变量的相互依赖性终止了Dymola模拟，并产生了非线性方程组

Question

我正在开发一个模型来描述双管网络的行为。该网络连接到一个水箱，根据外部质量流速从该水箱中注入或提取热量。任意假设加热和冷却的质量流速随时间变化。CCD_ 1的初始值与参数CCD_ 2相关联。然而，在不同的时间点，PipeTemp是根据最大函数来计算的。

问题是，由于变量PipeTemp依赖于使用PipeTemp值计算的其他时变变量，Dymola终止了模拟并产生以下错误：无法使用牛顿求解器求解非线性系统。

这个简单的模型可以很容易地在Excel中模拟，因为它能够处理单元格变量之间的相互依赖性。在Dymola中，为了避免非线性方程组，这个模型的变通方法是什么？

model FullyMixedTemperature
parameter Real StartTemp = 20;      //Assumed mixed temperature in the pipes
parameter Real dTpipe = 10;        //Temperature difference between the two pipes
parameter Real TankVol = 150;      //Total volume
Real DecreasingTemp;               //Mixed temperature in the pipe due to additional cooling mass flow rate
Real IncreasingTemp;               //Mixed temperature in the pipe due to additional heating mass flow rate
Real PipeTemp(start=StartTemp);    //Mixed temperature in the pipe
Real CoolFlowRate;                 //Additional cooling flow rate from external sources
Real HeatFlowRate;                 //Additional heating flow rate from external sources
equation 
CoolFlowRate=0.5*time;
HeatFlowRate=2*time;
PipeTemp = max(DecreasingTemp, IncreasingTemp);
DecreasingTemp= PipeTemp-(dTpipe*CoolFlowRate/TankVol);
IncreasingTemp= PipeTemp+(dTpipe*HeatFlowRate/TankVol);
end FullyMixedTemperature;

Answer 1

编写的模型没有意义。

由于dTPipe、HeatFlowRate、CoolFlowRate和TankVol都是非负PipeTemp0大于DecreasingTemp，因此方程折叠为：

PipeTemp=PipeTemp+dTPipe*HeatFlowRate/TankVol;

并且你不能从中计算CCD_ 12。

最接近的变体是，在每个采样点，我们计算一个新的PipeTemp，这将是：

model FullyMixedTemperature
parameter Real StartTemp = 20;      //Assumed mixed temperature in the pipes
parameter Real dTpipe = 10;        //Temperature difference between the two pipes
parameter Real TankVol = 150;      //Total volume
Real DecreasingTemp;               //Mixed temperature in the pipe due to additional cooling mass flow rate
Real IncreasingTemp;               //Mixed temperature in the pipe due to additional heating mass flow rate
Real PipeTemp(start=StartTemp);    //Mixed temperature in the pipe
Real CoolFlowRate;                 //Additional cooling flow rate from external sources
Real HeatFlowRate;                 //Additional heating flow rate from external sources
equation 
CoolFlowRate=0.5*time;
HeatFlowRate=2*time;
when sample(1,1) then
PipeTemp = max(pre(DecreasingTemp), pre(IncreasingTemp));
end when;
DecreasingTemp= PipeTemp-(dTpipe*CoolFlowRate/TankVol);
IncreasingTemp= PipeTemp+(dTpipe*HeatFlowRate/TankVol);
end FullyMixedTemperature;

但在我看来，你更可能想要一个两种流都有贡献的微分方程：

model FullyMixedTemperature
parameter Real StartTemp = 20;      //Assumed mixed temperature in the pipes
parameter Real dTpipe = 10;        //Temperature difference between the two pipes
parameter Real TankVol = 150;      //Total volume
Real PipeTemp(start=StartTemp);    //Mixed temperature in the pipe
Real CoolFlowRate;                 //Additional cooling flow rate from external sources
Real HeatFlowRate;                 //Additional heating flow rate from external sources
equation 
CoolFlowRate=0.5*time;
HeatFlowRate=2*time;
der(PipeTemp) =(dTpipe*HeatFlowRate/TankVol)-(dTpipe*CoolFlowRate/TankVol);
end FullyMixedTemperature;