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I'm reading a book about mathematical modelling of dynamic linear(in theory) systems.

As I know, measure simulation data and create a model of the system, is much better and gives a more exact mathematical model of the system.

My question for you is: Which one is best to focus on: State space model e.g MOESP algorithm or ARX, ARMAX models, which gives transfer functions.

They are both good. But estimate state space is a "new" method in the area of system identification, compared to estimate transfer functions.

My question for you is: What should I choose? Focus on state space model estimation or transfer function estimation?

I like state space models better that transfer functions because they give more information and they are not difficult to use. I can also convert a state space model to a transfer function by using the canonical forms.

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  • $\begingroup$ I didn't downvote your question. But I guess it is because it is not really clear what you are asking. You should narrow down your question and be more precise in your formulations. $\endgroup$ – MrYouMath Nov 6 '17 at 9:40
  • $\begingroup$ @MrYouMath My question is what is best for me - State space black box models or transfer function black box models. With black box models, you don't know the real physical structure of equations. My goal is to estimate mathematical models of dynamic systems. Hydraulic, mechanic, electric, thermal. The most standard systems in the industry. $\endgroup$ – Daniel Mårtensson Nov 6 '17 at 18:36
  • $\begingroup$ It totally depends on the system itself and the information it can provide you with. BTW, you do realize that transfer functions are for linear systems but state space models can cover nonlinear systems as well, right? $\endgroup$ – polfosol Nov 18 '17 at 6:51
  • $\begingroup$ I know that TF is for linear systems only and SS is for both nonlinear och both linear systems. But in this case, i'm want to estimate a linear model. $\endgroup$ – Daniel Mårtensson Nov 18 '17 at 10:46
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As you already mentioned, there is no right or wrong in this answer. I will point out some thoughts on your question anyway:

  • If you want to identify your system, always introduce as much structure as possible. The minimum information for all classical algorithms is the order of the system. If you have more above that, this is good! This might be: steady-state gain, time constant, etc.
  • Transfer functions are often more intuitive if you start working with dynamic systems. However, they are limited in use. First, it is in general very tedious to introduce a grey-box structure in transfer functions. This is easier in state space formulation. As you asked about black box, this might not refer to your case.
  • If you start working on MIMO systems, the state space representation becomes a very handy tool to find a compact representation of the shared dynamics. Again, this is very handy if you know at least a little bit about your system. In complete blackbox identification this might not matter.
  • The positive thing about ARMAX etc is that these algorithm are widely known and often implementations are available with the standard software, such as MATLAB. This is not the case for many state space identification algorithms.

To sum up, my advice for you is to go with the state space models. However, you should be aware that several control techniques easily applied for transfer function SISO designs can become quite tricky in case of the general state space formulation (e.g. adding an integral controller behaviour or analyze control design robustness). This is why so many industrial applications still stick to transfer function and PID approaches instead of state space and more advanced designs.

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