Open-loop Feedforward And Closed Loop Transfer Function

Open-loop transfer function and feedforward transfer function:

Fig: 1 closed loop system

Referring to Figure 1, the ratio of the feedback signal B(s) to the actuating error signal E(s) is called the open-loop transfer function. That is,

The ratio of the output C(s) to the actuating error signal E(s) is called the feedforward transfer function, so that

If the feedback transfer function H(s) is unity, then the open-loop transfer function and the feedforward transfer function are the same.

Closed-loop transfer function

For the system shown in Figure 1, the output C(s) and input R(s) are related as follows:

Eliminating E(s) from these equations gives

The transfer function relating C(s) to R(s) is called the closed-loop transfer function. This transfer function relates the closed-loop system dynamics to the dynamics of the feedforward elements and feedback elements.

From the above equation C(s) is given by

Thus the output of the closed-loop system clearly depends on both the closed-loop transfer function and the nature of the input.