How to solve State space equation with disturbance matrix
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I have three inputs in my system
Damper force (fs)
Gravitational force (g) (N X 1 matrix)
External disturbance (q) (N X 1 matrix)
u = [q g];
4 states in my system: x1, x2, x3 and x4 (4 X 1 matrix)
3 outputs: y1, y2 and y3. (3 X 1 matrix)
State and output equations are as follows
xdot = A.x + B.fs + E.u
y = C.x + D.fs + F.u
Now, I have obtained the damper force as a function of the system state and it is given below: fs=G[α{(x4/2)*mod(sign(x4)+sign(x4-x2))}+(1-α){(x2/2)*mod(sign(-x2 )+sign(x4-x2))}]
Here: G: is a constant, α: is a constant, sign – Signum function and x: is the state of the system
How do I solve this problem in Matlab and obtain simulation results for it.
Thanks. Shilp
回答（3 个）
Azzi Abdelmalek
2013-1-8
0 个投票
Rewrite your equation as
xdot=A.x+H.u1
with H=[B;E] and u1=[fs;q;g]
and
y=C.x+D1.u1 , with D1=[D;F]
Then use State Space block with parameters A,H,C,D1 with 3 inputs passed throug a MUX block to the SS block.
You will need to extract the values of x1, x2, x3 and x4. I don't know if you know how to do it?
You will also need to calculate fs using blocks, or an interpreted matlab function.
4 个评论
Shilp Dixit
2013-1-8
Azzi Abdelmalek
2013-1-8
Yes, I thought you were using Simulink (easier) , but you can do it with matlab control toolbox.
To get your states xi, tell us what is C? (it will be easy to find xi).
I see that your control law depends only on xi and constants, I guess those constants are solutions of a certain criterium. In your post there is no reference to any Lyapounov function
Shilp Dixit
2013-1-9
编辑：Shilp Dixit
2013-1-9
Shilp Dixit
2013-1-11
Phani kumar KSV
2014-10-24
0 个投票
the ' fs ' equation containing state variables ( x4,x2 ) Its better to combine the terms as
xdot=H.x+B.u1
with H=[A;E] and u1=[q;g]
and
y=C1.x+D.u1 , with C1=[C;F]
then proceed as mentioned by Azzi Abdelmalek above.
maddikayala venkateswarlu
2017-4-5
0 个投票
Hi all, I have A, B,C ,D, Input(u) and output(y) in the state space model. so my question here is is it possible to calculate state vector(x) with the input values. if possible can you please help me to calculate state vectors(x)..?
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2013-1-8
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