Modal observer design for a flexible motion system with state dependent sensor positions

This paper focuses on observer design for a flexible motion system with a state dependent output map. After rewriting the modal system to parameter varying form sufficient conditions are derived to obtain a parameter varying modal observer with bounded ℒ₂ gain. These conditions translate to linear matrix inequalities (LMIs) when the time derivative of the Lyapunov function is multiconvex. The derived theory is applied to a model of the Herringbone Pattern Planar Actuator (HPPA) where noise and input disturbance affect the system. Using the theory it is possible to estimate independent rigid body motion in six degrees of freedom (DoF) and two flexible modes.