id	summary	reporter	owner	description	type	status	priority	milestone	component	version	resolution	keywords	cc
4289	In OMPython the linearization doesn't result correct results	arunkumar palanisamy	arunkumar palanisamy	"Below, I summarize the linearization results for a standard reactor model from the literature. The model has 4 inputs, one output and 2 states. The order of the inputs, outputs and states have been read from the resulting file of the OM linearization routine.

The “theoretical calculation” result is the correct result. This result has been found by analytic computation of the Jacobians using Waterloo Maple (similar to Mathematica), and by subsequent insertion of values for the operating point of the system. I have also computed the Jacobians *numerically* using MATLAB, and the result is identical to the “exact” result. So there can be no doubt that the “theoretical” result is the correct result.

A comment on the theoretical result: the A matrix contains one positive and one negative eigenvalue. The positive eigenvalue indicates that the system in fact is unstable at the operating point. (Something similar would be found for an inverted pendulum…) However, I have used very accurate values for the initial states, and in my simulations using OM, there is no problem in simulating the system for 10 minutes with no observed drift in the operating point.

The A and B matrices found using linearization in OM are very different from the exact values. The C and D matrices are correct, though.

Result from OM Linearization:

  A= [-2.092050209205021,5.653416094580654e-077;
      -6.134270952087974e-075,-2.702332893209552e-077];

  B= [2.092050209205021,0,-0.4346639552067547,0;
      0,0,-0.4901435697186606,0];

  C= [0,0.01];

  D= [0,0,0,0];

Results from Handmade calculation and from matlab

   A =[4.3796 ,2.0921;
      -3.5715 ,-2.0000]

   B = [2.0921 ,1.0000 , 0, 0;
         0     ,0     ,0.5000,  100.0000]

   C= [0,0.01];

   D= [0,0,0,0];

"	defect	closed	high	Future	OMPython		fixed		Bernt.Lie@…