Controllers with Quadratic Stability and Performance for The Benchmark Problem of Wind-Excited Tall Building

by

S. Srivastava1, F. Jabbari,2 W.E. Schmitendoef3 and J.N. Yang4

1Graduate Student, Department of Mechanical and Aerospace Engineering University of California, Irvine, CA 92697, USA
2Associate Professor, Department of Mechanical and Aerospace Engineering University of California, Irvine, CA 92697, USA, email: FJABBARI@UCI.EDU, Phone: (714) 824 6433, Fax: (714) 824 8585
3Professor , Department of Mechanical and Aerospace Engineering University of California, Irvine, CA 92697, USA
4Professor, Department of Civil and Environmental Engineering University of California, Irvine, CA 92697, USA

Keywords: Quadratic Stability And Performance, Robustness, Reliability Corresponding

Abstract

Quadratic stability with performance control techniques are used to design controllers for the benchmark problem in the control of wind-excited tall building. The underlying quadratic stability framework can be used for a multi-criterion approach which allows inclusion of a variety of objectives simultaneously. In this paper, it is assumed that the building is equipped with the active mass driver (AMD), and several designs, which corresponds to different design tradeoffs, will be obtained and analyzed. The general solution and design of the compensator rely on convex optimization techniques, through a number of matrix inequalities which contain the desired compensator matrices. Incorporating robustness to parameter uncertainty, reliability with respect to the actuator malfunction and feasibility of adding semi-active devices will be considered. Inevitable modeling errors necessitate control techniques that possess suitable levels of robustness with respect to uncertainties in the structural model. Furthermore, the size and performance requirements associated with the actuator motivate study of the control methods that guarantee stability and performance in the presence of undesirable (different from ideal or nominal) behavior of the actuator. Finally, the advantages associated with semi-active devices serve as motivation for combining semi-active and active techniques for control of buildings subject to wind excitation.