A new time-domain robust anti-windup PID control scheme for vibration suppression of building structure

Abstract

Robustness is one of the main issues in the design of closed-loop control systems, and to provide it, considering the differences between the actual and mathematical models, effects of external disturbances and measurement noise is necessary. In this study, a new time-domain robust anti-windup proportional integral derivative (PID) control scheme for vibration suppression of building structure is introduced. Because of computational complexity in determining and tuning gains of the controller for each structural vibration modes in the conventional PID control methods. Such as modal analysis; the dynamic vibration equations of the structure are implemented in the state space form to consider the effects of all vibration modes of the structural system in the controlling gains simultaneously. Uncertainties in the structural stiffness parameter, sensing noise, input time-delay, and saturation windup of the actuator are considered in a new formulation. To ensure robust stability and performance of the proposed controller, the closed-loop transfer function from exogenous inputs to the controlled outputs is defined as in the standard form of the H∞ mixed sensitivity minimization criterion. The PID control gains are obtained by minimizing the infinity norm of the closed-loop transfer function of the control system in standard form. Based on numerical study of an 11-story benchmark structure equipped with an active tuned mass damper, the robustness and stability of the proposed controller are presented. This controller can reduce further the maximum displacement, velocity, and acceleration of the structure subjected to far field earthquakes with considering uncertainties by 16, 10, and 16%, respectively, compared to the conventional PID controller.