Predictive Optimal Linear Control of Elastic Structures during Earthquake. Part I

A predictive optimal linear control (POLC) algorithm is proposed for controlling the seismic responses of elastic structures. This algorithm compensates for time delay that occurs in real control application by predicting the structural response in the classical optimal linear control equation. The unique feature of this proposed POLC algorithm is that it compensates for time delay very effectively over a very wide range of time delay magnitudes. Numerical examples of single-degree-of-freedom structures are presented to study the performance of the proposed POLC system for various time delay magnitudes. Results show that a time delay always causes degradation of control efficiency, and POLC can greatly reduce this degradation. The effects of natural periods and damping of the structure, different earthquake characteristics and numerical integration schemes, and choices of control gains on the degradation induced by time delay are carefully studied in the analysis. Results show that using a larger time delay magnitude may give smaller structural responses, and this magnitude is independent of earthquake characteristics but dependent on the control gains. Finally, practical application of POLC is performed on a six-story moment-resisting steel frame. It is demonstrated that POLC maintains stability in multi-degree-of-freedom structures and at the same time it has a satisfactory control performance.