1. Scintillas System Dynamics Tutorial
Tim Broenink

2. Planning Introduction Lecture on SysDyn Break Exercises/Practice

3. Introduction Mostly repetition of the Lectures
Extra instructions, extra practice.
Basic Level, Not a substitution for study/official lectures
Promote understanding

4. Student Panel Evaluate understanding Promote questions 3-5 people

5. Calculations and mechanics
Lecture 2
Calculations and mechanics

6. Contents Calculations with bondgraphs, Based in causality Masons rule
Planar Mechanics

7. Calculations with bondgraphs
Why with bondgraphs
Causality
Signal-Flow (Diagrams)
Masons Rule

8. Calculations with bondgraphs
Why with bondgraphs
Directed graph
All directions for power, effort and flow are defined.
Causal
Goes from a model to computational instructions.
𝑒 1 =𝑛 𝑒 2 To 𝑒 1 ←𝑛 𝑒 2

9. Calculations with bondgraphs
Why with bondgraphs
𝑓 𝑠𝑓 = 𝑓 𝑅1 + 𝑓 𝑅2
𝑓 𝑅1 ← 𝑓 𝑠𝑓 − 𝑓 𝑅2
𝑒 𝑠𝑓 = 𝑒 𝑅1 = 𝑒 𝑅2
𝑒 𝑠𝑓 ← 𝑒 𝑅1
𝑒 𝑅2 ← 𝑒 𝑅1

10. Calculations with bondgraphs
Signal Flow
Bond contains 2 signals.
Effort, Flow
Direction is based on causality.
Extend with element and junction eqations.

11. Question What you should be able to do now
Create Bondgraphs and assing causality.
Identify signal flows from a bondgraph
Try for yourself:

12. Calculations with Bondgraphs
Masons Rule
Generate transfer function based on SFG/BG.
Shows effect of system on transfer function clearly.
For more information, see paper on BB.

13. Calculations with Bondgraphs
Masons rule
𝐻 𝑠 = 𝐺 𝑖 ∗ Δ 𝑖 Δ
𝐺 𝑖 is the forward path gain
Δ= 1− 𝐿 𝑖 𝐿 𝑖 𝐿 𝑗 − 𝐿 𝑖 𝐿 𝑗 𝐿 𝑘 etc.
Δ 𝑖 is the same as Δ but without the forward path in your SFG.
𝐿 𝑖 is a loop in the SFG/BG.

14. Calculations with bondgraphs
Masons RUle
How to apply
Create a causal bondgraph
Identify all loops
Identify all forward paths
Apply.

15. Calculations with bondgraphs
Masons rule
A small example
Transfer from 𝑒 𝑠𝑒 to 𝑒 𝑐 .
Identify loops and forward path
𝐺 1 = 1 𝑅 ∗ 1 𝑠𝐶 and 𝐿1=− 1 𝑅 ∗ 1 𝑠𝐶
Apply:
𝐻 𝑠 = 𝐺 1 ∗ Δ 1 Δ
Δ 1 =1, Δ=1−− 1 𝑠𝑅𝐶
𝐻 𝑠 = 1 𝑠𝑅𝐶 𝑠𝑅𝐶 = 1 𝑠𝑅𝐶+1

16. Question Can you do this?
Get a transfer function for the previous graph from the source to the voltage over the resistor.
Same for this one

17. Planar Mechanics Move Move Required for the project
Complete handout is on BB.
Content:
2D vs 3D, degrees of freedom
Free mass
Inertial Frames
Body fixed speed.
Velocity Transforms

18. Planar mechanics 2d vs 3d A single body: 2D, three DOF: 𝐷 𝑥 ,𝐷𝑦,ϕ
3D, six DOF: 𝐷 𝑥 , 𝐷 𝑦 , 𝐷 𝑧 , 𝜙,𝜃,𝜓
We will only use 2D.
Moddeling and simulation (Master course)

19. Planar Mechanics Free Mass A single mass in 2D space.
𝐷 𝑥 : Mass => I Element
𝐷 𝑦 : Mass => I Element
𝜙: Interia => I Element

