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The synthesis of optimal controllers for vibrational protection of large-scale structures with multiple actuation devices and partial state information is a challenging problem. In this study, the authors present a design strategy that allows computing this kind of controllers by using standard linear matrix inequality optimisation tools. To illustrate the main elements of the new approach, a five-story structure equipped with two interstory actuation devices and subjected to a seismic disturbance is considered. For this control setup, three different controllers are designed: an ideal state-feedback H ∞ controller with full access to the complete state information and two static output-feedback H ∞ controllers with restricted neighbouring state information. To assess the performance of the proposed controllers, the corresponding frequency responses are investigated and a proper set of numerical simulations are conducted, using the full scale North-South El Centro 1940 seismic record as ground acceleration input. The obtained results indicate that, despite the severe information constraints, the proposed static output-feedback controllers attain a level of seismic protection that is very similar to that achieved by the ideal state-feedback controller with complete state information.
References
-
-
1)
-
2. Li, H., Huo, L.: ‘Advances in structural control in civil engineering in China’, Math. Probl. Eng., 2010, , pp. 1–23.
-
2)
-
10. Xiang, P., Nishitani, A.: ‘Seismic vibration control of building structures with multiple tuned mass damper floors integrated’, Earthq. Eng. Struct. Dyn., 2014, 43, (6), pp. 909–925 (doi: 10.1002/eqe.2379).
-
3)
-
37. Palacios-Quinonero, F., Rubió-Massegú, J., Rossell, J.M., et al : ‘Semiactive-passive structural vibration control strategy for adjacent structures under seismic excitation’, J. Franklin Inst., 2012, 349, (10), pp. 3003–3026 (doi: 10.1016/j.jfranklin.2012.09.005).
-
4)
-
35. Du, H., Zhang, N., Naghdy, F.: ‘Actuator saturation control of uncertain structures with input time delay’, J. Sound Vib., 2011, 330, (18–19), pp. 4399–4412 (doi: 10.1016/j.jsv.2011.04.025).
-
5)
-
39. Park, K.S., Ok, S.Y.: ‘Hybrid control approach for seismic coupling of two similar adjacent structures’, J. Sound Vib., 2015, 394, pp. 1–17 (doi: 10.1016/j.jsv.2015.03.028).
-
6)
-
6. Oliveira, F., Morais, P., Suleman, A.: ‘Predictive control for earthquake response mitigation of buildings using semiactive fluid dampers’, Shock Vib., 2014, , pp. 1–14.
-
7)
-
16. Palacios-Quiñonero, F., Rubió-Massegú, J., Rossell, J.M., et al : ‘Discrete-time multioverlapping controller design for structural vibration control of tall buildings under seismic excitation’, Math. Probl. Eng., 2012, , pp. 1–20.
-
8)
-
29. Kurino, H., Matsunaga, Y., Yamada, T., et al : ‘High performance passive hydraulic damper with semi-active characteristics’, Proc. 13th World Conf. on Earthquake Engineering, Vancouver, Canada, 2004. , pp. 1–12.
-
9)
-
6. Shen, M.Q., Ye, D., Fei, S.M.: ‘Robust H∞ static output control of discrete Markov jump linear systems with norm bounded uncertainties’, IET Control Theory Appl., 2014, 8, (15), pp. 1449–1455 (doi: 10.1049/iet-cta.2013.1123).
-
10)
-
22. Palacios-Quiñonero, F., Rubió-Massegú, J., Rossell, J.M., et al : ‘Feasibility issues in static output-feedback controller design with application to structural vibration control’, J. Franklin Inst., 2014, 351, (1), pp. 139–155 (doi: 10.1016/j.jfranklin.2013.08.011).
-
11)
-
1. Spencer, B.F., Nagarajaiah, S.: ‘State of the art of structural control’, J. Struct. Eng., 2003, 129, (7), pp. 845–856 (doi: 10.1061/(ASCE)0733-9445(2003)129:7(845)).
