Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers

  • Ying, Z.G. (Department of Mechanics, Zhejiang University) ;
  • Ni, Y.Q. (Department of Civil and Structural Engineering, The Hong Kong Polytechnic University) ;
  • Ko, J.M. (Department of Civil and Structural Engineering, The Hong Kong Polytechnic University)
  • Received : 2007.08.03
  • Accepted : 2008.07.31
  • Published : 2009.01.25
⟨ Previous Next ⟩

Abstract

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.

Keywords

References

  1. Batterbee, D.C. and Sims, N.D. (2005), "Vibration isolation with smart fluid dampers: a benchmarking study", Smart Struct. Systems, 3, 235-256.
  2. Bratus', A., Dimentberg, M., Iourtchenko, D. and Noori, M. (2000), "Hybrid solution method for dynamic programming equations for MDOF stochastic systems", Dyn. Control, 10, 107-116. https://doi.org/10.1023/A:1008304230605
  3. Dimentberg, M.F., Iourtchenko, D.V. and Bratus', A.S. (2000), "Optimal bounded control of steady-state random vibrations", Probab. Eng. Mech., 15, 381-386. https://doi.org/10.1016/S0266-8920(00)00008-4
  4. Dimentberg, M., Iourtchenko, D. and Bratus', A. (2002), "Bounded control of random vibration: hybrid solution to HJB equations", Mechanica, 37, 129-141. https://doi.org/10.1023/A:1019679001288
  5. Housner, G.W., Bergman, L.A., et al. (1997), "Structural control: past, present, and future", ASCE J. Eng. Mech., 123, 897-971. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:9(897)
  6. Jansen, L.M. and Dyke, S.J. (2000), "Semiactive control strategies for MR dampers: comparative study", ASCE J. Eng. Mech., 126, 795-803. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:8(795)
  7. Jung, H.J., Choi, K.M., Park, K.S. and Cho, S.W. (2007), "Seismic protection of base isolated structures using smart passive control system", Smart Struct. Systems, 3, 385-403. https://doi.org/10.12989/sss.2007.3.3.385
  8. Kushner, J. (1978), "Optimality conditions for the average cost per unit time problem with a diffusion model", SIAM J. Control Optim., 16, 330-346. https://doi.org/10.1137/0316021
  9. Maiti, D.K., Shyju, P.P. and Vijayaraju, K. (2006), "Vibration control of mechanical systems using semi-active MR-damper", Smart Struct. Systems, 1, 61-80.
  10. Samali, B., Widjaja, J. and Reizes, J. (2006), "The controllable fluid dashpot damper performance", Smart Struct. Systems, 3, 209-224.
  11. Symans, M.D. and Constantinou, M.C. (1999), "Semi-active control systems for seismic protection of structure: a state-of-the-art review", Eng. Struct., 21, 469-487. https://doi.org/10.1016/S0141-0296(97)00225-3
  12. Ying, Z.G., Ni, Y.Q. and Ko, J.M. (2004a), "A new stochastic optimal control strategy for hysteretic MR dampers", Acta Mech. Solid. Sini., 17, 223-229.
  13. Ying, Z.G., Ni, Y.Q. and Ko, J.M. (2004b), "Non-linear stochastic optimal control for coupled-structures system of multi-degree-of-freedom", J. Sound Vib., 274, 843-861. https://doi.org/10.1016/S0022-460X(03)00610-2
  14. Ying, Z.G. and Zhu, W.Q. (2003), "Stochastic optimal control of hysteretic systems under externally and parametrically random excitations", Acta Mech. Solid. Sini., 16, 61-66.
  15. Ying, Z.G., Zhu, W.Q. and Soong, T.T. (2003), "A stochastic optimal semi-active control strategy for ER/MR dampers", J. Sound Vib., 259, 45-62. https://doi.org/10.1006/jsvi.2002.5136
  16. Zhu, W.Q., Huang, Z.L. and Yang, Y.Q. (1997), "Stochastic averaging of quasi-integrable Hamiltonian systems", ASME J. Appl. Mech., 64, 975-984. https://doi.org/10.1115/1.2789009
  17. Zhu, W.Q., Luo, M. and Dong, L. (2004), "Semi-active control of wind excited building structures using MR/ER dampers", Probabilistic Eng. Mech., 19, 279-285. https://doi.org/10.1016/j.probengmech.2004.02.011
  18. Zhu, W.Q., Ying, Z.G., Ni, Y.Q. and Ko, J.M. (2000) "Optimal nonlinear stochastic control of hysteretic systems", ASCE J. Eng. Mech., 126, 1027-1032. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:10(1027)
  19. Zhu, W.Q., Ying, Z.G. and Soong, T.T. (2001), "An optimal nonlinear feedback control strategy for randomly excited structural systems", Nonlinear Dyn., 24, 31-51. https://doi.org/10.1023/A:1026527404183

Cited by

  1. Semi-active control of seismic response of a building using MR fluid-based tuned mass damper vol.16, pp.5, 2015, https://doi.org/10.12989/sss.2015.16.5.807
  2. Semi-active structural fuzzy control with MR dampers subjected to near-fault ground motions having forward directivity and fling step vol.12, pp.6, 2013, https://doi.org/10.12989/sss.2013.12.6.595
  3. Active and semi-active control of structures – theory and applications: A review of recent advances vol.23, pp.11, 2012, https://doi.org/10.1177/1045389X12445029
  4. A review of non-linear structural control techniques vol.225, pp.4, 2011, https://doi.org/10.1177/2041298310392855
  5. Seismic Risk–Based Stochastic Optimal Control of Structures Using Magnetorheological Dampers vol.18, pp.1, 2017, https://doi.org/10.1061/(ASCE)NH.1527-6996.0000215
  6. Experimental Investigation of a Base Isolation System Incorporating MR Dampers with the High-Order Single Step Control Algorithm vol.7, pp.4, 2017, https://doi.org/10.3390/app7040344
  7. Probabilistic distribution of displacement response of frictionally damped structures excited by seismic loads vol.6, pp.4, 2009, https://doi.org/10.12989/sss.2010.6.4.363
  8. A dragonfly inspired flapping wing actuated by electro active polymers vol.6, pp.7, 2009, https://doi.org/10.12989/sss.2010.6.7.867
  9. Experiment of an ABS-type control strategy for semi-active friction isolation systems vol.8, pp.5, 2009, https://doi.org/10.12989/sss.2011.8.5.501
  10. Beam-rotating machinery system active vibration control using a fuzzy input estimation method and LQG control technique combination vol.10, pp.1, 2009, https://doi.org/10.12989/sss.2012.10.1.015
  11. Adaptive MR damper cable control system based on piezoelectric power harvesting vol.10, pp.1, 2009, https://doi.org/10.12989/sss.2012.10.1.033
  12. Semi-active control on long-span reticulated steel structures using MR dampers under multi-dimensional earthquake excitations vol.10, pp.6, 2009, https://doi.org/10.12989/sss.2012.10.6.557
  13. Optimal MR Damper-Based Semiactive Control Scheme for Strengthening Seismic Capacity and Structural Reliability vol.146, pp.6, 2020, https://doi.org/10.1061/(asce)em.1943-7889.0001768