Pitfalls and Guidelines for the Numerical Evaluation of Moderate-order System Frequency ResponseNASA, 1981 - 36 pages |
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