-
12)
-
3. Thenozhi, S., Yu, W.: ‘Advances in modeling and vibration control of building structures’, Annu. Rev. Control, 2013, 37, (2), pp. 346–364 (doi: 10.1016/j.arcontrol.2013.09.012).
-
13)
-
24. Jafarabad, A., Kashani, M., AdlParvar, M.R., et al : ‘Hybrid damping systems in offshore jacket platforms with float-over deck’, J. Constr. Steel Res., 2014, 98, pp. 178–187 (doi: 10.1016/j.jcsr.2014.02.004).
-
14)
-
20. Shu, Z., Lam, J.: ‘An augmented system approach to static output-feedback stabilization with H∞ performance for continuous-time plants’, Int. J. Robust Nonlinear, 2009, 19, (7), pp. 768–785 (doi: 10.1002/rnc.1348).
-
15)
-
15. Rubió-Massegú, J., Rossell, J.M.: ‘Decentralized static output-feedback H∞ controller design for buildings under seismic excitation’, Earthq. Eng. Struct. Dyn., 2012, 41, (7), pp. 1199–1205 (doi: 10.1002/eqe.1167).
-
16)
-
25. Cai, M., Xiang, Z., Karimi, H.R.: ‘Robust sampled-data H∞ control for vibration mitigation of offshore platforms with missing measurements’, Math. Probl. Eng., 2014, , pp. 1–10.
-
17)
-
9. Bitaraf, M., Hurlebaus, S.: ‘Semi-active adaptive control of seismically excited 20-story nonlinear building’, Eng. Struct., 2013, 56, pp. 2107–2118 (doi: 10.1016/j.engstruct.2013.08.031).
-
18)
-
42. Zhang, H., Wang, J.: ‘Robust two-mode-dependent controller design for networked control systems with random delays modelled by Markov chains’, Int. J. Control, 2015, volume 88, issue 12, pp. 2499–2509 (doi: 10.1080/00207179.2015.1048293).
-
19)
-
31. Zhang, H., Wang, R., Wang, J., et al : ‘Robust finite frequency H∞ static-output-feedback control with application to vibration active control of structural systems’, Mechatronics, 2014, 24, (4), pp. 354–366 (doi: 10.1016/j.mechatronics.2013.07.013).
-
20)
-
5. Iuliis, M.D., Faella, C.: ‘Effectiveness analysis of a semiactive base isolation strategy using information from an early-warning network’, Eng. Struct., 2013, 52, pp. 518–535 (doi: 10.1016/j.engstruct.2013.03.025).
-
21)
-
21. Rubió-Massegú, J., Rossell, J.M., Karimi, H.R., et al : ‘Static output-feedback control under information structure constraints’, Automatica, 2013, 49, (1), pp. 313–316 (doi: 10.1016/j.automatica.2012.10.012).
-
22)
-
17. Moerder, D.D., Calise, A.J.: ‘Convergence of a numerical algorithm for calculating optimal output feedback gains’, IEEE Trans. Autom. Control, 1985, 30, (9), pp. 900–903 (doi: 10.1109/TAC.1985.1104073).
-
23)
-
13. Boyd, S., Ghaoui, L.E., Feron, E., et al : ‘Linear matrix inequalities in system and control theory’ (SIAM Studies in Applied Mathematics, Philadelphia, 1994).
-
24)
-
34. Zhang, W., Chen, Y., Gao, H.: ‘Energy-to-peak control for seismic-excited buildings with actuator faults and parameter uncertainties’, J. Sound Vib., 2011, 330, (4), pp. 581–602 (doi: 10.1016/j.jsv.2010.09.001).
-
25)
-
33. Du, H., Lam, J., Sze, K.Y.: ‘Non-fragile H∞ vibration control for uncertain structural systems’, J. Sound Vib., 2004, 273, (4–5), pp. 1031–1045 (doi: 10.1016/S0022-460X(03)00520-0).
-
26)
-
23. Bakka, T., Karimi, H.R.: ‘H∞ static output-feedback control design with constrained information for offshore wind turbine system’, J. Franklin Inst., 2013, 350, (8), pp. 2244–2260 (doi: 10.1016/j.jfranklin.2013.05.028).
