Transfer function of the state space model

[zoom1]

I have a state space model along with an observer and state feedback.

I need to find the transfer function connecting the r (reference) to the y (output)

I have this model on simulink. I know the A,B,C,D matrices. So, I can get the TF for the stateSpace with ss2tf function of matlab. However, I couldn't find a way to obtain the TF of the observer.

Actually I am interested in the poles and zeros of the system. I though if I find the TF, I can get them. But if there is another way around for this, I would also welcome this method.

Thanks

 

[donpacino]

ok, so first what is the equation for a state observer?

 

[zoom1]

ok, so first what is the equation for a state observer?

x_head' = (A-LC)x_head + Bu + Ly

Where x_head is the estimated state array

 

[donpacino]

right...

So use that equation to get the transfer function.

so your A,B,C,D matrixs are the same in the observer as they are in the regular model (at least typically they are)
You should have chosen your L matrix (measurement vs model accuracy).

remember the observer is a MIMO system (multi input multi output)
so to find y/r there is no one simple command, you will have to be smart about how you use matlabas for any easy of finding the poles i'll give you this hint...in the regular state space model X'=AX+Bu
with direct state feedback, the new model is

X'=AX+B(u-KX)

X'=(A-BK)X+Bu

The old poles of the system were the eigenvalues of A. The new poles are the eigenvalues of A-BK
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knowing that, is there an easy way to find the poles of the observer

 

[alphy]

for your question. I understand the importance of finding the transfer function of a state space model and how it can provide valuable insights into the behavior of a system. In your case, you have a state space model with an observer and state feedback and you are looking to find the transfer function connecting the reference (r) to the output (y).

One way to obtain the transfer function for the observer is to first convert the state space model into a transfer function using the ss2tf function in Matlab. This will give you the transfer function from the reference (r) to the state variables (x). Then, you can use the state feedback gain matrix to obtain the transfer function from the state variables (x) to the output (y). Finally, you can combine these two transfer functions to get the overall transfer function from the reference (r) to the output (y).

Another method is to use the observer canonical form of the state space model, which is a special form that allows for easy calculation of the observer transfer function. This form can be obtained by rearranging the A, B, C, and D matrices of the state space model. Once you have the observer canonical form, you can use it to directly calculate the transfer function of the observer.

Additionally, if you are interested in the poles and zeros of the system, you can use the pole-zero cancellation method to find them. This involves finding the common factors in the transfer function and eliminating them to obtain the poles and zeros. Alternatively, you can also use the eigenvalues of the A matrix in the state space model to determine the poles of the system.

I hope this helps you in finding the transfer function and understanding the behavior of your system. Best of luck with your research!