Relation Between States and Outputs

Dear Jason,

I want to implment a LQR controller to minimize the load of wind turbine.

Questions:

To design a LQR the states of the system are needed and in this case, the outputs of the system are not the states. How can I obtain the states of the system from outputs? Moreover, I would also like to know what is the relationship between the states i.e. how do the states depend on each other?

Best Regards
SS

Dear Syed,

I agree that states and outputs are different things. But I don’t understand what you are asking–what model are you using that you need to understand the states?

Best regards,

Dear Jason,

Sorry I didn’t explained well the problem in the previous post.

Background:

I want to implment a LQR controller to minimize the load of wind turbine. For that purpose I did linearization for my system at 18m/s steady wind and then I have created MBC_A,MBC_B,MBC_C,MBC_D matrices through running getmats__f8 and mbc3 commands. I took the avg of above mentioned matrices through “MBC_Avg(B,C,D) = mean(MBC_(B,C,D), 3)” commands respectivly.

Problem:

Now to design a LQR the states of the system are needed explicitly or to understand them is important.

Relevent Information:

After linearization my I have 18 states due the following DOFs.

DOFs

True FlapDOF1 - First flapwise blade mode DOF (flag)
False FlapDOF2 - Second flapwise blade mode DOF (flag)
True EdgeDOF - First edgewise blade mode DOF (flag)
True GenDOF - Generator DOF (flag)
True TwFADOF1 - First fore-aft tower bending-mode DOF (flag)
True TwSSDOF1 - First side-to-side tower bending-mode DOF (flag)

The outputs I want to control are as follows respectively.

Outputs

“BldPitch1”
“BldPitch2”
“BldPitch3”
“Azimuth”
“YawBrTAxp”
“YawBrTAyp”
“RootMyb1”
“RootMyb2”
“RootMyb3”

Questions:

How can I obtain the states of the system from outputs? Moreover, I would also like to know what is the relationship between the states i.e. how do the states depend on each other? because nonlinear system gives only the outputs not the states and eventually i have to implement the controller to nonlinear system.

Note: I know that from total 18 states, state number 10 to 18 are the derivative of the 1st 9 states. But the question is how the 1st 9 states depend on each other? Any equation to obtain them form outputs or from each other will be helpful.

Best Regards
SS

Dear Syed,

States 1-9 (the 9 degrees of freedom (DOFs)) are independently needed to quantify the displaced configuration of the wind turbine. States 10-18 are the velocities i.e. the first time-derivatives of these DOFs. The states are interrelated through the second-time derivatives of the DOFs i.e. the accelerations through the system equations of motion i.e. the generalized system mass, damping, and stiffness matrices of the linearized model.

The linearized states are known through the solution of the linearized equations of motion. Alternatively, you could use a state estimator to approximate the states from the system outputs.

I hope that helps.

Best regards,

Dear Jason,
Thank you for your help and clearing my doubts.

I have noticed that In the OutListParameters file (in the ElastoDyn sheet) there are variables that relate exactly to the states.

But the problem is that when in simulink i try to extract that specific state from output it gives the following error:
“The expression: u(strmatch(‘Q_TFA1’, OutList)) has a syntax error”
can you help how to get rid of this error?

Best regards
SS

Dear Syed,

Is ‘Q_TFA1’ and the like included in your OutList?

Best regards,

Dear Jason,

I was doing this naive mistake.

Thank you for your real quick response.

Best regards
SS