1. Scintillas System Dynamics Tutorial
Tim Broenink

2. Planning Introduction Lecture on SysDyn Break Exercises/Practice
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3. Introduction Why this lecture? Extra instructions, extra practice.
Based on test 1
Promote understanding
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4. Student Panel A new (exiting and fun) way Evaluate understanding
Promote questions
3-5 people
Hopefully different next time.
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5. On the nature of dynamics
Lecture 1
On the nature of dynamics
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6. Contents Why SysDyn? Energy Units Generalizations Elements Storage
Transformations
BondGraphs

7. Why SysDyn Generalization of domain into a universal system.
Use Electrical knowledge for other domains.
Cross domain interactions.
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8. Energy Two universal units: Time [s] Energy [J] Power [J/s]
Basis for all dynamical systems.
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9. Energy The basis for all Domains Domain Energy per unit units per Time
Electrical
Volt [J/C]
Ampere [C/s]
Tanslation
Force [N]
Velocity [m/s]
Rotation
Torque [Nm]
Angular Velocity[rad/s]
Hydraulic
Pessure [N/m2]
Volume Flow [m3/s]
Note: 1[N] = 1 [J/m]
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10. Energy The basis for all domain 1 quantity for energy/X Effort
1 quantity for X/time
Flow
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11. Energy The basis for all Domains Domain unit Effort Flow Electrical
Charge
Volt [J/C]
Ampere [C/s]
Translation
Displacement
Force [N]
Velocity [m/s]
Rotation
Angle
Torque [Nm]
Angular Velocity[rad/s]
Hydraulic
Volume
Pressure [N/m2]
Volume Flow [m3/s]
Note: 1[N] = 1 [J/m]
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12. Question Can you answer this
Explain why Voltage and Force are analogs in dynamic systems.
Sort the following quantities into efforts and flows: Velocity, Torque, Pressure, Current, Force, Voltage
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13. Elements What to do with all that power
Elements refer to Ideal Physical Models (IPM).
A single relation between effort and flow.
A single physical component.
Modelled using multiple IPM.
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14. Elements Different groups 1-port Sources Dissipative Storage 2-port
Transformation
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15. Elements Sources Can Source or Sink infinite power
Hard to create in real life.
Model approximation.
Two options
Effort
Flow
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16. Elements Effort Sources Constant Variable Electrical Rotation
Translation
Hydraulics 𝑉 𝐼 𝑇 𝜔 𝐹 𝑣 𝑝 𝜙
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17. Elements Flow Sources Constant Variable Electrical Rotation
Translation
Hydraulics 𝐼 𝑉 𝜔 𝑇 𝑣 𝐹 𝜙 𝑝
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18. Elements Dissipative Power goes in, power is gone. (heat) Linear case:
𝐸𝑓𝑓𝑜𝑟𝑡=𝛼∗𝐹𝑙𝑜𝑤
𝑃𝑜𝑤𝑒𝑟= 𝐸𝑓𝑓𝑜𝑟 𝑡 2 𝑎 , 𝑃𝑜𝑤𝑒𝑟=𝐹𝑙𝑜 𝑤 2 ∗𝑎
A Resistance.
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19. Elements Resistance Equation Electrical 𝑉=𝑅∗𝐼 Rotation Translation
Hydraulics
𝑉=𝑅∗𝐼
T=𝑅∗𝜔
𝐹=𝑅∗𝑣
p=𝑅∗ϕ
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20. Question Can you answer this
What Electrical resistance needs to be connected to a voltage source, for the source to supply infinite power? And for a current source?
Does the previous case also hold for the Hydraulic domain? And for Mechanical rotation and translation?
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21. Elements Storage Storage of energy into an internal state
Intergrate over time [J/s] -> [J]
Required for dynamic behaviour.
Store two things
Effort
Flow
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22. Elements Storage Power goes in, Power comes out later.
Intergrate quantity into state
State results in other variable.
