Boundary Control for A Flexible Inverted Pendulum System Based on A Pde Model

A partial differential equation (PDE) model for a flexible inverted pendulum system (FIPS) is derived by the use of the Hamilton principle. To solve the coupling system model, a singular perturbation method was adopted. The PDE model was divided into a fast subsystem and a slow subsystem using the singular perturbation method. To stabilize the fast subsystem, a boundary control force was applied at the free end of the beam. It then was proven that the closed-loop subsystem is appropriate and exponentially stable. For the slow subsystem, a sliding mode control method was employed to design a controller and the Linear Matrix Inequality (LMI) method was used to design the sliding surface. It then was shown that the slow subsystem is exponentially stable.

[1]  Hamed Jafarian,et al.  Two-Time Scale Control and Observer Design for Trajectory Tracking of Two Cooperating Robot Manipulators Moving a Flexible Beam , 2007, 2007 American Control Conference.

[2]  Petar V. Kokotovic,et al.  Singular perturbations and order reduction in control theory - An overview , 1975, at - Automatisierungstechnik.

[3]  A. A. Rodriguez,et al.  An interactive flexible inverted pendulum modeling, simulation, animation, and real-time (MoSART) control environment for enhancing control design , 2003, Proceedings of the 2003 American Control Conference, 2003..

[4]  Ö. Morgül,et al.  On the Stabilization of a Flexible Beam with a Tip Mass , 1998 .

[5]  M. Vakil,et al.  Maneuver control of the multilink flexible manipulators , 2009 .

[6]  Fumin Zhang,et al.  Adaptive nonlinear boundary control of a flexible link robot arm , 1999, IEEE Trans. Robotics Autom..

[7]  Victor Etxebarria,et al.  SLIDING-MODE ADAPTIVE CONTROL FOR FLEXIBLE-LINK MANIPULATORS USING A COMPOSITE DESIGN , 2005, Cybern. Syst..

[8]  Petar V. Kokotovic,et al.  Singular perturbations and time-scale methods in control theory: Survey 1976-1983 , 1982, Autom..

[9]  Fumitoshi Matsuno,et al.  Simple Boundary Cooperative Control of Two One-Link Flexible Arms for Grasping , 2009, IEEE Transactions on Automatic Control.

[10]  Shuzhi Sam Ge,et al.  Improving regulation of a single-link flexible manipulator with strain feedback , 1998, IEEE Trans. Robotics Autom..

[11]  Mohammad Eghtesad,et al.  Vibration Control and Trajectory Tracking for General In-Plane Motion of an Euler–Bernoulli Beam Via Two-Time Scale and Boundary Control Methods , 2008 .

[12]  J. Prevost,et al.  A coupled sliding-surface approach for the trajectory control of a flexible-link robot based on a distributed dynamic model , 2005 .

[13]  Desineni S Naidu,et al.  Singular perturbations and time scales in control theory and applications: An overview , 2002 .

[14]  Jiali Tang,et al.  Modeling and Simulation of a Flexible Inverted Pendulum System , 2009 .

[15]  Fumitoshi Matsuno,et al.  Positioning Control of Flexible Inverted Pendulum Using Frequency-Dependent Optimal Servo System. , 1999 .

[16]  Linjun Zhang,et al.  Observer-based partial differential equation boundary control for a flexible two-link manipulator in task space , 2012 .

[17]  D. Naidu,et al.  Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey , 2001 .