1. ME 176
Control Systems Engineering
Time Response
Department of
Mechanical Engineering

2. System Response with Additional Poles:
Under certain conditions, a system with more than two poles or with zeros
can be approximated as a second-order system that has just two complex
"dominant poles".
Department of
Mechanical Engineering

3. System Response with Additional Poles:
Department of
Mechanical Engineering

4. System Response with Additional Poles:
Under certain conditions, a system with more than two poles or with zeros
can be approximated as a second-order system that has just two complex
"dominant poles".
How much larger should case 2 be to have effects of extra pole negligible
and thus have second order analysis applicable to this type of system?
Department of
Mechanical Engineering

5. System Response with Zeros:
Under certain conditions, a system with more than two poles or with zeros
can be approximated as a second-order system that has just two complex
"dominant poles".
---------------------------------> Zero : -3
---------------------------------> Dominant Pole
---------------------------------> Zero : -5
---------------------------------> Dominant Pole
---------------------------------> Zero : -10
---------------------------------> Dominant Pole
---------------------------------> Zero :None
---------------------------------> Dominant Pole
Department of
Mechanical Engineering

6. System Response with Zeros:
The closer the zero is to the dominant poles, the greater its effects on the
transient response. As the zero moves away from the dominant poles, the
response approaches that of the two pole system.
Department of
Mechanical Engineering

7. System Response with Zeros:
Analysis:
Derivative of Scale of
original response Orginal Response
Department of
Mechanical Engineering

8. System Response with Pole-Zero cancellation:
For a third-order transfer functions with a zero and a pole very close in
value, both cancel to result in a second-order transfer function.
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Department of
Mechanical Engineering