{"title":"Optimal Controllers with Actuator Saturation for Nonlinear Structures","authors":"M. Mohebbi, K. Shakeri","volume":37,"journal":"International Journal of Computer and Information Engineering","pagesStart":58,"pagesEnd":65,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/3659","abstract":"Since the actuator capacity is limited, in the real\r\napplication of active control systems under sever earthquakes it is\r\nconceivable that the actuators saturate, hence the actuator saturation\r\nshould be considered as a constraint in design of optimal controllers.\r\nIn this paper optimal design of active controllers for nonlinear\r\nstructures by considering actuator saturation, has been studied. The\r\nproposed method for designing optimal controllers is based on\r\ndefining an optimization problem which the objective has been to\r\nminimize the maximum displacement of structure when a limited\r\ncapacity for actuator has been used. To this end a single degree of\r\nfreedom (SDF) structure with a bilinear hysteretic behavior has been\r\nsimulated under a white noise ground acceleration of different\r\namplitudes. Active tendon control mechanism, comprised of prestressed\r\ntendons and an actuator, and extended nonlinear Newmark\r\nmethod based instantaneous optimal control algorithm have been\r\nused. To achieve the best results, the weights corresponding to\r\ndisplacement, velocity, acceleration and control force in the\r\nperformance index have been optimized by the Distributed Genetic\r\nAlgorithm (DGA). Results show the effectiveness of the proposed\r\nmethod in considering actuator saturation. Also based on the\r\nnumerical simulations it can be concluded that the actuator capacity\r\nand the average value of required control force are two important\r\nfactors in designing nonlinear controllers which consider the actuator\r\nsaturation.","references":"[1] B.F. Spencer and Nagarajaiah S., \"State of the art of structural control,\"\r\nASCE, J. Struct. Eng., vol.129, no.7, pp.845-856, 2003.\r\n[2] T. Kobori, N. Koshika, K. Yamada and Y. Ikeda, \"Seismic-responsecontrolled\r\nstructure with active mass driver system .part 1: Design\"\r\nEarthquake Eng. Struct. Dynamics, vol. 20, pp.133-149, 1991.\r\n[3] T. Kobori, N. Koshika, K. Yamada and Y. Ikeda, \"Seismic-responsecontrolled\r\nstructure with active mass driver system .part2:\r\nVerification,\"Earthquake Eng. Struct. Dynamics, vol.20, pp.151-166,\r\n1991.\r\n[4] T. T. Soong, Active structural control: theory and practice. Longman\r\nScientific & Technical, New York, 1990.\r\n[5] J. Ghaboussi and A. Joghataie, \"Active control of structures using\r\nneural networks,\" ASCE, J. Eng. Mech., 121(4):555-567, 1995.\r\n[6] A. Joghataie and A. Vahidi, \"Designing a general neuro controller for\r\nwater towers,\" ASCE, J.Eng. Mech, 126(6): 582-587, 2000.\r\n[7] A. Reinhorn, M. Manolis G. D. and C. Y. Wen, \"Active control of\r\ninelastic structures,\"ASCE, J. Eng. Mech., 113(3):315-333, 1987.\r\n[8] S.F. Masri, G.A. Bekey and T.K. Caughey, \"Optimal pulse control of\r\nflexible structures,\" ASME, J. App. Mech., 48(4):619-626, 1981.\r\n[9] J. N. Yang, F. X Long and D. Wong. , \"Optimal control of nonlinear\r\nstructures,\" Applied Mech., vol. 55, pp. 931-938, 1988.\r\n[10] J. N. Yang, Z. Li, A. Danielians and S. C. Liu, \"A seismic hybrid\r\ncontrol of nonlinear and hysteretic structures,\" ASCE, J. Eng. Mech.,\r\n118(7):1423-1440, 1992.\r\n[11] C. C. Chang and H. T., Yang Y., \"Instantaneous optimal control of\r\nbuilding frames,\" ASCE, J. Struct. Eng., vol.120, no. 4, pp.1307-1326,\r\n1994.\r\n[12] O.Bahar, M. R Banan, M. Mahzoon and Y.Kitagawa, \"Instantaneous\r\noptimal Wilson-\u256c\u00a9 control method,\"ASCE, J. Eng. Mech., vol.129,\r\nno.11, pp.1268-1276, 2003.\r\n[13] A. Joghataie and M. Mohebbi, \"Optimal control of nonlinear frames by\r\nNewmark and distributed genetic algorithms,\" Struct. Design Tall Spec.\r\nBuild., published online, 2009.\r\n[14] K. J. Bathe Finite element procedures. Prentice-Hall, Inc., New Gersey,\r\n1996.\r\n[15] J.H. Holland, Adaptation in natural and artificial systems. Ann Arbor:\r\nThe University of Michigan Press, 1975.\r\n[16] D. E. Goldberg, Genetic algorithms in search, optimization and machine\r\nLearning. Addison -Wesley Publishing Co., Inc. Reading, Mass, 1989.\r\n[17] Z. Michalewicz, Genetic algorithms + data structures=evolution\r\nprograms, New York: Springer-Verlag, 1996.\r\n[18] H. M\u251c\u255dhlenbein, M.Schomisch and J. Born, \"Parallel genetic algorithms\r\nas a function optimizer,\" Parallel Computing, no.17, pp.619-632, 1991.\r\n[19] T. Starkweather, D. Whitley and K. Mathias, \"Optimization using\r\ndistributed genetic algorithms,\" Springer - Verlag Lecture Notes in\r\nComputer Science, no.496, pp.176-185, 1990.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 37, 2010"}