计算科学 - Modelica“导数”标注问题 - 吾爱随笔录

我有关于使用“衍生”注释的问题，我想问你。让我们放一个样本。

方程是这样的：

z_level = LevelZ(time);

其中 LevelZ(time) 是一个外部 C 函数，还有 LevelZ_der(time) 和 LevelZ_der2(time) 是一阶和二阶导数。

代码是这样的，它运行良好......

function LevelZ_der2 
    input Real t; 
    input Real dt; 
    input Real ddt; 
    output Real res; 
external 
    res = LevelZ_der2(t); 
annotation(Library="...", Include="...");  
end LevelZ_der2; 

function LevelZ_der 
    input Real t 
    input Real dt 
    output Real res; 
external 
    res = LevelZ_der(t); 
annotation(derivative=LevelZ_der2, 
           Library="...", Include="...");  
end LevelZ_der; 

function LevelZ 
    input Real t 
    output Real res; 
external 
    res = LevelZ(t) 
annotation(derivative=LevelZ_der, 
           derivative(order=2)=LevelZ_der2, 
           Library="...", Include="...");  
end LevelZ;

...虽然出现了这些错误：

[C:/Users/Model/Model.mo:52:2-52:28:writable] Warning: Unused input variable dt in function .LevelZ_der2. 
[C:/Users/Model/Model.mo:52:2-52:28:writable] Warning: Unused input variable ddt in function .LevelZ_der2. 
[C:/Users/Model/Model.mo:52:2-52:28:writable] Warning: Unused input variable dt in function .LevelZ_der. 

Error: Derivative of expression 
Differentiate.differentiateExpSolve failed for z_level - LevelZ(time) 
is non-existent.

但是，如果代码是这样的，OpenModelica 模拟会忽略导数...

function LevelZ_der2 
    input Real t; 
    output Real res; 
external 
    res = LevelZ_der2(t); 
annotation(Library="...", Include="...");  
end LevelZ_der2; 

function LevelZ_der 
    input Real t 
    output Real res; 
external 
    res = LevelZ_der(t); 
annotation(derivative(zeroDerivative=t)=LevelZ_der2, 
           Library="...", Include="...");  
end LevelZ_der; 

function LevelZ 
    input Real t 
    output Real res; 
external 
    res = LevelZ(t) 
annotation(derivative(zeroDerivative=t)=LevelZ_der,  
           derivative(order=2)=LevelZ_der2, 
           Library="...", Include="...");  
end LevelZ;

...并出现此错误：

Error: Derivative of expression 
Differentiate.differentiateExpSolve failed for z_level - LevelZ(time) 
is non-existent.

什么是正确的方法，为什么？

最好的问候科尔多