H Control for Vibration Control of Civil Structures in Seismic Zones

The control of structural vibrations in seismic zones is an area of widespread research which seeks to reduce structural response and enhance structural integrity and occupant safety during seismic events. This research is devoted to the theory and application of H∞ state feedback optimal control to civil structures in the presence of actuator limitations and time varying parametric uncertainties. The primary goals when applying optimal control theory to civil structures is the maintenance of stability and the achievement of specific performance criteria, including control efficiency, in the face of random disturbances. Two important issues in achieving these goals are the consideration of non-linear actuator saturation effects and unknown, time varying, parametric uncertainties. Most importantly both of these issues must be addressed concomitantly within the same control design.

Robust H∞ state feedback controllers are developed here which achieve the desired H∞ norm bound while accounting for pre-specified bounds on the time varying parametric uncertainties. Stability of these controllers in the presence of non-linear actuator saturation can be proven through the construction of a Lyapunov function for the saturated control system using a non-linear state space model and new mathematical programming techniques. The primary goal of these controllers is the attenuation of response to mitigate damage to the structure.

Application of these newly developed algorithms to an actively controlled 33 story structure in Tokyo is discussed in the second part of this thesis. Robust H∞ controllers are developed for this structure using the active mass damping control system architecture in place on the structure. In addition, a tendon control system is designed. Both active controllers are designed using a control system design algorithm developed within this thesis. Finally, a passive base isolation system is developed and combined with the two active systems to create two different hybrid systems.

Simulation of these controllers for several select seismic inputs is performed to assess the relative effectiveness of these controllers for high rise civil structures. The robust H∞ controllers are found to outperform a conventional LQR controller which does not account for parametric variation of the structural parameters or actuator saturation. Comparison of the different robust H∞ control system architectures indicates that the hybrid systems are more suitable for tall structures due to their additional passive control mechanisms. In addition, the tendon control systems are shown to be more efficient than the active mass dampers (AMD's) for attenuating response with smaller control efforts. The overall result is that, for tall buildings, strictly active systems do not have the capacity to significantly impact peak responses of-the structure due to its overwhelming inertial forces that the structure may undergo relative to the control energies available through realistic actuators. However, the hybrid systems provide exceptional control, employing the active system to minimize response quantities that are unaffected by the passive system. These hybrid systems are able to accomplish this task with greater efficiency than the strictly active systems because lower control efforts are required.