Project topics and materials
Get Complete Project Material File(s) Now! »
Shape Memory Alloys (SMA)
Shape memory alloy consists of a group of materials that have the capability to return to a predefined shape or size when subjected to appropriate thermal input. Some examples of these alloys are NiTi, NiTiCu, CuAlNi, CuAlBe, NiMnGa, AuCd and Fe- Mn-Si. A shape memory alloy is able to remember its original configuration after it has been deformed by heating the alloy above characteristic transition temperature. This unique effect of returning to its original geometry after a large inelastic deformation is known as shape memory effect(SME)(Mosley & Mavroidis, 2001; Van Humbeeck, 2001). The SME behavior is due to a temperature and stress dependent transition in the material’s crystalline structure between two different phases ; a high temperature parent phase called austenite, and a low temperature product phase called martensite.
Let us consider the example of a straight SMA rod (Mavroidis, 2002). If the straight rod of SMA in its austenite i.e., high temperature phase is allowed to cool below the phase transition temperature, the crystalline structure will change to martensite. If the bar is then plastically deformed, for example by bending and then reheated above the phase transition temperature, it will return to its original straight configuration. This phenomenon can be explained in a simplified manner using the material’s crystalline arrangement as shown in Figure 5.2. At high temperature, the material is in a cubic austenite structure (Fig. 5.2-a). When cooling below the phase transition temperature, the crystalline structure changes to martensite having a lower crystal symmetry and a very typical twinned pattern (Fig. 5.2-b). Now, if sufficient stress is applied, the martensite structure is detwinned producing a large deformation at the crystal length scale (Fig. 5.2-c). This behaviour can be illustrated by studying the stress-strain curve for the martensite phase (Figure 5.3). For small stresses, the martensite- twinned structure in Figure 5.2-b behaves elastically from stage-0 to stage-1. At stage 1, the material yields and de-twinning occurs between stage-1 and stage-2. At stage-2 the martensitic structure is completely de-twinned as represented by Figure 5.2-c. Now a second elastic region starts from stage-2 and ends at stage-3. At stage 3, permanent plastic deformation begins that is not recoverable by the Shape Memory Effect. During the phase transition there is energy dissipation due to internal friction. As a result a thermal hysteresis occurs which can be seen in Figure 5.4-a. Starting at stage 1 the material is 100 % martensite. During heating the material composition follows the lower curve. When the temperature reaches As the austenite begins and continues until AF is reached and the material is 100 % austenite. If cooling occurs from stage 2 the material composition follows the upper curve. When the temperature drops to MS, martensite phase begins and continues until MF which is the original phase 100 % martensite. This thermal hysteresis can be seen in the strain/temperature relationship (Figure 5.4-b).
General Performance and Thermal Control of SMA element
The general design guidelines of SMA actuators in terms of performance is briefly discussed here. Performance of SMA actuators is to be understood in terms of dy- namic performance (input-output time response) and positioning accuracy which are considered to be typical requirements for certain applications such as robotic or any precision displacement actuator. The performance requirements of SMA actuators also rely heavily on aspects like energy efficiency or the stroke of the actuator element. For SMA actuators, the efficiency of the conversion of heat into mechanical work is very low. Theoretical Carnot value is itself very low for SMAs because the difference between high and low temperature is only a few tens of degrees. When considering friction and losses, this efficiency go down to about 1%. According to Reynaerts & Van Brussel (1998), a SMA actuator will never compete with conventional drive types, as it has been compared in Mavroidis et al. (2000) that the efficiency of an electrical actuator is 90% (for large systems). For hydraulic and pneumatic it is rare although possible to achieve efficiency above 60% and 30%, which is still higher compared to SMA actuators. But there are interesting applications where the disadvantages of SMA actuators can be ignored, and considering the performance point of view the design of SMA actuators has more prominent takers in applications such as robotic actuators, to name one of the many fields of applications. Commercially the two main groups of SMA alloys available are copper based alloys such as CuAlBe, CuAlNi alloys and NiTi alloys. Depending on the type of applica- tions and price of the final product the two major types of SMA alloys are utilized.
NiTi SMAs are more expensive than copper based alloys but fatigue resistance and functional properties are better. For applications such as “clamps” copper based alloys are preferred. In robotic applications NiTi based SMAs are preferred. NiTi has aconsiderably larger resistance than cooper-based alloys, so smaller current is sufficient in case of electrical resistive heating. The functional properties of NiTi are far better reproducible and has higher mechanical strength and allows a higher working stress. NiTi alloys have also appeared to have shown a higher work density (delivered work per unit volume) and have good corrosion resistive properties.
Modelling methods and Control
There is considerable interest in development of SMA actuators due to interesting advantages such as high power-to-weight ratio, low driving voltages and ability to produce large strains. These advantages have found them interesting applications in biomedical field (Sars et al., 2010), robotics (Cocaud et al., 2006) and space applications (Peng et al., 2008). However application to precise engineering systems are difficult due to the highly nonlinear relationship between output strain and input current. SMA ac- tuators have hard nonlinearities such as backlash like hysteresis and saturation due to SME. The efficiency of an SMA actuator depends on the accuracy of its control, which in turn depends on good reliable model which can be efficiently used to compensate the hysteretic nonlinearity and perform the control task. This section is entirely dedicated to study the various modelling and control methods popular among SMA actuators. Many models for SMA control have been proposed in literature, which can be coarsely classified into physical and phenomenological models. For specific problems, models describe the given hysteretic SMA system based on physical laws. Normally this is a difficult task and the resulting models are too complex to be used for prac- tical purposes. In general, engineering applications require alternative models which although not giving enough description about the physical behaviour of the system, do describe the Input-Output features. Such input-output models are useful for identification design and control purposes of systems involving such behaviours. These models are referred to as phenomenological models. This section briefly introduces the physical and phenomenological models. Although a large number of models could be classified in the physical and phenomenological category for studying the problem of hysteresis, only a few will be discussed here.
