Abstract
Actuators incorporating smart materials are competitive choices for micro-positioning devices, but they are difficult to control because of their nonlinearity and hysteresis. These actuators are shown to be passive using several different approaches. Using passivity, a class of stabilizing controllers is identified. A controller for velocity control is designed that optimizes tracking performance and evaluated experimentally. A different approach is used to establish stability and tracking when position control is required. Robust stability is obtained in both approaches since stability is not sensitive to actuator parameters.
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References
Akella, P., Wen, J.T.: Synthesized passive feedback control of sensor-rich smart structures — experimental results. In: Proceedings, IEEE conference on control applications, pp. 1098–1103 (1995)
Bertsekas, D.P.: Nonlinear Programming. Athena Scientific, Belmont, Massachusetts (1999)
Brokate, M., Sprekels, J.: Hysteresis and phase transitions. Springer, New York (1996)
Damaren, C.J., Oguamanam, D.C.: Vibration control of spacecraft box structures using a collocated piezo-actuator/sensor. Journal of Intelligent Material Systems and Structures 15, 369–374 (2004)
Gorbet, R.B., Wang, D.W.L., Morris, K.A.: Preisach Model Identification of a Two-Wire SMA Actuator. In: Proceedings of the 1998 IEEE International Conference on Robotics and Automation, vol. 3, pp. 2161–2167 (1998)
Gorbet, R.B., Morris, K.A., Wang, D.W.L.: Passivity-based stability and control of hysteresis in smart actuators. IEEE Transactions on control systems technology 9, 5–16 (2001)
Gorbet, R.B., Morris, K.A., Wang, D.W.L.: Control of Hysteretic Systems: A State-space Approach. In: Yamamoto, Y., Hara, S. (eds.) Learning, Control and Hybrid Systems, pp. 432–451. Springer, Heidelberg (1999)
Hughes, D., Wen, J.T.: Preisach Modelling of Piezocramic and Shape Memory Alloy Hysteresis. In: Proceedings of the 1995 IEEE Control Conference on Applications (1995)
Iyer, R.V., Tan, X., Krishnaprasad, P.S.: Approximate Inversion of the Preisach Hysteresis Operator with Application to Control of Smart Actuators. IEEE Transactions on Automatic Control 50, 798–810 (2005)
Logemann, H., Ryan, E.P., Shvartsman, I.: A class of differential-delay systems with hysteresis: asymptotic behaviour of solutions. Nonlinear analysis (to appear, 2007)
Logemann, H., Ryan, E.P., Shvartsman, L.: Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach. ESAIM — control, optimisation and calculus of variations 13, 458–483 (2007)
Nealis, J.M., Smith, R.C.: Robust control of a magnetostrictive actuator. In: Proceedings of SPIE, The International Society for Optical Engineering, vol. 5049, pp. 221–232 (2003)
Smith, R.C., Dapino, M.J., Seelecke, S.: Free energy model for hysteresis in magnetostrictive transducers. J. Appl. Phys. 93, 458–466 (2003)
Smith, R.C.: Smart Material Systems: Model Development. SIAM, Philadelphia (2005)
Tan, X., Baras, J.S.: Modeling and control of hysteresis in magnetostrictive actuators. Automatica 40, 1469–1480 (2004)
Valadkhan, S., Morris, K.A., Khajepour, A.: Passivity of magnetostrictive materials. SIAM Journal of applied mathematics 67, 667–686 (2007)
Valadkhan, S., Morris, K.A., Khajepour, A.: A review and comparison of hysteresis models for magnetostrictive materials. Journal of intelligent material systems and structures (submitted, 2007)
Valadkhan, S., Morris, K.A., Khajepour, A.: Stability and robust position control of hysteretic systems. IEEE Trans. Auto. Control (submitted, 2007)
Vidyasagar, M.: Nonlinear systems analysis. Prentice hall, Englewood Cliffs, New Jersey (1993)
Willems, J.C.: Dissipative dynamical systems, part I: General theory. Archives for Rational Mechanics and Analysis 45, 321–351 (1972)
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Valadkhan, S., Morris, K., Khajepour, A. (2008). Robust Control of Smart Material-based Actuators. In: Blondel, V.D., Boyd, S.P., Kimura, H. (eds) Recent Advances in Learning and Control. Lecture Notes in Control and Information Sciences, vol 371. Springer, London. https://doi.org/10.1007/978-1-84800-155-8_18
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DOI: https://doi.org/10.1007/978-1-84800-155-8_18
Publisher Name: Springer, London
Print ISBN: 978-1-84800-154-1
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