Hybrid Control of an Euler-Bernoulli Beam Using Direct Velocity Feedback and Wave-Filter-Based Active Wave Control

Abstract

Active wave control strategy enables the inactivation of vibration mode, which is valid for suppressing the vibration of a distributed parameter structure. However, when active wave control is applied, new vibration modes are produced in the uncontrolled region. To overcome this problem, this paper proposes a novel control strategy based on a hybrid combination of direct velocity feedback (DVFB) and active wave control. The two control methods have complementary qualities; DVFB is for improving the stability, and active wave control is for its unique control effects. First, a transfer matrix method in the Laplace domain is introduced to describe wave propagation phenomena of an Euler-Bernoulli beam. Then the wave filtering method which uses point sensors is presented. Based on the filtering method, the characteristic equation and control laws of the reflected wave absorbing control are derived. Next, the independence of the two control methods in the proposed hybrid control system is investigated by a numerical simulation. This is followed by the discussion of the stability problem of the hybrid control system via a Nyquist diagram method and three types of root loci. Finally, the control effects of the proposed control system are presented, demonstrating the validity of the proposed method.