Modeling, Control and Applications of Shape Memory Alloys Actuators Nguyen Trong Tai A thesis submitted to the school of Mechanical and Automative Engineering in fulfillment if the thesis requirements for the degree of Doctor of Philosophy in the Graduate School, University of Ulsan May 2011 ACKNOWLEDGMENTS First and foremost, I would like to express my sincerest gratitude to my supervisor, Prof. Ahn Kyoung Kwan, for his guidance, support and valuable advice throughout my study in University of Ulsan. I would like to thank Professors in the committee, Prof. Lee Byung Ryong, Prof.
Ha Cheol Keun, Assist. Choi Seung Tae and Dr. Jin Maolin for their suggestions and comments throughout the research. I would like to express my gratitude to my grandparents, my parents and my three brothers, who provided me with unconditional advice, support and love.
They have never been far from my heart. I would like to express special gratitude to my girl friend, Ms. Her patience, encouragement and support have been invaluable during my study. I would also like to thank all members in FPMI Lab, University of Ulsan, especially, Mr Yoon Jong Il, for their friendship and help during my study.
May 2011 Nguyen Trong Tai ii CONTENTS Abstract xiv 1.1 Shape Memory Alloys 3 1.2 Advantages and Limitations 3 1.3 Research Objectives and Approach 4 1. Shape Memory Alloys 7 2.1 The Phases of SMA 7 2.2 The Shape Memory Effect 10 2.1 History and Applications 15 2. SMA Actuator modeling 27 3.1 Joule heating and heat transfer 29 3.2 Phase transformation hysteresis 29 3.5 Block diagram and state variable form 30 3.6 Comparison of mathematical model and real model 31 3.3 SMA actuator identification using HFLANN 33 3.2 Structure of the Hysteresis Functional Link Artificial Neural Network 34 3.3 System identification using PSO 35 iii 3.4 SMA dynamic identification result 36 3. SMA hysteresis compensation using control algorithms 40 4.1 Optimized PID controller using Particle Swarm Optimization 40 4.1 PID gain parameters tuning using PSO 40 4.2 Sliding mode control 44 4.1 Description of problem 44 4.2 Sliding mode controller 44 4.3 Adaptive Fuzzy Sliding mode control 48 4.1 Design of fuzzy controller 48 4.2 Stability, Learning law and reaching control signal 50 4.4 Adaptive RBF neural network controller 56 4.1 Structure of RBF neural network 56 4.2 RBF neural network training and stability 56 4.1 The k-mean algorithm for centre adjustment 57 4.2 Stability, weight adaption, and reaching control signal 57 4.5 Output feedback Direct Adaptive Control using Kalman filter 63 4.1 Description of problem 63 4.2 Linearization feedback control 63 4.3 Direct Adaptive Controller using RBF neural network 64 4.4 SMA states estimation using Kalman filter 65 4.5 Direct Adaptive Control stability with Kalman Filter estimator 67 4.6 PID Adaptive Sliding mode control 73 4.1 Description of problem 73 4.2 Design of PID Sliding mode controller 73 4.3 Choice of the value of Sliding controller Gain 75 iv 4.7 Model Predictive control based HFLANN 82 4.1 Idea of model based predictive control 82 4.2 Predictive control based HFLANN 82 4.8 Model Predictive control based online linearization identification model 93 4.1 System Online identification 93 4.2 Derivation of predictor and calculation of control signals 94 4.3 The solution of step coefficient matrix and free response 97 4.
