OpenModelica船舶装卸龙门架小车逆模型编译报错求助

背景 #

研究船舶装卸龙门架小车X轴驱动系统：龙门架在码头轨道移动，承载32吨起重机小车，可起吊50吨载荷，仅关注X轴运动。已完成正向模型（输入电机扭矩，输出小车运动），但逆模型（输入小车速度曲线，输出电机转速）编译报错。

正向模型代码 #

model chariot_portique
  constant Real rpm_max = 1450.0;
  constant Real v_max = 3.0;
  
  Modelica.Mechanics.Rotational.Components.IdealGearR2T idealGearR2T(ratio = (rpm_max*2*Modelica.Constants.pi/60)/v_max)  annotation(
    Placement(visible = true, transformation(origin = {28, -36}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.Rotational.Components.LossyGear lossyGear(lossTable = [0, 0.8, 0.8, 0, 0], ratio = 1)  annotation(
    Placement(visible = true, transformation(origin = {-6, -36}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
  Modelica.Mechanics.Translational.Components.Mass mass(m = 82000)  annotation(
    Placement(transformation(origin = {98, -36}, extent = {{-10, -10}, {10, 10}})));
  Modelica.Blocks.Sources.CombiTimeTable combiTimeTable(extrapolation = Modelica.Blocks.Types.Extrapolation.HoldLastPoint, table = [0, 0; 0, 1520; 4, 1520; 4, 0; 8, 0; 8, -974; 12, -974; 12, 0; 16, 0; 16, -1520; 20, -1520; 20, 0; 24, 0; 24, 974; 28, 974; 28, 0; 32, 0], tableOnFile = false) annotation(
    Placement(transformation(origin = {-40, -66}, extent = {{-80, 20}, {-60, 40}})));
  Modelica.Mechanics.Rotational.Sources.Torque torque annotation(
    Placement(transformation(origin = {-74, -36}, extent = {{-10, -10}, {10, 10}})));
  Modelica.Mechanics.Rotational.Sensors.MultiSensor multiSensor_moteur annotation(
    Placement(transformation(origin = {-38, -36}, extent = {{-10, -10}, {10, 10}})));
  Modelica.Mechanics.Translational.Sensors.MultiSensor multiSensor_chariot annotation(
    Placement(transformation(origin = {64, -36}, extent = {{-10, -10}, {10, 10}})));
equation
  connect(lossyGear.flange_b, idealGearR2T.flangeR) annotation(
    Line(points = {{4, -36}, {18, -36}}));
  connect(combiTimeTable.y[1], torque.tau) annotation(
    Line(points = {{-99, -36}, {-86, -36}}, color = {0, 0, 127}));
  connect(torque.flange, multiSensor_moteur.flange_a) annotation(
    Line(points = {{-64, -36}, {-48, -36}}));
  connect(multiSensor_moteur.flange_b, lossyGear.flange_a) annotation(
    Line(points = {{-28, -36}, {-16, -36}}));
  connect(idealGearR2T.flangeT, multiSensor_chariot.flange_a) annotation(
    Line(points = {{38, -36}, {54, -36}}, color = {0, 127, 0}));
  connect(mass.flange_a, multiSensor_chariot.flange_b) annotation(
    Line(points = {{88, -36}, {74, -36}}, color = {0, 127, 0}));
  annotation(
    experiment(StopTime = 32),
    uses(Modelica(version = "4.0.0")),
  Diagram(coordinateSystem(extent = {{-200, -100}, {200, 100}})),
  Icon(coordinateSystem(extent = {{-200, -100}, {200, 100}})),
  version = "",
  __OpenModelica_simulationFlags(lv = "LOG_STDOUT,LOG_ASSERT,LOG_STATS", s = "dassl", variableFilter = ".*"));
end chariot_portique;

逆模型代码 #

model chariot_portique_inverse
  constant Real rpm_max = 1450.0;
  constant Real v_max = 3.0;
  Modelica.Blocks.Sources.CombiTimeTable combiTimeTable( table = [0, 0; 4, 3; 8, 3; 12, 0; 16, 0; 20, -3; 24, -3; 28, 0; 32, 0], tableOnFile = false) annotation(
    Placement(transformation(origin = {92, -66}, extent = {{80, 20}, {60, 40}}, rotation = -0)));
  Modelica.Mechanics.Translational.Sensors.MultiSensor multiSensor_chariot annotation(
    Placement(transformation(origin = {60, -36}, extent = {{-10, -10}, {10, 10}})));
  Modelica.Mechanics.Rotational.Components.IdealGearR2T idealGearR2T(ratio = (rpm_max*2*Modelica.Constants.pi/60)/v_max) annotation(
    Placement(transformation(origin = {28, -36}, extent = {{-10, -10}, {10, 10}})));
  Modelica.Mechanics.Rotational.Components.LossyGear lossyGear(lossTable = [0, 0.8, 0.8, 0, 0], ratio = 1) annotation(
    Placement(transformation(origin = {-6, -36}, extent = {{-10, -10}, {10, 10}})));
  Modelica.Mechanics.Translational.Sources.Speed speed(exact = true)  annotation(
    Placement(transformation(origin = {126, -36}, extent = {{10, -10}, {-10, 10}})));
  Modelica.Mechanics.Rotational.Sensors.MultiSensor multiSensor_moteur annotation(
    Placement(transformation(origin = {-44, -36}, extent = {{-10, -10}, {10, 10}})));
  Modelica.Mechanics.Translational.Components.Mass mass(m = 82000, s(start = 0), v(start = 0), a(start = 0))  annotation(
    Placement(transformation(origin = {90, -36}, extent = {{-10, -10}, {10, 10}})));
equation
  connect(lossyGear.flange_b, idealGearR2T.flangeR) annotation(
    Line(points = {{4, -36}, {18, -36}}));
  connect(multiSensor_moteur.flange_b, lossyGear.flange_a) annotation(
    Line(points = {{-34, -36}, {-16, -36}}));
  connect(idealGearR2T.flangeT, multiSensor_chariot.flange_a) annotation(
    Line(points = {{38, -36}, {50, -36}}, color = {0, 127, 0}));
  connect(combiTimeTable.y[1], speed.v_ref) annotation(
    Line(points = {{152, -36}, {138, -36}}, color = {0, 0, 127}));
  connect(mass.flange_a, multiSensor_chariot.flange_b) annotation(
    Line(points = {{80, -36}, {70, -36}}, color = {0, 127, 0}));
  connect(mass.flange_b, speed.flange) annotation(
    Line(points = {{100, -36}, {116, -36}}, color = {0, 127, 0}));
  annotation(
    experiment(StopTime = 32),
    uses(Modelica(version = "4.0.0")),
    Diagram(coordinateSystem(extent = {{-200, -100}, {200, 100}})),
    Icon(coordinateSystem(extent = {{-200, -100}, {200, 100}})),
    version = "",
  __OpenModelica_simulationFlags(lv = "LOG_STDOUT,LOG_ASSERT,LOG_STATS", s = "dassl", variableFilter = ".*"));
end chariot_portique_inverse;

