Dead-Beat Control of the Constraint Stabilization Method for Numerical Integration of Multibody Mechanical Systems

• Main Authors: Shu-Kai Chen, 陳書愷
• Other Authors: 林仕亭
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/67044906204947535926

碩士 === 國立中興大學 === 機械工程學系所 === 103 === The objective of this thesis is to resolve the stability problem for the numerical integration of constrained multibody mechanical systems. The dynamic equations of motion of the constrained multibody mechanical system is a mixed differential-algebraic equation(DAE) which contains external forces, constraint reaction forces as well as acceleration of the generalized coordinates of the system. In applying numerical integration methods to solve the mixed differential-algebraic equation, the constraint equation and its first and second derivatives must be satisfied simultaneously. That is, the generalized coordinates are dependent. Direct integration methods do not consider this dependency and constraint violation occurs. To solve this problem, Baumgarte proposed a constraint stabilization method in which a velocity term and a position term were added in the second derivative of the constraint equation. The disadvantage of this method is that there is no known reliable method for selecting the coefficients of the position and velocity term. Improper selection of these coefficients can lead to erroneous results. In this paper, we will use the so-called pseudo-integration equation to analyse the constraint stabilization method for numerical integration. Dead-beat Control of the stability analysis methods in digital control theory will be used to give correct choice of the control law for the Adams-bashforth and Adams Predictor-Corrector integration methods.