transfer function zeros are more than poles

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aiman
aiman 2023-11-22
评论： Sam Chak 2023-11-23
Hello,can someone help me explainig how to implement this transfer function
2 s^2 + 30 s + 100
------------------
s
in simulink ?

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Sam Chak
Sam Chak 2023-11-23
Hi @aiman
You can try these configurations (2 methods). Both should produce nearly the same output signals.
  2 个评论
aiman
aiman 2023-11-23
Thanks @Sam Chak the second approach works fine but how did you find the filter value ?
The first configration gave this error :
Component:Simulink | Category:Block diagram warning
An error occurred while running the simulation and the simulation was terminated
Caused by:
  • Derivative of state '1' in block 'Simulink2/Transfer Fcn' at time 1.0000000000001645 is not finite. The simulation will be stopped. There may be a singularity in the solution. If not, try reducing the step size (either by reducing the fixed step size or by tightening the error tolerances)
Sam Chak
Sam Chak 2023-11-23
Hi @aiman
No errors were identified in the 1st method (referred to as the unrealizable ideal config) as demonstrated in my block configuration. However, your error message tells that an error occurred in the block 'Simulink2/Transfer Fcn'. My proposed block configuration above (Method 1) does not have any block named 'Transfer Fcn'. My assumption is that you might have connected the unrealizable ideal config to the 'Transfer Fcn' block. This connection seems to cause the Simulink system to blow up at time 1.0000000000001645. But this is no longer irrelevant to the original question that you asked.
The 2nd method (realizable practical config) is an approximation of the unrealizable ideal config. In the 1st method (unrealizable ideal config), the expression can be rewritten as:
.
Believe it or not, I did not attempt to calculate the filter value; instead, I directly plugged in a very large value, 1 million. The reason for this is that if the filter coefficient, N, in the PID Controller block (realizable practical config), is very large, then the practical derivative term approximates the ideal derivative term, as shown in the expression:
.

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