Please read this two pictures in File, It is in Chinese I took it from a paper but the symbol and expression is worldwide and international. For a system, select sliding mode valuable as S=c1e1+c2e2......en.
What if I want to know the value of S' (dot(s)) ? In this paper, It gives the expression of S'. It derives from the error state space by letting en'=xn'-dot^n(yd)=f(x)+bu-dot^n(yd), But can I get it in an easier way?
Let see, e1=x1-yd| yd is the reference signal and x1 is the output of the system,y=x1. e2=dot(e1),e3=dot(e2)=dot(dot(e1))......So, in this way, we can get the value of S and its higher order time differentiates. I think it may work and the final value we get should be the same numerically.
What's your opioions? Thank you very much!
If you agree with me, I have another doubt.
In the simulink model of that paper, It calculated dot(s) by that expression it gave, Why didn't it use differentiator to get dot(s)? It seems it doesn't want to introduce more differentiators into its system.
Hi Dawn,
I can see where you're coming from. You are trying to generalize that
\dot{en} = \dot{xn} − yd(n) = x1(n) − yd(n) .
However,
\dot{xn} ≠ x1(n) because of
\dot{xn} = ∂(x) + β(x)u + η.
It seems they are writing s_dot in terms of the output and input (in closed loop) of the system. Notice that the first part of s_dot , d(x)+beta(x)*u+eta looks as the plant and the substracting part (including the summation terms) seems to be the output and feedback effects,
OK,Thanks Yew-Chung Chak and Ricardo Zavala-Yoe so much.
from my present opinion, if the model is clear enought, we can use terms of input and output to build dot...e. But if the transfer function contains noise or other unknown disturbance, it stops us. So in this case ,have to use differentiator to get dot...e.
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