1. Performance of Second Order Systems

2. Why Consider Second Order Systems
There are two main aspects in Control System design
Design using a highly accurate model
Taking care of all minor details
Considering all elements in the system
The Controller based on highly accurate model maybe very complex

3. Design using performance specifications
The controller can be designed based on the desired performance specifications.
Instead of considering the exact model of the system the response is considered.
The system response of second order system can reflect in general the response of even higher order systems.

4. The Time Response the transient response disappears with time
the steady-state response exists a long time after input is applied

5. Transient and Steady State
Transient Response
Steady State Response

6. Test Input Signals

7. Step Input

8. Ramp input

9. Parabolic Input

10. Input Signals Summary Test Signals Purpose Impulse stability test Step
transient response test
Ramp
tracking capability test
Parabolic
faster tracking capability test

11. How to find the response analytically
For a given transfer function, the response can be found easily by taking the Laplace inverse of the Product of the input and the transfer function

12. How to find…. Example

13. response

14. Step Response