State space to transfer function conversion and vice versa

Hi,

So, I have following piece of code. It simulates a simulink file 'model' (which I cannot provide as an attachment), then creates a state space representation of the model which is saved as variable 'sys_ss_inacc_frommodel'. The problem that I am facing is that when I convert this state space representation to TF representation i.e variable 'systf' and then back to state space i.e variable 'sys_ss_acc', the two State space representations are different.

can someone please clarify what mistake I am making here?

clc

io = getlinio(model);

%% Specify the operating point % Use the model initial condition op = operpoint(model);

%% Linearize the model sys_ss_inacc_frommodel = linearize(model,io,op); sys_ss_inacc_frommodel=minreal(sys_ss_inacc_frommodel) %% Plot the resulting linearization

systf=tf(sys_ss_inacc_frommodel)

%creat ss again from systf beause for some reason ss of sys is different. %discuss with reinhold. sys_ss_acc=ss(systf) sys_ss_acc=minreal(sys_ss_acc)

Answer 1

[Sebastian Castro]

This can happen and is completely expected.

Transfer functions are defined as the relationship between inputs and outputs, whereas state-space models contain two separate relationships: inputs to states and states to outputs.

For this reason, a single transfer function can be expressed as an infinite combination of state-space realizations. While your two state-space models look different, they should contain the same system dynamics.

This is part of the reason why people often convert state-space models into different canonical forms, such as modal, observability, etc. This ensures that you always get the same structure for state-space realizations.

- Sebastian