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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    Can you type the equations instead of the screenshots? – percusse Jun 11 at 14:43
  • What are the parameters for tf:trasnfer_function? – Arash Jun 13 at 23:06
  • 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. – Sulivan Küttler Jun 15 at 21:16

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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