Open-Loop Transfer Function

Open-Loop Transfer Function

          The open loop transfer function is defined as the overall transfer function of the forward path elements. Consider an open loop control system consisting of several elements having individual transfer function such F₁(D), F₂(D), F₃ (D)  as shown on in Fig.,  

Fig. Open loop control system.

 Thus

                                    = F1 (D ) X F2 (D ) X F3 (D ) = KG (D)

The simplified block diagram of the open loop transfer function is shown in Fig.,

Fig. Simplified open loop control system.

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.

EXERCISES

EXERCISES

1. Define the following terms: 

         (a) Response    (b) Process control     (c) Process Controller

         (d) Regulator   (e) Transducer             (f) Feedback

2. Explain different types of Automatic Control Systems? Explain with an example. 

3. Discuss the importance of block diagrams in control systems. 

4. Draw the block diagrams for the following control systems: 

      (a) A simple carburettor, 

      (b) A thermostatically controlled electric furnace. 

5. What is a transfer function ? 

6. Derive Open - loop and closed - loop transfer functions?