I'm doing some prework for a control design of a system, and have started using SymPy. In my previous job I used MATLAB. In my system I have a matrix A, with these parameters: s= symbols('s') V = 20000 #[m^3 volume in tank] K_qo = 20000/(35*60) C = np.pi * 20.25**2 a0 = K_qo/(0.06*C) a1 = K_qo/V T = 0.02 A = Matrix([[-a0, 0, 0,0,0], [0, -a1, 1,1,1], [0, 0, -1/T ,0, 0], [0, 0, 0, -1/T, 0], [0, 0, 0, 0, -1/T] ]) I want to calculate the state transition matrix $ \phi $ To find this matrix I have to do this matrix manipulation: $ \phi = [sI-A]^{-1} $ When i use the method='LA' i get the expected expression (second order). But if I use other methods, or the default method I get a higher order expression (fifth order) when my coefficient has a lot of decimals (I think). ie.: G=C*((s*eye(5)-A).inv(method='LU'))*B gives my expected result but G=C*((s*eye(5)-A).inv())*B gives a total different answer. Could any of you help me understand why this is happening? I want to try to avoid this in the future. This system was pretty simple, so I could kind of tell something was off. But in larger more complex systems I would not necessarily catch this. Continue reading...
