Active vibration control of flexible structure by frequency-shaped sliding mode control with μ synthesis theory

This paper proposes a new design method for a sliding mode control system using μ synthesis theory. This concept is based on a frequency-shaped approach. A general hyperplane consists of a reference model without dynamics. Therefore, a conventional sliding mode control system often becomes unstable due to spillover phenomena of high frequency caused by high-speed switching. The proposed design method suppresses such spillover phenomena because of frequency shaping. Also, it has good robustness on the hyperplane to realize a minimum value of H∞ norm and the structured singular value from some noise to state variables. We have just applied this new method to the flexible structure of a test rig with four stories such as a high-rise building. We have obtained good performance from simulations and experiments.