Multivariable predictive control for vibrating structures: An application

Abstract This paper proposes the use of Model Predictive Control (MPC) to control a fast mechanical system. In particular an MPC strategy is applied to a laboratory flexible arm to perform a fast positioning of the end-effector with limited oscillations during the maneuver. The on-line implementation of a fast MPC is obtained with an ad hoc platform based on C++ and MATLAB while the MPC tuning is based on a non-linear model identified and validated with experimental data. The effectiveness of the proposed method is highlighted with some suitable experiments performed on the plant. In particular the comparison with a Linear Quadratic Regulator stresses the advantage of the MPC capability to explicitly handle input and state constraints.This feature guarantees smaller displacements that imply a structure stress reduction.

[1]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[2]  Bruno Siciliano,et al.  A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators , 1988, Int. J. Robotics Res..

[3]  Miguel Ayala Botto,et al.  Approaches for dynamic modelling of flexible manipulator systems , 2003 .

[4]  V. Zanotto,et al.  Vibration reduction in a flexible link mechanism through the synthesis of an MPC controller , 2009, 2009 IEEE International Conference on Mechatronics.

[5]  D. Lovekin,et al.  DESIGN AND ANALYSIS OF A FACILITY FOR FREE – FLOATING FLEXIBLE ROBOTIC MANIPULATORS , 2000 .

[6]  Alessandro Gasparetto,et al.  Model Predictive Control of a Flexible Links Mechanism , 2010, J. Intell. Robotic Syst..

[7]  Riccardo Scattolini,et al.  Architectures for distributed and hierarchical Model Predictive Control - A review , 2009 .

[8]  Wayne J. Book,et al.  Structural flexibility of motion systems in the space environment , 1993, IEEE Trans. Robotics Autom..

[9]  R. H. Cannon,et al.  Initial Experiments on the End-Point Control of a Flexible One-Link Robot , 1984 .

[10]  Paolo Rocco,et al.  Multiobjective Onboard Experiment for Advanced Researches on Robotics, Control Systems and Materials Behaviour , 2001 .

[11]  Bruno Siciliano,et al.  Direct adaptive control of a one-link flexible arm with tracking , 1989, J. Field Robotics.

[12]  M. Balas,et al.  Feedback control of flexible systems , 1978 .

[13]  Eduardo Bayo,et al.  Inverse Dynamics and Kinematics of Multi- Link Elastic Robots: An Iterative Frequency Domain Approach , 1989, Int. J. Robotics Res..

[14]  Paolo Rocco,et al.  Two-time scale visual servoing of eye-in-hand flexible manipulators , 2006, IEEE Transactions on Robotics.

[15]  Giovanni Mimmi,et al.  Theoretical and experimental sensitivity analysis of extra insensitive input shapers applied to open loop control of flexible arm , 2009 .

[16]  Carlos Canudas de Wit,et al.  Friction Models and Friction Compensation , 1998, Eur. J. Control.

[17]  M. Gurtin,et al.  An introduction to continuum mechanics , 1981 .

[18]  M. Hassan,et al.  Active vibration control of a flexible one-link manipulator using a multivariable predictive controller , 2007 .

[19]  M. Vidyasagar,et al.  Control of a Class of Manipulators With a Single Flexible Link: Part I—Feedback Linearization , 1991 .

[20]  Mouhacine Benosman,et al.  Control of flexible manipulators: A survey , 2004, Robotica.

[21]  Carlos Canudas de Wit,et al.  Theory of Robot Control , 1996 .

[22]  L. Meirovitch.  Analytical Methods in Vibrations , 1967 .

[23]  Atsushi Konno,et al.  Development of a flexible dual-arm manipulator testbed for space robotics , 1990, EEE International Workshop on Intelligent Robots and Systems, Towards a New Frontier of Applications.

[24]  Peter Eberhard,et al.  DYNAMIC ANALYSIS OF FLEXIBLE MANIPULATORS, A LITERATURE REVIEW , 2006 .

[25]  Miguel Ayala Botto,et al.  Vibration control of a very flexible manipulator system , 2005 .

[26]  M. O. Tokhi,et al.  Hybrid control schemes for input tracking and vibration suppression of a flexible manipulator , 2003 .

[27]  V. Feliu,et al.  A new design methodology for passivity-based control of single- link flexible manipulators , 2007, 2007 IEEE/ASME international conference on advanced intelligent mechatronics.