Modelica linear analysis

Question

I am new into Modelica/Dymola-modeling. I started to model fluid models for my master-thesis (pipes, heaters, control). My professor suggested: Check the eigenvalues of the systems and the ratio of them (and if the systems is stiff). So did the following:

• Linear analysis
• Full linear analysis
• SimulationSetup: linearizeAtInitial = false; t_linearize = 1000 (that the system is in operation mode (after initialization)

The simulation restuls are Ok.

But the linear analysis says: The system is not stable --> what does that mean?

And regarding eigenvalues i get the following result:

I have to say that I am not really into numerics. So these are my questions:

1. Does that mean that the system has 23 eigenvalues?
2. If I want to specify how "stiff" the system is, I guess i have to check the biggest and smallest value?
3. What are the eigenvalues 12-23 --> not stable, not stabilizable, not detectable?

Any recommendations for a (simple) introduction book/chapter that explains general things like :linearication of Models, eigenvalues, etc.?

Thank you very much for your help.

Answer 1

实部 < 0 的特征值是稳定的；而最小的和最大的之间的比率可以看作是“刚度”。

实部 > 0 的特征值显然是不稳定的。

实部 == 0 的特征值更复杂；它们被写成“不稳定”——但处于稳定和不稳定之间的边界。

由于虚部也为零，因此它们是纯积分器，并且可以看作是积分器的流体罐；这解释了为什么你有这么多的特征值为零。（如果虚部不为零，则它们是无阻尼振荡器。）

因此，我将跳过分析中的零特征值。

“可检测/可控制”是指您的模型具有输出和输入（并且可稳定是它们的组合）的情况。