LTI state-space model discretization using Modelica integralExp function not working

Question

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:

model ssDiscretization
  import Modelica.Math.Matrices;
  // Continuous LTI state-space model of pendulum: L=1, m=1, g=9.81
  Real A[2,2] = [0, 1; -9.81, 0] "system matrix";
  Real B[2,1] = [0; 1] "input matrix";
  // Discretization with sampling time 0.1 s
  Real Ad[2,2] = Matrices.exp(A,0.1) "T = 0.1 s";
  Real Bd[2,1] = Matrices.inv(A)*(Ad - identity(2))*B;
end ssDiscretization;

method #2:

model ssDiscretization
  import Modelica.Math.Matrices;
  // Continuous LTI state-space model of pendulum: L=1, m=1, g=9.81
  Real A[2,2] = [0, 1; -9.81, 0] "system matrix";
  Real B[2,1] = [0; 1] "input matrix";
  // Discretization with sampling time 0.1 s
  Real Ad[2,2];
  Real Bd[2,1];
  (Ad,Bd) = Matrices.integralExp(A,B,0.1) "T = 0.1 s";
end ssDiscretization;

Oliver

Answer 1

You forgot the equation keyword in example 2. It still won't work in OpenModelica since it seems to have a problem with the alias na=size(A,1) in that function but you could easily fix the source code to make that work.

model ssDiscretization
  import Modelica.Math.Matrices;
  // Continuous LTI state-space model of pendulum: L=1, m=1, g=9.81
  Real A[2,2] = [0, 1; -9.81, 0] "system matrix";
  Real B[2,1] = [0; 1] "input matrix";
  // Discretization with sampling time 0.1 s
  Real Ad[2,2];
  Real Bd[2,1];
equation // This was missing
  (Ad,Bd) = Matrices.integralExp(A,B,0.1) "T = 0.1 s";
end ssDiscretization;