state space model with constant term

2013 1 30
2 个回答
回答已采纳
更新时间：2020 4 8
9 次查看（30 天）

0 个投票

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
显示 无 隐藏 无

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.

请先登录，再进行评论。

请先登录，再回答此问题。

 采纳的回答

Azzi Abdelmalek
Azzi Abdelmalek 2013-1-30

0 个投票

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
显示 -1更早的评论 隐藏 -1更早的评论

Nikolaj Goodger
Nikolaj Goodger 2013-1-30
Thankyou. This put me on the right track and I was able to get a solution :-)

请先登录，再进行评论。

更多回答（1 个）

Hesam Mazaheri
Hesam Mazaheri 2018-5-28
编辑：Hesam Mazaheri 2018-5-28

0 个投票

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)

类别

在 帮助中心 和 File Exchange 中查找有关 State-Space Control Design and Estimation 的更多信息

产品

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by