For example: 𝑞= 𝐼 𝑑𝑡 , 𝑉=𝑞/𝐶
Total energy = 𝑃 𝑑𝑡 = 𝑉∗𝐼 𝑑𝑡 = 𝑞 2 𝐶
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23. Elements Storage- Different types Store either Effort -> p-type
Generalized momentum
Flow -> q-type
Generalized displacement
Same behaviour, different equations
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24. Elements Storage – Q-type Stored quantity State Output
𝐼 𝑖𝑛𝑡𝑜 𝑐ℎ𝑎𝑟𝑔𝑒 [𝑞]
𝑉= 𝑞 𝐶
Electrical
Rotation
Translation
Hydraulics
𝑇= 𝜃 𝐶 , T=𝜃∗𝐾
𝜔 𝑖𝑛𝑡𝑜 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 [𝜃]
𝐹= 𝑥 𝐶 , F=𝑥∗𝐾
𝑣 𝑖𝑛𝑡𝑜 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 [x]
𝜙 𝑖𝑛𝑡𝑜 𝑣𝑜𝑙𝑢𝑚𝑒 [𝑣]
𝑝= 𝑣 𝐶
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25. Elements Storage – P-type Stored quantity State Output
𝑉 𝑖𝑛𝑡𝑜 𝑓𝑙𝑢𝑥 𝑙𝑖𝑛𝑘𝑎𝑔𝑒 𝜆
𝐼= 𝜆 𝐿
Electrical
Rotation
Translation
Hydraulics
𝑣= 𝐿 𝐽
𝑇 𝑖𝑛𝑡𝑜 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 impulse [𝐿]
𝑣= 𝑝 𝑚
𝐹 𝑖𝑛𝑡𝑜 𝑖𝑚𝑝𝑢𝑙𝑠𝑒 [p]
𝑝 𝑖𝑛𝑡𝑜 𝑓𝑙𝑢𝑖𝑑 𝑖𝑚𝑝𝑢𝑙𝑠𝑒 𝑓𝑝
𝜙=𝜌∗ 𝐿 𝐴 ∗𝑓𝑝
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26. Question Can you answer this?
Give the element equation of a ideal mass.
Why would it be usefull, or not to define a third type of storage?
Given a spring, what quantities would change when a exact copy of the spring is added next to it?
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27. Elements Transformers 2-port
Power continuity, Power goes in, power comes out the other side
Usually works via other domain
So e1*f1 = e2*f2
Two solutions:
Transformer
Gyrator
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28. Elements Transformer Relates Effort to effort, Flow to flow.
For electrical:
𝑉 𝑖𝑛 =𝑛∗ 𝑉 𝑜𝑢𝑡
Power continuity then results in:
𝐼 𝑜𝑢𝑡 =𝑛∗ 𝐼 𝑖𝑛
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29. Elements Transformer Element Equations Other domain
𝑉 𝑖𝑛 =𝑛∗ 𝑉 𝑜𝑢𝑡 , 𝐼 𝑜𝑢𝑡 =𝑛∗ 𝐼 𝑖𝑛
𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐
Electrical
Rotation
Translation
Hydraulics
𝑇 𝑖𝑛 =𝑛∗ 𝑇 𝑜𝑢𝑡 , 𝜔 𝑜𝑢𝑡 =𝑛∗ 𝜔 𝑖𝑛
𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛
𝐹 𝑖𝑛 =𝑛∗ 𝐹 𝑜𝑢𝑡 , 𝑣 𝑜𝑢𝑡 =𝑛∗ 𝑣 𝑖𝑛
𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛
𝑝 𝑖𝑛 =𝑛∗ 𝑝 𝑜𝑢𝑡 , 𝜙 𝑜𝑢𝑡 =𝑛∗ 𝜙 𝑖𝑛
𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛
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30. Elements Gyrator Relates Effort to Flow, Flow to Effort.
For electric motor:
𝑉 𝑖𝑛 =𝑛∗ 𝑣 𝑜𝑢𝑡
Power continuity then results in:
𝐹 𝑜𝑢𝑡 =𝑛∗ 𝐼 𝑖𝑛
Usually works cross domain
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31. Elements Transformer From domain From domain Element Equations
𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙
𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐
𝑇 𝑖𝑛 =𝑛∗ 𝜙 𝑜𝑢𝑡 , 𝑝 𝑜𝑢𝑡 =𝑛∗𝜔
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙
𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛
𝑉 𝑖𝑛 =𝑛∗ 𝜔 𝑜𝑢𝑡 , 𝐹 𝑜𝑢𝑡 =𝑛∗ 𝐼 𝑖𝑛
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32. Question Can you answer this
Can you make a transformer using three gyrators?
Design a two transformers using a different domain then in slide 29.
