The dynamic equations of motion of the constrained multibody mechanical system are mixed differential-algebraic equations (DAEs). The numerical solution of the DAE systems solved using ordinary-differential equation (ODE) solvers may suffer from constraint drift phenomenon. To solve this problem, Baumgarte proposed a constraint stabilization method in which a position and velocity terms were added in the second derivative of the constraint equation. Baumgarte’s method is a proportional-derivative (PD) type controller design. In this paper, an controller is included to form a proportional-integral-derivative (PID) controller so that the steady state error of the numerical integration can be reduced. Stability analysis methods in the digital control theory are used to find out the correct choice of the coefficients for the PID controller.
Skip Nav Destination
e-mail: stlin@dragon.nchu.edu.tw
Article navigation
October 2011
Technical Briefs
A PID Type Constraint Stabilization Method for Numerical Integration of Multibody Systems
Shih-Tin Lin,
Shih-Tin Lin
Department of Mechanical Engineering,
e-mail: stlin@dragon.nchu.edu.tw
National Chung-Hsing University
, Taichung 40227, Taiwan
Search for other works by this author on:
Ming-Wen Chen
Ming-Wen Chen
Department of Mechanical Engineering,
National Chung-Hsing University
, Taichung 40227, Taiwan
Search for other works by this author on:
Shih-Tin Lin
Department of Mechanical Engineering,
National Chung-Hsing University
, Taichung 40227, Taiwane-mail: stlin@dragon.nchu.edu.tw
Ming-Wen Chen
Department of Mechanical Engineering,
National Chung-Hsing University
, Taichung 40227, TaiwanJ. Comput. Nonlinear Dynam. Oct 2011, 6(4): 044501 (6 pages)
Published Online: April 14, 2011
Article history
Received:
April 25, 2010
Revised:
September 21, 2010
Online:
April 14, 2011
Published:
April 14, 2011
Citation
Lin, S., and Chen, M. (April 14, 2011). "A PID Type Constraint Stabilization Method for Numerical Integration of Multibody Systems." ASME. J. Comput. Nonlinear Dynam. October 2011; 6(4): 044501. https://doi.org/10.1115/1.4002688
Download citation file:
Get Email Alerts
Cited By
Numerical Simulation Method for the Rain-Wind Induced Vibration of the Three-Dimensional Flexible Stay Cable
J. Comput. Nonlinear Dynam
A Numerical Study for Nonlinear Time-Space Fractional Reaction-Diffusion Model of Fourth-Order
J. Comput. Nonlinear Dynam (March 2025)
An Investigation of Dynamic Behavior of Electric Vehicle Gear Trains
J. Comput. Nonlinear Dynam (March 2025)
Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method
J. Comput. Nonlinear Dynam (March 2025)
Related Articles
Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems
J. Comput. Nonlinear Dynam (January,2008)
Scaling of Constraints and Augmented Lagrangian Formulations in Multibody Dynamics Simulations
J. Comput. Nonlinear Dynam (April,2009)
A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations
J. Comput. Nonlinear Dynam (July,2006)
Stabilization of Baumgarte’s Method Using the Runge-Kutta Approach
J. Mech. Des (December,2002)
Related Proceedings Papers
Related Chapters
Boundary Layer Phenomenon for the Nonlinear Dynamical Systems with High-Speed Feedback
International Conference on Advanced Computer Theory and Engineering, 4th (ICACTE 2011)
Auto-Tuning Method of PIDA Controller Based Ongain Margin and Phase Margin
International Conference on Mechanical Engineering and Technology (ICMET-London 2011)
Accommodation and Stability of Alloying Elements in Amorphous Grain Boundaries of Zirconia
Zirconium in the Nuclear Industry: 20th International Symposium