How to solve State space equation with disturbance matrix

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

Answer 1

[Azzi Abdelmalek]

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.

[Shilp Dixit]

Hi,

Thanks for your reply.

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. - Is this for MATLAB or Simulink

You will need to extract the values of x1, x2, x3 and x4. I don't know if you know how to do it? - No, i dont know how to do that. That is my prime concern. extract x1 to x4.

You will also need to calculate fs using blocks, or an interpreted matlab function. - Could you please throw some more light on this method

I was trying to solve this using the sliding mode approach and lyapunov function approach but am unable to combine my control law (equation of U) and lyapunov function.

Thanks.

[Azzi Abdelmalek]

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]

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]

hi,

any further help based on the documents and function snippets?

Thanks in advance.

Answer 2

[Phani kumar KSV]

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.

Answer 3

[maddikayala venkateswarlu]

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)..?