Feedback Controller Design Based on $H_{\infty}$ Control Theory in Dynamically Substructured System

Hybrid experimental systems are a promising approach to conduct a wide variety of vibration tests for the structures, where the system combines an actual experiment for the substructure using the actuators with a numerical simulation using mathematical model. The correspondence of boundary displacement between numerical structure and physical structure is required to accurately evaluate the vibration responses in the test. To accomplish the purpose, a dynamically substructured system as a control design framework has been proposed, where the control structure consists of two-degree-of-freedom control with a feedforward compensator and a simple proportional feedback compensator. However, the proportional compensator has the performance limitation for the experimental system with resonant vibrations and/or delay components. This paper introduces $H_{\infty}$ control theory as an approach of feedback compensator design in the dynamically substructured system. In the design, the stability margin of the system is explicitly considered by adding the condition based on the stability margin and circle condition to the mixed sensitivity problem. The designed control system is verified by conducting the experiments using a laboratory experimental setup with a basic mass-spring-damper system.