20. Planar Mechanics Inertial Frames Trown Ball
Rotation has no influence on the direction of motion.
I elements in fixed world
𝑉 𝑦,𝑤𝑜𝑟𝑙𝑑
𝑉 𝑦,𝑏𝑎𝑙𝑙
𝑉 𝑥,𝑏𝑎𝑙𝑙
𝑉 𝑥,𝑤𝑜𝑟𝑙𝑑

21. Planar Mechanics Inertial Frames
Transformation from World frame or Local frame is simple.
𝑉 𝑥,𝑏𝑎𝑙𝑙 = cos 𝜙 ∗ 𝑉 𝑥,𝑤𝑜𝑟𝑙𝑑 + sin 𝜙 ∗ 𝑉 𝑦,𝑤𝑜𝑟𝑙𝑑
𝑉 𝑦,𝑏𝑎𝑙𝑙 = cos 𝜙 ∗ 𝑉 𝑦,𝑤𝑜𝑟𝑙𝑑 − sin 𝜙 ∗ 𝑉 𝑥,𝑤𝑜𝑟𝑙𝑑
Can be moddeled as a Modulated TF
𝑉 𝑥,𝑏𝑎𝑙𝑙 𝑉 𝑦,𝑏𝑎𝑙𝑙 = cos⁡(𝜙) sin⁡(𝜙) −sin⁡(𝜙) cos⁡(𝜙) 𝑉 𝑥,𝑤𝑜𝑟𝑙𝑑 𝑉 𝑦,𝑤𝑜𝑟𝑙𝑑
Due to power continuity:
𝐹 𝑥,𝑤𝑜𝑟𝑙𝑑 𝐹 𝑦,𝑤𝑜𝑟𝑙𝑑 = cos⁡(𝜙) sin⁡(𝜙) −sin⁡(𝜙) cos⁡(𝜙) 𝐹 𝑥,𝑏𝑎𝑙𝑙 𝐹 𝑦,𝑏𝑎𝑙𝑙
𝑉 𝑦,𝑤𝑜𝑟𝑙𝑑
𝑉 𝑥,𝑏𝑎𝑙𝑙 𝜙
𝑉 𝑥,𝑤𝑜𝑟𝑙𝑑

22. Body to world, multibonds
Planar Mechanics
Inertial Frames
Body to world
Body to world, multibonds

23. Planar Mechanics Body Fixed Speed
Speed relative to body center of mass (COM),
In COM: Only speed
Outside of COM: Speed and rotation.

24. Planar MEchanics Body fixed speeds
𝐷 𝑥,𝑃1 𝐷 𝑦,𝑃1 = 𝐷 𝑥,𝐶𝑂𝑀 𝐷 𝑦,𝐶𝑂𝑀 + 𝑥 𝑝 𝑦 𝑝 𝜙
Velocity then becomes: 𝑉 𝑥,𝑃1 𝑉 𝑦,𝑃1 = 𝑉 𝑥,𝐶𝑂𝑀 𝑉 𝑦,𝐶𝑂𝑀 + −𝑦 𝑥 𝜔

25. Planar MEchanics
Body fixed Speed

26. Check What you should be able to do Create Model of Ideal free mass
Create Model for arbitrary points on that mass.
Transform between coordinate frames.

27. What can you do with these models?
Attach more rigid bodies
Must be done in world space.
Beware of causal relations.
Attach other impedances
Eg springs, resistances.

28. Planar Mechanics Velocity Transform Linear spring, in 2d Situation
How does the spring behave?
Spring Velocity = Derivative of Length.
Spring Length:
𝐷 𝑥 2 + 𝐷 𝑦 2
Spring Velocity:
1 2 𝐷 𝑥 2 + 𝐷 𝑦 2 ∗ 2𝑉 𝑦
Dus MTF: 𝑉 𝑠𝑝𝑟𝑖𝑛𝑔 = 𝐷 𝑥 2 + 𝐷 𝑦 2 ∗ 𝑉 𝑦

29. Coffee Break

30. Practice makes perfect
Assignments
Practice makes perfect

31. Assignments Teaching assistants: Berjan Westerdijk Martijn Schouten
Tim Broenink
Roel Mentink

32. Assignments
New sets of assignments: C (Masons rule) and D (Planar Mechanics).
Also handout on planar mechanics (also on BB).
Found on:
Or here.

33. Practice makes perfect
Vrimibo
Practice makes perfect