Optimal control parameterization for displacement and acceleration demands, and local post-yield constitutive responses

This paper uses a COntroller Optimal Parameterization algorithm, as developed herein, to control displacement and acceleration responses in otherwise highly nonlinear steel shear-frame buildings using Displacement-Optimization (DO) and Acceleration-Optimization (AO) sub-routines. Optimal weighing parameters are used to converge the global and local constitutive responses to prescribed elastic performance levels in order that structural damage – measured in terms of post-yield global displacements, local post-yield strains, and plastic spread lengths – does not occur. The CO-OP routine is embedded into an existing nonlinear time-history analysis that is applied to inelastic structures in order to subsequently enable these structures to displace elastically and to respond at lower accelerations. Numerical examples are used to demonstrate the ability of CO-OP to reduce the maximum calculated displacement and acceleration in steel shear frames subjected to the El Centro earthquake by 92% and 19%, respectively, and by 98% and 75%, respectively, under the Hyogo-ken Nambu earthquake in comparison to an uncontrolled nonlinear frame. When the CO-OP method is tuned to reducing the peak acceleration in an elastic frame, the peak demands are substantially smaller than those of the uncontrolled frame. Finally, analyses of SDOF and MDOF structures show significant reduction of displacements (up to 62% and 27%, respectively) in comparison to a time-varying LQR (TVLQR) method, and significant reduction in accelerations and control energy (35% and 33%, respectively) in comparison to a published approach that utilizes additional parameters and a constraining control force.