Dear researchers;
I need to build a state space model for a three storey building in Simulink MATLAB: the equation of motion of the building is given by:
Mx'' + Cx' + Kx = Tf - MAx''g
The building is equipped with a damper that produces a force represented by (f).
Dear Mehdi.
The building is also exposed to earthquake x"_g (ground acceleration), I think that the state space of above equation can be written as:
x_1=x; x_2=x_1\prime; x_3=x_2\prime= (1/M) * (Tf - K*x_1 - C*x_2 -MA*x_g\pprime)
in which, x_g\pprime is replaced with the second derivative of ground displacement of an earthquake. It is the input of your system.
Dear Mohammad;
Since the structure is a 3 story building M, C and K are Matrix [M] [C] and [K], T is the distribiton vector of the dampers force and A is a unit vector
how the state space equation will be ?
Dear Mehdi,
If [M], [C] and [K] are Matrix, then x_1, x_2 and x_3 are vector, It is common for multi-input / multi-output systems (MIMO). I suggest you see the example (2.7) of the Chi-Tsong Chen's Book that I attached it.
thank you deat Nikos and Mohammed
i will see and let you know about the results
The state vector should be taken as z=(x1 x1' x2 x2' x3 x3')
Then from the guven eqn u can formulate z'=Az+Bu
where u is the input force
Dear researchers : what is [A] and [B] or how can I write [A] and [B].
Other think while using Simulink state space block, the bloc is juste giving:
X' = Ax + Bu
Y = Cx + Du
but in the attached paper that you will find in this document the state space equation is given like this:
Z'= Az+ Bf + Ex''g
Y = Cz + Df + v
how can I intreduce the E matrix in the simulink state space bloc ? and how can I also intreduce the v ?
best regards
Hi Mahdi,
I am recently studying on the same subject with you. It is hard to visualize and understand all system. Sometimes I have problem with that. Can you please check out word file that attached in the post? I hope this help you.
Best regards,
Osman
Dear Osman
Thanks you for your answer, this questions is a two year old question, nowadays things are very clear for me. However I'm very thankful to you for taking time and writing the explication for me.
Kind regards.
Dear Osman and Mahdi,
I would like to thank you for the discussion you did about the use of state space block in SIMULINK. Now I am facing the same problem as the one of Mahdi. I am solving nonlinear equations for base isolated buildings(by Lead core rubber bearing : LCRB). So, according to the word document that Osman attached, it seems there is no need to use the existing block in SIMULINK. Right?
@Mahdi, if there is another way to use the existing block in SIMULINK, I would love to know it from you. Thanks!!
- Badges
- Science topic