SMA Applications on SMA cylinder and climbing robot 104 5.1 Actuator design using SMA springs 104 5.1 SMA Spring design 105 5.2 Bias springs Design 106 5.3 Design of the SMA cylinder 107 5.3 Cylinder position and force control 110 5.2 A climbing robot using elastomer adhesive and SMA wires 113 5.1 Researches of climbing robot 113 5.3 Design of the robot 116 5.1 Design of the robot 116 5.2 Force and moment distribution 118 5.1 Summary of achievements and contributions 125 6.2 Future works 126 References 127 Publications 135 Appendix: Properties of Flexinol and NiTi 136 vi LIST OF FIGURES Figure 1.1: The locus of power density vs. weight of actuators.1: Stress-strain curves for the two primary phases of SMA 8 Figure 2.2: Hysteresis curve of SMA Actuator 9 Figure 2.3: One-way shape memory effect 11 Figure 2.4: Two-way shape memory effect 12 Figure 2.5: Pseudoelasticity effect 13 Figure 2.6: Stress dependence of transformation temperatures 13 Figure 2.7: (a) SMA linear joint configurations, (b) SMA revolute joint configurations 14 Figure 2.8: Medical applications of SMA actuator 16 Figure 2.9: Industrial applications of SMA actuator 17 Figure 2.10: Schematic of the Preisach model 22 Figure 2.11: The Preisach plane 22 Figure 3.1: Experimental control setup 27 Figure 3.2: Photo of Experimental model 28 Figure 3.3: Block diagram of SMA mathematical model 31 Figure 3.4: Original state block of SMA actuator 31 Figure 3.5: New state block of SMA actuator 31 Figure 3.6: Comparison of mathematical and real model responses at frequency 1/15Hz 32 Figure 3.7: Hysteresis curve of experimental SMA actuator at frequency 1/15Hz 32 Figure 3.8: Hysteresis operator and its hysteresis nonlinear function 34 Figure 3.9: Model of SMA hysteresis dynamic using HFLANN 35 Figure 3.10: Model Identification diagram 36 Figure 3.11: Flowchart of parameters optimization using PSO 37 Figure 3.12: SMA dynamic identification – Identification result 38 Figure 3.13: Validation result with control input at 1/15Hz 38 Figure 4.1: Flowchart of tuning PID gain parameters using PSO 41 Figure 4.2: Results of PID gain parameters tuning after 100 iterations using PSO 42 Figure 4.3: The PID Control result with respect to the best PID gain parameters 42 Figure 4.4: PID Control result with respect to the multi-step reference 43 Figure 4.5: Control result with respect to sinusoidal reference 44 Figure 4.6: Control result using SMC with respect to multi-step response 46 vii Figure 4.7: Control result using SMC with respect to sinusoidal reference 47 Figure 4.8: Structure of the Fuzzy inference 48 Figure 4.9: Input and output membership functions 49 Figure 4.10: Block diagram of AFSMC 52 Figure 4.11: Control result with respect to multi-step reference using AFSMC 54 Figure 4.12: Control result with respect to sinusoidal reference using AFSMC 54 Figure 4.13: Hysteresis curve after using AFSMC 55 Figure 4.14: Control result with respect to saw-teeth reference using AFSMC 55 Figure 4.15: Structure of the RBF neural network 56 Figure 4.16: Block diagram of RBFSMC 59 Figure 4.17: Initial of center distribution of RBF neural network 59 Figure 4.18: Control result with respect to multi-step reference using RBFSMC 60 Figure 4.19: Control result with respect to sinusoidal reference using RBFSMC 61 Figure 4.20: Hysteresis curve after applying RBFSMC 61 Figure 4.21: Control result with respect to saw-teeth reference using RBFSMC 62 Figure 4.22: Structure of RBF neural network 64 Figure 4.23: Flowchart of DAC with modified KF 66 Figure 4.24: Block diagram of DAC with modified KF 67 Figure 4.25: Effect of Weighting matrix and number of neurons to control performance 68 Figure 4.26: Position control with respect to sinusoidal reference (1/15Hz) in simulation 69 Figure 4.27: Position control with respect to multistep reference 69 Figure 4.28: SMA displacement and estimated states using KF 69 Figure 4.29: Position control with respect to multi-step reference using DAC with KF 70 Figure 4.30: Position control with respect to sinusoidal reference using DAC with KF 71 Figure 4.31: