Session: 07-01-05: General Dynamics, Vibration, and Control

Paper Number: 116650

116650 - Extended Absolute Vibration Suppression Controllers 

Flexible structures appear in diverse engineering applications, ranging from small scale actuators and sensors to large mechanical, space and even civil engineering systems such as bridges and buildings. In some cases the flexibility is an unavoidable consequence while in others it is a result of a deliberate design, aiming at utilizing their main advantage which is light weight. It is worth noting that flexible is a relative term, depending both on the excitation bandwidth and the accepted level of vibration. Tighter performance requirements in terms of speed and accuracy require therefore including the flexible modes in models of systems that could otherwise be considered as rigid.

In a series of publications [1-4] by the second author and his research group a comprehensive modeling and control method for flexible structures was presented. The model is given in terms of an exact, infinite dimension transfer functions, from point application to point measurement. They have a very clear structure, consisting of delays and low order rational terms. The transfer functions have a clear interpretation from physical point of view. The different terms represent the travelling wave in the system and their reflections from the boundaries. This is in contrast with the finite element method (FEM) approach which can be interpreted as finite dimension approximation of the standing waves.

Feedback control has two important tasks in flexible structure design: adding ”artificial rigidity” for tracking systems, and absorbing energy. The paper uses the Absolute Vibration Suppression (AVS) controller which belongs to the family of dedicated control approaches that use the physical properties of flexible structures. In particular the control strategy stems directly from the transfer function and can be described as being a sink  to the traveling waves. This is in contrast with the approach of generic mathematical control laws that in theory can be applied to all dynamic systems, regardless of their physical origin.

Two assumptions were made in previous research. One is that the actuation and the measurement are at a single point. In practice, in particular the actuation, is distributed on an area that might not be negligible.  The second is that of a single control action that is applied at the boundary. Both assumptions are removed in this work and the general case is investigated. The correct extension to AVS control, which maintains its fundamental properties was formulated and analyzed.   

 

[1]        Halevi, Y., Control of flexible structures governed by the wave equation using infinite dimensional transfer functions”, ASME Journal of Dynamic Systems, Measurement, and Control, (2005) 127: 579-588.

[2]        Peled, I., O’Connor, W., and Halevi, Y., On the relationship between wave based control, absolute vibration suppression and input shaping, Mechanical Systems and Signal Processing, (2013) 39( 1): 80–90.

[3]        Sirota, L. and Halevi, Y., Fractional order control of the two-dimensional wave equation, Automatica, (2015) 59:152–163.

[4]        Sirota, L., Halevi, Y. and Krstic M., On the relationship between the absolute vibration suppression and back-stepping methods in control of the wave equation with possibly unstable boundary conditions, American Control Conference, Boston, MA ,(2016).

Presenting Author: Yoram Halevi Shenkar

Presenting Author Biography: Yoram Halevi is the Dean of Engineering at Shenkar and Professor emeritus at the Technion. He is a Fellow of ASME.

Authors:

Shahar Levin Technion
Yoram Halevi Shenkar