I'm sorry, but as a text-based AI, I cannot directly sketch images. However, I can describe the typical shape of the underdamped time response of a second-order feedback control system subjected to a unit step input.
In an underdamped system, the response starts from the initial state and initially overshoots the steady-state value before settling down. The response consists of a series of oscillations known as damped oscillations. The number of oscillations and their damping ratio depend on the system's parameters.
The typical shape of the underdamped time response can be described as follows:
1. The response starts at zero and rapidly rises initially in the positive direction.
2. It overshoots the steady-state value (typically around 1 for a unit step input) and reaches a maximum value known as the peak overshoot.
3. After reaching the peak overshoot, the response starts oscillating around the steady-state value.
- The amplitude of the oscillations gradually decreases over time.
- The oscillation frequency is determined by the system's natural frequency.
- The damping ratio determines how quickly the oscillations decay.
4. Eventually, the response settles down and approaches the steady-state value from below.
- The settling time depends on the system's damping ratio.
- The response may never completely reach the steady-state value due to the presence of damping.
To visualize the underdamped time response, you can search online for "underdamped second-order system step response" to find plots and diagrams that illustrate the behavior.
sketch the underdamped time response of a typical second order feedback control system subjected to a unit step input
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