Tutorial: Co-Simulation with MotionSolve

With MotionView software, create the geometry for the inverted pendulum.

1. Launch MotionView and create a new model.
2. Add three points of geometry to the model with the following names and locations:

   Point	X	Y	Z
   PivotCenter	300	0	0
   PendulumCenter	350	0	300
   Z-Direction	400	0	600

3. Save your model as Inverted_Pendulum.mdl.

Add the pendulum and cart to your model.

1. Insert a body entity and label it Cart.
2. For the Cart, set the CM Coordinates to the point PivotCenter.
3. Insert a second body entity and label it Pendulum.
4. For the Pendulum, set the CM Coordinates to the point PendulumCenter, and the Z-axis to the direction of point ZDirection.
5. Enter the following inertial properties for the bodies:

   Body	ID	Mass (kg)	Ixx(kg-mm^2)	Iyy(kg-mm^2)	Izz(kg-mm^2)
   Cart	b_0	0.45	100	100	100
   Pendulum	b_1	0.2	32	32	32

Add a revolute and translational joint to the model.

1. Insert a revolute joint, label it PendulumPivot, and set the Connectivity parameters as follows:

   

2. Set the Initial Conditions as follows:

   

3. Insert a translational joint, label it CartTranslation, and set the Connectivity parameters as follows:

   

4. Set the Initial Conditions as follows:

   

Graphics are essential for understanding the model behavior in an animation.

1. Insert a cylinder graphic and label it Rail.
2. For the Connectivity parameters, set the parent body to Ground Body; origin to Global Origin; and direction to vector Global X.
3. Set the Properties as follows:

   

4. Insert a sphere graphic, and label it Pendulum.
5. For Connectivity parameters, set the parent body to Pendulum, and set the origin to PendulumCenter.
6. For Properties, set the radius to 20.
7. Insert a cylinder graphic, and label it Rod.
8. For Connectivity parameters, set the parent body to Pendulum; set the origin to PendulumCenter; set the direction to the point PivotCenter.
9. Set the Properties as follows:

   

10. Insert a box graphic, and label it Cart.
11. For Connectivity parameters, set the Type to Center; set the Parent Body to Cart; set the Origin Point to PivotCenter; set the Z axis direction to Vector Global Z; set the ZX plane direction to Vector Global X.

    

12. Set the Properties as follows:

    

Apply translational forces to the Cart.

1. On the Connectivity tab, add the force, frc_0, label it Control Force, and set the Connectivity properties as follows:

   

2. On the Connectivity tab, add a second force, frc_1, label it PivotTorque, and set the Connectivity properties as follows:

   

3. Select File > Save As Model, and save your model with the name: Inverted_Pendulum_Tutorial.mdl.

1. Create two solver variables: ControlForce (varname: sv_0) and PivotTorque (varname: sv_1) as follows:

   

   

2. Connect the two solver variables to the forces you created in the previous section, Adding Forces.
   As you see in the following figure, on the Trans Properties tab for ControlForce, for Fx, select Expression, and for f, enter: `VARVAL({sv_0.id})`. This expression specifies the ControlForce to be the first solver variable, sv_0. This variable sets the control signal sent from Activate to be the control force acting on the translational joint of the Cart.

   

3. Verify that the varnames match (sv_0): From the Expression Builder, select the solver variable by name and enter its ID as you see in the following figure:

   

4. On the Rot Properties tab for PivotTorque, for Ty, select Expression, and then for f, enter:`VARVAL({sv_1.id})`. This expression sets the PivotTorque as the second solver variable, sv_1, which specifies the control signal sent from Activate as the torque acting on the rotation of the pendulum.

   

5. Insert three additional solver variables: AngularDeviation, AngularRate and CartPosition.
6. For AngularDeviation, enter sv_2. For Type, select Expression, and enter: `RTOD(AY({b_1.cm.idstring}))`, where b1 is the ID of the Pendulum body. Note that the AY function returns the Angle about the Y axis of the marker specified as the argument. The units of the angle are in radians, therefore, apply the RTOD function to convert Radians TO Degrees.
7. For Angular Rate, enter sv_3. For Type, select Expression, and enter:`RTOD(WY({b_1.cm.idstring}))`, where b2 is the ID of the Pendulum body.
8. For Car Position, enter, sv_4. For Type, select Expression, and enter: `DX({b_0.cm.idstring})-300`, where b1 is the ID of the cart body.
9. Insert two solver arrays. Label them ControlInput and PlantOutput.

