[M]x'' + [C]x' + [K]x =[D] F - [M]x"g
Hello Dear resaerchers ;
I'm traying to solve a mouvement equation of MDOF mouvement building, this building is equiped with MR dampers so the mouvement equation is in this way:
what is the best methode i can use to solve this equation in matlab or simulink then to controle the force of the damper with a fuzzy logic algorithme at the same time ?
best regards
Hi Mehdi,
Hope you are well.
The common method that I have always used, is on the basis of the following equation that is a rearrangement of your aforementioned one:
X"=inv(M)*(DF-MX"g-CX'-KX)
in this way, you have to write a function the output of which is X" that would need to be integrated to yield X' and X. After that, these two must be fed back to the function so that it can calculate M (if a function of X), CX' and KX. Evidently, this function has two inputs: DF and X"g. This whole can simulate the motion of your system as it yields the state variables and can get effected by the considered inputs.
Feel free to contact me if any questions remain.
Best,
Hamed
Dear Hamed
What if I can do that using Simulink blocs ? what do you think ? is it possible ?
Dear Mehdi,
If your system is (almost-)continuous and its coefficients are time-invariant, I believe that the best way to do it is to rewrite your equations of motion on a space-state representation of the type
z' = Az + Bu
y = Cz + Du
Using your equation, the matrices A, B, C and D would be:
A = [ -[M-1][C] -[M-1][K]
[E] [0] ]
B = [ [M-1][D] -[E]
[0] [0] ]
C = [E]
D = [0]
where [E] and [0] are, respectivelly, identity and zeros matrices of convenient sizes. The vectors z and u in your case are:
z = [ X'; X]
u = [F; X''g]
Save the matrices above to your workspace and feed them into the Space-State block available in Simulink. You can then use the u vector as an input to such block. The output will be the z vector.
ode45 is a good choice to solve this problems, assuming that your matrices are time-invariant and that F is bounded and sufficiently smooth.
Hope this helps.
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