Receptance-Based Partial Pole Assignment for Asymmetric Systems Using State-Feedback

Many structures or machines interact with some internal nonconservative forces and present asymmetric systems in which the stiffness and damping matrices are asymmetric. Examples include friction-induced vibration and aeroelastic flutter. Asymmetric systems are prone to flutter instability as a result of the real parts of some poles becoming positive when certain system parameters vary. This paper presents a receptance-based inverse method for assigning a number of complex poles of second-order damped asymmetric systems while keeping other unassigned poles unchanged. It uses state-feedback (active damping and active stiffness) to shift the poles to desired locations where all poles have negative real parts. Receptances at only a small, limited number of degrees-of-freedom of the underlying symmetric system are required. Simulated numerical examples indicate that this is an effective method and is capable of assigning negative real parts to unstable poles to stabilise an otherwise unstable second-order dynamic system.