Question

The range of steady state value for the rise time of underdamped system is

• A. 0 to 90%
• B. 10 to 90%
• C. 0 to 100%
• D. 10 to 100%

Hint:

Common time-domain specifications: \[ t_r = \text{Rise Time} \] \[ t_p = \text{Peak Time} \] \[ t_s = \text{Settling Time} \] \[ M_p = \text{Maximum Overshoot} \] For an underdamped system, rise time is usually measured from \(0%\) to \(90%\) of the final value.

Answer 1

The Correct Option is A

Concept: Rise time is one of the important time-domain specifications of a control system. It indicates how quickly the system response reaches its final value after the application of a step input. For an underdamped second-order system, rise time is defined as the time required for the response to rise from \(0%\) to \(90%\) of its final steady-state value.

Step 1: Recall the definition of rise time.
Rise time is the interval required for the output response to move from its initial value to a specified percentage of its final value. \[ t_r=\text{Time required to reach }90%\text{ of final value} \] for an underdamped system.

Step 2: Identify the standard range.
For underdamped systems, rise time is measured between \[ 0% \quad \text{and} \quad 90% \] of the steady-state value.

Step 3: Select the correct option.
Therefore, \[ \boxed{\text{Rise Time Range} = 0% \text{ to } 90%} \] Hence, \[ \boxed{\text{Correct Option (A)}} \]