Selective modal control for vibration reduction in flexible structures. (English) Zbl 1352.93015
Summary: The design of a controller for selective reduction of vibrations in flexible low-damped structures is presented. The objective of the active feedback control law is to increase damping of selected modes only, in frequency regions where a disturbance is likely to produce largest effect. Moreover, the stabilizing controller is required to be band-pass, in order to filter out high-frequency sensor noise and low-frequency accelerometer drift, and stable to increase robustness to uncertain parameters. The control design is based on the inverse optimal design approach, through the solution of a matrix Stein equation, resulting in the solution of an optimal \(\mathcal{H}_\infty\) control problem. A grey-box identification approach of the authors is employed for obtaining the model from experimental data or from detailed Finite Element Model (FEM) simulators. The problem of optimal actuator/sensor location is also addressed. Detailed simulation results are provided to show the effectiveness of the strategy.
MSC:
| 93A15 | Large-scale systems |
| 93B35 | Sensitivity (robustness) |
| 93B36 | \(H^\infty\)-control |
| 70Q05 | Control of mechanical systems |
| 70J50 | Systems arising from the discretization of structural vibration problems |
Keywords:
large scale optimization problems and methods; vibration control for flexible structures; optimization-based controller synthesis; infinite-dimensional systems; identification methodsReferences:
| [1] | Anderson, B. D.O.; Liu, Y., Controller reduction: concepts and approaches, IEEE Transactions on Automatic Control, 34, 8, 802-812 (1989) · Zbl 0698.93034 |
| [2] | Balas, M. J., Trends in large space structure control theory: Fondest hopes, wildest dreams, IEEE Transactions on Automatic Control, 27, 3, 522-535 (1982) · Zbl 0496.93007 |
| [3] | Calafiore, G.; Carabelli, S.; Bona, B., Structural interpretation of transmission zeros for matrix second-order systems, Automatica, 33, 4, 745-748 (1997) · Zbl 0924.73166 |
| [6] | Cavallo, A.; De Maria, G.; Natale, C.; Pirozzi, S., Gray-box identification of continuous-time models of flexible structures, IEEE Transactions on Control Systems Technology, 15, 5, 967-981 (2007) |
| [7] | Cavallo, A.; De Maria, G.; Natale, C.; Pirozzi, S., Robust control of flexible structures with stable bandpass controllers, Automatica, 44, 5, 1251-1260 (2008) · Zbl 1283.93093 |
| [8] | Cavallo, A.; De Maria, G.; Natale, C.; Pirozzi, S., (Active control of flexible structures: from modeling to implementation. Active control of flexible structures: from modeling to implementation, Advances in industrial control (2010), Springer) · Zbl 1271.74001 |
| [9] | Cavallo, A.; De Maria, G.; Setola, R., A sliding manifold approach for the vibration reduction of flexible systems, Automatica, 35, 10, 1689-1696 (1999) · Zbl 0939.74042 |
| [10] | Cavallo, A.; May, C.; Minardo, A.; Natale, C.; Pagliarulo, P.; Pirozzi, S., Active vibration control by a smart auxiliary mass damper equipped with a fiber bragg grating sensor, Sensors and Actuators A: Physical, 153, 2, 180-186 (2009) |
| [11] | Cavallo, A.; Natale, C.; Pirozzi, S.; Visone, C., Limit cycles in control systems employing smart actuators with hysteresis, IEEE/ASME Transactions on Mechatronics, 10, 2, 172-180 (2005) |
| [12] | Fanson, J. L.; Caughey, T. K., Positive position feedback control for large space structures, American Institute of Aeronautics and Astronautics, 28, 4, 717-724 (1990), 2015/10/21 |
| [13] | Junkins, J. L.; Kim, Y., Introduction to dynamics and control of flexible structures (1993), AIAA · Zbl 0891.93001 |
| [14] | Khalil, H. K., Nonlinear systems (2002), Prentice Hall · Zbl 0626.34052 |
| [15] | Khoshnood, A. M.; Moradi, H. M., Robust adaptive vibration control of a flexible structure, ISA Transactions, 53, 4, 1253-1260 (2014), Disturbance Estimation and Mitigation |
| [16] | Klein, A.; Spreij, P., On the solution of stein’s equation and Fisher’s information matrix of an ARMAX process, Linear Algebra and its Applications, 396, 1-34 (2005) · Zbl 1085.15017 |
| [17] | Ran, A. C.M.; Reurings, M. C.B., A fixed point theorem in partially ordered sets and some applications to matrix equations, Proceedings of the Americal Mathematical Society, 132, 1435-1443 (2004) · Zbl 1060.47056 |
| [18] | Skogestad, S.; Postlethwaite, I., Multivariable feedback control: analysis and design (2005), John Wiley & Sons · Zbl 0842.93024 |
| [19] | Zhou, K.; Doyle, J. C., Essentials of robust control (1998), Prentice Hall International |
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