High Performance Force Control for Shape Memory Alloy (SMA) Actuators

Transcription

1 High Performance Force Control for Shape Memory Alloy (SMA) Actuators Roy Featherstone (reporting the work of Yee Harn Teh) Dept. Information Engineering, The Australian National University R. Featherstone, Y. H. Teh 2008 Roy Featherstone 1

2 The Shape Memory Effect An alloy exhibiting the shape memory effect has the following property: it can be deformed easily when cold, but returns to its original shape when heated. The shape recovery process is accompanied by large forces, which can be harnessed to perform mechanical work. 2

3 The Shape Memory Effect The effect is caused by a transformation between two crystal phases: 1. an austenite crystal phase, which is stable at higher temperatures, and 2. a martensite crystal phase, which is stable at lower temperatures. Austenite crystals are cubic: Martensite crystals are monoclinic: or 3

4 The Shape Memory Effect hot cooling cold warming deform 4

5 The Shape Memory Effect 100% martensite ratio 0% M f A s thermal hysteresis M s A f temperature 5

6 SMA Actuators SMA wires are easily stretched when cool force sensors but recover their original shape when heated antagonisticpair actuator 6

7 SMA Actuators Advantages mechanically simple large force outputs high forcetoweight ratio cheap clean silent sparkfree easily miniaturized Disadvantages inefficient low strain slow hard to control accurately a better control system can fix these 7

8 Force Control System power limit R L P max,l P max,r power limit R R F cmd differential force controller P diff map P L P R left SMA right SMA F L F diff F diff P com anti overload F R anti slack 8

9 Force Control System P max,l P max,r power limit R L P L = P com max(0,p diff ) power P R = P com limit max(0,p diff ) R R F cmd differential force controller P diff map P L P R left SMA right SMA F L F diff F diff P com anti overload F R anti slack 9

10 Differential Controller power limit R L P max,l P max,r power limit R R F cmd differential force controller P diff map P L P R left SMA right SMA F L F diff F diff P com anti overload F R anti slack 10

11 Differential Controller P max,l P max,r differential force controller T d s max 1 min F cmd K p max min P diff F diff 1 T i s 11

12 Behaviour of the Plant The smallsignal AC response of nickeltitanium SMA approximates to a firstorder lowpass filter. Gain varies with mean stress and strain in a 78 db range Phase is independent of stress and strain 78 db gain phase Cutoff frequency varies with wire diameter 12

13 What Happened to the Hysteresis? 13

14 A Problem When Flexinol TM wires are used in an antagonisticpair actuator, they quickly develop a twoway shape memory effect, in which the wires actively lengthen as they cool, even if the tension on the wire is zero. Symptom: Remedy: The wires can become slack as they cool. An antislack mechanism that maintains a minimum tension on both wires at all times. 14

15 AntiSlack Mechanism power limit R L P max,l P max,r power limit R R F cmd differential force controller P diff map P L P R left SMA right SMA F L F diff F diff P com anti overload F R anti slack 15

16 AntiSlack Mechanism power limit R L P max,l P max,r power limit R R F cmd differential force controller P diff map P L P R left SMA right SMA F L F diff F diff P com anti overload F R anti slack 16

17 AntiSlack Mechanism P com K as min F L F R antislack F min 17

18 AntiSlack Mechanism P com K as min F L F R out F min in 18

19 without antislack with antislack Reference Actual Reference Actual Differential Force (N) Differential Force (N) Time (s) x 103 Time (s) Differential Force Error (N) Time (s) Differential Force Error (N) Time (s) 19

20 Another Problem We want the actuator to be as fast as possible. The speed can be increased by means of a faster heating rate, and/or a faster cooling rate. A faster heating rate is more beneficial and easier to implement. problem: how to achieve faster heating without risk of overheating? 20

21 Why Focus on Heating? Excerpt from Flexinol TM data sheet: Diameter (mm) Current (ma) Contraction Time (sec) Off Time 70C Off Time 90C If we use the recommended safe heating currents then, for a thin wire, heating takes longer than cooling. 21

22 Rapid Electrical Heating To obtain a rapid response from an SMA wire, we need a heating strategy that allows large heating powers when there is no risk of overheating, but allows only a safe heating power when there is a risk of overheating. This can be accomplished by measuring the electrical resistance of the wire, and calculating a heating power limit as a function of the measured resistance 22

23 Resistance Electrical Resistance vs. Temperature The electrical resistance (of nitinol) varies with the martensite ratio, and therefore also with temperature, because the resistivity of the martensite phase is about 20% higher than the resistivity of the austenite phase. heating ~20% cooling Temperature 23

24 Calculating the Power Limit 1. Choose a threshold resistance, R th, which is equal to the hot resistance of the wire plus a safety margin. R th safety margin operating temperature too hot 24

25 Calculating the Power Limit 2. Calculate the power limit, P max, as a function of the measured resistance, R meas. R ramp P max R th unsafe power levels P high P safe safe R meas 25

26 Rapid Heating Mechanism power limit R L P max,l P max,r power limit R R F cmd differential force controller P diff map P L P R left SMA right SMA F L F diff F diff P com anti overload F R anti slack 26

27 without rapid heating with rapid heating 3 Reference Actual 3 Reference Actual 2 2 Differential Force (N) Differential Force (N) Time (s) Left SMA Right SMA Time (s) Left SMA Right SMA Force (N) 3 Force (N) Time (s) Time (s) 27

28 Yet Another Problem Rapid heating can produce excessively high tensions on the wires, which can cause damage. remedy: an antioverload mechanism that cuts the heating power if the tension goes too high. 28

29 AntiOverload Mechanism power limit R L P max,l P max,r power limit R R F cmd differential force controller P diff map P L P R left SMA right SMA F L F diff F diff P com anti overload F R anti slack 29

30 AntiOverload Mechanism power limit R L P max,l P max,r power limit R R F cmd differential force controller P diff map P L P R left SMA right SMA F L F diff F diff P com anti overload F R Yee Harn s version anti slack 30

31 AntiOverload Mechanism K ao max F L F R antioverload F max 31

32 without antioverload with antioverload 3 Reference Actual 3 Reference Actual 2 2 Differential Force (N) Differential Force (N) Time (s) Left SMA Right SMA Time (s) Left SMA Right SMA Force (N) 3 Force (N) Time (s) Time (s) 32

33 Conclusion A new architecture for highperformance force control of antagonisticpair SMA actuators has been presented, comprising a PID controller for accurate control of the actuator s output force (i.e., the differential force); an antislack mechanism to enforce a minimum tension on both wires; a rapidheating mechanism that allows faster heating rates, but protects the wires from overheating; and an antioverload mechanism that protects the wires from mechanical overload. 33

34 Epilogue This control system has been found to work in the presence of large motion disturbances, and it has been used as the inner loop in a position control system that achieves high setpoint accuracy. For more details, see Yee Harn s Ph.D. thesis Y. H. Teh & R. Featherstone, "An Architecture for Fast and Accurate Control of Shape Memory Alloy Actuators", Int. J. Robotics Research, 27(5):595611, Acknowledgement: The experimental results graphs appearing in this talk are taken from Yee Harn s Ph.D. thesis. 34