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Control of a magnetostrictive actuator with feedforwarding inverted hysteresis
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e1757–e1759
Control of a magnetostrictive actuator with feedforwarding inverted hysteresis Young-Woo Parka,*, Min-Cheol Lima, Do-Youn Kimb b
a Chungnam National University, 220 Kung-Dong, Yusong-Gu, Daejeon 305-764, South Korea LG Chemical, Ltd., Battery Research and Development, P.O. Box 61, Yusong-Gu, Science Town, Daejeon, South Korea
Abstract This paper proposes a systematic approach for an accurate control of the Terfenol-D actuator taking into account hysteresis, modeled by applying the classical Preisach operator with memory curve. A desired input displacement is calculated by using the hysteresis inverter, which is fed into the actuator. Then the PI compensator corrects the error between the commanded and actual displacements. Experiments with the step responses show that the PI controller settles in 70 ms and the hybrid controller in 20 ms. It means that the concurrent application of two control schemes is effective to control the actuator. r 2004 Elsevier B.V. All rights reserved. PACS: 75.80.+q; 75.60.Ej Keywords: Terfenol-D; Magnetostriction; Hysteresis; Preisach operator; Hysteresis inversion
1. Introduction
2. Controller design
Magnetostriction is a phenomenon consisting in the deformation of a ferromagnetic material when it experiences an applied magnetic field. The magnetostrictive materials (e.g., Terfenol-D) have been widely studied for mechanical actuation purposes, thanks to their ability to exert high forces. Nevertheless, hysteresis in the magnetostrictive materials hinders the wider applicability of them in actuators. The use of a non-linear model or non-linear inverse model in a control configuration has been shown to significantly enhance the performance of the hysteretic materials [1,2]. Thus, this paper proposes a systematic approach for an accurate control of the Terfenol-D actuator taking into account the hysteresis effect.
Hysteresis in Terfenol-D is modeled by applying the classical Preisach operator with memory curve, and formulated, according to Ref. [3], as ZZ yðtÞ ¼ G½xðtÞ ¼ mða; bÞgab ½xðtÞ da db; ð1Þ
*Corresponding author. Tel.: +82-42-821-6874; fax: +8242-823-4919. E-mail address: [email protected] (Y.-W. Park).
where G½xðtÞ is the Preisach operator, gab is a relay operator, a and b are up and down relay’s switching values ðaXbÞ; and mða; bÞ is a weight function to be determined by a suitable identification procedure. The weight function is determined by measuring the first order reversal curves experimentally. It is assumed that the input range is ½umin ; umax : The input is increased to umax and then decreased to umin : Then some piecewise monotone continuous input uðtÞ; tA½0; T; and the output wðtÞ is measured. In this work, the input is the current to the Terfenol-D actuator and the output is the corresponding displacement from the Terfenol-D actuator, as shown in Fig. 1. The hysteresis inversion algorithm for the resulting Preisach operator is called closest match algorithm [4].
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.988
ARTICLE IN PRESS Y.-W. Park et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e1757–e1759
e1758
actual displacements. The proposed control scheme is shown in Fig. 2.
The closest match algorithm tries to find the input yielding the closest match to the desired output rather to find the exact match to the desired output. Also, PI control scheme is incorporated into the full control scheme as a compensator. Using these concepts, the controller is built on a PC with a data acquisition board, and contains the hysteresis inverter and PI compensator. A desired input displacement is calculated by using the hysteresis inverter. The calculated input displacement is fed into the Terfenol-D actuator, and then the PI compensator corrects the error between the input and
3. Experimental procedure Experiments are performed to show the effectiveness of the proposed control schemes. Experimental setup consists of the Terfenol-D actuator, a coil driver for current amplification, power supply, an ADE MicroSense 3401 capacitive sensor with the resolution of 1 nm for the displacement measurement, and a controller. Two experiments are performed with the step responses; one is controlled by using the PI control and the other by using the PI control with hysteresis inversion.
4 3.5 Displacement (µm)
3
4. Experimental results and discussion
2.5
Figs. 3(a) and (b) show the step responses with the PI controller and with the hybrid (PI+hysteresis inversion) controller, respectively. In each figure, the inset marked as (b) is the enlargement of the inset marked as (a). It is found that the tracking accuracy with the hybrid controller is better that with the PI controller. It is also found that the response time with the hybrid controller is faster than that with the PI controller. That is, it settles in 70 ms with the PI controller and that in 20 ms with the hybrid controller. This is because of the capability of the Preisach model to predict and linearize the hysteresis.
