June 24, 2007
June 24, 2007
June 27, 2007
12.1252.1 - 12.1252.9
RULE BASED MODELING OF DYNAMIC SYSTEMS AND COMPUTATION OF TRANSFER-FUNCTIONS WITH “MATLAB”
The dynamic systems are in general modeled by Newton’s force method or Lagrange’s energy method. In this paper a rule based procedure is given as an alternate method for simple linear systems. The resulting equations in matrix form can be used as input in the analytical computation of transfer functions with MATLAB software. Integration of rule based modeling of dynamic systems and analytical computation of transfer functions with MATLAB provides a viable pedagogical tool for undergraduate education in Linear System Control.
Linear Vibrations and Linear System Control are relatively difficult courses in undergraduate curriculum for Aerospace, Mechanical as well as Electrical engineering students. The primary difficulty lies in developing the equations of motion from given physical system. In applying the Newton’s force method, one should have good understanding of degree of freedom and free body diagram. In applying the energy method, one should have good understanding of kinetic energy, potential energy, and damping energy. Although some students have very good grasp of these principles, majority of the class have trouble in application of these concepts. The computation of transfer functions in analytical form requires the knowledge of partial fractions and Laplace Transforms. Manual computation of transfer functions is rather laborious for even some simple systems. MATLAB software can be easily used for this purpose and it is efficient in applying Laplace Transform in order to find the transfer function.
Rules for Modeling
1. Degrees of Freedom: (a) Every degree of freedom [Xi] is associated with a mass [Mi]; (b) A degree of freedom without a real mass is associated with a virtual mass of zero magnitude (or zero-mass).
2. Stiffness Matrix: (a) Diagonal elements of the matrix [Kii] are sum of the values of stiffness connected to each mass [Mi], including the zero-mass. (b) The Off- diagonal terms [Kij] are negative and equal to sum of the values of stiffness connected in between mass [Mi] and [Mj].
3. Damping Matrix: (a) Diagonal elements of the matrix [Cii] are sum of the values of damping connected to each mass [Mi], including the zero-mass. (b) The Off- diagonal terms [Cij] are negative and equal to sum of the values of damping connected in between mass [Mi] and [Mj].
Karunamoorthy, S., & Mallikarjuna, H. (2007, June), Rule Based Modeling Of Dynamic Systems And Computation Of Transfer Functions With "Matlab" Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. https://peer.asee.org/3074
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