ABSTRACT

We have used the Taylor series linearization scheme a number of times to enable us to obtain analytical approximate solutions for nonlinear systems. It is clear that such approximations get inaccurate if the system variables move too far from the chosen operating point, but it is not obvious how far is "too far." Some appreciation of the accuracy of linearization is useful to us, since it is so widely applied. We can develop such an appreciation by comparing analytical linearized solutions with "exact" nonlinear solutions obtained by simulation. You might be saying: "Why bother with approximations when we can easily get exact results by simulation?" You should remember that simulation gets only numerical results, never any formulas that show relations among physical parameters that are so useful in design. Linearized analytical solutions can provide such relations.