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.