Performance of Second Order Systems Why Consider Second

Performance of Second Order Systems

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

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

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

Transient and Steady State Transient Response Steady State Response

Test Input Signals

Step Input

Ramp input

Parabolic Input

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

How to find the response analytically l 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

How to find…. Example

response

Step Response