Abstract
There are many research studies in the literature that have been devoted to active control of human-induced vibrations in civil engineering structures. This technology has been implemented in floors and footbridges in order to improve their vibration serviceability performance. Most of these works have focused on single-input single-output (SISO) controller schemes, i.e. comprising of a single sensor and actuator pair. Their closed-loop stability properties expressed in terms of the gain margin (GM) and phase margin (PM) can easily be evaluated from techniques such as root locus studies of the closed-loop systems and Nyquist contour plots.
For multiple-input multiple-output (MIMO) controller schemes, i.e. systems with multiple sets of actuators and sensors, evaluation of their stability properties is not so obvious and most past researches hardly show this although it is taken into account in one way or another. This is the focus of this work. It presents a study of MIMO stability of a control set-up comprising of two sensors and actuators and further reviews what might be regarded as the appropriate controller gains for velocity based controllers. The approaches used to evaluate the stability properties of this control scheme comprise of comparative studies covering the generalized Nyquist criterion, plots of eigenvalues of the closed-loop system and relative gain arrays (RGA). A limiter on the actuator displacement to disturbance loop both for SISO and MIMO studies is introduced to reduce potential stroke saturation.
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References
Díaz, I.M., Pereira, E., Hudson, M.J., Reynolds, P.: Enhancing active vibration control of pedestrian structures using inertial actuators with local feedback control. Eng. Struct. 41, 157–166 (2012). doi:10.1016/j.engstruct.2012.03.043
Hanagan, L.M.: Practical implications of optimizing an active floor vibration controller. In: IMAC XXVIII, Jacksonville, FL, 189–194 (2010) doi:10.1007/978-1-4419-9831-6_20
Moutinho, C., Cunha, A., Caetano, E. Implementation of an active mass damper to control vibrations in a “ lively ” footbridge. In: III ECCOMAS Thematic Conference on Smart Structures and Materials, III ECCOMAS thematic conference on smart structures and materials, W.Ostachowicz, J. Molnicki--Szule, C. Mota Soares et al. (eds.) Gdansk, Poland, July 9–11, 2007
Nyawako, D., Reynolds, P., Hudson, M.J.: Findings with AVC design for mitigation of human induced vibrations in office floors. In: IMAC XXXI, Society for Experimental Mechanics (SEM), Orange County, CA, 2013
Pereira, E., Díaz, I.M., Hudson, E.J., Reynolds, P.: Optimal control-based methodology for active vibration control of pedestrian structures. Eng. Struct. 80, 153–162 (2014). doi:10.1016/j.engstruct.2014.08.046
Hanagan, L.M., Murray, T.M.: Active control approach for reducing floor vibrations. J. Struct. Eng. 123(11), 1497–1505 (1997). doi:10.1061/(ASCE)0733-9445(1997)123:11(1497)
González Díaz, C., Gardonio, P.: Feedback control laws for proof-mass electrodynamic actuators. Smart Mater. Struct. 16(5), 1766–1783 (2007). doi:10.1088/0964-1726/16/5/031
Diaz, I.M., Pereira, E., Zanuy, C., Alen, C.: A comparative study of SISO and MIMO control strategies for floor vibration damping. In: SMART2013, Torino, Italy, 2013
Gardonio, P., Elliot, S.J.: Smart panels for active structural acoustic control. Smart Mater. Struct. 13, 1314–1336 (2004)
Elliot, S.J., Gardonio, P., Sors, T.C., Brennan, M.J.: Active vibroacoustic control with multiple local feedback loops. J. Acoust. Soc. Am. 111(2), 908–915 (2002)
Desoer, C.A., Wang, Y.T.: On the generalized Nyquist stability criterion. IEEE Trans. Autom. Control 25(2), 187–196 (1980)
Barmanj, J.F., Katzenelson, J.: A generalized Nyquist-type stability criterion for multivariable feedback systems. Int. J. Control 20(4), 593–622 (1974). doi:10.1080/00207177408932763
Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control: Analysis and Design, 2nd edn. John Wiley and Sons publishers ISBN:978-0-470-01167-6 (2005)
Chen, D., Seborg, D.E.: Relative gain array analysis for uncertain process models. AIChE J. 48(2), 302–310 (2002)
RGA (controls wiki). Accessed online at https://controls.engin.umich.edu/wiki/index.php/RGA
Nyawako, D.S., Reynolds, P.: Observer-based controller for floor vibration control with optimization algorithms. J. Vib. Control 1–16 (2015). doi:10.1177/1077546315581229
Acknowledgements
The authors would like to acknowledge the financial assistance provided by the UK Engineering and Physical Sciences Research Council (EPSRC) through a responsive mode grant (Ref. EP/H009825/1), and a Leadership Fellowship Grant (Ref. EP/J004081/2).
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Nyawako, D., Reynolds, P., Hudson, E. (2016). Stability of MIMO Controllers for Floor Vibration Control. In: Di Miao, D., Tarazaga, P., Castellini, P. (eds) Special Topics in Structural Dynamics, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29910-5_20
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DOI: https://doi.org/10.1007/978-3-319-29910-5_20
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