Implementation of a Feasible Control Design Process Incorporating Robustness Criteria for Wind-Excited High-Rise Buildings

In this paper, a control design process incorporating robustness criteria is developed specifically for wind-excited high-rise buildings and its feasibility is experimentally verified by implementing on a four degree-of-freedom scaled (1:300) model of a high-rise building through wind tunnel tests in along-wind and across-wind directions. For feasibility toward mature application, considerations in the control design process are made as practical and thorough as possible. The main features of the proposed design process include a suitable identification scheme that can realistically model wind loads and the possible interaction between control devices and structure, as well as a systematic way of incorporating robustness criteria in the controller for reducing tracking error, rejecting noise, attenuating disturbance, and maintaining stability in the presence of system uncertainty. To account for the complexity of wind load in system identification, wind spectrum is obtained through the high-frequency force-balance tests, and the corresponding state space wind model is constructed. The nominal system with the robustness criteria employed is transformed into a generalized $H_{\infty }$ control problem that can be further converted into a set of linear matrix inequalities (LMIs). Consequently, strictly proper output feedback $H_{\infty }$ controllers are thus determined by a simpler solution procedure in searching the solution of LMIs. As observed from experimental results, the performances of proposed $H_{\infty }$ controllers are quite remarkable and comparable to those of classical linear quadratic Gaussian (LQG) controllers. Additionally, the proposed controllers are numerically demonstrated to be more robust than classical LQG controllers under the existence of system uncertainty. This successful implementation shows that the design process and robust controllers proposed are feasible for wind-excited high-rise buildings and the resulting control performance is promising.