Model reduction for active structural vibration control

The protection of civil structures has been a challenging research topic, in order to avoid human, economic and material losses. Into the active vibration control there are different techniques and approaches to reduce structural responses due to natural hazards. Hence, obtaining accurate mathematical models from structure and structure-actuator is very important. Normally these models result in high order systems particularly if the structures become large, therefore dealing with such systems represent some difficulties. This paper presents a useful methodology to reduce linear high order systems models, to obtain an under damped second order system with time delay which describes the general behavior of the high order system, simplifying the controller design. To evaluate the methodology effectiveness, we consider a sixth-order system which represents a test structure with two stories including an active mass damper. Additionally, a Proportional- Integral-Derivative controller is designed based on the reduced model but presenting favourable results when applied to the original system. The simulations show that the controller and the actuator reduce the structural displacements positively. The comparisons between uncontrolled and controlled structure are shown considering records of El Centro earthquake. Finally the proposed methodology demonstrates an effective way to deal with such systems.