Multi-Mode Vibration Suppression in MIMO Systems by Extending the Zero Placement Input Shaping Technique: Applications to a 3-DOF Piezoelectric Tube Actuator

Piezoelectric tube actuators are extensively used in scanning probe microscopes to provide dynamic scanning motions in open-loop operations. Furthermore, they are employed as micropositioners due to their high bandwidth, high resolution and ease of excitation. However, these piezoelectric micropositioners exhibit badly damped vibrations that occur when the input excites the dynamic response, which tends to degrade positioning accuracy and performance. This paper deals with vibrations’ feedforward control of a multi-degrees of freedom (DOF) piezoelectric micropositioner in order to damp the vibrations in the direct axes and to reduce the cross-couplings. The novelty in this paper relative to the existing vibrations feedforward controls is the simplicity in design approach, the minimal number of shaper impulses for each input required to damp all modes of vibration at each output, and the account for the strong cross-couplings which only occur in multi-DOF cases. A generalization to a multiple degrees of freedom actuator is first proposed. Then simulation runs on a 3-DOF piezoelectric tube micropositioner have been effectuated to demonstrate the efficiency of the proposed method. Finally, experimental tests were carried out to validate and to confirm the predicted simulation.

[1]  Micky Rakotondrabe,et al.  Simultaneous suppression of badly damped vibrations and cross-couplings in a 2-DoF piezoelectric actuator by using feedforward standard H∞ approach , 2015, Commercial + Scientific Sensing and Imaging.

[2]  Philippe Lutz,et al.  Robotic microassembly and micromanipulation at FEMTO-ST , 2013 .

[3]  Gerber,et al.  Atomic Force Microscope , 2020, Definitions.

[4]  Micky Rakotondrabe,et al.  Bouc–Wen Modeling and Inverse Multiplicative Structure to Compensate Hysteresis Nonlinearity in Piezoelectric Actuators , 2011, IEEE Transactions on Automation Science and Engineering.

[5]  Sudarshan P. Bhat,et al.  Solutions to Point-to-Point Control Problems using Laplace Transform Technique , 1990, 1990 American Control Conference.

[6]  Micky Rakotondrabe.  Smart Materials-Based Actuators at the Micro/Nano-Scale , 2013 .

[7]  Micky Rakotondrabe.  Classical Prandtl-Ishlinskii modeling and inverse multiplicative structure to compensate hysteresis in piezoactuators , 2012, 2012 American Control Conference (ACC).

[8]  P. Lutz,et al.  Development, Modeling, and Control of a Micro-/Nanopositioning 2-DOF Stick–Slip Device , 2009, IEEE/ASME Transactions on Mechatronics.

[9]  D. Croft,et al.  Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application , 2001 .

[10]  Ian R. Petersen,et al.  Resonant Controller Design for a Piezoelectric Tube Scanner: A Mixed Negative-Imaginary and Small-Gain Approach , 2014, IEEE Transactions on Control Systems Technology.

[11]  M. Rakotondrabe,et al.  Characterizing piezoscanner hysteresis and creep using optical levers and a reference nanopositioning stage. , 2009, The Review of scientific instruments.

[12]  Philippe Lutz,et al.  Hysteresis and vibration compensation in a nonlinear unimorph piezocantilever , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[13]  Lucy Y. Pao.  Multi-input shaping design for vibration reduction , 1999, Autom..

[14]  Micky Rakotondrabe,et al.  Characterization, Modeling and H∞ control of n-DOF Piezoelectric Actuators: application to A 3-DOF Precise Positioner , 2016 .

[15]  G. Schitter,et al.  Active Damping of a Piezoelectric Tube Scanner using Self-Sensing Piezo Actuation. , 2010, Mechatronics : the science of intelligent machines.

[16]  Warren P. Seering,et al.  Preshaping Command Inputs to Reduce System Vibration , 1990 .

[17]  Micky Rakotondrabe,et al.  Bouc–Wen Modeling and Feedforward Control of Multivariable Hysteresis in Piezoelectric Systems: Application to a 3-DoF Piezotube Scanner , 2015, IEEE Transactions on Control Systems Technology.

[18]  Philippe Lutz,et al.  Feedforward and IMC-feedback control of a nonlinear 2-DOF piezoactuator dedicated to automated micropositioning tasks , 2011, 2011 IEEE International Conference on Automation Science and Engineering.

[19]  Santosh Devasia,et al.  A Survey of Control Issues in Nanopositioning , 2007, IEEE Transactions on Control Systems Technology.

[20]  Warren P. Seering,et al.  Using input command pre-shaping to suppress multiple mode vibration , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[21]  Micky Rakotondrabe.  Modeling and compensation of multivariable creep in multi-DOF piezoelectric actuators , 2012, 2012 IEEE International Conference on Robotics and Automation.

[22]  Warren P. Seering,et al.  A zero-placement technique for designing shaped inputs to suppress multiple-mode vibration , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[23]  Tarunraj Singh,et al.  Robust time-optimal control - Frequency domain approach , 1994 .

[24]  Junqiang Xi,et al.  Special Issue on “Recent Developments on Modeling and Control of Hybrid Electric Vehicles” , 2016 .

[25]  L.Y. Pao,et al.  A Tutorial on the Mechanisms, Dynamics, and Control of Atomic Force Microscopes , 2007, 2007 American Control Conference.

[26]  Micky Rakotondrabe,et al.  Multi-mode vibration suppression in 2-DOF piezoelectric systems using zero placement input shaping technique , 2015, Commercial + Scientific Sensing and Imaging.