Design spectra for actively controlled structures based on convex models

Preliminary design of an actively controlled structure requires a simple procedure for analysis and performance evaluation. A response spectrum technique applied to simplified models of complex structures can provide such a procedure. The spectra required for preliminary evaluation of a controlled structure include, besides the usual response parameters (displacement, acceleration, base shear), the control resource parameters, such as the size and capacity of hydraulic actuators, power requirements and energy consumption. This paper presents an approach for the development of design spectra based on a classical optimal control law and convex models of uncertainty. Analytical expressions are derived at each step so that one can obtain the values of basic design parameters of the control system without the need for a response history analysis. Based on these parameter values, preliminary design can be initiated and system cost can be estimated.