How 2nd order systems (those with 2 energy storing elements) respond to step inputs.
- is the undamped frequency of the system response
- Indicates the speed of the response
- is the damping factor
- Indicates the shape of the response
- Forces response is the response to a non-zero input, namely
- Initial conditions are zero, it ,
- The response is the solution to a non-homogeneous second order differential equation
There are 4 different cases for system response:
The response of a system to the same input with varying damping factors is shown in the graph below, from the data book. The equations are also given in the data book.
The system is not damped at all and is just a normal sinusoidal wave.
The amplitude of the sinusoidal output decreases slowly over time to a final "steady state" value.
This gives the fastest response, where the output rises to its final steady state value.
The output rises slowly to its steady state value