ABSTRACT
We have already seen that a DC position servo can be modeled by the use of third-order differential equations. A second-order model of this system is only an approximation of what is really happening, so why explore it? The simple answer is that control engineers communicate via the “language” of the second-order system. Statements like “You need more damping” or “There is too much gain” are very common in control work. These statements must be taken seriously, because a third-order system behaves much like one of second order, provided that two roots of the characteristic equation “dominate” the system response to standard test inputs. The dominant roots are those that are closest to the origin of the s-plane, along the negative real axis. Concentrating attention on these two roots can give the control engineer an intuitive feeling for how the system behaves. Fortunately, the second-order system has been well characterized and lends itself to manual solution using preplotted graphs, charts, and Laplace transform tables. We now proceed to investigate a second-order approximation of a DC position servo. Our discussion is limited to proportional control only, so that results are easily compared when the system is subjected to step, ramp, and sinusoidal inputs.
