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When I describe a simple system with spring-damper feedback with 4 states variables, I obtain a transfer function or canonical form of this transfer function with 3 poles and a reduced form with order 3. Why ? some state variables can be contracted ? You can see code from from maxima

first part enter image description here

second part enter image description here

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    $\begingroup$ Can you type the equations instead of the screenshots? $\endgroup$ – percusse Jun 11 '18 at 14:43
  • $\begingroup$ What are the parameters for tf:trasnfer_function? $\endgroup$ – Arash Jun 13 '18 at 23:06
  • $\begingroup$ The input is I and the output is speed1. The transfer function is correct but the problem is that the canonical form give a matrix smaller than the number of state variables. $\endgroup$ – Sulivan Küttler Jun 15 '18 at 21:16
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Your question and approach is unclear but from what I understand, you had a fourth order transfer function and when you transformed it into canonical form, you got a third order system. If this is indeed the case, it is not unusual. You are probably obtaining a minimum realization of the system (happens with pole-zero cancellations).

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