Table of contents :
I Résumé étendu
1 Introduction
1.1 Introduction générale
1.2 Alliage à Mémoire de Forme (AMF)
1.3 Actionneurs à Alliage à Mémoire de Forme
1.4 Modélisations et commandes
1.4.1 Commandes avec modèles constitutifs
1.4.2 Commande à partir de modèles phénomènologiques
1.4.3 Méthodes classiques sans modèles explicites
1.5 Contribution de la thèse
2 Modélisation
2.1 Introduction
2.2 Modélisation des systèmes linéaires invariants
2.2.1 Modèle discrets en environnement déterministe
2.2.2 Environnement stochastique
2.3 Identification
2.3.1 Moindres carrés
2.3.2 Moindres carrés récursifs
2.4 Base des fonctions de Laguerre
2.4.1 Intérêt
2.4.2 Base orthonormale des fonctions de Laguerre discrètes
2.4.3 Propriétés
2.4.4 Modèle de Volterra-Laguerre
2.5 Etude expérimentale
2.5.1 Critères d’évaluation
2.5.2 Actionneur simple
2.5.3 Actionneur antagoniste
2.6 conclusion
3 Commande
3.1 Commande adaptative prédictive
3.1.1 Principe de la commande prédictive
3.1.2 Commande prédictive avec modèle de Laguerre
3.1.3 Stabilité et robustesse
3.1.4 Validation expérimentale
3.2 Commande modifiée
3.2.1 Principe
3.2.2 Stabilité
3.2.3 Validation expérimentale
3.3 conclusions
4 Conclusion
4.1 Résumé du travail
4.1.1 Identification
4.1.2 Commande
4.2 Perspectives
4.2.1 Améliorations à apporter
4.2.2 Limites de l’approche « boite noire »
II Version Anglaise
5 Introduction
5.1 Introduction to Actuators
5.2 Shape Memory Alloys (SMA)
5.3 Shape Memory Alloy (SMA) Actuators
5.3.1 General Performance and Thermal Control of SMA element
5.3.2 Different Types of SMA Actuator
5.4 Modelling methods and Control
5.4.1 Physical Modeling and Nonlinear Control
5.4.2 Phenomenological Model and Inverse Control
5.4.3 Control without using Explicit Model: Linear Control
5.5 Summary of modelling and control methods and their interaction
5.6 Contribution of this Thesis
5.7 Outline of the Thesis
6 Modelling
6.1 Introduction
6.2 Models of linear time invariant processes
6.2.1 Discrete model in deterministic environment
6.2.2 Modelling the disturbances
6.3 Identification
6.3.1 Least squares
6.3.2 Recursive least squares
6.3.3 Adaptive recursive least squares
6.4 Laguerre function basis
6.4.1 Motivation
6.4.2 Discrete Laguerre orthonormal basis
6.4.3 Some properties of the Laguerre function basis
6.5 Experimental Study
6.5.1 Validation of Model in Prediction Error Method
6.5.2 Single Wire Actuator
6.5.3 Open loop Identification of the single actuator
6.5.4 Experimental Setup: Antagonistic Actuator
6.6 Conclusion
7 Adaptive Predictive Control
7.1 Introduction
7.2 Closed Loop Identification (Offline/Non-Adaptive)
7.3 Introduction to Predictive control
7.3.1 Closed loop Identification (Non-Adaptive) for MPC
7.4 Predictive control as Receding Horizon Problem
7.5 Stability and Robustness
7.6 Control of SMA using Classical Laguerre Predictive (CLaP) Control: Experimental Results
7.6.1 Position Control using 2nd order linear Laguerre model with CLaP method
7.6.2 Position Control using 5th order linear Laguerre model with CLaP method
7.7 CLaP method using RLS estimation with Directional Forgetting factor 142
7.7.1 Directionnal Forgetting Factor Recursive Least Squares
7.7.2 Methodology
7.7.3 Position Control using 5th order linear Laguerre model with CLaP- DFRLS method
7.7.4 Influence of Prediction Horizon (Hp) and Control weights (Q,R) 144
7.7.5 ClaP-DFRLS using 2nd order
7.7.6 Influence of Thermal Disturbance and Ambient Temperature
7.8 Conclusion and Perspective on CLaP-DFRLS
7.9 Modified Adaptive Predictive Control
7.9.1 Main Results
7.9.2 Stability analysis
7.10 Control of SMA using Modified Laguerre Predictive (MLaP) Control:
7.10.1 Position Control using 5th order linear Laguerre model with MLaP method
7.10.2 Position Control using 2nd order linear Laguerre model with MLaP method
7.11 Discussions
7.11.1 Influence of prediction horizon
7.11.2 Perturbation Rejection
7.12 Antagonistic Actuator control
7.12.1 Open loop charateristics
7.13 Experimental results and discussion
7.13.1 Position Control
7.13.2 Influence of Prediction Horizon
7.14 Antagonistic setup: Discussion
7.15 Conclusion
8 Conclusion
8.1 Summary of this work
8.2 Contributions
8.2.1 Modeling for Control
8.2.2 Adaptive control of SMA actuator
8.3 Unsolved problems and Future Directions
8.3.1 Optimal Actuator design
8.3.2 Modeling Problem
8.3.3 Control Problem
