- #1
Payam30
- 46
- 1
Hi,
I have a 2nd order of sliding mode observer of the form:
[tex] \dot{\hat{x}} = \hat{f}(x,t) + \delta f + \Psi(u,y) +[ \frac{d \Omega}{dx}]^{-1} \upsilon[/tex]
where ##\upsilon##:
[tex] \upsilon_1= \alpha_1 \lambda_1^{1/2} | y_1 -\hat{x}_1|^{1/2}*sign(y_1 -\hat{x}_1)[/tex]
[tex]\upsilon_2= \alpha_2 \lambda_1*sign(\upsilon_1)[/tex]
[tex] \upsilon_3= \alpha_3 \lambda_2^{1/2} | y_2 -\hat{x}_2|^{1/2}*sign(y_2 -\hat{x}_2)[/tex]
[tex]\upsilon_4= \alpha_4 \lambda_2*sign(\upsilon_3)[/tex]
...
where ##y_{1,2}## is the output and and ##x_{1,2}## are the estimations of measurable outputs. How do I find the correct gain of sliding mode observer?
##\delta f## is the uncertainties and ##[ \frac{d \Omega}{dx}]^{-1} ## is some mathematical stuff based on transformations. The main question is how do you find the proper gain of an observer by linearizing a system?
Do I linearize the plant and observer? and then what graphs should I look at to find the appripriate gains?
Thanks in advance
I have a 2nd order of sliding mode observer of the form:
[tex] \dot{\hat{x}} = \hat{f}(x,t) + \delta f + \Psi(u,y) +[ \frac{d \Omega}{dx}]^{-1} \upsilon[/tex]
where ##\upsilon##:
[tex] \upsilon_1= \alpha_1 \lambda_1^{1/2} | y_1 -\hat{x}_1|^{1/2}*sign(y_1 -\hat{x}_1)[/tex]
[tex]\upsilon_2= \alpha_2 \lambda_1*sign(\upsilon_1)[/tex]
[tex] \upsilon_3= \alpha_3 \lambda_2^{1/2} | y_2 -\hat{x}_2|^{1/2}*sign(y_2 -\hat{x}_2)[/tex]
[tex]\upsilon_4= \alpha_4 \lambda_2*sign(\upsilon_3)[/tex]
...
where ##y_{1,2}## is the output and and ##x_{1,2}## are the estimations of measurable outputs. How do I find the correct gain of sliding mode observer?
##\delta f## is the uncertainties and ##[ \frac{d \Omega}{dx}]^{-1} ## is some mathematical stuff based on transformations. The main question is how do you find the proper gain of an observer by linearizing a system?
Do I linearize the plant and observer? and then what graphs should I look at to find the appripriate gains?
Thanks in advance