Most control design methods are based on the optimization technique of the performance of the system through minimizing the control energy under certain constraint. The genetic algorithm (GA) has been applied as an effective search technique to many optimization problems. In this paper, a fuzzy logic controller (FLC) is designed to evaluate the active control force in a ATMD controller system for reducing the response of high rise buildings subjected to earthquake excitations. In order to optimize the FLC parameters, a genetic algorithm optimizer is used. In order to investigate the performance of the proposed control strategies in reducing the structural responses under earthquake loadings, a typical medium-size multi-story building in the city of Rasht in the north of Iran, is chosen as an example problem.

The tuned mass damper (TMD) is a classical engineering control device consisting of a mass, a spring, and a viscous damper attached to a vibrating main system in order to attenuate any undesirable vibration. The natural frequency of a TMD is tuned to a frequency close to one of the natural frequencies of the main system. Thus, there are three main parameters in a TMD system: TMD mass, TMD stiffness coefficient and TMD damping ratio. In ATMD control system in comparison with the TMD system an additional control force is also needed.

In order to solve the governing equation of motion of the system (with and without the control devices) the standard state-space form is used. For designing the ATMD system, its parameters, especially the active control force, should be optimized to obtain the maximum reduction in structural dynamic response. For this purpose, the following methods have been used: a fuzzy logic control system, and a genetic-fuzzy control system.

Fuzzy logic allows objects to have a continuous truth value. Fuzzy logic enables the use of linguistic directions as a basis for control and are generally very capable of handling uncertain systems. The design of a fuzzy controller involves decisions about the number of important design parameters that should be determined before that actual control starts. These parameters are the fuzzy sets in the rules, the rules themselves, scaling factors in input and output, inference methods, and defuzzification procedures. In this investigation, the fuzzy controller will couple the point-valued MAX-MIN fuzzy inference engine product rule to combine the membership values for each rule (Mamdani type), and the center of area (COA) defuzzifier scheme to obtain the crisp value.

In a genetic algorithm the basic idea is to maintain a population of chromosomes (representing candidate solutions to the problem being solved) that evolves over time through a process of competition and controlled variation. The operators applied by the GA, can be described as: chromosome representation; initial population; fitness function; crossover; and mutation. To minimize the peak value of the top story displacement due to the given earthquake excitations, a multi objective function is used.

All of the FLC parameters and ATMD parameters have been optimized. For comparison, the parameters of the active controller system are calculated by the FLC method and GFLC. In this paper, fuzzy controller design procedure for the ATMD system uses crisp data directly from a model of the building. This data is then converted into a linguistic or fuzzy membership functions through the fuzzification process. The controller is designed based on two input variables (displacement and the velocity of the top story), each having five trapezoidal membership functions, and one output variable (active external control force) with seven triangular membership functions. To investigate the effectiveness of the proposed control systems for different disturbances, twenty-five different seismic motions have been used in the numerical simulations. From the results of the study, it is found that:

1. The GFLC system is more effective than the fuzzy controller system.
2. The reduction ratio obtained is much more sensitive to the weighting coefficients considered in fuzzy associative memory (FAM) rules.
3. The GA optimizer is a very powerful tool to optimize the FLC system by considering simultaneously as many parameters as desired.
4. The multi objective optimizer is much more effective than that of the single objective optimizer.

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