Linearization Tool

[htessaro]

Dear Dr Cui,

First, congratulation on the amazing work with ANDES.

I am wondering if ANDES offers the possibility of linearization of the used system. Is it possible to obtain a linearized system for a particular operation point after the definition of the system? Thanks.

Best regards
Heitor José Tessaro

[cuihantao]

Hi Heitor, Thank you. The eigenvalue analysis routine does the Linearization. You can call system.EIG.run() at any point after initializing the dynamics. If you want to linearization the system following a disturbance, set the tome domain simulation end time to the desired time, simulate it, and run system.EIG.run(). Regards, Hantao Cui

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On Jun 24, 2021, 8:21 AM -0400, heitortessaro ***@***.***>, wrote: Dear Dr Cui, First, congratulation on the amazing work with ANDES. I am wondering if ANDES offers the possibility of linearization of the used system. Is it possible to obtain a linearized system for a particular operation point after the definition of the system? Thanks. Best regards Heitor José Tessaro — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub, or unsubscribe.

[htessaro]

Thank you Dr Cui,

With the system.EIG.run() function, I would obtain the system eigenvalues. However, is it possible to get the state-space matrices from the linearized system?

My objective is to design a centralized controller. The design method requires the state-space matrices from the linearized system. For this reason, I ask the question above.

Best regards,
Heitor

[cuihantao]

@heitortessaro , sorry for the late response.

ANDES generates the state matrix A from the linearized system. You should be able to manually generate the B matrix by taking the derivative of your input w.r.t. the states and place the derivatives at the corresponding indices.

ss.EIG.run() # run the eigenvalue analysis routine
As = ss.EIG.As  # As is the state matrix A
names = ss.EIG.x_name  # the corresponding variable names 

Note that the variable names in ss.EIG.x_name is not always the same as ss.dae.x_name. A state variable will be moved to the end if it causes numerical singularity (associated with zero time constants, just like an algebraic variable). For details, see the code in eig.py.