Keywords: active control structures, continuous control, bounded control, response reduction, modified bang-bang controller, chattering effect.

This paper considers nonlinear controllers for controlling buildings subject to earthquake excitations. The controller utilises continuous function to approximate the bang-bang type controller. It is to be noted that although much progress has been achieved in structural control of civil engineering structures [1,2,3,4,5], most algorithms are linear control with the assumption that there is no limit in magnitude of the control energy. However, maximum capacity of the control device is limited. Therefore, designing controllers that include the bounded nature of the device is desirable. Only a few researchers consider bounded controller for active control of civil engineering structures [6,7,8,9,10]. In this paper modified bang-bang controllers considered in [8,10] is approximated by using a continuous function [11]. A hyperbolic function is used in this present application. Such controllers are capable of alleviating high-speed switching effect that are present in the traditional bang-bang controllers.

Numerical simulations to active control systems under several input disturbances from various earthquakes are then presented by using MATLAB [12] and SIMULINK [13]. Numerical simulations show the potential benefit of using the proposed controller to reduce the structural response subject to earthquake excitations.

Numerical comparison with the bang-bang type controller shows that the effectiveness of the proposed controller is almost the same. However, the high-speed switching command that usually occurs in the bang-bang type controller might be avoided.

Numerical simulation under particular earthquake acceleration, but different level of the actuator capacity, shows that the controller tends to utilise the maximum capacity of the actuator when the maximum capacity of the actuator is reduced. Thence, it resembles the bang-bang controller. However, by adjusting the weighting variable in the controller, the high-speed switching control command might be alleviated.

1

G.W. Housner, L.A. Bergman, T.K. Caughey, A.G. Chassiakos, R.O. Claus, S.F. Masri, R.R., Skelton, T.T., Soong, B.F. Spencer, J.T.P. Yao, "Structural control: past, present, and future", Journal of Engineering Mechanics, 123(9), 897-971, 1997. doi:10.1061/(ASCE)0733-9399(1997)123:9(897)

2

T.T. Soong, "Active structural control: theory and practice", Longman Wiley, London, England, 1990.

3

B.F. Spencer Jr., J. Suhardjo and M.K. Sain, "Frequency domain optimal control strategies for aseismic protection", Journal of Engineering Mechanics, 120, 135-159, 1994. doi:10.1061/(ASCE)0733-9399(1994)120:1(135)

4

W.E. Schmitendorf, F. Jabbari and J.N. Yang, "Robust control techniques for building under earthquake excitations", Earthquake Engineering and Structural Dynamics, 23(5), 539-552, 1994. doi:10.1002/eqe.4290230506

5

Y. Arfiadi and M.N.S. Hadi, "Optimal direct (static) output feedback controller using real coded genetic algorithms", Computers and Structures, 79, 1625-1634, 2001. doi:10.1016/S0045-7949(01)00041-4

6

S.J. Dyke, B.F. Spencer Jr., M.K. Sain and J.D. Carlson, "Experimental verification of semi-active structural control strategies using acceleration feedback", Proceedings of the 3rd International Conference on Motion and Vibration Control, Vol. III, 291-296, Chiba, Japan, September 1-6, 1996.

7

D.P. Tomasula, B.F. Spencer Jr., M.K. Sain, "Nonlinear control strategies for limiting dynamic response extreme", Journal of Engineering Mechanics, 122(3), 218-229, 1996. doi:10.1061/(ASCE)0733-9399(1996)122:3(218)

8

Z. Wu and T.T. Soong, "Modified bang-bang control law for structural control implementation", Journal of Engineering Mechanics, 122(8), 771-777, 1996. doi:10.1061/(ASCE)0733-9399(1996)122:8(771)

9

T. Nguyen, F. Jabbari and S. de Miguel, "Controller designs for seismic-excited buildings with bounded actuators", Journal of Engineering Mechanics, 124(8), 857-865, 1998. doi:10.1061/(ASCE)0733-9399(1998)124:8(857)

10

B. Bhartia and I. Nagashima, "Saturation control of building with AMD of bounded capacities", The 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference , La Jolla, CA, April 19-22, 1993.

11

N. Mostaghel and T. Davis, "Representations of Coulomb friction for dynamic analysis", Earthquake Engineering and Structural Dynamics, 26, 541-548, 1997. doi:10.1002/(SICI)1096-9845(199705)26:5<541::AID-EQE660>3.3.CO;2-N

12

I.E. Kose, W.E. Schmitendorf, F. Jabbari, J. N. Yang, "H_infinity seismic response control using static output feedback", Journal of Engineering Mechanics, 22(7), 651-659, 1996. doi:10.1061/(ASCE)0733-9399(1996)122:7(651)

13

"Matlab Control System Toolbox", The Math Works, Inc., Natick, MA, 1996.

14

"Using SIMULINK", The Math Works, Inc., Natick, MA, 1996.

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