Neural network-based micropositioning control of smart shape memory alloy actuators
Introduction
Miniaturization has created the need of compact smart material-based actuators to power mechanical devices built at smaller scales. Shape memory alloys (SMA) are one of the most promising smart materials used in this kind of new actuators. Those actuators have a high power to weight ratio and have found applications in many areas (Pons, 2005) including micromechatronics and light robotics (Majima et al., 2001).
The shape memory effect in SMA is based on the transition caused between two solid phases: one of them of low temperature (martensite) and the other one of high temperature (austenite) (Fig. 1). This variation in the microscopic structure induces shape changes in the material, particularly in its length, if the sample is wire-shaped. This property can be used to generate motion or force in electromechanical devices by electrically heating the material.
SMA have traditionally been used as “on–off” electromechanical actuators, because of the intrinsic difficulty in controlling accurately the martensite–austenite proportion. This is due to the fact that the microscopic rearrangements involved in the structural changes take place quite sharply and in a highly complex and nonlinear fashion. The main difficulty in controlling these materials is caused by the hysteretic behavior of the phase transition. A memoryless controller is insufficient for a correct design due to the memory of the system under control. One possible solution to this problem would be to develop an accurate model for the thermo-mechanical behavior of the material, based on already developed mathematical models of hysteresis (Mayergoyz, 2003), as it has been done for other materials (Smith, 2005). From this point, an inverse model could be generated, and implemented in the controller, in order to compensate the system's hysteresis (Gang Tao and Kokotović, 1996). However, good models of phase transitions, ready to be used in a control loop, are by no means easily obtainable.
In this paper a nickel–titanium alloy (Nitinol) SMA wire will be considered as a micropositioning actuator. An electric current is applied through the wire to heat it to induce the phase transition and the consequent contraction. When the material cools off, the wire stretches again, provided that a sufficient tensile strain is applied. As pointed out before, an approach to the control of these materials can be based on hysteretic nonlinear compensation of the actuator's input–output characteristics, by using approximate inverse models of its hysteresis. In this paper two experimental approaches are described for this purpose: a linear compensation based on introducing a phase shift in the system, and a nonlinear one based on neural networks (NNs) appropriately trained to learn the system's inverse hysteresis from experimental data.
In the first approach, the system hysteresis is essentially considered as a phase lag between a periodic input signal and the corresponding output signal (Cruz-Hernández and Hayward, 2001) and, therefore, we implement a compensating stage that shifts the necessary phase angle to approximately cancel the system nonlinearities. This can be accomplished by linear means and inserted in a conventional proportional-integral (PI) control loop.
The nonlinear approach to the hysteresis compensation is based on NNs. NNs are usually employed within a control-systems context as modelling tools to approximate either the unknown plant's direct or the inverse dynamics, exploiting the network's well-known capability of nonlinear mapping to any desired accuracy (Narendra and Parthasarathy, 1990, Funahashi, 1989). Thus, they are ideal tools to implement a nonlinear inverse hysteresis compensation (Antsakis, 1990). In this work, we have experimentally trained NN to cancel the intrinsic nonlinearities of the Nitinol wire. The trained NN, having learned the inverse hysteresis behavior, is inserted in a PI with antiwindup control loop.
Both compensation methods are implemented and closed-loop tested on an experimental SMA-based laboratory positioning device. Experimental closed-loop results obtained (a) without compensation, (b) using phase lead compensation, and (c) using NN inverse hysteresis approximation are presented and their respective performance merits are discussed. It is shown that the NN approach compares favorably to the other methods in terms of precision and required control effort.
The paper is structured as follows: Section 2 describes the underlaying principles of the proposed hysteresis compensation methods: phase shift and NN learning of the hysteresis inverse. Section 3 describes the laboratory SMA-based micropositioning setup used to perform the experiments. Section 4 describes the implementation of the compensating methods and the experimental results obtained. The relevant discussion is included for all the control strategies, in terms of accuracy and control effort. Finally, Section 5 resumes the conclusions of the investigation.
Section snippets
Phase shift
The hysteresis effects observed in SMA can be seen as a phase lag between a periodic input and the corresponding output. Thus, the hysteresis compensation can be performed by introducing a compensating phase shift, for instance, by means of the “phaser” operator proposed by Cruz-Hernández and Hayward (2001), which modifies the phase but not the gain of the signal:
Note that this operator can be viewed as the counterpart of a gain, which modifies the
Experimental setup
The Nitinol wire that we have used for the control experiments has a diameter of 0.15 mm and its length, in the low temperature phase, is 75 mm. The scheme of the experimental setup used is depicted in Fig. 4(a). The wire is suspended vertically from a fixed support. It is Joule-heated using a voltage-controlled home-made current source. The current flowing through the wire is accurately determined by the voltage drop in a calibrated resistor. To measure the shrinking of the wire and therefore
Experimental results and discussion
An example of the SMA wire hysteresis measured in the experimental setup is shown in Fig. 5. This particular curve was obtained with a sinusoidal current with a period of 40 s flowing through the wire. Its amplitude is limited to 0.4 A to avoid overheating and degradation of the wire. The maximum contraction experienced by the wire is 2.9 mm and sharp changes in length are observed at about 0.3 A in the ascending branch and 0.15 A in the descending one.
All the control experiments that are presented
Conclusions
The difficulty in smoothly controlling the austenite–martensite proportion in SMA implies that these materials are mainly used in practice as “on–off” actuators. In this work, it has been experimentally shown that, despite the nonlinear and hysteretic characteristics of the material phase transitions, SMA wires can be successfully controlled to be used in micropositioning applications with micrometer accuracy by including the hysteresis effects in a nonlinear control scheme.
Inverse models have
Acknowledgments
The authors are grateful to CICYT for partial support of this work through project DPI2005-03121. They also wish to thank the Basque Government for Grant BFI05.283 and financial support under ACTIMAT project.
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