Nonlinear optimal control for reducing vibrations in civil structures using smart devices

Abstract

The frequently excessive vibrations presented in civil structures during seismic events or service conditions may result in users\' discomfort, or worst, in structures failure, producing economic and even human casualties. This work contributes in proposing the synthesis of a nonlinear optimal control strategy for semiactive structural control, with the main characteristic that the synthesis considers both the structure model and the semiactive actuator nonlinear dynamics, which produces a nonlinear system that requires a nonlinear controller design. The aim is to reduce the unwanted vibrations in the response of civil structures, by means of intelligent fluid semiactive actuator such as the Magnetorheological Damper (MRD), which is a device with a low level of power consumption. The civil structures for which the proposed control methodology can be applied are those admitting a state-dependent coefficient factorized representation model, such as buildings, bridges, among others. A scaled model of a three storey building is analyzed as a case study, whose dynamical response involves displacement, velocity and acceleration of each one of the storeys, subjected to the North-South component of the September 19th., 2017, Puebla-Morelos (7.1M), Mexico earthquake. The investigation rests on comparing the structural response over time for two different conditions: with no control device installed and with one MRD installed between the first floor and the ground, where a nonlinear optimal signal for the MRD input voltage is determined. Simulation results are presented to show the effectiveness of the proposed controller for reducing the building\'s dynamical response.