The transfer function belongs to the static digital model. In engineering, transfer function (also called system function, transfer function and network function, and the drawn curve is called transfer curve) is a mathematical expression used to fit or describe the input-output relationship of black box model (positive imitation system).
Usually, the transfer function is the input-output relationship of linear time-invariant system (LTI) with space or time frequency as variables under zero initial condition and zero equilibrium point.
Transfer function refers to the ratio of Laplace transform (or Z transform) of linear system response (output) to Laplace transform of excitation (input) under zero initial condition. Let G(s)=Y(s)/U(s), where Y(s) and U(s) are Laplace transforms of output and input respectively.
Transfer function is one of the basic mathematical tools to describe the dynamic characteristics of linear systems. The main research methods of classical control theory-frequency response method and root locus method-are based on transfer function. Transfer function is one of the main tools to study classical control theory.
The transfer function is mainly used in three aspects:
1. Determine the output response of the system. For the system whose transfer function G(s) is known, the output response y(s) of the system can be directly determined by G (s) u(s) by Laplace inverse transformation method after the input action U (s) is given.
2. Analyze the influence of system parameter change on output response. For the closed-loop control system, the root locus method can easily analyze the influence of the change of the open-loop gain of the system on the pole and zero positions of the closed-loop transfer function, so that the influence on the output response can be further estimated.
3. Used in the design of control system. When designing directly from the open-loop transfer function of the system, the root locus method is used. When designing according to frequency response, frequency response method is adopted.