Genetic Algorithm Based Approach for Actuator Saturation Effect on Nonlinear Controllers

In the real application of active control systems to mitigate the response of structures subjected to sever external excitations such as earthquake and wind induced vibrations, since the capacity of actuators is limited then the actuators saturate. Hence, in designing controllers for linear and nonlinear structures under sever earthquakes, the actuator saturation should be considered as a constraint. In this paper optimal design of active controllers for nonlinear structures by considering the actuator saturation has been studied. To this end a method has been proposed based on defining an optimization problem which considers the minimizing of the maximum displacement of the structure as objective when a limited capacity for actuator has been used as a constraint in optimization problem. To evaluate the effectiveness of the proposed method, a single degree of freedom (SDF) structure with a bilinear hysteretic behavior has been simulated under a white noise ground acceleration of different amplitudes. Active tendon control mechanism, comprised of pre-stressed tendons and an actuator, and extended nonlinear Newmark method based instantaneous optimal control algorithm have been used as active control mechanism and algorithm. To enhance the efficiency of the controllers, the weights corresponding to displacement, velocity, acceleration and control force in the performance index have been found by using the Distributed Genetic Algorithm (DGA). According to the results it has been concluded that the proposed method has been effective in considering the actuator saturation in designing optimal controllers for nonlinear frames. Also it has been shown that the actuator capacity and the average value of required control force are two important factors in designing nonlinear controllers for considering the actuator saturation.

Authors:

• M. Mohebbi
• K. Shakeri

Keywords:

• Active control
• Actuator Saturation
• Nonlinear
• Optimization.

References:

[1] B.F. Spencer and Nagarajaiah S., "State of the art of structural control,"
ASCE, J. Struct. Eng., vol.129, no.7, pp.845-856, 2003.
[2] T. Kobori, N. Koshika, K. Yamada and Y. Ikeda, "Seismic-responsecontrolled
structure with active mass driver system .part 1: Design"
Earthquake Eng. Struct. Dynamics, vol. 20, pp.133-149, 1991.
[3] T. Kobori, N. Koshika, K. Yamada and Y. Ikeda, "Seismic-responsecontrolled
structure with active mass driver system .part2:
Verification,"Earthquake Eng. Struct. Dynamics, vol.20, pp.151-166,
1991.
[4] T. T. Soong, Active structural control: theory and practice. Longman
Scientific & Technical, New York, 1990.
[5] J. Ghaboussi and A. Joghataie, "Active control of structures using
neural networks," ASCE, J. Eng. Mech., 121(4):555-567, 1995.
[6] A. Joghataie and A. Vahidi, "Designing a general neuro controller for
water towers," ASCE, J.Eng. Mech, 126(6): 582-587, 2000.
[7] A. Reinhorn, M. Manolis G. D. and C. Y. Wen, "Active control of
inelastic structures,"ASCE, J. Eng. Mech., 113(3):315-333, 1987.
[8] S.F. Masri, G.A. Bekey and T.K. Caughey, "Optimal pulse control of
flexible structures," ASME, J. App. Mech., 48(4):619-626, 1981.
[9] J. N. Yang, F. X Long and D. Wong. , "Optimal control of nonlinear
structures," Applied Mech., vol. 55, pp. 931-938, 1988.
[10] J. N. Yang, Z. Li, A. Danielians and S. C. Liu, "A seismic hybrid
control of nonlinear and hysteretic structures," ASCE, J. Eng. Mech.,
118(7):1423-1440, 1992.
[11] C. C. Chang and H. T., Yang Y., "Instantaneous optimal control of
building frames," ASCE, J. Struct. Eng., vol.120, no. 4, pp.1307-1326,
1994.
[12] O.Bahar, M. R Banan, M. Mahzoon and Y.Kitagawa, "Instantaneous
optimal Wilson-╬© control method,"ASCE, J. Eng. Mech., vol.129,
no.11, pp.1268-1276, 2003.
[13] A. Joghataie and M. Mohebbi, "Optimal control of nonlinear frames by
Newmark and distributed genetic algorithms," Struct. Design Tall Spec.
Build., published online, 2009.
[14] K. J. Bathe Finite element procedures. Prentice-Hall, Inc., New Gersey,
1996.
[15] J.H. Holland, Adaptation in natural and artificial systems. Ann Arbor:
The University of Michigan Press, 1975.
[16] D. E. Goldberg, Genetic algorithms in search, optimization and machine
Learning. Addison -Wesley Publishing Co., Inc. Reading, Mass, 1989.
[17] Z. Michalewicz, Genetic algorithms + data structures=evolution
programs, New York: Springer-Verlag, 1996.
[18] H. M├╝hlenbein, M.Schomisch and J. Born, "Parallel genetic algorithms
as a function optimizer," Parallel Computing, no.17, pp.619-632, 1991.
[19] T. Starkweather, D. Whitley and K. Mathias, "Optimization using
distributed genetic algorithms," Springer - Verlag Lecture Notes in
Computer Science, no.496, pp.176-185, 1990.