How to solve State space equation with disturbance matrix

Question

Shilp Dixit 2013-1-8

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回答： maddikayala venkateswarlu 2017-4-5

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

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Answer 1

Azzi Abdelmalek 2013-1-8

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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.

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Shilp Dixit 2013-1-9

编辑：Shilp Dixit 2013-1-9

Hi.

I am posting links for the document and code so far. I have just written a random function for U and fs but my actual aim is to replace fs with the control law.

The document will explain my thought process

Document < https://www.dropbox.com/s/70tmggzo7hz85uu/Quarter%20Car%20Model%20with%20SMC_v1.0.docx https://www.dropbox.com/s/70tmggzo7hz85uu/Quarter%20Car%20Model%20with%20SMC_v1.0.docx>

Basic Code http://pastebin.com/j5XudXTa

extra functions

http://pastebin.com/F1EmZ3En

http://pastebin.com/MEhaxdUh

Thanks.

Shilp Dixit 2013-1-11

hi,

any further help based on the documents and function snippets?

Thanks in advance.

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Answer 2

Phani kumar KSV 2014-10-24

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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.

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Answer 3

maddikayala venkateswarlu 2017-4-5

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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)..?