Active control devices, such as active mass dampers, are mainly employed for the reduction of wind-induced vibrations in high-rise buildings, with the final aim of satisfying vibration serviceability limit state requirements and of meeting appropriate comfort criteria. When such active devices, normally operating under wind loads associated with short return periods, are subjected to seismic events, they can experience large amplitude vibrations and exceed stroke limits. This may lead to a reduced performance of the control system that can even worsen the performance of the whole structure. In this paper, a nonlinear control strategy based on a modified direct velocity feedback algorithm is proposed for handling stroke limits of an active mass driver (AMD) system. In particular, a suitable nonlinear braking term proportional to the relative AMD velocity is included in the control law in order to slowdown the device in the proximity of the stroke limits. Experimental and numerical free vibration tests are carried out on a scaled-down five-story frame structure equipped with an AMD to demonstrate the effectiveness of the proposed control strategy. 1. Introduction Active control systems are in principle very effective for the mitigation of the structural response, especially for high-rise buildings and flexible structures that may experience significant wind-induced vibrations [1, 2]. However, their use in practical applications is still limited by the physical bounds of the devices. In the case of strong earthquakes, the limits of the actuators may be exceeded, forcing the system to operate in a nonlinear mode for which it was not designed, thus worsening the performance of the controlled structure. The physical bounds of the actuators include both the control force limits and the stroke limits. The problem of force saturation has been deeply studied in the literature. Some approaches deal with preventing saturation of the control signal by designing the control system to always operate below its limits in the framework of linear control [3]. Another category of control methods accounts for system limitations directly in the control algorithm. Chase et al. [4] modified the H∞ control method through the addition of nonlinear state-dependent terms in order to model the actuators saturation and the uncertainties in the parameters of the system. Indrawan et al. [5] developed the bound-force control method which excludes the control-effort penalty from the performance index defined in the case of LQR control, defines it at the end of each time interval, and
References
[1]
I. Venanzi and A. L. Materazzi, “Acrosswind aeroelastic response of square tall buildings: a semi-analytical approach based of wind tunnel tests on rigid models,” Wind & Structures, vol. 15, no. 6, pp. 495–508, 2012.
[2]
I. Venanzi and A. L. Materazzi, “Multi-objective optimization of wind-excited structures,” Engineering Structures, vol. 29, no. 6, pp. 983–990, 2007.
[3]
A. Forrai, S. Hashimoto, H. Funato, and K. Kamiyama, “Robust active vibration suppression control with constraint on the control signal: application to flexible structures,” Earthquake Engineering & Structural Dynamics, vol. 32, no. 11, pp. 1655–1676, 2003.
[4]
J. G. Chase, S. E. Breneman, and H. A. Smith, “Robust H∞ static output feedback control with actuator saturation,” Journal of Engineering Mechanics, vol. 125, no. 2, pp. 225–233, 1999.
[5]
B. Indrawan, T. Kobori, M. Sakamoto, N. Koshika, and S. Ohrui, “Experimental verification of bounded-force control method,” Earthquake Engineering & Structural Dynamics, vol. 25, no. 2, pp. 179–193, 1996.
[6]
J. R. Cloutier, “State-dependent Riccati equation techniques: an overview,” in Proceedings of the American Control Conference, pp. 932–936, Albuquerque, NM, USA, 1997.
[7]
B. Friedland, “On controlling systems with state-variable constraints,” in Proceedings of the American Control Conference, pp. 2123–2127, Philadelphia, Pa, USA, 1998.
[8]
A. L. Materazzi and F. Ubertini, “Robust structural control with system constraints,” Structural Control and Health Monitoring, vol. 19, no. 3, pp. 472–490, 2012.
[9]
J.-H. Kim and F. Jabbari, “Actuator saturation and control design for buildings under seismic excitation,” Journal of Engineering Mechanics, vol. 128, no. 4, pp. 403–412, 2002.
[10]
J. Mongkol, B. K. Bhartia, and Y. Fujino, “On Linear-Saturation (LS) control of buildings,” Earthquake Engineering & Structural Dynamics, vol. 25, no. 12, pp. 1353–1371, 1996.
[11]
Z. Wu and T. T. Soong, “Modified bang-bang control law for structural control implementation,” Journal of Engineering Mechanics, vol. 122, no. 8, pp. 771–777, 1996.
[12]
C.-W. Lim, “Active vibration control of the linear structure with an active mass damper applying robust saturation controller,” Mechatronics, vol. 18, no. 8, pp. 391–399, 2008.
[13]
I. Nagashima and Y. Shinozaki, “Variable gain feedback control technique of active mass damper and its application to hybrid structural control,” Earthquake Engineering & Structural Dynamics, vol. 26, no. 8, pp. 815–838, 1997.
[14]
M. Yamamoto and T. Sone, “Behavior of active mass damper (AMD) installed in high-rise building during 2011 earthquake off Pacific coast of Tohoku and verification of regenerating system of AMD based on monitoring,” Structural Control and Health Monitoring, vol. 21, no. 4, pp. 634–647, 2013.
[15]
I. Venanzi, F. Ubertini, and A. L. Materazzi, “Optimal design of an array of active tuned mass dampers for wind-exposed high-rise buildings,” Structural Control and Health Monitoring, vol. 20, pp. 903–917, 2013.
[16]
I. Venanzi and A. L. Materazzi, “Robust optimization of a hybrid control system for wind-exposed tall buildings with uncertain mass distribution,” Smart Structures and Systems, vol. 12, no. 6, pp. 641–659, 2013.
[17]
F. Ubertini, I. Venanzi, G. Comanducci, and A. L. Materazzi, “On the control performance of an active mass driver system,” in Proceedings of the AIMETA Congress, Turin, Italy, 2013.
[18]
EN 1993-1-1 Eurocode 3: Design of steel structures—part 1-1: General rules and rules for buildings, 2005.
