MATLAB: Tf2ss and ss(sys) gives different results

Control System Toolboxstate-space

This code gives different results. However the tfs are the same. Can anybody exxplain it why?

   [A1,B1,C1,D1]=tf2ss([25.61 6.2],[24.78 29.74 6.202])
    sys=tf([25.61 6.2],[24.78 29.74 6.202]);
    ss(sys)

Best Answer

This is explained in the doc page for ss. Please click here, and scroll down to click on "Algorithms" in the "More About" section.

Arkadiy

Related Solutions

MATLAB: Conversion from State Space to TF and then back to State Space

Some points:

Don't do "algebra" with tf variables, use the functions series, parallel and feedback.

sys_mimo1 = ss(sys_mimo) is going to convert the tf model to a ss model, I don't think there is a need for the extra step with ssdata.

This one here

sys_mimo_tf(1,2) = sys_mimo_tf(1,2)*feedback(sys_mimo_tf(1,2),C);

is probably not doing what you want it to, it will give you the transfer function

sys_mimo_tf(1,2)^2 /  1 + sys_mimo_tf(1,2)*C

so that's probably where many extra states come from. You should expect 2 extra states per added PID.

Lastly, look at the Hankel Singular Values or a similar measure to figure out whether there might be a lot of almost unobservable/almost uncontrollable states in your resulting model. That would indicate numerical issues.

MATLAB: Do state space and its equivalent transfer function models yield different step responses

Hi there,

Examine the state-space model sys_ss:

>> sys_ss

Note that it has a non-unity E matrix. This happens because your H, a pure derivative, is improper. The connect command represents that block as a two-state ss with a non-unity E matrix - a descriptor ss. When connect builds the interconnected system, it preserves those states, so it yields a descriptor system.

And that means that your call to ss2tf, which only uses A,B,C, and D, is missing part of the dynamics of the system. sys_tf doesn't represent the same dynamics as sys_ss.

This is one of the reasons that ss2tf is not a great command to use when converting from ss to tf form. Try this instead:

>> sys_tf = tf(sys_ss)

This time when you plot the step responses, they match up. Also, tf removes those two extra states.

You can also reduce and simplify sys_ss into explicit form (E = 1) using the 'explicit' option of the ss command:

>> sys_ss_ex = ss(sys_ss,'explicit')

Now all of the system dynamics are described by A,B,C, and D.

For more information about explicit and descriptor state-space models, see the reference page for ss.

>> doc ss

Hope this helps!

Best Answer

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MATLAB: Conversion from State Space to TF and then back to State Space

MATLAB: Do state space and its equivalent transfer function models yield different step responses

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