Transfer Functions, Block Diagrams and the s-Plane

Abstract

Transfer functions are input–output relationships in the Laplace domain. They are multiplicative operators. Multiplying a transfer function by the Laplace transform of an input variable yields the corresponding output variable. A block diagram represents input–output relationships graphically. The operators are contained within rectangular “blocks.” The input and output variables, or “signals,” are the lines which connect blocks. Block diagrams can combine transfer functions representing mathematical operations, such as differentiation, with transfer functions created from system equations, to predict the response of systems created by interconnection. Feedback loops allow calculation of the difference between the commanded value and the response of the system, which is termed the error signal, and is the basis of feedback control. The s-plane is a complex plane, in which the real and imaginary axes are the components of the eigenvalues of a system. The association between regions of the s-plane with the homogeneous response of a system allows the s-plane to be used as a graphical design tool.