1.3 Motivation and Objective
1.3.1 Organization of the Present Work
• chapter 2 : The complete description of the Shape Memory Alloy (SMA) is presented in this chapter. Two interesting phenomena namely, Shape memory effect and Pseudo- elasticity or Super-elasticity, with the underlying mechanism are discussed. The stress and temperature dependent phase transformation, dictating the extraordinary behavior of SMA are discussed. In this context, the phase diagram is also introduced. The phenomenological constitutive relation and the associated phase kinetics, that are used in this work, are described. The algorithms required for selection of transformation domain as well for updating the memory parameters, that are adopted in this work are also presented. Finally, determination of the temperature of the SMA wire, subjected to resistive heating and convective cooling, following a heat balance equation is also discussed.
• chapter 3 : The development of the Extended Kalman Filter for exploring the self- sensing capability of the SMA wire actuator is presented in this chapter. Two systems, having linear and nonlinear stiffnesses, respectively, are considered to be actuated by the SMA wire actuator. The mathematical models of these two systems, as required for the Kalman filter, are presented. The model comprises of heat balance equation and the constitutive relation of the SMA wire coupled with the stiffness of the system.
Next, the implementation of the Kalman filter using two numerical schemes, namely implicit and explicit methods, are discussed. Then the computational advantage of the using implicit scheme over the explicit one is illustrated. Finally, the EKF estimated response of the systems is compared with the response obtained from the model, to validate the potential of the developed EKF model.
• chapter 4 : The experimental set-up developed to test the performance of the EKF model is presented. The set-up comprises of an SMA actuated system, a data acqui- sition system, voltage divider circuit, and a displacement sensor. The voltage divider circuit is designed and developed to measure the electrical resistance of the SMA wire online. The displacement sensor measures the response of the system being actuated by the SMA wire. Two systems are considered. The first one is a linear spring being stretched by the SMA wire actuator, and the second one comprises of a flexible beam being bent by an SMA wire place above the surface of the beam. In the latter case, the force-displacement relation as offered to the SMA wire actuator is non-linear; as the beam is designed to undergo large deformation. For different voltage signals applied across the SMA wire, the system response as estimated by the EKF, using the experi- mentally measured resistance of the SMA wire, and are compared with the measured response of the systems.
• chapter 5 : In this chapter, the development and implementation of an Unscented
Kalman filter model for a linear spring biased SMA wire actuator are discussed. It starts with the mathematical details involved in an UKF, followed by the detailed steps required to implement the same for self-sensing application of the SMA wire actuators.
The UKF estimated system response are compared with that of the same obtained using EKF. Though it offers the same level of accuracy as in case of EKF, however, it is found to be computationally less rigorous as compared to the EKF.
• chapter 6 : In this chapter, couple of steps are reported to improve the accuracy of the estimation. Firstly, the transformation temperatures of the SMA wire is obtained following a DSC test. Next, an artificial neural network has been developed based on the EKF estimation and is found to perform better in comparison to another artificial neural network trained only based on experimental data. Then an attempt has been made to take care of the various uncertainties in the model as well as the parameters using variable process noise covariance. However, this approach failed to improve the estimation accuracy. Finally, two uncertain parameters are augmented with EKF model so as to estimate the same along with the state variables. In this approach, a drastic improvement in the estimation accuracy is observed.
• chapter 7 : In this chapter, the implementation details of the developed EKF model in a low end hardware, namely, Arduino Uno, is presented. The details of the set-up are discussed followed by a couple of responses that has been obtained using the Arduino board.
• chapter 8: In this chapter the research contribution of the work has been summarized and the possible extensions of the current work are presented.
Chapter 2
Modelling of Shape Memory Alloy (SMA) Wire Behavior
2.1 Introduction
Shape Memory Alloys (SMAs) are basically metallic alloys, undergo large deformation un- der external load at low temperature and can recover the same upon heating above certain temperature. This capability of remembering its initial undeformed shape, renders these group of metallic alloys the name Shape Memory Alloy. This particular phenomenon is known as Shape Memory Effect. In general, this is widely used in actuator applications, pipe couplings, valves, circuit breakers etc. Another interesting behavior, these group of alloys offer, is referred as Pseudo-Elasticity or Super-Elasticity. Above a certain temper- ature, the material exhibits large deformation with external load and successively recovers the same upon unloading. It is used in biomedical applications, where a member can un- dergo large strain without an effective change in stiffness and can recover completely once
the external load is withdrawn. The Shape Memory Effect (SME) and Pseudo-Elasticity (PE) or Super-Elasticity (SE) emerge because of the reversible solid-solid phase transforma- tion among various variants of Martensite [M], and Austenite [A]. In this chapter, a brief overview of these phenomena and the underlying mechanics are presented. Then the avail- able phenomenological model to simulate these phenomena are discussed.