Robust H∞ Control of Building Structures with Time Delay

In this paper, a robust H∞ controller for a building structure with a time delay is studied. Firstly, the motion equation of the structural system with an explicit time delay is introduced. Then, the state space representation of a dynamic equation without any explicit time delay is deduced by a specific integral transformation to the time-delay equation. Secondly, a robust control method is applied to the H∞ time-delay controller design and, due to the compensation of the time delay, the proposed controller contains not only the state term of the current step, but also a linear combination of some former steps of the control. Finally, numerical simulations and comparisons of a six-story building using the proposed time-delay controller are carried out. The simulation results indicate that the control performance will deteriorate if the time delay is not taken into account in the control design. The proposed H∞ time-delay controller in this paper can effectively compensate for a time delay in order to get better control effectiveness. Besides, this delay controller is robust to both structural parameter and time delay uncertainties.