Pitfalls and Guidelines for the Numerical Evaluation of Moderate-order System Frequency ResponseNASA, 1981 - 36 pages |
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Page 22
... equation 22 , which is of the form of equation 19 , are the values of z which satisfy the determinantal equation 17 : det [ H ( z ) ] = 0 These can then be used to rewrite this equation in the desired factor polynomial form : det [ H ...
... equation 22 , which is of the form of equation 19 , are the values of z which satisfy the determinantal equation 17 : det [ H ( z ) ] = 0 These can then be used to rewrite this equation in the desired factor polynomial form : det [ H ...
Page 25
... write the transfer function G ( s ) given in equation 31 as a truncated partial fraction expansion as a ratio of polynomials both given in factored polynomial form . The denominator is the least common denominator ; since all B , in ...
... write the transfer function G ( s ) given in equation 31 as a truncated partial fraction expansion as a ratio of polynomials both given in factored polynomial form . The denominator is the least common denominator ; since all B , in ...
Contents
POLYNOMIAL AND RATIONAL FORMS FOR TRANSFER | 4 |
SYSTEM EQUATIONS PRIMARY DATA | 16 |
REDUCED ORDER SYSTEM EQUATIONS | 23 |
Common terms and phrases
accuracy associated with equation B₂ block diagram C₁ C₂ companion matrix complex plane computed results COMPUTED)/EXACT D₁ damped digits double precision eigenanalysis eigensystem EISPACK exact solution factored polynomial form follow-on frequency domain ill-conditioned computing problem ill-conditioned problems initial data input instinctive methods large order large-order systems low order low-degree polynomials MATRIX ELEMENTS matrix exponential matrix inversion matrix of polynomials method of Leverrier method Reference moderate to large moderate-order systems NASA Neumann and Goldstine Non-Oscillatory System numerator polynomial numerical error analysis numerical methods obtaining transfer functions order state variable oscillatory systems partial fraction expansion Pitfalls and Guidelines polynomials in power POLYRT COMPUTED ROOTS poorly-conditioned power series form present results associated primary data quasi-upper triangular QZ-algorithm QZ-method rational functions Reference 14 root-finding algorithm round-off error simulation models stable algorithm subroutine summarize a large system definition data System Frequency Response system order increases Table theory tions transfer function matrix well-conditioned system