ABSTRACT
We prefer analytical methods since they produce formulas for the solution, whereas computer methods produce only tables of numbers, or graphs. Formula solutions show directly how system parameters affect system response. This information is most useful for design purposes, where we are trying to find the best combination of system parameters. Computer solutions can provide similar information but only with repeated trials, using different combinations of parameters. When there are many parameters, such "search" methods can become expensive. A common approach is to first linearize our equations, to allow analytical solution, even though we get approximate results. Using the formula solutions to help us arrive at an optimum set of parameters, we "rough out" a trial design. Using these trial parameter values, we go to digital simulation, including now some or all of the nonlinear or time-varying-coefficient effects. In a complex system we may add one nonlinearity at a time, so that we appreciate its effect without the confusing presence of others. Because the superposition theorem of linear differential equations does not apply here, we finally need to include all the significant nonlinearities. That is, the effect of one nonlinearity may be changed by the simultaneous presence of another.
