### MU-SYNTHESIS BASED ACTIVE ROBUST VIBRATION CONTROL OF AN MRI INLET

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#### Abstract

In this paper, a robust control technique based on μ-synthesis is employed in order to investigate the vibration control of a funnel-shaped structure that is used as the inlet of a magnetic resonance imaging (MRI) device. MRI devices are widely subjected to the vibration of the magnetic gradient coil which then propagates to acoustic noise and leads to a series of clinical and mechanical problems. In order to address this issue and as a part of noise cancellation study in MRI devices, distributed piezo-transducers are bounded on the top surface of the funnel as functional sensor/actuator modules. Then, a reduced order linear time-invariant (LTI) model of the piezolaminated structure in the state-space representation is estimated by means of a predictive error minimization (PEM) algorithm as a subspace identification method based on the trust-region-reflective technique. The reduced order model is expanded by the introduction of appropriate frequency-dependent weighting functions that address the unmodeled dynamics and the augmented multiplicative modeling uncertainties of the system. Then, the standard D-K iteration algorithm as an output-feedback control method is used based on the nominal model with the subordinate uncertainty elements from the previous step. Finally, the proposed control system implemented experimentally on the real structure is to evaluate the robust vibration attenuation performance of the closed-loop system.

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Yao, G.Z., Mechefske, C.K., Rutt, B.K., 2005, Vibration analysis and measurement of a gradient coil insert in a 4T MRI, Journal of Sound and Vibration, 285, pp. 743-758.

Rutt, B.K., 2003, Safety issues in MRI, The 11th Scientific Meeting of the International Society for Magnetic Resonance in Medicine, Toronto, Canada.

Mechefske, C.K., Geris, R., Gati, J.S., Rutt, B.K., 2002, Acoustic noise reduction in a 4T MRI scanner, Magnetic Resonance Materials in Physics, Biology and Medicine, 13, pp. 172-176.

Turner, R., 1993, Gradient coil design: a review of methods, Magnetic Resonance Imaging, 1, pp. 903-920.

Katsunuma, A., Takamori, H., Sakakura, Y., Hamamura, Y., Ogo, Y., Katayama, R., 2002, Quiet MRI with novel acoustic noise reduction, Magnetic Resonance Materials in Physics, Biology and Medicine, 13, pp. 139-144.

Edelstein, W.A., Mallozzi, R.P., Hedeen, R.A., El-Hamamsy, S.-A., Miller, M.L., Thompson, P.S., Ackermann, R.A., Amm, B.C., Fura, J.P., Radziun, M.J., Dean, D.E., Mansell, S.T., Purgill, D.A., Vavrek, R.M., 2002, Low noise MRI scanner, US 6437568 B1, Grant Application number US 09/676,945.

Wu, Y., Chronik, B.A., Bowen, C., Mechefske, C.K., Rutt, B.K., 2000, Gradient-induced acoustic and magnetic field fluctuation in a 4T whole-body MR imager, Magnetic Resonance in Medicine, 44, pp. 532-536.

McJury, M., Stewart, R.W., Crawford, D., Tomas, E., 1997, The use of active noise control (ANC) to reduce acoustic noise generated during MRI scanning: some initial results, Magnetic Resonance Imaging, 15(3), pp. 319-322.

Park, S.H., Kim, H., Chung, S.C., Chung, S.T., Chung, Y., Moon, C.W., Sin, C.H., Wong, E.K., Cho, Z.H., 1997, Analysis of acoustic noise in MRI, Magnetic Resonance Imaging, 15(7), pp. 815-822.

Price, D.L., De Wilde, J.P., Papadaki, A.M., Curran, J.S., Kitney, R.I., 2001, Investigation of Acoustic Noise on 15 MRI Scanners from 0.2 T to 3 T, Journal Of Magnetic Resonance Imaging, 13, pp. 288-293.

Edelstein, W.A., Hedeen R.A., Mallozzi, R.P., El-Hamamsya, S.-A., Ackermann, R.A., Havens, T.J., 2002, Making MRI Quieter, Magnetic Resonance Imaging, 20, pp. 155-163.

Mechefske, C.K., Geris, R., Gati, J.S., Rutt, B.K., 2002, Acoustic noise reduction in a 4 T MRI scanner, Magnetic Resonance Materials in Physics, Biology and Medicine, 13, pp. 172-176.

Oveisi, A., Gudarzi, M., Mohammadi, M.M., Doosthoseini, A., 2013, Modeling, identification and active vibration control of a funnel-shaped structure used in MRI throat, Journal of Vibroengineering, 15(1), pp. 1392-8716.

Mechefske, C.K., Shao, W., 2007, Analytical modeling of noise in MRI scanners, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 307-311.

Pribil, J., Pribilova, A., Frollo, I., 2012, Analysis of spectral properties of acoustic noise produced during magnetic resonance imaging, Applied Acoustics, 73, pp. 687-697.

Hurwitz, R., Lane, S.R., Bell, R.A., Brant-Zawadzki, M.N., 1989, Acoustic analysis of gradient-coil noise in MR imaging, Radiology, 173, pp. 545-548.

