How to simplify this function?

Hi,

I want to create u as a function of two variables x1 and x2 with the conditions as follows: if true

    U = G(a.s1+(1-a).s2);

    % Here
    % G is a constant
    % a is a constant
    % s1 and s2 are functions of x1 and x2 and are described below

end

if true

    % s1 as func. of x1,x2
    if x1(x1-x2) >= 0
       s1 = x1;
    else
       s1 = 0;

    % s2 as func. of x1, x2
    if -x2(x1-x2) >= 0
       s2 = x2;
    else
       s2 =0;
    end

end

To achieve this is I wrote a modified Signum function(modsign): http://tny.cz/e67c7d01

and use it to define the parameter U as

if true

    U = G(a*x1*modsign(x1(x1-x2),0) + (1-a)*x2*modsign(-x2(x1-x2),0));

end

Please suggest a better and simpler way to do it. Preferably I want U, s1 and s2 as functions of x1 and x2 without using this convoluted way that I have used.

Thanks.

Shilp

[Walter Roberson]

Are you sure that you want to index x1 by the difference between x1 and x2?

x1(x1-x2)

is an indexing operation.

Perhaps you want multiplication in there?

x1 * (x1-x2)

??

[Shilp Dixit]

Sorry about the confusion. I want multiplication everywhere.

Answer 1

[Thorsten]

Note that x times y is coded x*y in Matlab.

I would go straigthforward

function U = myfunction(x1, x2)
G = 1.0; % replace with your constants 
a = 0.5;

if x1*(x1 - x2) >= 0
  s1 = x1;
else
  s1 = 0;
end

if -x2*(x1 - x2) >= 0
  s2 = x2;
else
  s2 =0;
end

U = G*(a*s1 + (1-a)*s2);

[Shilp Dixit]

Hi Thorsten,

Thanks for your answer. Now here lies my problem.

1. U control input for the system.

2. x1 and x2 are states of the system.[x1, x2, x3, x4]

I wanted to create U as a function of x so that could create a lyapunov function to solve my sliding mode control surface. Entire problem is as follows:

1. Problem statement http://sdrv.ms/WMjL9a

2. Codes: http://pastebin.com/q651xg3q

http://pastebin.com/NufKuL22

http://pastebin.com/WWiD9y7r

Perhaps these will explain what I am trying to do better.

Thanks.

Shilp

Answer 2

[Thorsten]

Hi Shilp, please try to ask a more detailed, more Matlab specific question, may be then I could provide some help.

[Shilp Dixit]

Hi,

I would be glad with some help in sliding mode control and its solution via lyapunov function in matlab.

I have a sliding surface as

if true

    % Sliding Surface
    S = C.x
    % C is 1X4 and x is 4X1.
    % Ideally C.x = 0

    % lyapunov function
    V = 0.5*S^2 % 0.5 times S squared

    % differentiating w.r.t x
    V' = S.S'
    % lyapunov function criteria
    S.S' < 0 for all S ~=0

end

How do I find out the coeff of matrix C using this method in MATLAB.

Thanks. Shilp