state space model with constant term

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Nikolaj Goodger
Nikolaj Goodger 2013-1-30
评论： Asser Mohamed 2020-4-8
If i linearize a nonlinear system model of the form
dx/dt=f(x,u) so that it can be written in the form
dx/dt=Ax+Bu+constant
What is the best way to handle the constant if I want to create an lqr regulator or an observer? For example the system below?
A=[0 1 0;0 0 1;0 0 0] B=[0;0;1] Constant=[0;1;0]
  2 个评论
Shashank Prasanna
Shashank Prasanna 2013-1-30
This is not technically a state space representation. Could you give some information on what the constant is? is it an initial condition? Or atleast share what the f(x,u) looks like.
Nikolaj Goodger
Nikolaj Goodger 2013-1-30
f(x,u) could be a nonlinear model of the form dx1/dt=x2 dx2/dt=x3^2 dx3/dt=u
If I then want to linearize the system at the point t0_x1,t0_x2,t0_x3 I end up with
dx1/dt=x2
dx2/dt=(x3-t0_x3)*2*t0_x3+t0_x3^2
dx3/dt=u
So then I could write in the form
dx/dt=Ax+Bu+constant where
A=[0 1 0;0 0 2*t0_x3;0 0 0] B=[0;0;1] constant=[0 t0_x3^2-t0_x3 0]
but as Azzi said i can consider the constant as a disturbance.

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采纳的回答

Azzi Abdelmalek
Azzi Abdelmalek 2013-1-30
You can consider a constant as a disturbance signal. You can calculate your lqr regulator without this constant, but you should add to your system an integrator which will eliminate the effect of any disturbance signal. (m integrators for m outputs)
  1 个评论
Nikolaj Goodger
Nikolaj Goodger 2013-1-30
Thankyou. This put me on the right track and I was able to get a solution :-)

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更多回答（1 个）

Hesam Mazaheri
Hesam Mazaheri 2018-5-28
编辑：Hesam Mazaheri 2018-5-28
hello, regarding your answer, how can i model this disturbance as an constant to the system in m-file by defining matrices A,B,C,D as ss, how can I add this constant term. after linearing a nonlinear system, my state space is like this: Xdot=Ax+Bu+G1(Constant term) y=Cx+Du+G2(another constant term)

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