Transfer Function is the ratio of Laplace transform of the output to the Laplace transform of the input, assuming all initial conditions zero.
- In general
- Where x is the input of the system and y is the output of the system.
- When order of the denominator polynomial is greater than the numerator polynomial the transfer function is said to be ‘proper’. Otherwise it is ‘improper’.
Properties of Transfer Function
Transfer function can be used to check
- The stability of the system from characteristic equation.
- Time domain and frequency domain characteristics of the system.
- Output of the system for any given input.
- Poles/zeros of the system.
Advantages of Transfer Function
- It gives the gain of the given system.
- Integral and differential equations can be converted into simple algebraic equations.
- Once the transfer function is known the output of the system can be determined for any input.
- Poles and zeros can be found out by transfer function and they play important role in response of the system.
Disadvantages of Transfer Function
- Transfer function is valid only for Linear Time Invariant (LTI) systems.
- In transfer function initial conditions are neglected hence initial conditions loose their importance.
- It does not give any idea how the present output is progressing.