Question

What are the step response specifications?

Answer 1

The step response of a system shows how it reacts when a step input (typically a sudden change in input from 0 to a constant value, like 1) is applied. This is commonly used in control systems and signal processing to understand the dynamic behavior of the system.

The key step response specifications include:

1. **Rise Time (Tr)**:
   - The time it takes for the system’s output to rise from a lower specified percentage of the final value (often 10%) to a higher specified percentage (often 90%).
   - It gives an indication of how quickly the system responds to the input change.

2. **Peak Time (Tp)**:
   - The time it takes for the system to reach the maximum value of its output after the step input is applied.
   - For underdamped systems, this is when the output first reaches its highest point before settling.

3. **Overshoot (Mp)**:
   - The amount by which the system's response exceeds its final value, typically expressed as a percentage.
   - A high overshoot indicates that the system is too responsive or “overreacting” to the input change.

4. **Settling Time (Ts)**:
   - The time it takes for the system's output to stay within a certain percentage (usually 2% or 5%) of its final value and remain there.
   - It shows how long it takes the system to stabilize after the initial change.

5. **Steady-State Value**:
   - The final value of the system's output after it has settled.
   - For a step input, this should be the constant value of the input unless the system is unstable or there are other issues.

6. **Delay Time (Td)**:
   - The time it takes for the system’s output to initially respond to the step input (typically the time when the output first starts to increase noticeably).

Each of these specifications helps describe how a system responds in terms of its speed, accuracy, and stability when subjected to a step input.