ABSTRACT
We still cannot be sure that these calculations are accurate, so we compare the analytical solution with that given by SIMULINK simulation. Using Eq. (6-59) we get
for the "perfect" system's response. Figure 6-5 shows simulation results for both the perfect and not-quite-perfect systems, simulated as two cascaded second-order systems and also as single fourth-order systems. All four response curves lie essentially on top of each other. The fourth-order models should of course respond exactly like their respective cascaded second-order models. The not-quite-perfect system has coefficients so close to those of the perfect system that its response, though not exactly the same, is so close we can't see the difference on the graph. When we graph Eq. (6-60) (or a similar equation obtained for the "not-quite-perfect system") we again duplicate the curve of Fig. 6-5. We see thus that "repeated" roots require extra care, but we can get analytical solutions if that is desired. If we are satisfied with simulation (numerical integration of the differential equations), then no special efforts are needed.
