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shox2005

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cont...

shox2005 5
July 02 2013
> 

lin_model3 := Linearize(sys3, [u(t)], [phi(t), x(t), y(t), theta(t)], lin_point3)

(18)

The state-space object given by lin_model3[1] can be used to construct a stabilizing controller using linear control theory.

soo it ends here where is the state space matrix A B C D

this is the example in maple 15...

shox2005 5
July 02 2013
> 

with(DynamicSystems)

> 

sys3 := [diff(x(t), t) = y(t), diff(theta(t), t) = phi(t), diff(y(t), t) = -(-3*cos(theta(t))*sin(theta(t))*g-2*u(t)+2*m*L*sin(theta(t))*phi(t)^2)/(-3*cos(theta(t))*m+2*M+2*m), diff(phi(t), t) = -(3*(-sin(theta(t))*g*M-sin(theta(t))*g*m-m*u(t)+m^2*L*sin(theta(t))*phi(t)^2))/((-3*cos(theta(t))*m+2*M+2*m)*m*L)]

sys3 := [diff(x(t), t) = y(t), diff(theta(t), t) = phi(t), diff(y(t), t) = -(-3*cos(theta(t))*sin(theta(t))*g-2*u(t)+2*m*L*sin(theta(t))*phi(t)^2)/(-3*cos(theta(t))*m+2*M+2*m), diff(phi(t), t) = -3*(-sin(theta(t))*g*M-sin(theta(t))*g*m-m*u(t)+m^2*L*sin(theta(t))*phi(t)^2)/((-3*cos(theta(t))*m+2*M+2*m)*m*L)]

 (16)

Linearization point is given by:

> 

lin_point3 := [phi(t) = 0, x(t) = 0, y(t) = 0, theta(t) = 0, u(t) = 0]

lin_point3 := [phi(t) = 0, x(t) = 0, y(t) = 0, theta(t) = 0, u(t) = 0]

 (17)
> 

lin_model3 := Linearize(sys3, [u(t)], [phi(t), x(t), y(t), theta(t)], lin_point3)

(18)

The state-space object given by lin_model3[1] can be used to construct a stabilizing controller using linear control theory.

my question here where is the state spaceee ...?????? the 4 matrix A B C D

this is the equations...

shox2005 5
July 02 2013

New_Microsoft_Office.docx  thns for ur help

thnx for ur answer ....

shox2005 5
July 02 2013

i want to ask 2 question 1st : i ahve maple 15 so i see the examples about linearization thats what i found

> 

with(DynamicSystems)
> 

sys3 := [diff(x(t), t) = y(t), diff(theta(t), t) = phi(t), diff(y(t), t) = -(-3*cos(theta(t))*sin(theta(t))*g-2*u(t)+2*m*L*sin(theta(t))*phi(t)^2)/(-3*cos(theta(t))*m+2*M+2*m), diff(phi(t), t) = -(3*(-sin(theta(t))*g*M-sin(theta(t))*g*m-m*u(t)+m^2*L*sin(theta(t))*phi(t)^2))/((-3*cos(theta(t))*m+2*M+2*m)*m*L)]

sys3 := [diff(x(t), t) = y(t), diff(theta(t), t) = phi(t), diff(y(t), t) = -(-3*cos(theta(t))*sin(theta(t))*g-2*u(t)+2*m*L*sin(theta(t))*phi(t)^2)/(-3*cos(theta(t))*m+2*M+2*m), diff(phi(t), t) = -3*(-sin(theta(t))*g*M-sin(theta(t))*g*m-m*u(t)+m^2*L*sin(theta(t))*phi(t)^2)/((-3*cos(theta(t))*m+2*M+2*m)*m*L)]

 (16)

Linearization point is given by:

> 

lin_point3 := [phi(t) = 0, x(t) = 0, y(t) = 0, theta(t) = 0, u(t) = 0]

lin_point3 := [phi(t) = 0, x(t) = 0, y(t) = 0, theta(t) = 0, u(t) = 0]

 (17)
> 

lin_model3 := Linearize(sys3, [u(t)], [phi(t), x(t), y(t), theta(t)], lin_point3)

(18)

The state-space object given by lin_model3[1] can be used to construct a stabilizing controller using linear control theory.

 

then  i want to get the state space where is it ......... A B C D  how can i get these matrix    in the examples in maple 15 it ends here.

 

 

 

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2nd one was about the quad copter

plz look at this  he get the state space model to equation froem 3.22 to 3.27 3.27New_Microsoft_Office.docxNew_Microsoft_Office.docxNew_Microsoft_Office.docxNew_Microsoft_Office.docx

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