#### Year

2000

#### Degree Name

Doctor of Philosophy

#### Department

Faculty of Engineering

#### Recommended Citation

Arfiadi, Yoyong, Optimal passive and active control mechanisms for seismically excited buildings, Doctor of Philosophy thesis, Faculty of Engineering, University of Wollongong, 2000. http://ro.uow.edu.au/theses/1836

#### Abstract

Optimisation methods for designing passive and active control mechanisms of buildings under earthquake loading is developed in this thesis. In designing passive and active control devices, the performance indices developed in the modern control theory are utilised in conjunction with genetic algorithms. These performance indices include linear quadratic regulator (LQR), Lı, H_{2} and H_{∞} norms.

Various passive and active control systems are solved by using the methods developed in this research. In passive control applications, tuned mass damper, multi tuned mass damper and hybrid base isolation-mass damper systems are solved numerically. The methods have shown to be more advantageous than the available methods so far. In optimising passive tuned mass damper systems, for example, it is not necessary to transform the structure into a single mode model as usually done in the available methods. In this case, the optimisation developed in this research may utilise the actual building model in the optimisation process. In addition, in optimising the passive control systems, the designer has the flexibility to choose the regulated output the response to be minimised in a systematic fashion similar to the active control systems. In active control optimisation, the direct (static) output feedback, where only limited number of sensors are installed at strategic locations without an observer, has been solved in a simple way. Output feedback is preferred as the number of sensors to be used can be reduced substantially. This is in contrast to full state feedback controllers that require all states, i.e., all displacements and velocities of the structure to be for the feedback. Output feedback considered in this research is static (direct) output feedback instead of dynamic output feedback controllers. In dynamic output feedback controllers, although utilise a limited number of sensors, an online computation is required to estimate the observer state, while in direct (static) output feedback controllers, the gain can be multiplied directly with the measurement output without obtaining the observer state. Therefore, solving direct (static) output feedback controllers in a simple fashion as demonstrated in this research is important in active control design.

In solving passive and active control optimisation problems, the genetic algorithm is used as an optimiser. Binary and real coded genetic algorithms are used for the optimisation process. For the passive control system, the binary coded GA is usually sufficient to solve the problems. In active control system, the domain of the controller gain is usually unknown. Although it may be possible to estimate the domain of the stabilising controller through the Routh-Hurwitz criterion, for the MIMO (multi-input-multi-output) systems such as multi degree of freedom system, this procedure is burdensome. Therefore, real coded GA, which is able to search the larger and unknown domain of the solution through the appropriate crossover and mutation procedures, is developed and used to solve the active control optimisation.

Most recent active control studies have considered only two-dimensional structures. However, not all buildings can be modelled as plane structures. When the building is asymmetric, a three dimensional analysis is necessary. In this research, a three-dimensional analysis of building systems is developed. The building is assumed to have a rigid floor in the horizontal direction such that the building possesses two horizontal displacements perpendicular to each other and one rotation with respect vertical axis. In forming the stiffness matrix, Global Frame Coordinate Systems and Global Building Coordinate Systems are defined. Elemental stiffness matrices of three dimensional frame elements are first transformed and assembled into Global Frame Coordinate Systems. In assembling the stiffness matrix and load vector into Global Frame Coordinate Systems, the order of degrees of freedom is arranged such that degrees of freedom that do not relate to the floor displacement can be easily condensed out. A static condensation technique may be employed to retain only degrees of freedom associated with the floor displacements. A transformation matrix is developed to transform these retained displacements at each joint to the displacements of the floor associated with Global Building Coordinate Systems. While the location of the Global Building Coordinate System can be located anywhere, for simplicity, these coordinate systems are located at the centre of mass of every floor such that the diagonal form of the mass matrix can be obtained. The Hamilton principle is then employed in order to include the passive and active control devices into equations of motion. The optimisation procedure developed for two-dimensional structures is used to optimise passive and active control devices of three-dimensional buildings. From the numerical simulation to the structure employing passive tuned mass damper, active tuned mass damper and active bracing systems that is optimised using the procedure developed in this research, it is shown that such systems are capable of reducing the response of the structure.