second order to first order
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Hello, I'm trying to convert this system to as described here:
This is my attempt but not sure...any help will be greatly appreciated. Thanks
syms x(t)
eqn = diff(x,2) + diff(x,t)*x == u;
V = odeToVectorField(eqn)
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Sam Chak
2022년 8월 24일
I suspect that your 2nd-order ODE was incorrectly written. Please check. If it is a linear damped spring system, then the equation should be:
and it can be converted to the state-space form as shown below:
omega = 2;
zeta = sqrt(3)/4;
sympref('AbbreviateOutput', false);
syms x(t) y(t) u
eqn = diff(x, 2) + 2*zeta*omega*diff(x) + (omega^2)*x == (omega^2)*u;
[V, S] = odeToVectorField(eqn)
From the result, and , and so, the state-space model can be constructed accordingly:
A = [0 1; -4 -sqrt(3)];
B = [0; 4];
C = [1 0];
D = 0;
sys = ss(A, B, C, D)
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