Effect of Response Related Weighting Matrices on Performance of Active Control Systems for Nonlinear Frames

In this paper, the effect of various arrangements of displacement, velocity and acceleration related weighting matrices on the performance of active control systems on nonlinear frames has been studied. Different arrangements of weighting matrices and feedback combinations of the response have been considered to design the active controllers using a single actuator for reducing the response of an eight-storey bilinear hysteretic frame under white noise excitations. The nonlinear Newmark-based instantaneous optimal control algorithm has been used, where the distributed genetic algorithm (DGA) is employed to determine the proper set of weighting matrices. For each set of feedback and weighting matrices, the active control system has been designed with the optimal weights determined. Here, the objective is to minimize the maximum control force required to reduce the maximum structural drift to a value below the desired level. The numerical results of simulation show that, for the cases studied, the use of different arrangements of weighting matrices in the proposed method for the performance index of the active control law has no significant impact on the performance of the active control system. However, the type of response feedback combination included in the control law considerably affects the performance, and the controllers designed based on velocity feedback have been found to be more effective. It was also shown that for all the weight-cases, using the full feedback of response can lead to design controllers that require minimum control force to reduce the structural response with more online measurements. The robustness of the designed controllers for different weighting matrices arrangements and feedback combinations has also been tested under a number of real earthquake excitations with the results discussed.