Gravitation | Programme permettant de visualiser l'interaction

I need to perform a ZOH discretization of a continuous LTI state-space model in OpenModelica (OMEdit). I tried two ways of doing this:

1. using matrix exponential (Matrices.exp function) for calculating discretized A matrix (A_d) and subsequent calculation of discretized B matrix (B_d) following equation: B_d = A^-1 (A_d - I) B, where I is identity matrix; This algebraic equation can be solved either by direct calculation of matrix inversion (Matrices.inv function) or, more efficiently, by solving for B_d matrix using Matrices.solve2 function: Bd = Matrices.solve2(A,(Ad-identity(2))), thus avoiding calculation of matrix inversion. However, in both cases A matrix must be invertible, what generally (and very often) doesn't hold.
2. using Matrices.integralExp function which should return both discretized matrices (A_d, B_d) and should work for general matrix A, whether invertible or singular; However, this function does not work for me - it returns error message: "No viable alternative near token: (".

I attach code for both methods for demonstration purpose. The state space model represents a very simple second-order system of linearized pendulum with length 1 m, mass 1 kg and gravitational acceleration 9.81 m/s². Sampling time for discretization is 0.1 s. The first code works fine (A is invertible in this particular case) but the second code doesn't. Does anybody know what am I doing wrong? I'd be grateful for any advice.

method #1:

this is my first post! With that in mind, if I need to add anything more than what is below, please let me know. Thank you!

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Codes are:

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Here is the code that was given to me:

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