J. C. Wu

Control of seismic-excited buildings using active variable stiffness systems

Abstract It has been demonstrated that active variable stiffness (AVS) systems may be effective for response control of buildings subjected to earthquake excitations. The applications of active variable stiffness systems involve nonlinear control in which control theories for linear systems are not applicable. Based on the theory of variable structure system (VSS) or sliding mode control (SMC), control methods are presented in this paper for applications of active variable stiffness systems to seismic-excited buildings. In addition to full-state feedback controllers, general static output feedback controllers as well as simple output feedback controllers using only collocated sensors are presented. The principle of active variable stiffness control is interpreted based on the concept of the dissipation of hysteretic energies. Simulation results indicate that the control methods presented are robust and the performance of static output feedback controllers is comparable to that of the fullstate feedback controllers. Simulation results further indicate that the active variable stiffness systems, using locking and unlocking devices, are effective in reducing the interstorey drifts of seismicexcited buildings. However, the floor acceleration of the building may increase significantly, depending on the structure design and earthquake excitation.

Reduced-order H∞ and LQR control for wind-excited tall buildings

Abstract Because of the large number of degrees-of-freedom involved in modeling wind-excited tall buildings, three reduced-order control methods are presented and their performances are investigated systematically. These include the state reduced-order control, critical-mode control and simple modal control. The important issues associated with reduced-order control, control spillover and observation spillover have been addressed. Both the robust H ∞ and linear quadratic regulator ( LQR ) control algorithms have been used. Applications of static output feedback controllers, that utilize only a limited number of sensors without an observer, are also investigated for practical implementations of control devices on wind-excited structures. The spatially correlated wind loads, as defined by a cross-power spectral density matrix, have been used to compute the stochastic response of the full-order tall building to demonstrate the performance of each control method. Numerical results indicate that as long as enough modes are considered in the reduced-order system, the performance for both state reduce-dorder control and critical-mode control are comparable to that of the full-order control. However, the performance of the simple modal control for reducing the acceleration response of wind-excited buildings is not satisfactory because of the spillover effects. Simulation results further indicate that static output controllers for reduced-order systems provide a possibility for reducing the required number of sensors. From the practical implementation standpoint, the state reduced-order control may be preferable to the critical-mode control, since it does not require an observer.

Sliding mode control with compensator for wind and seismic response control

Recently, it has been demonstrated that control techniques based on sliding mode control (SMC) are robust and their performances are quite remarkable for applications to active/hybrid control of seismic-excited linear, non-linear or hysteretic civil engineering structures. In this paper, sliding mode control methods are further extended by introducing a compensator. The incorporation of a compensator provides (i) a convenient way of making trade-offs between control efforts and specific response quantities of the structure through the use of linear quadratic optimal control theory, and (ii) a convenient design procedure for static output feedback controllers to facilitate practical implementations of control systems. Since civil engineering structures generally involve excessive degrees of freedom, a controller design based on a full-order system may be difficult, in particular for wind-excited tall buildings. In this paper, three reduced-order control methods have been used and their performances have been investigated. Applications of sliding mode control with compensators to active control of buildings subject to either earthquakes or strong wind gusts have been demonstrated through numerical simulations. Simulation results show that the performance of the sliding mode controller with compensators for the reduced-order system is quite close to that of the controller based on the full-order system as long as enough vibrational modes are taken into account in the reduced-order system.

LQG control of lateral–torsional motion of Nanjing TV transmission tower

The 310 m Nanjing TV transmission tower in China will be installed with an active mass driver on the upper observation deck in order to reduce the acceleration responses under strong wind gusts. This paper presents the linear–quadratic–Gaussian (LQG) control strategy using acceleration feedback to reduce the tower responses under coupled lateral–torsional motion. Emphasis is placed on the practical applications, such as the limitations on actuator peak force and stroke, limited number of sensors, etc. The along- and across-wind components of the wind velocity are defined by the cross-power spectra. In the simulation analysis, both deterministic and stochastic approaches have been used, and the power spectral density, rms values and peak values of response quantities have been computed. Comparisons of the responses of the TV tower due to wind loads from different angles of attack have been made. Simulation results demonstrate that (i) the performance of the active mass driver using the LQG control strategy is remarkable in reducing coupled lateral-torsional motions of the tower, and (ii) the LQG strategy is robust with respect to uncertainties in the angle of attack of wind loads. The LQG strategy is suitable for the full-scale implementation of active mass driver on Nanjing Tower. Copyright

Non-linear control strategies for Duffing systems

The Duffing oscillator is a useful model for the non-linear behavior of structural systems. This paper studies the applications of two control strategies to Duffing oscillators; namely, an optimal polynomial control and robust sliding mode control. An advantage of the polynomial controller investigated is that, for a given appropriate weighting matrices, the gain matrices for different orders of the controller can be computed easily by solving Riccati and Lyapunov equations. It is demonstrated through numerical simulation results that the stability region of the softening Duffing system can be expanded rapidly by the optimal polynomial controller and the entire state space of the closed-loop system becomes asymptotically stable when the gain matrix reaches a certain level. On the other hand, the closed-loop softening system is always asymptotically stable in the entire state space for the robust sliding-mode controller. The performances of both controllers, in terms of the system response reduction and the required control effort, have been studied through numerical simulations. Simulation results indicate that the performance of the optimal polynomial controller presented in this paper in reducing the response of the Duffing systems is comparable to a polynomial controller proposed recently in the literature. In comparison with polynomial controllers, the performance of robust sliding-mode control is quite remarkable.

