Pole assignment using state feedback with time delay in friction-induced vibration problems

The dynamic behavior of friction-induced vibration problems is governed by second-order differential equations having asymmetric matrices, due to the coupling of structures and external loads, which are functions of some parameters. Asymmetric systems are prone to unstable vibration (flutter) as a parameter reaches a critical value. Placement of these unstable poles to the left-hand half of the complex pole plane for stabilization can be achieved by active (feedback control) and passive means (structural modification). Moreover, placement of poles is also done to achieve the desirable dynamic response and system performance. However, such active pole assignment 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 by using state-feedback control while considering a constant time-delay in the feedback control loop. The control strategy is based on receptances of the symmetric part of the asymmetric open-loop system (without time delay), which can be easily obtained from transfer function measurements. This method does not require the knowledge of mass, damping and stiffness matrices, and hence circumvents the modeling errors (finite element or reduced order). In this research, with numerical examples, it is shown that by means of active state feedback control and by using a relatively small number of available receptances, open-loop poles of the asymmetric system can be assigned precisely. The stability of the closed-loop system is analyzed by computing primary closed-loop poles and the associated critical time delay.