Pole Assignment for Asymmetric Systems Using State-feedback with Time Delay

Linear, friction-induced vibration and aeroelastic flutter problems are governed by second-order differential equations of motion in which the stiffness matrix and often damping matrix are asymmetric. Asymmetric systems are prone to unstable vibration (flutter) as a parameter reaches a critical value, when the real part of a pair of complex poles crosses the vertical imaginary axis of the s-plane from left to right. It is important and useful to shift the unstable poles to the left-hand half of the complex pole plane for stability. Pole assignment by means of active control introduces inherent time delays in the feedback control loop. This paper presents a method for assigning complex poles to second-order damped asymmetric systems using state-feedback control with time-delay. It is based on receptances of the symmetric part of the asymmetric system without time delay, which is easier to measure than the receptances of the asymmetric system. Knowledge of mass, damping and stiffness matrices, though useful, is not required, and hence modelling errors such as from the finite element method can be avoided. Simulated numerical examples indicate that by means of active damping and active stiffness and using a small number of receptances of the symmetric part of the asymmetric system, n (n being the number of degrees-of-freedom of the whole system) pairs of complex poles of the asymmetric system can always be assigned precisely with or without time delay.