The inverted pendulum model prerequisites

[AbdulrhmnGhanem]

A note to my future self
What I am doing here is quite against my policy of doing the least necessary amount of quality work, but I am doing it as a partial fulfillment of my Master's degree secondary goal: to be proficient in model, simulation, and control using Julia. Otherwise, I would just use the ABCD matrix of the model and would call it a day.

To follow a TDD approach, I need a verified model of an inverted pendulum to compare the newly created model against it. To do so I need to:

• Run the inverted pendulum from Wolfram System Modeler #12

The WSM model is a Modelica model, which means I need to

• Run the WSM using OMJulia.jl #13

OMJulia relies on Open Modelica, so I have to figure out a way to

• Install Open Modelica in an easily reproducible way #14

Here is a quick summary of the components used in the model

1. Modelica.Icons.Library - This is a built-in icon library.
2. PlanarMechanics.Parts.Body - Represents the mass of the pendulum and the cart in planar mechanics.
3. PlanarMechanics.Parts.Fixed - Represents a fixed point in planar mechanics.
4. PlanarMechanics.Parts.FixedTranslation - Represents the length of the pendulum in planar mechanics.
5. PlanarMechanics.PlanarWorld - Represents the planar world in planar mechanics.
6. PlanarMechanics.Joints.Revolute - Represents a revolute joint in planar mechanics.
7. PlanarMechanics.Joints.Prismatic - Represents a prismatic joint in planar mechanics.
8. Modelica.Mechanics.Rotational.Sensors.AngleSensor - Represents an angle sensor in rotational mechanics.
9. Modelica.Blocks.Math.MatrixGain - Represents a matrix gain block for control.
10. Modelica.Mechanics.Translational.Sensors.PositionSensor - Represents a position sensor in translational mechanics.
11. Modelica.Mechanics.Rotational.Sensors.SpeedSensor - Represents a speed sensor in rotational mechanics.
12. Modelica.Mechanics.Translational.Sensors.SpeedSensor - Represents a speed sensor in translational mechanics.
13. PlanarMechanics.Sources.WorldForce - Represents a world force source in planar mechanics.

Other auxiliary components

15. Modelica.Blocks.Interfaces.RealOutput - Represents real output signals for various components.

16. Real - Represents real numbers for storing values.

17. Modelica.SIunits.Mass - Represents mass values in SI units.

18. Modelica.SIunits.Inertia - Represents inertia values in SI units.

19. Modelica.SIunits.Angle - Represents angle values in SI units.

20. Modelica.SIunits.Length - Represents length values in SI units.

21. Modelica.SIunits.Position - Represents position values in SI units.

22. Modelica.SIunits.Acceleration - Represents acceleration values in SI units.

23. Modelica.SIunits.AngularAcceleration - Represents angular acceleration values in SI units.

The PlanarMechanics.* components are provided via https://github.com/dzimmer/PlanarMechanics which is missing for ModelingToolkitStandardLibarary. So I have to add the following to MTKStdLib

• Add PlanarMechanics/components/Fixed to MTKStdLib #16
• Add PlanarMechanics/components/Body (Mass) to MTKStdLib #15
• Add PlanarMechanics/components/FixedTranaslation to MTKStdLib #17
• Add PlanarMechanics/joints/Revolute to MTKStdLib #18
• Add PlanarMechanics/joints/Prismatic to MTKStdLib #19
• Add PlanarMechanics/sources/force to MTKStdLib #20
• Add Measure demo #27 (as a validation for the component implementation, it isn't related to the pendulum model directly.)

Here is a PR that added the Mechnaical.Transitional module for inspiration and pitfalls SciML/ModelingToolkitStandardLibrary.jl#85

only then I can start building the model using ModelingToolkit. oouf 😫

[AbdulrhmnGhanem]

PlanarMechanics_ReferenceResults

[AbdulrhmnGhanem]

Merging SciML/ModelingToolkitStandardLibrary.jl#220 means all the required components are upstream in the ModelingToolkitStandardLibrary.