A novel approach of active control of structures based on the critically damped condition

In this research, the active control of structures based on the critically damped condition was proposed for reducing displacements and drifts of structures under seismic loading. In this approach, the second-order dynamic equation is converted into a first-order dynamic equation and a first-order derivative operator with the same constants, which satisfy critically damped conditions of the system. Based on this concept and using the defined performance index, the feedback gain matrix of the structural velocity is obtained. In the method of active control of structures based on the critically damped condition, the control force, which is the linear definition of the feedback gain matrix and the structural velocity, is exerted on the structure in each time step. Four types of numerical examples are examined to the comparison verification of active control of structures based on the critically damped condition with the classical linear optimal control, standard model predictive control, and other methods proposed in several references. Programming and calculations are done by Mathcad prime mathematical software.