while a preliminary study was performed to determine a composite lamina with appropriate unidirectional properties. An optimization was then completed to find an ideal composite layup. This optimization also included the design of a passive torque tube used to properly balance the twist generated by the SMA against that required in the wing. Localized buckling in the twisted wing was also considered and avoided. The product of this optimization was a composite wing that twisted while considering constraints of stress on the SMA. To validate the controllable use of SMA actuators, testing was completed on a scaled wing model fitted with a rapid prototype shell.

There are two different ways of using shape memory alloy (SMA) wire as an actuator for shape control of flexible structures: it can be either embedded within the composite laminate or externally attached to the structure. As the actuator can be placed at different offset distances from the beam, external actuators produce more bending moment and, consequently, considerabnle shape changes with the same magnitude of actuation force compared with the embedded type. Such a configuration also provides faster heat transfer rate owing to convection, which is very important in shape control applications that require a highfrequency response of SMA actuators. Although combination and physics-based modeling of externally attached SMA actuator wires and strips have been considered by many researchers, these studies have some drawbacks, which, if neglected, result in a number of errors in the theoretical results compared with experimental results. These shortcomings are considering the linear Euler-Bernoulli beam theory, not deriving the actuation force of the SMA from the constitutive equations, and taking into account the effect of only one SMA wire actuation force on, for example, the structure. These assumptions may lead to erroneous theoretical modeling results compared with experimental results. In this study, the aforementioned difficulties of attaching SMA actuators to the smart structures have been addressed. In other words, instead of linear beam theory, nonlinear beam theory is used in system modeling and, therefore, the proposed method and results are valid in large deflection and rotation behavior of beam. Also, in comparison to many other analyses that the effect of only one SMA wire is investigated, in the present research the effect of all active and inactive SMA wires is considered. Accordingly, the result of this paper can easily be generalized to the structure with several SMA wire actuations. Moreover, with the purpose of having practical applications in modeling and control, the heat transfer equations of all SMA wires are considered in the analysis and, as a result, the control inputs of the presented model are SMA wire electric currents rather than SMA temperatures. First, a flexible beam actuated by two active SMA actuators is modeled. Then, the Brinson constitutive equations and thermoelectric equations for SMA materials are coupled with the nonlinear beam behavior, and the coupled system of equations is numerically solved for some particular practical cases. Finally, the numerical results of the model simulation are verified against the experimental results using a test setup to validate the proposed model prediction. The implemented method used in this paper can be easily extended to the more complex smart structure with numerous externally attached SMA wires.

Transient heat transfer behavior of one-dimensional symmetric thermoelectric SMA actuators

In Part II of this two-part study, system simulations and experimental correlations of a Shape Memory Alloy (SMA) based vibration isolation device (briefly described in Part I) has been presented. This device consists of layers of preconstrained SMA tubes undergoing pseudoelastic transformations under transverse dynamical loading. In Part II, detailed description of the prototype vibration isolation device, its experimental setup, and actual experimental test results are presented. An extensive parametric study has been conducted on a nonlinear hysteretic dynamical system, representing this vibration isolation device utilizing a physically based simplified SMA model and a Preisach model (an empirical model based on system identification) developed in Part I. Both the physically based simplified SMA model and the modified Preisach model have been utilized to perform experimental correlations with the results obtained from actual testing of the device. Based on the investigations, it has been shown that variable damping and tunable isolation response are major benefits of SMA pseudoelasticity. Correlation of numerical simulations and experimental results has shown that large amplitude displacements causing phase transformations of SMA components present in such a device are necessary for effective reduction in the transmissibility of such dynamical systems. It has also been shown that SMA-based devices can overcome performance trade-offs inherent in typical softening spring-damper vibration isolation systems. In terms of numerically predicting the experimental results, it has been shown that the Preisach model gave relatively accurate results due to better modeling of the actual SMA tube behavior. However, for a generic parametric study, the physically based simplified SMA model has been found to be more useful as it is motivated from the constitutive response of SMAs and hence, could easily incorporate different changes in system conditions.

This paper describes development of a motion controller for Shape Memory Alloy (SMA) actuators using a dynamic model generated by a neuro-fuzzy inference system. This kind of smart alloy is known to have a unique characteristic in that its shape can be controlled by temperature that can be varied by passing a current through it. Using SMA actuators, it would be possible to design miniature mechanisms for a variety of applications. Today SMA is used for valves, latches, and locks, which are automatically activated by heat. However it has not been used as a motion control device due to difficulty in the treatment of its highly non-linear strain-stress hysteresis characteristic which is further influenced by its temperature. In this project, a dynamic model of a SMA actuator is developed using ANFIS, a neuro-fuzzy inference system provided in MATLAB environment. Using neuro-fuzzy logic, the system identification of the dynamic system is performed by observing the change of state variables (displacement and velocity) responding to a known input (voltage across the SMA actuator). Then, using the dynamic model, the estimated input voltage required to follow a desired trajectory is calculated in an open-loop manner. The actual input voltage supplied to the SMA actuator is the sum of this open-loop input voltage and an input voltage calculated from an ordinary PD control scheme. This neuro- fuzzy logic-based control scheme is a very generalized scheme that can be used for a variety of SMA actuators. Experimental results are provided to demonstrate the potential for this type of controller to control the motion of the SMA actuator.

We have developed a discretely actuated steerable probe for percutaneous procedures. We propose use of shape memory alloy (SMA) actuators in our design due to their small size and high power density. SMAs are attractive actuators when large forces or displacements are required and limited spaces are available. SMA actuators are shape-setted to an arc shape and mounted on the outer surface of the probe to generate bending action upon thermal actuation. SMA can recover large deformation on thermal activation and recovery strain of SMA is related to its temperature. Hence, we propose controlling the temperature of the SMA actuators for position control of the probe by heating up the SMA wires at each joint. Pulse width modulation (PWM) based control scheme is used to be able to control all SMA wires simultaneously. PWM is implemented via use of a switching circuit. Proposed controller is validated through an experiment to heat up the SMA wires to a desired temperature. Another experiment is carried out inside gelatin to mimic the motion of the probe inside soft tissue. PWM control was successfully implemented and we were able to demonstrate local actuation of the steerable probe.