   

10. The ControlInput solver array includes both the PivotTorque and ControlForce solver variables. Set the properties as follows:

    

11. The PlantOutput solver array includes the following solver variables: AngularDeviation, AngularRate and CartPosition. Set the Plant Output properties as follows:
    
12. To help you select the proper solver variable names, click and a panel appears:

    

13. Save your model as Inverted_Pendulum_Tutorial.mdl.

Simulate the MBS model in MotionSolve and validate that it performs as required.

1. From the Run panel, select: Save and run current model.
2. Select the folder icon, and enter a path and name for saving the MotionSolve model (XML file). The name is your choice, but a good practice is to use the same root name as your MotionView model. The solver run requires the XML file. When entering the path, note that the default directory of the tutorial may not be writable, and you may need to specify a different directory or change the write permissions on the directory.
3. From the Run panel, save your model as an XML file. This file is used for the solver run as well as the Activate model. Alternatively, you can run the MotionView .mdl file, and name it Inverted_Pendulum_Tutorial.xml.

   

4. Animate the results from the simulation and confirm that the model works as intended before continuing to the next steps. The controller is not yet connected to the model, therefore the input force and torque are zero.

   

1. On the ribbon, select File > New.
2. From the Palette Browser, select Activate > CoSimulation, then drag and drop one MotionSolve block into the current diagram.
3. In the diagram, on the MotionSolve block, double-click. From the dialog that appears, define the following block properties:

   For this property	Do this
   XML or MDL input file name	Copy and paste the path to your MotionView .mdl model or MotionSolve .xml file.
   Output MRF file name	Enter a path to an output multi-body results file.
   Direct feedthrough	Clear the check box for this option. Direct feedthrough defines if the outputs of a block are directly affected by the inputs. An example is a gain block where y = K*u, which causes algebraic loops. If this result is not desired, clear the check box to break the loops.

   Note: The following parameters are populated automatically after you load the input model, *.mdl or *.xml:

   This parameter	Is defined with this value
   Input Row Size	The value 2 indicates that two signals from the Activate model are supplied to the MotionSolve model. These signals correspond to the solver array PlantInput, with variables PivotTorque and ControlForce.
   Output Row Size	The value 3 indicates that the MotionSolve model sends out three signals from one port, which is why the Demux block is added to separate the signals. The signals correspond to the solver array ControlOutput with variables AngularRate, AngularDeviation and CartPosition.

4. In the Palette Browser from Activate > MathOperations, drag and drop one Sum block into the diagram.
5. In the Palette Browser, from Activate > Routing, drag and drop one Demux and one Mux block into the diagram.
6. On the DeMux block, double-click, and in the block dialog, for Number of outputs, enter 3.
7. Do one of the following:
   • Create a super block that includes a function to limit an angle between -180º and 180º. An example is shown below.

     

   • Alternately, add an OmlCustomBlock. In the block dialog box, select the SimFunction tab, and enter the following function in Function Code:

     
     function OmlBlockFunction(block,flag)
      angle=vssGetInPortData(block,1);
      if flag==vssBlockOutputUpdateFlag
        x= mod(angle(1),360);
        if(x>180)
          x=-360+x;
        end
        vssSetOutPortData(block,1,x,vssGetOutputDataType(block,1));
       end
     end

8. In the Palette Browser, from Activate > SignalViewers, drag and drop three Scope blocks into the diagram.
   The Scope blocks correspond to the responses of AngularDeviation, AngularRate and CartPosition. Define the scope block parameters for axis and curve properties for these responses.
9. In the Palette Browser, from Activate > Dynamical, drag and drop two PID blocks into the diagram.
10. Select the first PID block. From the Property Editor, select General > Name, and enter the name PID1_AngularDeviation.
11. Select the second PID block. From the Property Editor, select General > Name, and enter the name: PID2_CartPosition
12. On the block, PID1_AngularDeviation, double-click, and enter these values for the parameters:

    

    Note:

    • Proportional Gain multiplies the error signal by a constant gain Kp.
    • Integral Gain multiplies the sum history of error with integral gain Ki.
    • Derivative Gain multiplies the rate of change of error with gain Kd.
13. On the block, PID2_CartPosition, double-click. In the dialog, define the parameters:

    

14. In the Palette Browser, from Activate > SignalGenerators, drag and drop one Constant block into the diagram.
15. On the Constant block, double-click. In the dialog, for Constant, enter 0.
16. Select the Constant block, and copy and paste it into your diagram so that you have a duplicate.
17. All of the required blocks are now present. Assemble and link the blocks in the diagram as follows:

    

18. Experiment with the diagram and try to modify the PID gain parameters to see their effect on the simulation.