Application of Stochastic Control System in Structural Control

AbstractStochastic control of a building frame subjected to earthquake excitation and fixed with an Active Tuned Mass Damper (ATMD) is presented in this paper. The control forces are computed using stochastic control algorithm. It is assumed that the system is partially observed and measurement error is present as a Gaussian white noise. The excitation is also assumed as a Gaussian white noise and the expected value of the state of the system is controlled using the Astrom's algorithm. The algorithm is obtained using dynamic programming technique leading to a recursive formulation. The equations used for calculating the control force are similar to the Algebraic Riccati's Equation (ARE). An eight storey building frame is taken as an example in which Gaussian white noise with zero mean is considered as excitation. The analysis is simulated using MATLAB with synthetically generated time history of acceleration as an excitation. Results obtained for various response quantities are presented. The results show comparison between the controls achieved by the stochastic algorithm and Linear Quadratic Gaussian (LQG) regulator