Abstract
H ∞ full information control method for structural vibration suppression with control delay is proposed within a discrete-time framework. Firstly, the continuous-time system equation with control delay is discretized by precise computation of matrix exponentials. By introducing an appropriate extended state vector, the time-delay system is transformed into standard discrete forms without time delays. Then a controller is designed based on the discrete time H ∞ full information control theory. The controller consists of a regular feedback closed-loop and a feed-forward compensator which utilizes external excitation signals measured in real time. The feed-forward plus feedback controller has better performance than feedback only controllers. The feedback loop of the deduced controller contains linear combinations of former control inputs besides the current state feedback terms. Thus the proposed method is applicable to large time-delay cases. Considering the complexity of the transformed system, a 2 N algorithm is introduced to search the optimal attenuation level and evaluate the control law. The present algorithm can be executed parallel, which makes the design of H ∞ controllers very convenient. Finally, numerical simulations of a three-story structure control are implemented. Time-delay effects on the optimal attenuation level are given to show that it is an important factor for system stability. Simulation results demonstrate the feasibility and effectiveness of the proposed control method.