В этом примере показано, как найти установившуюся рабочую точку для модели Simscape™ Multibody™ с помощью findop с основанным на проекции оптимизатором. Результаты проверяются с помощью симуляции.
Откройте модель Simulink.
mdl = 'scdbackhoeTRIM';
open_system(mdl)
Прежде, чем создать спецификацию рабочей точки, сконфигурируйте модель, чтобы использовать начальное условие модели.
set_param(mdl,'LoadExternalInput','off') set_param(mdl,'LoadInitialState','off')
Создайте объект спецификации рабочей точки по умолчанию.
ops = operspec(mdl);
Наложите ограничения на выходные параметры.
ops.Outputs(1).Known = true(10,1); ops.Outputs(1).y(1) = 0; % Bucket angle ops.Outputs(1).y(3) = 50; % Upper angle ops.Outputs(1).y(5) = -50; % Lower angle ops.Outputs(1).y(7) = 0; % Base angle ops.Outputs(1).y(9) = -45; % Support angle
Сконфигурируйте опции оптимизатора для обрезки. Установите 'OptimizerType' опция к 'graddescent-proj', который является основанным на проекции оптимизатором для обрезки, который осуществляет непротиворечивость физических состояний модели. Чтобы отобразить прогресс для обрезки, установите 'DisplayReport' опция к 'iter'.
opt = findopOptions('OptimizerType','graddescent-proj',... 'DisplayReport','iter'); opt.OptimizationOptions.MaxFunEvals = 20000;
Найдите установившуюся рабочую точку, которая соответствует этим спецификациям. Следующая команда занимает несколько минут.
[op,rpt] = findop(mdl,ops,opt);
Optimizing to solve for all desired dx/dt=0, x(k+1)-x(k)=0, and y=ydes. (Maximum Error) Block --------------------------------------------------------- (4.50000e+01) scdbackhoeTRIM/Out1 (3.88972e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Right/Revolute Joint Arm (3.25130e+00) scdbackhoeTRIM/Plant/Backhoe Arm/Arm-Bucket Joint (2.92756e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.90835e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.87033e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.88039e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.75915e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.82770e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.83204e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.77134e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.77170e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.66093e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (1.91196e+00) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (1.48418e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.48194e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.92844e+00) scdbackhoeTRIM/Out1 (1.47015e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.46951e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47048e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47087e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47081e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47072e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47065e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47067e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47062e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47044e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47049e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47044e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47035e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.47009e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.46945e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.46915e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.46650e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.45218e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.43599e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.39092e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.32192e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.32141e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34505e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34732e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34643e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34590e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34577e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34579e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34598e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34609e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34550e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.34208e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.33732e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (1.21415e+00) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (5.03874e-01) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (5.04915e-01) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (3.02028e-01) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (2.00116e-01) scdbackhoeTRIM/Out1 (2.80354e-01) scdbackhoeTRIM/Out1 (8.41676e-02) scdbackhoeTRIM/Plant/Lower Arm to Mounting Assembly (9.96485e-02) scdbackhoeTRIM/Plant/Lower Arm to Mounting Assembly (1.04079e-01) scdbackhoeTRIM/Plant/Lower Arm to Mounting Assembly (9.08181e-02) scdbackhoeTRIM/Out1 (8.72986e-02) scdbackhoeTRIM/Out1 (2.96463e-02) scdbackhoeTRIM/Plant/Backhoe Arm/Upper-Lower Arm Joint (9.04872e-03) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (2.39393e-03) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Right/Revolute Joint Arm (1.28775e-03) scdbackhoeTRIM/Plant/Backhoe Arm/Hydraulic Actuator Lower - Upper Arm/Prismatic Joint (1.61736e-04) scdbackhoeTRIM/Plant/Mounting Assembly/Mounting Base and Support Arms/Support Arm Left/Revolute Joint Arm (1.59106e-04) scdbackhoeTRIM/Plant/Hydraulic Actuator Mounting - Lower Arm/Prismatic Joint (1.70351e-05) scdbackhoeTRIM/Plant/Cylinder Base to Mounting Plate (2.39957e-05) scdbackhoeTRIM/Plant/Hydraulic Actuator Mounting - Lower Arm/Prismatic Joint (1.49012e-05) scdbackhoeTRIM/Plant/Hydraulic Actuator Mounting - Lower Arm/Hydraulic Actuator/Simulink-PS Converter1 (7.45058e-06) scdbackhoeTRIM/Plant/Backhoe Arm/Hydraulic Actuator Lower - Upper Arm/Hydraulic Actuator/Simulink-PS Converter1 (7.45058e-06) scdbackhoeTRIM/Plant/Backhoe Arm/Hydraulic Actuator Lower - Upper Arm/Hydraulic Actuator/Simulink-PS Converter1 Operating point specifications were successfully met.
Симулируйте модель от вычисленного устойчивого состояния.
set_param(mdl, 'LoadExternalInput','on') set_param(mdl, 'ExternalInput','getinputstruct(op)') set_param(mdl, 'LoadInitialState','on') set_param(mdl, 'InitialState','getstatestruct(op)') sim(mdl)
Открытый осциллограф, чтобы смотреть результаты.
open_system([mdl, '/Joint Angle Trajectories'])
Результаты симуляции показывают, что эти пять углов обрезаются к их ожидаемым значениям, однако траектория отклоняется немного в зависимости от времени из-за числового шума и нестабильности. Можно стабилизировать углы с помощью контроллеров обратной связи.
bdclose(mdl)