Hysteresis curve after applying DAC with KF 72 Figure 4.32: Position control with respect to saw-teeth reference using DAC and KF 72 Figure 4.33: Nonlinear and hysteresis behavior 73 Figure 4.34: Block diagram of PIDSMC 76 Figure 4.35: Step reference control results using PIDSMC in simulation 76 Figure 4.36: Schematic of PIDSMC in Matlab 77 Figure 4.37: Position control with respect to multi-step reference using PIDSMC 78 Figure 4.38: Position control with respect to sinusoidal reference at 1/30Hz using PIDSMC 79 viii Figure 4.39: Position control with respect to sinusoidal reference at 1/15Hz using PIDSMC 79 Figure 4.40: Position control with respect to saw-teeth reference using PIDSMC 80 Figure 4.41: Hysteresis curve after applying the PIDSMC 80 Figure 4.42: Control result of PIDSMC in the conditions of external load 81 Figure 4.43: Basic idea of model based predictive control 82 Figure 4.44: Predictive Control Block diagram using HFLANN 83 Figure 4.45: Flowchart of HFLANN based Predictive control 86 Figure 4.46: Control results with respect to sinusoidal reference with three cases of different learning rate 87 Figure 4.47: Comparison of errors and control input is three cases of learning rate 87 Figure 4.48: Control result with respect to multi-step reference ( λ = 0.49: Control results with respect to the multi-step reference 88 Figure 4.50: Control result with respect to sinusoidal reference at frequency 1/30Hz 89 Figure 4.51: Control result with respect to sinusoidal reference at frequency 1/15Hz 90 Figure 4.52: The hysteresis curve after applying HFLANN Predictive controller 90 Figure 4.53: Control result with respect to saw-teeth reference 91 Figure 4.54: Comparison of control result in different load conditions 92 Figure 4.55: Matlab schematic diagram of GPC applied to SMA cylinder 100 Figure 4.56: Control result with respect to sinusoidal reference at 1/150Hz using GPC 101 Figure 4.57: Online linearized model parameters tuning 101 Figure 4.58: Control results with respect to sinusoidal reference at frequency 1/70Hz, 1/30Hz and in load condition at 4N 102 Figure 4.59: Hysteresis curves after applying GPC 102 Figure 4.60: Position control results with respect to multi-step reference 103 Figure 5.1: SMA spring deflection – (a) Extension, (b) Compression 104 Figure 5.2: SMA spring with bias spring 106 Figure 5.3: SMA Cylinder design tool and cylinder parameters result 108 Figure 5.4: Experimental SMA cylinder configuration 109 Figure 5.5: Photo of Experimental SMA cylinder 109 Figure 5.6: Setup for SMA cylinder control 110 Figure 5.7: SMA Cylinder and force sensor 110 Figure 5.8: Cylinder position control with respect to sinusoidal reference at frequency 1/70Hz 111 Figure 5.9: Cylinder position control with respect to sinusoidal reference at frequency 1/30Hz 111 ix Figure 5.10: Cylinder position control with respect to multi-step response 112 Figure 5.11: Cylinder exerted force control at position 4mm 112 Figure 5.13: Gecko feet structure and artificial dry adhesion 115 Figure 5.14: Gecko adhesive system 115 Figure 5.15: The climbing robot structure 117 Figure 5.16: Robot legs structure and adhesive distribution 117 Figure 5.17: Robot operation principle 117 Figure 5.18: Robot force and moment distribution 118 Figure 5.19: PDMS adhesion pressure versus preload pressure 119 Figure 5.20: PDMS adhesion torque versus adhesive area 119 Figure 5.21: Photo of the robot 120 Figure 5.22: The implementation control block diagram 121 Figure 5.23: Photo of V/I Converter and Electric circuit 121 Figure 5.24: Robot operating control principle 122 Figure 5.25: Photos of robot operation 123 x LISTS OF TABLES Table 2.1: Systems with Shape Memory Alloy [7] 8 Table 3.1: List of experimental devices and parameters 28 Table 3.2: Parameters of SMA mathematical model 32 Table 4.1: DAC and KF parameters 69 Table 5.1: Climbing robot – List of devices 120 Table A. 1: Technical data of Flexinol actuator wires. 2: Selected properties of NiTi alloys, taken from Johnson Matthey, Inc 138 Table A.
3: Properties of different SMA alloys (by AMT).