Steady-State Simulation with Projection-Based Trim Optimizer
This example shows how to find a steady-state operating point for a Simscape™ Multibody™ model using findop with a projection-based optimizer. Results are verified using simulation.
Open Model
Open the Simulink model.
mdl = 'scdbackhoeTRIM';
open_system(mdl)
Define Operating Point Specifications
Before creating an operating point specification, configure the model to use the model initial condition.
set_param(mdl,'LoadExternalInput','off') set_param(mdl,'LoadInitialState','off')
Create a default operating point specification object.
ops = operspec(mdl);
Impose constraints on the outputs.
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
Configure Trim Options
Configure trim optimizer options. Set the 'OptimizerType' option to 'graddescent-proj', which is a projection-based trim optimizer that enforces consistency of the model physical states. To display trim progress, set the 'DisplayReport' option to 'iter'.
opt = findopOptions('OptimizerType','graddescent-proj',... 'DisplayReport','iter'); opt.OptimizationOptions.MaxFunEvals = 20000;
Trim Model
Find the steady-state operating point that meets these specifications. The following command takes a few minutes.
[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.
Simulate Model
Simulate the model from the computed steady state.
set_param(mdl, 'LoadExternalInput','on') set_param(mdl, 'ExternalInput','getinputstruct(op)') set_param(mdl, 'LoadInitialState','on') set_param(mdl, 'InitialState','getstatestruct(op)') sim(mdl)
Open scope to inspect results.
open_system([mdl, '/Joint Angle Trajectories'])
The simulation results show that the five angles are trimmed to their expected values, however the trajectory deviates slightly over time due to numerical noise and instability. You can stabilize the angles using feedback controllers.
bdclose(mdl)