In Control Systems, a Unity Feedback System is a closed-loop control system in which the feedback transfer function is equal to unity . In this type of system, the output signal is fed back directly to the input without any amplification or attenuation.
Table of Contents
Definition
A unity feedback system is a feedback control system in which the feedback transfer function
is equal to 1.
\[
H(s) = 1
\]
This means the entire output is returned to the summing junction and compared with the reference input.
Basic Components
- \(R(s)\) – Reference input
- \(G(s)\) – Forward path transfer function
- \(C(s)\) – Output of the system
- \(H(s)\) – Feedback transfer function
For a unity feedback system:
\[
H(s) = 1
\]
Closed Loop Transfer Function
The general closed-loop transfer function of a feedback system is
\[
\frac{C(s)}{R(s)} = \frac{G(s)}{1 + G(s)H(s)}
\]
Since in a unity feedback system \(H(s) = 1\), the transfer function becomes
\[
\frac{C(s)}{R(s)} = \frac{G(s)}{1 + G(s)}
\]
Error Signal
The error signal is the difference between the reference input and the feedback signal.
\[
E(s) = R(s) – C(s)
\]
Working Principle
- The reference input \(R(s)\) is applied to the system.
- The output \(C(s)\) is fed back directly to the summing point.
- The error signal \(E(s)\) is generated by comparing input and feedback.
- The system processes the error through the forward transfer function \(G(s)\).
- The output adjusts continuously to reduce the error.
Advantages of Unity Feedback System
- Simple mathematical analysis.
- Widely used in control system problems.
- Helps determine steady-state error constants such as \(K_p\), \(K_v\), and \(K_a\).
Example
If the forward transfer function is
\[
G(s) = \frac{10}{s + 2}
\]
For a unity feedback system, the closed-loop transfer function becomes
\[
\frac{C(s)}{R(s)} = \frac{10}{s + 12}
\]