Vibration Control on a Pulse and Ramp Driven System with Friction

This paper investigates the sufficient stability condition of a three-phase proportional gain, pulse, and ramp (PPR) controller for pointing systems under the influence of friction. With the ramp and pulse schemes integrated, the PPR controller has been demonstrated to be an effective control strategy for fast and precise pointing applications. In this paper the LuGre model is used to derive the upper bounds of the ramp slope Sr for the sufficient stability condition to suppress vibrations around the [—0.5, +0.5] μm target region. Our study reveals that the frictional stiffness σ 0 and the micro viscous damping coefficient σ 1 in the LuGre model are required for the bounds of Sr . With the derived bounds of Sr , the Lyapunov direct method is applied to prove the stability of the PPR controller.

[1]  Nurkan Yagiz,et al.  Fuzzy Sliding Modes with Moving Surface for the Robust Control of a Planar Robot , 2005 .

[2]  Horst Ecker,et al.  Stability Analysis of Open-loop Stiffness Control to Suppress Self-excited Vibrations , 2005 .

[3]  Pi-Cheng Tung,et al.  Fast Pointing Control for Systems With Stick-Slip Friction , 2004 .

[4]  Nasser Sadati,et al.  Variable Structure Control with Adaptive Fuzzy Sliding Surface , 2006 .

[5]  Vincent Hayward,et al.  Single state elastoplastic friction models , 2002, IEEE Trans. Autom. Control..

[6]  Carlos Canudas de Wit,et al.  A survey of models, analysis tools and compensation methods for the control of machines with friction , 1994, Autom..

[7]  Jan Swevers,et al.  An integrated friction model structure with improved presliding behavior for accurate friction compensation , 1998, IEEE Trans. Autom. Control..

[8]  Dirk Söffker,et al.  RETRACTED: Modeling and Control of an Elastic Ship-mounted Crane Using Variable Gain Model-based Controller , 2007 .

[9]  Clark J. Radcliffe,et al.  Robust nonlinear stick-slip friction compensation , 1991 .

[10]  Shui-Shong Lu,et al.  Dual mode control of a system with friction , 1999, IEEE Trans. Control. Syst. Technol..

[11]  Keith W. Buffinton,et al.  Pulse Width Control for Precise Positioning of Structurally Flexible Systems Subject to Stiction and Coulomb Friction , 2004 .

[12]  Phil R Dahl,et al.  Measurement of Solid Friction Parameters of Ball Bearings , 1977 .

[13]  Pi-Cheng Tung,et al.  Studies of Stick-Slip Friction, Presliding Displacement, and Hunting , 2002 .

[14]  Masayoshi Tomizuka,et al.  Adaptive Pulse Width Control for Precise Positioning Under the Influence of Stiction and Coulomb Friction , 1988 .

[15]  Jan Swevers,et al.  Modification of the Leuven integrated friction model structure , 2002, IEEE Trans. Autom. Control..

[16]  Andrew A. Goldenberg,et al.  Fuzzy logic controller for accurate positioning of direct-drive mechanism using force pulses , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[17]  Paolo Rocco,et al.  Single and multistate integral friction models , 2004, IEEE Transactions on Automatic Control.

[18]  Carlos Canudas de Wit,et al.  A new model for control of systems with friction , 1995, IEEE Trans. Autom. Control..

[19]  Paul I. Ro,et al.  Model Reference Adaptive Control of Dual-Mode Micro/Macro Dynamics of Ball Screws for Nanometer Motion , 1993 .