Qiu, J., Tani, J., 1995, Vibration control of a cylindrical shell used in MRI equipment, Smart Materials and Structures, 4, pp. 75-81.

Nestorović, T., Koppe, T.H., Gabbert, U., 2005, Active vibration control using optimal LQ tracking system with additional dynamics, International Journal of Control, 78(15), pp. 1182 – 1197.

Nestorović, T., Koppe, T.H., Gabbert, U., 2006, Vibration control of a funnel-shaped shell structure with distributed piezoelectric actuators and sensors, Smart Materials and Structures, 15(4), pp. 1119-1132.

Jaensch, M., Lamperth, M.U., 2007, Development of a multi-degree-of-freedom micro positioning, vibration isolation and vibration suppression system, Smart Materials and Structures, 16, pp. 409-417.

Roozen, N.B., Koevoets, A.H., den Hamer, A.J., 2008, Active vibration control of gradient coils to reduce acoustic noise of MRI systems, IEEE/ASME Transactions on Mechatronics, 13(3).

Li, M., Lim, T.C., Lee J.H., 2008, Simulation study on active noise control for a 4-T MRI scanner, Magnetic Resonance Imaging, 26, pp. 393-400.

Oveisi, A., Gudarzi, M., 2015, Application of auto-tuning Ziegler-Nichols PID control in chaotic vibration suppression of a beam with nonlinear boundary conditions, Latin American Applied Research, 45, pp. 179-184.

Oveisi, A., Gudarzi, M., 2013, Adaptive sliding mode vibration control of a nonlinear smart beam: a comparison with self-tuning Ziegler-Nichols PID controller, Journal of Low Frequency Noise, Vibration and Active Control, 32(1+2), pp. 41-62.

Kerschena, G., 2006, Past, present and future of nonlinear system identification in structural dynamics, Mechanical Systems and Signal Processing, 20(3), pp. 505-592.

Oveisi, A., Nestorović, T., 2016, Robust observer-based adaptive fuzzy sliding mode controller, Mechanical Systems and Signal Processing, DOI: 10.1016/j.ymssp.2016.01.015.

Ljung, L., 1999, System Identification: Theory for the User, Prentice Hall, New Jersey, USA.

Hasheminejad, S.M., Oveisi, A., 2015, Active vibration control of an arbitrary thick smart cylindrical panel with optimally placed piezoelectric sensor/actuator pairs, International Journal of Mechanics and Materials in Design, 12(1), pp. 1-16.

van Overschee, P., de Moor, B.L., 2012, Subspace identification for linear systems: theory-Implementation-Applications, Kluwer Academic Publishers Group, Dordrecht, The Netherlands.

Gabbert, U., Köppe, H., Nestorović, T., Seeger, F., 2003, Modelling, simulation and optimal design of lightweight structures, Proceedings of the Adaptronic Congress, Wolfsburg, Germany.

Shampine, L.F., 1986, Some Practical Runge-Kutta Formulas, Mathematics of Computation, 46(173), pp. 135-150.

Oveisi, A., Nestorović, T., 2014, Robust mixed H2/H∞ active vibration controller in attenuation of smart beam, Facta Universitatis Series: Mechanical Engineering, 12(3), pp. 235-249.

Byrd, R.H., Schnabel, R.B., 1988, Approximate solution of the trust region problem by minimization over two-dimensional subspaces, Mathematical Programming, 40, pp. 247-263 .

Sorensen, D.C., 1997, Minimization of a large-scale quadratic function subject to a spherical constraint, SIAM Journal on Optimization, 7(1), pp. 141-161.

Gudarzi, M., Oveisi, A., Mohammadi, M.M., 2012, Robust active vibration control of a rectangular piezoelectric laminate flexible thin plate: An LMI-based approach, International Review of Mechanical Engineering, 6(6), pp. 1217-1227.

Gudarzi, M., Oveisi, A., 2014, Robust control for ride comfort improvement of an active suspension system considering uncertain driver’s biodynamics, Journal of Low Frequency Noise Vibration and Active Control, 33(3), pp. 317-340.

Limebeer, D.J.N., Green, M., 2010, Linear robust control, Dover Books on Electrical Engineering, Dover Publications.

Gu, D.-W., Petkov, P., Konstantinov, M.M, 2013, Robust control design with MATLAB, Advanced Textbooks in Control and Signal Processing, Springer-Verlag, London, UK.

Packard, A., Doyle, J.C, Balas, G., 1993, Linear multivariable robust control with a μ perspective, ASME Journal of Dynamic Systems, Measurement and Control, 115(2), pp. 310-319.

Lin, F., 2007, Robust control design: an optimal control approach, 1st edition, Wiley-Interscience.

Gudarzi, M., 2015, μ-Synthesis Controller Design for Seismic Alleviation of Structures with Parametric Uncertainties, Journal of Low Frequency Noise, Vibration and Active Control, 34(4), pp. 491-512.

Oveisi, A., Shakeri, R., 2016, Robust reliable control in vibration suppression of sandwich circular plates, Engineering Structures, 116, pp. 1–11.

DOI: https://doi.org/10.22190/FUME1601037O

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