Predictive Optimal Linear Control of Inelastic Structures during Earthquake. Part II

The predictive optimal linear control (POLC) algorithm derived in the companion paper is extended to analyze the controlled responses of inelastic structures by incorporating the force analogy method (FAM). While POLC is very effective in compensating for the negative effect of time delay for elastic structures, the FAM is very efficient in performing the inelastic analysis. Different from conventional inelastic analysis methods of changing stiffness, the FAM analyzes inelastic structures by varying the structural displacement field, and therefore the state transition matrix needs to be computed only once. This greatly simplifies the computation and makes inelastic analysis readily applicable to the POLC algorithm. Numerical simulation is performed on a single-degree-of-freedom system to demonstrate the applicability of the POLC algorithm. Results show that the proposed control algorithm has feasibility for any inelastic structures for various control gains. Even though the control efficiency deteriorates with increase in time delay magnitudes, POLC maintains structural stability over a relatively wide range of time delay magnitudes. Finally, a computer model of a six-story moment-resisting steel frame is analyzed to show that POLC has a good control result on real inelastic structures, particularly in reducing the structural damages experienced during the earthquake.