Vibration Control for a Cantilever Beam with an Eccentric Tip Mass Using a Piezoelectric Actuator and Sensor

A novel model using the transfer matrix method for multibody system (TMMMS) is put forward to describe the dynamic characteristics of a cantilever beam that has a concentrated mass at its tip under axial excitations. The theoretical analysis and numerical results demonstrate that this model has some advantages, such as for a small matrix and a higher computational speed. Based on this model a control system, which is composed of a LQG controller, a piezoelectric actuator, and a sensor for the cantilever beam is proposed, theoretically analyzed, and experimentally verified. The experimental results show that the proposed controller with the piezoelectric actuator can effectively reduce the vibration of the cantilever beam with an eccentric tip mass. The piezoelectric sensor can measure vibration responses with high-accuracy. Therefore, this new model gives a broad range of possibilities for model-based controller design and implementation.

[1]  André Preumont,et al.  Vibration Control of Active Structures: An Introduction , 2018 .

[2]  Jinjun Shan,et al.  Slewing and vibration control of a single-link flexible manipulator by positive position feedback (PPF) , 2005 .

[3]  Hans Wagner,et al.  Natural frequencies of a uniform cantilever with a tip mass slender in the axial direction , 1976 .

[4]  G. Song,et al.  Vibration suppression of a spacecraft flexible appendage using smart material , 1998 .

[5]  William Singhose,et al.  Command shaping for flexible systems: A review of the first 50 years , 2009 .

[6]  Carlos F. Matt.  Simulation of the transverse vibrations of a cantilever beam with an eccentric tip mass in the axial direction using integral transforms , 2013 .

[7]  Xiaoting Rui,et al.  Automatic Deduction Theorem of Overall Transfer Equation of Multibody System , 2014 .

[8]  Xiaoting Rui,et al.  Transfer matrix method for linear multibody system , 2008 .

[9]  Carlos A. Rossit,et al.  Free vibrations of a cantilever beam with a spring-mass system attached to the free end , 2001 .

[10]  M. Yaman.  Adomian Decomposition Method for Solving a Cantilever Beam of Varying Orientation with Tip Mass , 2007 .

[11]  J.A. De Abreu-Garcia,et al.  Tracking control of a piezoceramic actuator with hysteresis compensation using inverse Preisach model , 2005, IEEE/ASME Transactions on Mechatronics.

[12]  Carlos F. Matt.  On the application of generalized integral transform technique to wind‐induced vibrations on overhead conductors , 2009 .

[13]  James L. Fanson,et al.  An experimental investigation of vibration suppression in Large Space Structures using positive position feedback , 1987 .

[14]  William Singhose,et al.  Command Generation for Flexible Systems by Input Shaping and Command Smoothing , 2010 .

[15]  C.W.S. To,et al.  Vibration of a cantilever beam with a base excitation and tip mass , 1982 .

[16]  Gangbing Song,et al.  Experimental Robustness Study of Positive Position Feedback Control for Active Vibration Suppression , 2002 .