Classical design in the frequency domain

Frequency domain analysis is concerned with the calculation or measurement of the steady-state system output when responding to constant amplitude, variable frequency sinusoidal input. Steady-state errors, in terms of amplitude and phase, relate directly to the dynamic characteristics—that is, the transfer function of the system. The Bode diagram technique uses asymptotes to quickly construct frequency response diagrams by hand. The construction of diagrams for high-order systems is achieved by simple graphical addition of the individual diagrams of the separate elements in the system. An important difference between analysis of stability in the s-plane and stability in the frequency domain is that, in the former, system models in the form of transfer functions need to be known. In the latter, however, either models or a set of input-output measured open-loop frequency response data from an unknown system may be employed. There are a few obvious relationships between the frequency response and time response of closed-loop systems: as bandwidth increases, the time response will be more rapid—that is, the settling time will decrease and larger the closed-loop peak, more oscillatory will the time response be.