2 1.5 1 0.5 0 -0.5 -0.5
0
0.5 1 Voltage (V)
1.5
2
Fig. 1. First-order reversal curve obtained from the experiments.
5. Conclusions Hysteresis in the Terfenol-D hinders the wider applicability of them in actuators. In this work, hysteresis inversion with PI control is proposed and applied to the Terfenol-D actuator. The hysteresis is modeled by using the classical Preisach operator with
Fig. 2. A proposed control scheme.
Displacement (µm)
3.5
Target Disp Actual Disp
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3
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2.5
2
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(b)
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0 1850
0 2000
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4000
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1900
2000
4500
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0.1 0
2500
3000
2000
3500
Time (ms)
Fig. 3. Step response with: (a) PI controller, (b) hybrid controller.
4000
4500
ARTICLE IN PRESS Y.-W. Park et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e1757–e1759
memory curve. Experimetal results show that the tracking accuracy and response time with the hybrid controller are better than those with the PI controller. Therefore, it can be concluded that the concurrent application of two control schemes is effective to control the Terfenol-D actuator.
Acknowledgements This work was supported by Grant No. R05-2001000-01092-0 from the Basic Research Program of the Korea Science and Engineering Foundation.
e1759
References [1] J. Schaefer, H. Janocha, Compensation of hysteresis in solid-state actuators, Sensors and Actuators A: Physical 49 (1–2) (1995) 97. [2] P. Ge, M. Jouaneh, Generalized Presach model for hysteresis nonlinearity of piezoceramic actuators, Precis. Eng. 20 (1997) 99. [3] I.D. Mayergoyz, Mathematical Models of Hysteresis, Springer, New York, NY, 1991 (Chapter 4). [4] X. Tan, R. Venkataraman, P.S. Krishnaprasad, Control of hysteresis: theory and experimental results, Technical Research Report at University of Maryland TR 2001-30, 2001.
Journal of Magnetism and Magnetic Materials 272–276 (2004) e1757–e1759
Control of a magnetostrictive actuator with feedforwarding inverted hysteresis Young-Woo Parka,*, Min-Cheol Lima, Do-Youn Kimb b
a Chungnam National University, 220 Kung-Dong, Yusong-Gu, Daejeon 305-764, South Korea LG Chemical, Ltd., Battery Research and Development, P.O. Box 61, Yusong-Gu, Science Town, Daejeon, South Korea
Abstract This paper proposes a systematic approach for an accurate control of the Terfenol-D actuator taking into account hysteresis, modeled by applying the classical Preisach operator with memory curve. A desired input displacement is calculated by using the hysteresis inverter, which is fed into the actuator. Then the PI compensator corrects the error between the commanded and actual displacements. Experiments with the step responses show that the PI controller settles in 70 ms and the hybrid controller in 20 ms. It means that the concurrent application of two control schemes is effective to control the actuator. r 2004 Elsevier B.V. All rights reserved. PACS: 75.80.+q; 75.60.Ej Keywords: Terfenol-D; Magnetostriction; Hysteresis; Preisach operator; Hysteresis inversion
1. Introduction
2. Controller design
Magnetostriction is a phenomenon consisting in the deformation of a ferromagnetic material when it experiences an applied magnetic field. The magnetostrictive materials (e.g., Terfenol-D) have been widely studied for mechanical actuation purposes, thanks to their ability to exert high forces. Nevertheless, hysteresis in the magnetostrictive materials hinders the wider applicability of them in actuators. The use of a non-linear model or non-linear inverse model in a control configuration has been shown to significantly enhance the performance of the hysteretic materials [1,2]. Thus, this paper proposes a systematic approach for an accurate control of the Terfenol-D actuator taking into account the hysteresis effect.
