The Use of Parameter Influence Coefficients in Computer Analysis of Dynamic Systems

Abstract

A new computer technique is described which yields the partial derivatives of problem variables with re spect to pertinent system parameters simultaneously with the solution of the original system differential equations. These derivatives, known as parameter influence coefficients, are valuable to the analyst in enhancing his understanding of system characteris tics. If the problem solution x(t, λ) and the parameter influence coefficient ∂x/∂λ (t, λ) is known for a par ticular operating point where λ= λ₀, then it is pos sible to make a first-order prediction of system behavior at a neighboring point having the new parameter value λ₁ = λ₀ + Δλ. Similar predictions can be made if not one but several parameters are to be varied. Thus, the knowledge of parameter in fluences often helps to reduce the total number of computer runs required in a parametric system study. Typical applications of the technique are: linear ex trapolation in the neighborhood of a known solution, determination of design tolerances of a system, and prediction of critical parameter values and stability boundaries. The most useful application pertains to systems disturbed by random noise where normally a very large number of computer runs would be re quired to analyze the system on a statistical basis in a variety of operating conditions. Several illustrative examples are presented in the paper.