solving state variable equation in matlab
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hello i am trying this eqution :
dx/dt=A*x+B*u
y=C*x
while A is matrix 4X4,B is matrix 4X1,C is matrix 1X4,and u is constant , how do i find X ? if X should be matrix of 4X1 , and how do i draw graph of x ?
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Answers (4)
M
on 22 Oct 2017
WHat do you want to do exactly ?
If you want to simulate your system with a given input, you can use specific function, such as step, impulse etc...
You can also solve your ODE system with the matlab ode45 solver.
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Star Strider
on 25 Oct 2017
Your integrated differential equation is the matrix exponential, given by the expm function (in both base MATLAB and the Symbolic Math Toolbox).
The integration of your system is:
dx/dt = A*x + B*u % Time-Domain Differential Equation
y = C*x
sX = A*X + B*U % Laplace Transformed System
Y = C*X
sX - A*X = B*U % Rearrange
Y = C*X
(s*I -A)*X = B*U % Combine Terms, ‘I’ Is The Identity (‘eye’) Matrix
Y = C*X
X = inv(s*I - A)*B*U % Solve For ‘X’ (Do Not Use ‘inv’), Illustration Only Here
Y = C*X
Y = C*(inv(s*I - A)*B*U) % Substitute
y(t) = C*expm(A*t)*B*u(t) % Inverse Laplace Transform To Get Solved Differential Equation
This is straightforward to calculate in a loop.
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