Hysteresis in Terfenol-D is modeled by applying the classical Preisach operator with memory curve, and formulated, according to Ref. [3], as ZZ yðtÞ ¼ G½xðtÞ ¼ mða; bÞgab ½xðtÞ da db; ð1Þ
*Corresponding author. Tel.: +82-42-821-6874; fax: +8242-823-4919. E-mail address: [email protected] (Y.-W. Park).
where G½xðtÞ is the Preisach operator, gab is a relay operator, a and b are up and down relay’s switching values ðaXbÞ; and mða; bÞ is a weight function to be determined by a suitable identification procedure. The weight function is determined by measuring the first order reversal curves experimentally. It is assumed that the input range is ½umin ; umax : The input is increased to umax and then decreased to umin : Then some piecewise monotone continuous input uðtÞ; tA½0; T; and the output wðtÞ is measured. In this work, the input is the current to the Terfenol-D actuator and the output is the corresponding displacement from the Terfenol-D actuator, as shown in Fig. 1. The hysteresis inversion algorithm for the resulting Preisach operator is called closest match algorithm [4].
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.988
ARTICLE IN PRESS Y.-W. Park et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e1757–e1759
e1758
actual displacements. The proposed control scheme is shown in Fig. 2.
The closest match algorithm tries to find the input yielding the closest match to the desired output rather to find the exact match to the desired output. Also, PI control scheme is incorporated into the full control scheme as a compensator. Using these concepts, the controller is built on a PC with a data acquisition board, and contains the hysteresis inverter and PI compensator. A desired input displacement is calculated by using the hysteresis inverter. The calculated input displacement is fed into the Terfenol-D actuator, and then the PI compensator corrects the error between the input and
3. Experimental procedure Experiments are performed to show the effectiveness of the proposed control schemes. Experimental setup consists of the Terfenol-D actuator, a coil driver for current amplification, power supply, an ADE MicroSense 3401 capacitive sensor with the resolution of 1 nm for the displacement measurement, and a controller. Two experiments are performed with the step responses; one is controlled by using the PI control and the other by using the PI control with hysteresis inversion.
4 3.5 Displacement (µm)
3
4. Experimental results and discussion
2.5
Figs. 3(a) and (b) show the step responses with the PI controller and with the hybrid (PI+hysteresis inversion) controller, respectively. In each figure, the inset marked as (b) is the enlargement of the inset marked as (a). It is found that the tracking accuracy with the hybrid controller is better that with the PI controller. It is also found that the response time with the hybrid controller is faster than that with the PI controller. That is, it settles in 70 ms with the PI controller and that in 20 ms with the hybrid controller. This is because of the capability of the Preisach model to predict and linearize the hysteresis.
2 1.5 1 0.5 0 -0.5 -0.5
0
0.5 1 Voltage (V)
1.5
2
Fig. 1. First-order reversal curve obtained from the experiments.
5. Conclusions Hysteresis in the Terfenol-D hinders the wider applicability of them in actuators. In this work, hysteresis inversion with PI control is proposed and applied to the Terfenol-D actuator. The hysteresis is modeled by using the classical Preisach operator with
Fig. 2. A proposed control scheme.
Displacement (µm)
3.5
Target Disp Actual Disp
3
3
2.5
2.5
2
0.5
2
(b)
0.6
1.5
0.4
0.3
1
(b)
0.5
0.4
1.5
Target Disp Actual Disp
3.5
0.3
1
0.2
0.2 0.1
0.5
(a)
0 1850
0 2000
(a)
0.5
2500
1950
3000
0
2050
3500
Time (ms)
4000
(a)
1900
2000
4500
(b)
0.1 0
2500
3000
2000
3500
Time (ms)
Fig. 3. Step response with: (a) PI controller, (b) hybrid controller.
4000
4500
ARTICLE IN PRESS Y.-W. Park et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e1757–e1759
memory curve. Experimetal results show that the tracking accuracy and response time with the hybrid controller are better than those with the PI controller. Therefore, it can be concluded that the concurrent application of two control schemes is effective to control the Terfenol-D actuator.
Acknowledgements This work was supported by Grant No. R05-2001000-01092-0 from the Basic Research Program of the Korea Science and Engineering Foundation.
e1759
References [1] J. Schaefer, H. Janocha, Compensation of hysteresis in solid-state actuators, Sensors and Actuators A: Physical 49 (1–2) (1995) 97. [2] P. Ge, M. Jouaneh, Generalized Presach model for hysteresis nonlinearity of piezoceramic actuators, Precis. Eng. 20 (1997) 99. [3] I.D. Mayergoyz, Mathematical Models of Hysteresis, Springer, New York, NY, 1991 (Chapter 4). [4] X. Tan, R. Venkataraman, P.S. Krishnaprasad, Control of hysteresis: theory and experimental results, Technical Research Report at University of Maryland TR 2001-30, 2001.