Bab 5 slide 2

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1st Revision 2007 Taufik

Cal Poly State University, San Luis Obispo 146

Damping Ratio and Closed Loop Frequency Response

Relationship exists between systems transient response and its closedloop frequency response

Example: Given a frequency response of a second order system, i.e. thatobtained from Bode Plot, we could determine the damping ratio, naturalfrequency, and hence the transfer function

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Obtaining Damping Ratio, Natural Frequency and Transfer Function fromFrequency Response Plot with a peaking characteristic:

1. From Frequency Response Plot, determine the Mp and p.2. Apply Equation #2 to get the Damping Ratio using the Mp found in step 13. Apply Equation #3 to get the Natural Frequency n using the p found in step

1 and found in step 24. Once Damping Ratio from step 2 and the Natural Frequency n from step 3are obtained, then the Systems Transfer Function is:

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% O.S. and Mp

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Response Speed and Closed Loop Frequency Response

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Permissible Locations of Poles of Second Order System

Recall: Second Order System

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Lets try two cases: 1. Poles at 0.5 j3 (which would NOT be in the permissible locations)

An example of the transfer function would be T(s) = 1/(s^2 + s + 9.25)2. Poles at 3 j5 (which would BE in the permissible locations)

An example of the transfer function would be T(s) = 1/(s^2 + 8s + 25)

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System Type

is the number of PURE INTEGRATIONS in the FORWARD PATH

Example: A Unity Feedback System

Then, the System Type is the value of n in the Denominator.Other Examples:

For the above Unity Feedback System:

Bab 5 slide 2

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