Control experiments on two SMA based micro ... - Semantic Scholar

C o n t r o l E x p e r i m e n t s on t w o S M A based micro-actuators N. Troisfontaine, Ph. Bidaud and P. Dario* Laboratoire de Robotique de Paris 10-12 Av. de l'Europe -78140 V~lizy - France * ARTS Lab. - MiTech Lab. Pisa Ital.v e-mail : troisfontaine,bidaud(@robot.uvsq.fr

Abstract: In this paper, two different control technics for SMA actuators are proposed : a position control and a temperature one. The position controller is based on a two stage ( P and PI) structure. The temperature controller uses a PID with a lag compensator in the feedback loop. Both of these simple technics have been designed for integration in micro-actuators. They have been experimented and have shown good performances with regard to perturbations in environmental conditions.

1. I n t r o d u c t i o n In recent years, Shape Memory Alloy (SMA) actuation has been considered in numerous proposals for micro-actuators. Its capacities in both tensile stress (up to 250 MPa) and motion range (up to 6% of its length) make it very attractive for micro-robotic applications. Basically. SMA actuators exploit a phase transformation in the alloy, called martensite transformation, by heating a n d / o r applying external stress. At high temperature, an SMA wire is basically elastic. At low temperature, in the martensite phase, it exhibits an elasto-plastic behavior. Restoring the initial length of an SMA actuator after heating requires an external bias force. This force is usually produced by the use of either an antagonist SMA actuator or a pre-stressed spring. Cyclic transitions between the austenite phase and the martensite phase are highly non linear with large hysteresis. Repeated heating/cooling process a n d / o r applied stress variations induce major and minor loops and lead to great difficulties for controlling the actuator position. Moreover. the SMA a~'tuator behavior is influenced by thermal exchanges. Experiments have clearl.v shown that open loop control is not suitable for robotic applications [1] [2]. Only a limited number of approches for controlling SMA actuator can be consider positively when taking into account integration constraints for microsystems (i.e number of sensors and controller hardware have to be minimized) [2]. In this paper, position and temperature feedback control schemes are proposed and experimented. Their good performances and their remarkable simplicit.v open perspectives for integration in micro-actuator structures. They have been designed for two SMA based micro-actuators. An inter-phalangeal actuator fi~r

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dexterous micro-grippers [1] and a steerable endoscope [3].

Photo 1 : Inter-phalangeal actuator for dexterous micro grippers In micro-grippers, joint positions have to be accurately controlled in order to perform precise manipulation tasks. This need justifies the integration of a position sensor. In this context, a minimal controller may use a single position feedback loop.

Photo 2 : Steerable endoscope tip The steerable endoscope is for applications in computer-assisted arthroscopy (photo 2). The endoscope tip trajectory is remotely controll~'d through a joystick and visual video feedback. However. in order to preserve the system controllability, to avoid thermal drift, and to maintain the desire'd bending, the actuator temperature has to be controlled. Thus. only a temperature sensor is integrated in the actuator and temperature measurement is used to obtain the feedback loop.

Both SMA actuators have been implemented by using Ni-Ti(50%/50(/, ) wires. The bias force is produced, in the first one by all elastic ~'lement. and in the second one, by a second wire mounted ill all antagonist mode.

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2. O p e n l o o p e x p e r i m e n t s 2.1. Principle In [1], a mathematical model has been proposed and experimentally validated to describe the thermo-mechanical behavior of an SMA wire. This model expresses the strain of the wire e as a function of the two parameters governing the martensite transformation : the temperature T and the applied stress or. Since e relies directly on the displacement x produced by the SMA actuator, the system can be considered as having two inputs variables (T,a) and one output (x). The applied stress depends on the force produced by the bias element and the external force applied to the SMA actuator. The temperature is generated by Joule effect with an electrical current controlled by a transistor (see fig. 2.1). The electrical resistance in the wire depends upon the transformation state. For this reason, it is preferable to use electrical power P~t,, rather than electrical voltage (u) [2]. The open loop control scheme takes the form described on the figure 2.1. Considering $~he hight non-linearity of the actuator, a simple transistor has been prefered to a P W M driver to minimize the complexity of the electronic circuit. F

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with time varying parameters, an experimental approch has been prefered tbr analizing the actuator dynamics.

