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Technical Briefs

A PID Type Constraint Stabilization Method for Numerical Integration of Multibody Systems

[+] Author and Article Information
Shih-Tin Lin

Department of Mechanical Engineering, National Chung-Hsing University, Taichung 40227, Taiwanstlin@dragon.nchu.edu.tw

Ming-Wen Chen

Department of Mechanical Engineering, National Chung-Hsing University, Taichung 40227, Taiwan

J. Comput. Nonlinear Dynam 6(4), 044501 (Apr 14, 2011) (6 pages) doi:10.1115/1.4002688 History: Received April 25, 2010; Revised September 21, 2010; Published April 14, 2011; Online April 14, 2011

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 Iintegrator 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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A slider crank system

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Figure 2

Error of the first constraint equation and its derivative

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Figure 3

Error of the first constraint equation for PID and PD type methods

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