Abstract
When calculating the transient response of a control loop by means of the classical differential-equation method, the solution of the characteristic equation and the determination of the integration constants becomes extremely difficult for complicated configurations. If the operational calculus, i.e., the Laplace transformation, is applied, the constants of integration are produced automatically as long as definite but meaningful initial conditions are assumed, and the calculating work is simplified considerably. Even with this method, however, the roots of the characteristic equation must still be found. This presupposes that the equation can be expressed analytically, and that it can be solved, which is not always the case, as for example, if the equation is transcendental. Graphical methods have been developed for such cases, which allow the determination of the transient output response with sufficient approximation and with a moderate amount of calculating work. These methods, based on the frequency response, will be treated in detail in this paper, and their practical application will be demonstrated by means of a few problems.
