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pozmogov
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Convert Differential Equations to Spate Space

pozmogov
さんによって質問されました 2019 年 7 月 9 日
最新アクティビティ Star Strider
さんによって コメントされました 2019 年 7 月 10 日
I have a system of differential equations, which I would like to convert to spate-space representation:
s = [x(2);
(x(4)*x(6)*(p.Iyy-p.Izz)-(u(1)+u(2)+u(3)+u(4))*p.IR*x(4)...
+(p.b*p.l*(u(2)^2-u(4)^2)))/p.Ixx;
x(4);
(x(2)*x(6)*(p.Izz-p.Ixx)+(u(1)+u(2)+u(3)+u(4))*p.IR*x(2)...
+(p.b*p.l*(u(3)^2-u(1)^2)))/p.Iyy;
x(6);
(x(4)*x(2)*(p.Ixx-p.Iyy)+(p.d*(u(1)^2+u(3)^2-u(2)^2-u(4)^2)))/p.Izz;
x(8);
((p.b*(u(1)^2+u(2)^2+u(3)^2+u(4)^2))*(sin(x(1))*sin(x(5))...
+cos(x(1))*sin(x(3))*cos(x(5))))/p.mass;
x(10);
((p.b*(u(1)^2+u(2)^2+u(3)^2+u(4)^2))*(cos(x(1))*sin(x(3))*sin(x(5))...
-sin(x(1))*cos(x(5))))/p.mass;
x(12);
((p.b*(u(1)^2+u(2)^2+u(3)^2+u(4)^2))*(cos(x(1))*cos(x(3)))-p.mass*p.g)/p.mass];
The confusing moment for me is that there are multiplication of state variables (e.g. x(4)*x(6)), so I don't know how to write it down in A matrix.
Is it possible to convert such system to state-space? Could you hint the way how it should look like?
Thank you in advance for your answer!

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1 件の回答

Star Strider
回答者: Star Strider
2019 年 7 月 9 日
 採用された回答

In order to convert your equations to a state-space representation, you need to linearise them. This involves taking the Jacobian. I refer you to Linearization of Nonnlinear Systems to guide your efforts. The Symbolic Math Toolbox (that was not available when I encountered this) can likely help you significantly.
There are several other such references that reveal themselves in an Interweb search.

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pozmogov
2019 年 7 月 10 日
Thank you very much for your answer! Really helpful.
Star Strider
2019 年 7 月 10 日
As always, my pleasure!

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