编译错误信息 #

仿真进程失败，退出代码0xffffffffffffffff。
在时间t=0时求解非线性系统47失败。如需更多信息，请使用-lv LOG_NLS。
仿真因初始化时的断言终止
同伦求解器全主元：初始化时矩阵（接近）奇异。
仍继续执行。如需更多信息，请使用-lv LOG_NLS_V。
欠定线性系统无法求解！
同伦求解器全主元：初始化时矩阵（接近）奇异。
欠定线性系统无法求解！
同伦求解器全主元：初始化时矩阵（接近）奇异。
欠定线性系统无法求解！
非线性系统47求解失败：t=0
为以下部分迭代变量设置合适的初始值可能有所帮助

问题原因 #

1. 系统欠定，约束不足：逆模型仅在平移端添加了Speed驱动源，但旋转端（lossyGear、multiSensor_moteur）处于自由状态，无任何驱动或约束，导致系统存在冗余自由度，求解时矩阵奇异。
2. 初始化缺失：仅给Mass设置了初始值，但旋转侧的角度、转速等变量未设置初始约束，加剧了初始化阶段的求解难度。

解决办法 #

方案1：运动学逆解（推荐，高效无冗余） #

直接通过齿轮运动学比例关系，从小车速度计算电机转速，无需保留动力学组件：

model chariot_portique_inverse_fixed
  constant Real rpm_max = 1450.0;
  constant Real v_max = 3.0;
  constant Real gear_ratio = (rpm_max*2*Modelica.Constants.pi/60)/v_max; // 电机转速与小车速度的比例

  Modelica.Blocks.Sources.CombiTimeTable combiTimeTable( 
    table = [0, 0; 4, 3; 8, 3; 12, 0; 16, 0; 20, -3; 24, -3; 28, 0; 32, 0], 
    tableOnFile = false
  ) annotation(Placement(transformation(origin = {92, -66}, extent = {{80, 20}, {60, 40}})));
  
  Modelica.Mechanics.Translational.Sources.Speed speed(exact = true) annotation(
    Placement(transformation(origin = {126, -36}, extent = {{10, -10}, {-10, 10}})));
  
  Modelica.Mechanics.Translational.Components.Mass mass(m = 82000, s(start = 0), v(start = 0)) annotation(
    Placement(transformation(origin = {90, -36}, extent = {{-10, -10}, {10, 10}})));
  
  // 增益模块实现运动学比例转换
  Modelica.Blocks.Math.Gain gearGain(k = gear_ratio) annotation(
    Placement(transformation(origin = {-20, -36}, extent = {{-10, -10}, {10, 10}})));
  
  // 观测电机转速
  Modelica.Blocks.Sinks.Scope motorSpeedScope annotation(
    Placement(transformation(origin = {-60, -36}, extent = {{-20, -20}, {20, 20}})));
equation
  connect(combiTimeTable.y[1], speed.v_ref) annotation(
    Line(points = {{152, -36}, {138, -36}}, color = {0, 0, 127}));
  connect(mass.flange_b, speed.flange) annotation(
    Line(points = {{100, -36}, {116, -36}}, color = {0, 127, 0}));
  // 从小车实际速度计算电机转速
  connect(speed.v_actual, gearGain.u) annotation(
    Line(points = {{116, -36}, {0, -36}}, color = {0, 0, 127}));
  connect(gearGain.y, motorSpeedScope.u[1]) annotation(
    Line(points = {{-10, -36}, {-40, -36}}, color = {0, 0, 127}));
  annotation(
    experiment(StopTime = 32),
    uses(Modelica(version = "4.0.0")));
end chariot_portique_inverse_fixed;

方案2：保留动力学结构，补充约束与初始值 #

若需保留原动力学组件，需给旋转侧变量添加初始值并闭合约束环：

• 给lossyGear的法兰添加初始角度和转速：lossyGear.flange_a.phi(start=0), lossyGear.flange_a.w(start=0)
• 给multiSensor_moteur的对应变量设置初始值
• 确保旋转端无自由自由度，可添加虚设的转速约束或反馈

关键提示 #

• 若仅需运动学逆解（从轨迹反推电机转速），优先用方案1，避免动力学组件带来的求解复杂度
• 若需动力学逆解（从轨迹反推所需电机扭矩），需确保系统是闭环结构，平移端的约束能传递到旋转端，同时旋转端需有对应的动力学反馈

内容的提问来源于stack exchange，提问作者scls