Response-spectrum-based design method for gain-scheduling control of active base-isolated structures with nonlinear viscous dampers

The response-spectrum-based design method has been developed for linear active base-isolation to eliminate numerical simulations and trial-and-error testing. On the other hand, gain-scheduling is an effective control method for nonlinear systems and provides a way to apply linear system design methods. In this paper, we extend the response-spectrum-based design method to incorporate the gain-scheduling control strategy for active base-isolated structures with nonlinear viscous dampers (NVDs), aiming to effectively control these structures and simplify the design process. The gain scheduling of the controller is achieved based on the linear time-varying damping coefficient of NVDs. The active base-isolated structure with NVDs is described as a pseudo linear parameter varying model. The stability of the system is proven and analyzed using a common Lyapunov function. Moreover, this paper proposes a control-force spectrum for estimating the maximum required control force without numerical simulations. Numerical examples are used to validate the effectiveness of the proposed spectra. Finally, we also detail the design process and verify the design method through a design example. The results show that this method directly determines the design parameters from the spectra and satisfies the design criteria of response and control force without numerical simulations, offering a promising design approach for active control of buildings with nonlinear energy dissipating devices.