Insertion of negative feedback in control system affects

Negative feedback system:

Negative Feedback is a process by which a fraction of the opposite output signal is used as an input.

Effect of negative feedback:

• Negative feedback stabilizes the control system by counteracting the changes due to any reason.
• Negative feedback reduces the overall gain of the system, with the degree of reduction being related to the open-loop gain.
• Negative feedback reduces distortion noise, sensitivity to external change, as well as improves the system bandwidth and input and output impedance.

Analysis:

Since the negative feedback improves the stability of the system, the time required to settle the response is reduced i.e. setting time is reduced and the transient response decay very fast.

Transient Response of control system:

Settling time:

It is time required for the response to use and reach to the tolerance band.

For 2% tolerance band:

\({t_s} = 4\tau = \frac{4}{{\xi \;{\omega _n}}}\)

For 5% tolerance band:

\({t_s} = 4\tau = \frac{3}{{\xi \;{\omega _n}}}\) 

Thus due to negative feedback transient response decay very fast.