Robust controller analysis and synthesis with consideration of various uncertainties for building structures

The H∞ control method is one of the most widely used methods of robust control theory, in which system stability can be guaranteed by using linear matrix inequalities (LMIs) and Lyapunov theory. The presence of various
uncertainties such as parametric uncertainty, time delay, sensors/actuators faults and failure is inevitable in the active control of the building structures. This paper focuses on the uncertain structural control system, in which
the controller synthesis process is complicated by a set of uncertainties and the generation of large and sparse matrices. Synthesizing a sub-optimal controller for this uncertain structural control system is done according to the new approach and to validate it, a comparison with the controller of critically damped conditions(CD) as an ideal state is performed. In order to compare the two mentioned controllers, two 3- and 8-story shear structures excited by synthetic earthquake are considered to assess the responses. The simultaneous presence of various types of uncertainties is examined and their effects on the results are investigated. The results indicate that the sub-optimal designed H∞ robust controller displays good robustness against time delay; however, parametric
uncertainty was evaluated as an unfavorable effect for the allowable time delay. Despite the negative impact of the parametric uncertainties, it was illustrated that the nominal sensors/actuators faults do not affect the allowable time delay.