How to simplify this function?

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Shilp Dixit
Shilp Dixit 2013-1-18
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
  2 个评论
Walter Roberson
Walter Roberson 2013-1-18
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
Shilp Dixit 2013-1-18
Sorry about the confusion. I want multiplication everywhere.

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回答（2 个）

Thorsten
Thorsten 2013-1-18
编辑：Thorsten 2013-1-18
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);
  1 个评论
Shilp Dixit
Shilp Dixit 2013-1-18
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

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Thorsten
Thorsten 2013-1-18
Hi Shilp, please try to ask a more detailed, more Matlab specific question, may be then I could provide some help.
  1 个评论
Shilp Dixit
Shilp Dixit 2013-1-18
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

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