Control of sliding-isolated buildings using dynamic linearization

Abstract The method of dynamic linearization is presented for the control of seismic-excited buildings isolated by a fractional-type base sliding system. The dynamic behaviour of the building equipped with a base sliding isolation system is highly nonlinear. The method of dynamic linearization is to synthesize the control vector such that the response of the building matches that of a spicified template system, where the dynamic behaviour of the template system is well known. Applications of the method of dynamic linearization to a sliding-isolated building require only a few sensors for the entire control system, making the control method very easy for practical implementation. A shaking table experimental program was conducted to demonstrate the validity of the control method presented. For the shaking table tests, a three-storey 1 4 - scaled building model is mounted on a base mat supported by four frictional bearings. Numerical simulation results under ideal control environments indicate that the performance of the dynamic linearization method is remarkable. However, experimental results show a moderate degradation of the control performance due to noise pollution and system time delays. It is observed that control of sliding-isolated buildings is quite sensitive to a system time delay.

Applications of sliding mode control to benchmark problems

In this paper, both the methods of continuous sliding mode control (CSMC) and continuous sliding mode control with compensators (CSMC&C) have been applied to two benchmark structures, namely, a building model equipped with an active mass driver system, and a building model equipped with an active tendon system. The CSMC&C strategy is a modification of CSMC to facilitate the design of static output feedback controllers and to provide a systematic tuning of the control effort. Due to the structural identification scheme used in the benchmark problems, in which the state variables are fictitious, one cannot take the full advantages of static output feedback controllers. As a result, an observer is used in CSMC, whereas a low-pass filter is incorporated for each measurement in CSMC&C. The purpose of using low-pass filters in CSMC&C is to transform the benchmark problems into strictly proper systems. The main advantage of the CSMC&C method is that the on-line computational effort is reduced since the dimension of filters and compensator is much smaller than that of an observer. Simulation results based on the CSMC and CSMC&C methods are presented and compared with that of the LQG method. Robustness of stability and noise rejection for each controller design are also illustrated by examining the loop transfer function. Simulation results for the benchmark problems indicate that the control performances for LQG, CSMC and CSMC&C are quite comparable.

Modeling of an actively braced full-scale building considering control–structure interaction

Recently, the application of active control to seismic-excited buildings has attracted international attention. To demonstrate the practical applicability of active control, we have conducted experimental tests using a full-scale three-storey building equipped with active bracing systems on the shake table at the National Center for Research on Earthquake Engineering (NCREE), Taiwan. Experimental results indicate that the control-structure interaction (CSI) effect is significant. A state-space analytical model of this actively controlled building taking into account the CSI effect is established in this paper using a system identification technique based on curve-fitting of transfer functions. To verify the accuracy of the analytical model for simulating the controlled response, four sets of linear quadratic Gaussian (LQG) controllers using acceleration feedback are designed and further experimental tests are conducted for comparison. It is demonstrated that the correlations between the simulation and experimental results are remarkable. The construction of an accurate analytical model is important for active control, and such an analytical model can be used for future benchmark studies of different control algorithms based on numerical simulations.

Application of optimal polynomial controller to a benchmark problem

In this paper, we investigate the performance of optimal polynomial control for the vibration suppression of a benchmark problem; namely, the active tendon system. The optimal polynomial controller is a summation of polynomials of different orders, i.e., linear, cubic, quintic, etc., and the gain matrices for different parts of the controller are calculated easily by solving matrix Riccati and Lyapunov equations. A Kalman-Bucy estimator is designed for the on-line estimation of the states of the design model. Hence, the Linear Quadratic Gaussian (LQG) controller is a special case of the current polynomial controller in which the higher-order parts are zero. While the percentage of reduction for displacement response quantities remains constant for the LQG controller, it increases with respect to the earthquake intensity for the polynomial controller. Consequently, if the earthquake intensity exceeds the design one, the polynomial controller is capable of achieving a higher reduction for the displacement response at the expense of control efforts. Such a property is desirable for the protection of civil engineering structures because of the inherent stochastic nature of the earthquake.

Control of Lateral-Torsional Motion of Nanjing TV Transmission Tower

The 310 m Nanjing TV transmission tower in China will be installed with an active mass driver on the upper observation deck in order to reduce the acceleration responses under strong winds. This paper presents the Linear Quadratic Gaussian (LQG) control strategy using acceleration feedback to reduce the tower response. Emphasis is placed on the practical applications, such as the limitations on actuator peak force and stroke, limited number of sensors, etc. The along-wind and across-wind components of the wind velocity are defined by the Davenport cross-power spectra. The power spectral density and rms of acceleration responses of the TV transmission tower equipped with an active mass driver have been computed. Simulation results demonstrate that the performance of the LQG control strategy is remarkable in reducing the coupled lateral-torsional motions of the tower and it is suitable for the full-scale implementation of active mass driver on Nanjing Tower.