2.2. Thermo-mechanical behavior sensibility analysis The strain inducing the output motion in SMA actuators depends upon thermomechanical conditions. In order to control the actuation process, the SMA behavior has to be analyzed. In [1], we proposed an analytical thermo-mechanical model for SMA actuators. We have experimentally verified for SMA wires, that their strain e can l)e described by : O"

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K and Tm depend on the transformation way. R1 and R2 rely on the material history. For more details on this model and its identification, see [11. The response to variations in thermo-mechanical conditions can be estimate from the model sensitivity to both parameters temperature T ansd stres. From the relationship : 0e • 0e .

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We can observe that temperature and strain variations vary in opposite direction, while stress and strain variations vary in same direction. This is true even in discontinuities caused by changes in transformation directions. It is important to notice that both partial derivatives are strongly dependent on the operative point, on the transformation way (i.e foward and reverse tranf(~rmations) as well as on the material history (throught R1 and R~). In position control of the SMA actuators, only the temperature can be considered as control variable. Stress variations in position control has to be compensated through au adequate temperature variation° An important feature, which is not reflected by the model, is the natural damping. The material experimentally exhibits a behavior that we call natural damping in the thermomechanical loading variations. This "damping" comes from internal friction in the phase transformation process and is dissipated in thermal energy. When both phases are present simultaneously, the internal damping effect can induce oscillations in control. This is due to coupling between temperature corrections

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coming from the position controller and internal temperature variations.

2.3. Environmental conditions sensibility analysis The SMA actuator dynamics rely mainly on the ambient temperature and convection mode. Open-loop experiments over a large set of different environmental conditions is a direct way to access to sensitivity analysis.

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Figure 2. Open loop experiments Ill figure 2-a, a very large perturbation is observed when switching the convection mode in a short time. On figure 2-b, experiments are performed in a limited ambient volume. The drift on output position is induced by a drift on the surrounding temperature caused by heat propagation. This ambient temperature rising also modifies the falling response time. and it can make the actuator uncontrollable after a limited number of cycles. It is also clear that the falling response time increases when the volume of ambiant air decreases. The two main conclusions for this analysis are : 1. open-loop control is not suitable for SMA actuators. 2. thermal exchanges have to be controlled. 3. T e m p e r a t u r e feedback control 3.1. C o n t r o l l e r d e s i g n Thermal exchanges can be controlled by a temperature feedback loop. Since the SMA wire strain is a function of temperature, applied stress and its transformation history, temperature feedback is not suitable to control the output position of the SMA actuators. Nevertheless. it can be sufficient in case of teleoperated systems such as the steering end-effector. The temperature measurement of the wire is not strictly necessary. A thermocouple with a 50tim diameter has been glued on the wire with a thermal conductive paste. The measured temperature is in fact the average temperature of the interface between the wire and the surrounding air. Moreover.

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by considering the heat propagation phenomena, the measure reflects the average temperature of the wire with a time delay in which the response time of the thermocouple can be neglected. To compensate this time delay, a lag compensator is integrated in the feedback loop (fig. 3).

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Figure 3. Temperature feedback control structure 3.2. E x p e r i m e n t a l results To evaluate the performances of the proposed controller, experiments were performed on wires with 100ttm in diameter which activation temperature is 7 0 ° C in the 10xl0xl0 m m 3 volume. 0.8

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Figure 4. Temperature feedback control for three different orders. tn figure 4, it can be noticed that the output position signal is established before the temperature signal because of heat propagation phenomena. In comparison to open loop experiments, the system response time is reduced in by a ratio of 40. This allows to maintain the system in a position controlled over a long period of time. The major drawback of temperature feedback control is that very small perturbations on environmental conditions can produce large variations in the output position. Figure 5 shows that a temperature perturbations, not perceptible by the thermocouple, modifies the strain (which is not compensated) in the SMA actuator because of its hysteresis.

