MAE 340 Lecture Notes - Lecture 5: Derived Row, Settling Time, The Roots
11 Oct 2017
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Document Summary
We have established the critical role of the roots of the characteristic equation in analyzing the behavior of the homogeneous solution of an lti ode. We will soon see that these roots are also critical in the particular solutions. The roots of the characteristic equation are the most important information in dynamic systems. For a ce with known numerical coe cients, we can nd roots numerically in matlab, on our calculators, etc. Suppose we know that the characteristic equation for a system is. 4 + 10 3 + 35 2 + 50 + 24 = 0. Using a root- nding function such as roots, we can easily nd the roots: But now suppose that the characteristic equation comes from a system still under design, with a design parameter. C that has not yet been selected, and the characteristic equation is still in the form of, say, 4 + 10 3 + c 2 + 50 + 24 = 0.
