Research on the multi objective optimization robust algorithm based on the reduced order model

Due to the excessive number of degrees of freedom in actual building structures, controller design and real-time execution become challenging. Model order reduction is an effective approach to reduce model complexity while satisfying the engineering accuracy requirements. The degree of matching between the reduced-order model and the full-order model significantly affects the control performance of the reduced-order controller. Addressing the challenges posed by parameter uncertainty and model uncertainty resulting from model reduction is crucial for maintaining system performance. This paper proposes a multi-objective optimization robust control algorithm based on the reduced-order controller, utilizing robust H2/H∞ optimal guaranteed cost control (OGCC) theory and linear matrix inequality (LMI) method. Based on the reduced-order model with uncertainty, the necessary and sufficient conditions for the existence of the proposed OGCC are established and proved. By introducing a deterministic H2 performance upper bound, the controller design problem is transformed into a standard convex optimization problem with LMI constraints, facilitating the solution process. Using the finite element software ABAQUS as the simulation platform, the effectiveness of the proposed algorithm is tested by a real engineering case of lateral-torsional coupled wind vibration control for a super high-rise building with large length-width ratio. The results indicate that the proposed OGCC algorithm significantly outperforms the LQR control algorithm based on the nominal model and has stronger robustness for model uncertainty and parameter uncertainty.