In control theory, a closed-loop transfer function is a mathematical function describing the net result of the effects of a feedback loop on the input signal to the plant under control. Overview The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, images, or other types of data streams. An example of a closed-loop transfer function is shown below: The summing node and the G(s) and H(s) blocks can all be combined into one block, which would have the following transfer function: is called feedforward transfer function, is called feedback transfer function, and their product is called the Open loop transfer function. Derivation We define an intermediate signal Z (also known as error signal) shown as follows: Using this figure we write: Now, plug the second equation into the first to eliminate Z(s): Move all the terms with Y(s) to the left hand side, and keep the term with X(s) on the right hand side: Therefore, See also Federal Standard 1037C Open-loop controller Open-Loop Transfer Function Control_theory#Closed-loop_transfer_function References Classical control theory Cybernetics