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4. Position feedback loop

4.1. Controller design In [1], we proposed a feedback position control based on a switching structure. This solution is generaly well adapted to non linear systems but it leads to oscillations on the output position. These oscillations are intrinsic to the ccmtroller structure. Hayward & al. [2, 4] exploited a variable structure with three gain levels. T h e y studied the onset of limited cycles which can be avoided with small gains. As said before, they are also due to damping in the material. This last point forces to select a smallest gain around the desired position, especially if it corresponds to a transformation state with both phases. Consequently. it leads to a significant steady state error. Here, we propose to apply a feedback position loop with a two-stage controller by defining a boundary layer around the desired position as described in figure

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In this controller: • when the position error is large, a high proportional gain is applied with a low pass filter. This reduces the velocity when the position error is closed the boundary layer. • In the layer, a PI controller is applied to minimize the steady state error with a smallest proportional gain. Gorbet & al. have studied the/:2 stability of shape memory alloy actuated position control systems with PI controller [5]. Their stability analysis concludes that gain optimization is difficult. The stability of the system depends upon the thermo-mechanical and the thermal models used. Consequently, controller parameters were set experimentally. 4.2. E x p e r i m e n t a l r e s u l t s Experiments were performed in same conditions as for temperature control. The two-stage variable controller provides very good position accuracy. We can see that the control voltage u is adapted to environmental conditions and decreases slowly when the surrounding temperature increases. 0.9 08

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When we applied a full range motion sinus command (8-a), the maximum frequency value is low (0.1Hz) but performances can be improved by using only the half range motion. In this case, the maximum frequency value is approximatily the double (8-b). Moreover, this controller has been tested for different values of the ambient temperature and has demonstrated good reproductibility.

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Figure 8. tracking sinus trajectory 4.3. C o m p a r i s o n s in d y n a m i c p e r f o r m a n c e s b e t w e e n t h e t w o control technics It is clear that temperature feedback does not allow to control the displacement of the SMA actuator. But, if we consider the experimental results represented in figure 9-a made in the same conditions for both control technics to obtain at least the same output position (in dotted line temperature feedback control). we can observe that the falling response time is smallest in case of temperature feedback control. This is due to a drift on wire temperature in case of position feedback control (fig. 9-b). As a matter of fact, to maintain the desired position, the control voltage u variations produce minor thermal cycles. f

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feedback loop to improve the dynamic performances of SMA actuator. Results will be presented in a future communication.

5. Conclusions We have proposed here two different modes for SMA micr-actuator control depending on the concerned robotic application. Experimental results have shown good performances of both technics with regard to external perturb~,tions. In both case, experimental tests have proved that thermal exchanges limit dynamic performances and they have to be considered during the design of such actuators. Dynamic performances can be improved by (1) adapting activation temperatures of the alloy to the working conditions and its geometr.v~ (2) not exploiting the full range of the maximum available motion produced by the wire, (3) choosing body material with good thermal properties, and (4) controlling forced convection phenomena inside the volume of the micro-system.

References [1] N. Troisfontaine, P. Bidaud, and G. Morel, "A new inter-phalangeal actuator for dexterous micro-grippers," in International confernce on Robotics and Automation, Albuquerque USA, IEEE, 1997. [2] D. Grant and V. Hayward, "Design of shape memory alloy actuator with high strain and variable structure control," in IEEE International Conference on Robotic and Automation, Nagoya, pp. 2305-2312, 1995. [3] P. Dario, C. Paggetti, N. Troisfontaine, E. Papa~ T. Ciucci, M. Carrozza. and M. Marcacci, "A miniature steerable end-effector for application in an integrated system for computer-assisted arthroscopy," in International confernce on Robot~c.~ and Automation, Albuquerque USA, IEEE, 1997. [4] D. Grant and V. Hayward, "Controller for a high strain shape menory alloy actuator:quentching of limit cycles," in IEEE International Conference on Robotic and Automation, Albuquerque, pp. 254-259, 1997. [5] R. Gorbet and D. Wang, "General stability criteria for a shape memory alloy position control system," in IEEE International Conference on Robotic and Automation, Nagoya, pp. 2313-2319., 1995.