Linearizing y''(t) + y'(t) + y(t) = u²(t) - 1 about y=0, u=1

[ktoobi]

urgent help for Linearization

Dear All,

y" (t)+ y'(t)+y(t)=u²(t)-1

Linearize the system about y(t)=0, u(t)=1, for all t>= 0

can we say that this equation is already linear at the given point

which will be y" (t)+ y'(t)+0=1-1 => y" (t) + y'(t)= 0

and no need for linearization.

 

[trambolin]

No. What you do is only valid for that point (0,1). You need to have a linear system around this point mimicking almost the nonlinear system in a neighborhood hence your input function must be linearized.

 

[ktoobi]

thank you a lot, so how to start solving this system?

do i have to get the state-space representation of this system first? or what?

 

[trambolin]

State representation is also helpful but, you can walk away with just linearizing the input function.

http://en.wikipedia.org/wiki/Linear_approximation

 

[ktoobi]

any hint on that?

 

[trambolin]

$f(x) = x^2$ is your function to be linearized.

 

[ktoobi]

Thank you a lot