-
27)
-
12. Wang, Y.: ‘Time-delayed dynamic output feedback H∞ controller design for civil structures: a decentralized approach through homotopic transformation’, Struct. Control Health, 2011, 18, (2), pp. 121–139 (doi: 10.1002/stc.344).
-
28)
-
18. Syrmos, V.L., Abdallah, C.T., Dorato, P., et al : ‘Static output feedback – a survey’, Automatica, 1997, 33, (2), pp. 125–137 (doi: 10.1016/S0005-1098(96)00141-0).
-
29)
-
14. Wang, Y., Lynch, J.P., Law, K.H.: ‘Decentralized H∞ controller design for large-scale civil structures’, Earthq. Eng. Struct. Dyn, 2009, 38, (3), pp. 377–401 (doi: 10.1002/eqe.862).
-
30)
-
27. Chopra, A.K.: ‘Dynamics of structures. Theory and applications to earthquake engineering’ (Prentice-Hall, New Jersey, 2007, 3rd edn.).
-
31)
-
38. Palacios-Quiñonero, F., Rubió-Massegú, J., Rossell, J.M., et al : ‘Vibration control for adjacent structures using local state information’, Mechatronics, 2014, 24, (4), pp. 336–344 (doi: 10.1016/j.mechatronics.2013.08.001).
-
32)
-
4. Thenozhi, S., Yu, W.: ‘Stability analysis of active vibration control of building structures using PD/PID control’, Eng. Struct., 2014, 81, pp. 208–218 (doi: 10.1016/j.engstruct.2014.09.042).
-
33)
-
21. Zhang, H., Wang, J.: ‘State estimation of discrete-time Takagi–Sugeno fuzzy systems in a network environment’, IEEE Trans. Cybern., 2015, 45, (8), pp. 1525–1536 (doi: 10.1109/TCYB.2014.2354431).
-
34)
-
40. Zhang, D., Wang, X.: ‘Static output feedback control of networked control systems with packet dropout’, Int. J. Syst. Sci., 2012, 43, (4), pp. 665–672 (doi: 10.1080/00207721.2010.517873).
-
35)
-
7. Zhang, C., Ou, J.: ‘Modeling and dynamical performance of the electromagnetic mass driver system for structural vibration control’, Eng. Struct., 2015, 82, pp. 93–103 (doi: 10.1016/j.engstruct.2014.10.029).
-
36)
-
28. Balas, G.J., Chiang, R.Y., Packard, A.K., et al : ‘MATLABTM Robust control Toolbox 3. User's guide’ (MathWorks Inc., Natick, , 2012).
-
37)
-
8. Lei, Y., Wu, D.T., Liu, L.J.: ‘A decentralized structural control algorithm with application to the benchmark control problem for seismically excited buildings’, Struct. Control Health, 2013, 20, (9), pp. 1211–1225 (doi: 10.1002/stc.1529).
-
38)
-
30. Chen, Y., Zhang, W., Gao, H.: ‘Finite frequency H∞ control for building under earthquake excitation’, Mechatronics, 2010, 20, (1), pp. 128–142 (doi: 10.1016/j.mechatronics.2009.11.001).
-
39)
-
32. Hao, Y., Duan, Z.: ‘Static output-feedback controller synthesis with restricted frequency domain specifications for time-delay systems’, IET Control Theory A, 2015, 9, (10), pp. 1608–1614 (doi: 10.1049/iet-cta.2014.1000).
-
40)
-
11. Lynch, J.P., Wang, Y., Swartz, R.A., et al : ‘Implementation of a closed-loop structural control system using wireless sensor networks’, Struct. Control Health, 2008, 15, (4), pp. 518–539 (doi: 10.1002/stc.214).
-
41)
-
19. Cao, Y.Y., Lam, J., Sun, Y.X.: ‘Static output feedback stabilization: an ILMI approach’, Automatica, 1998, 34, (12), pp. 1641–1645 (doi: 10.1016/S0005-1098(98)80021-6).
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