This paper developed multi-objective optimization design of proportional–derivative (PD) and proportional–integral–derivative (PID) controllers for seismic control of high-rise buildings. The case study is an 11-story realistic building equipped with active tuned mass damper (ATMD). Four earthquakes and nine performance indices are taken into account to assess the performance of the controllers. To create a good trade-off between the performance and robustness of the closed-loop structural system, a non-dominated sorting genetic algorithm, NSGA-II, is employed. To evaluate the degree of robustness of the controllers, four structural models with uncertainties in the nominal model of the structure is considered. For comparison purposes, a linear quadratic regulator (LQR) controller is also designed in the numerical simulations. Simulation results show that the proposed PD and PID controllers significantly perform better than the LQR in reduction of structural responses. Also, it is shown that the LQR does not provide a good performance in strong earthquakes. However, PD and PID controllers are able to significantly reduce structural responses. Moreover, it is shown that the PID has a better performance than the PD. The results also show that the proposed controllers are capable of maintaining a desired performance in the presence of modeling errors. They also have several advantages over modern controllers in terms of simplicity and reduction of required sensors and computational resources in tall buildings.
