Robust analysis of the designed controller based on the critically damped condition

The necessity of ensuring the robustness of the systems against uncertainties has been raised with the growth and development of active control systems based on classical and modern control theory. Therefore, the foundation of robust control theory has established as a new control theory. The H_∞ control method is one of the most widely used methods of this theory, in which system stability can be guaranteed by using linear matrix inequalities and Lyapunov theory. In this paper, the robustness of the active control system based on the critically damped conditions(CD), which is one of the latest control algorithms based on modern control theory, is investigated and it is compared with the controller designed by the H_∞ method. Due to the presence of various uncertainties in control systems such as parametric uncertainties, time delay, sensor/actuator faults, and actuators failure, the robust analysis of active control system based on the critically damped conditions and robust H_∞ controller synthesis is performed. In order to compare the two mentioned methods, two 3- and 8-story shear structures are considered to evaluate the responses. The obtained results show that the efficiency of the CD control method in controlling the acceleration of the structure is better than the H_∞ control method. But comparing the allowable time delay of control systems, the H_∞ control method provides better results.