Question

Specified tolerance band of transient damped oscillation

Answer 1

Explanation:

It is the time required for the response to reach the steady state and stay within the specified tolerance bands around the final value. In general, the tolerance bands are 2% and 5%. The settling time is denoted by ts.

The settling time for 5% tolerance band is -

ts=3δωn=3τ

The settling time for 2% tolerance band is -

ts=4δωn=4τ

Where, τ is the time constant and is equal to 1δωn.

Both the settling time ts and the time constant τ are inversely proportional to the damping ratio δ.

Both the settling time ts and the time constant τ are independent of the system gain. That means even the system gain changes, the settling time ts and time constant τ will never change.