Closed - Loop Transfer Function

Closed - Loop Transfer Function

          The closed - loop transfer function is defined as the overall transfer function of the entire control system. It is a mathematical expression (algorithm) describing the net result of the effects of a closed (feedback) loop. Consider a closed loop transfer function or feedback loop consisting of several elements as shown on Fig.,

Fig Closed-loop transfer function.

Now, for the forward path element, we know that

where      K G (D ) = F1 (D ) X F2 (D ) X F3 (D)

On rearranging, we get

               θo = K G ( D )θi − K G ( D)θo

or             [1 + K G ( D )] θo = K G ( D)θi

          The above expression shows the transfer function for the closed-loop control system. Thus the block diagram may be further simplified as shown in Fig., where the entire system is represented by a single block.

Fig. Simplified closed-loop system.