State representation : I have less order of canonical form than state variables

Question

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

second part

Answer 1

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).