Control system are normally designed to be Underdamped.

Explanation:

Underdamped control systems have a response that oscillates around the desired setpoint before settling down. This type of response is desirable in many control applications as it allows for a faster response time while avoiding overshoot and instability. The key characteristics of underdamped systems are:

1. Oscillatory Response: Underdamped systems exhibit oscillations in their response. This means that the output of the system will initially overshoot the desired setpoint and then oscillate around it before settling down.

2. Fast Response Time: Underdamped systems have a faster response time compared to overdamped and critically damped systems. This means that they can reach the desired setpoint more quickly, which is often desirable in control applications.

3. No Steady-State Error: Underdamped systems are capable of reaching the desired setpoint accurately without any steady-state error. Steady-state error refers to the difference between the desired setpoint and the actual output of the system after it has settled.

4. No Oscillations at Steady State: Underdamped systems will eventually settle down and reach a steady-state where the oscillations around the desired setpoint become smaller and smaller. This ensures that the system remains stable and does not exhibit sustained oscillations.

Advantages of Underdamped Control Systems:

- Faster response time: Underdamped systems can respond more quickly to changes in the input or setpoint, making them suitable for applications where a fast response is required.

- No steady-state error: Underdamped systems are capable of accurately reaching the desired setpoint without any steady-state error.

- Stability: Underdamped systems are stable and do not exhibit sustained oscillations at steady state.

Disadvantages of Underdamped Control Systems:

- Overshoot: Underdamped systems initially overshoot the desired setpoint, which may not be desirable in some applications where precise control is required.

- Oscillations: Underdamped systems exhibit oscillations around the desired setpoint, which may introduce instability or unwanted vibrations in certain applications.

- Sensitivity to disturbances: Underdamped systems may be more sensitive to disturbances or noise in the system, leading to erratic behavior or inaccurate control.

In conclusion, control systems are typically designed to be underdamped due to their faster response time, absence of steady-state error, and overall stability. However, the design of a control system should be carefully considered based on the specific requirements and constraints of the application.