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33. Bondgraphs
Graph, BondGraph
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34. Bondgraphs Why Bondgraphs Bondgraph Elements Junctions (0, 1)
Causality

35. Why bondgraphs Dynamic systems based on energy.
Keep energy flows together,
A bond:
Energy
Effort
Flow
Direction
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36. Why Bondgraphs Power transmission
Bond graps provide information about 2 quantities (actually power)
Resistor Example
Bond equations:
Element Equation
Conclusion: 𝑉 𝑏𝑜𝑛𝑑 = 𝐼 𝑏𝑜𝑛𝑑 𝑃 𝑏𝑜𝑛𝑑 = 𝑉 𝑏𝑜𝑛𝑑 2 𝑅
𝐼 𝑏𝑜𝑛𝑑 = 𝐼 𝑅
𝑉 𝑏𝑜𝑛𝑑 = 𝑉 𝑅
𝑉 𝑅 =𝑅 ∗ 𝐼 𝑅
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37. Why bondgraphs Direction Bondgraphs signify power flow.
Direction defines positive power direction:
Resistor consumes power:
Resistor generates power:
Negative power is generated
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38. Elements Based on the last 30 minutes or so 1-ports Resistors (R)
Sources (Effort, Flow)
Storage (p-type,q-type)
2-ports
Transformers
Gyrators
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39. Elements Resistor Icon: R Parameter: R Element equation: 𝑒=𝑓∗𝑅
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40. Elements Sources Source of Effort Icon: Se Parameter: e (effort)
Equation: 𝑒=𝑒, 𝑓=𝑤ℎ𝑎𝑡𝑒𝑣𝑒𝑟
Source of Flow
Icon: Sf
Parameter: f (flow)
Equation: 𝑓=𝑓, 𝑒=𝑤ℎ𝑎𝑡𝑒𝑣𝑒𝑟
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41. Question Can you answer this?
Give equations for the following systems:
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42. Elements Storage Elements Q-type element Symbol C Parameter: C
Equations: q= 𝑓 𝑑𝑡,𝑒= 𝑞 𝑐
P-type element
Symbol I
Parameter: I
Equations: p= 𝑒 𝑑𝑡,𝑓= 𝑞 𝐼
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43. Elements Tranformers Tranformer Symbol: Parameter: n
Equations 𝑒 1 =𝑛 ∗ 𝑒 2 , 𝑓 2 =𝑛∗ 𝑓 1
Gyrator
Equations 𝑒 1 =𝑛 ∗ 𝑓 2 , 𝑒 2 =𝑛∗ 𝑓 1
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44. Junctions Connecting things up N-ports 0 junction Common effort
Sum of flows, dependant on direction
1 junction
Common flow
Sum om efforts, dependant of direction
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45. Question Can you answer this?
Equivalent electrical system for these bondgraphs:
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46. Causality The cause for all this
Turning a equation model, into a calulation model:
Without causality, a set of equations:
𝑒 𝑟 = 𝑒 𝑠𝑒 , 𝑓 𝑒𝑠 = 𝑓 𝑟 , 𝑓 𝑟 = 𝑒 𝑟 𝑅
With causality, a set of operations
𝑒 𝑟 ← 𝑒 𝑠𝑒 , 𝑓 𝑟 ← 𝑒 𝑟 𝑅 , 𝑓 𝑒𝑠 ← 𝑓 𝑟
Causallity is independant of the direction of the bond.
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47. Causality Meaning of the bar Side of the bar:
Effort is applied to this side and a flow comes back.
Side without the bar
Flow is apploed to this side and a effort comes back.
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48. Question Can you answer this
What causality must a source of effort have? And a source of flow?
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49. Causality Prefered causality
The causality of sources elements is fixed
Can be determined from the equations.
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50. Causality Prefered causality
The causality of storage elements determine the type of equation
Intergral <preffered for simulation
Differential
Eg: e← 1 𝐶 𝑓 𝑑𝑡 𝑓←𝑐 𝑑𝑒 𝑑𝑡
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51. Causality Dependant causality
Transformers and gyrators have a causality that depends on the other port:
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52. Causality Dependant causality Junctions have a dependant causality
Only one bond can determine effort
1 junction
Only one bond can determine flow
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53. Causality assignment Start with: Fixed causality
Fill in all dependant causalities
Next, prefered causality
Next, pick one.
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54. Question Can you answer this
Assign causality to the following schematics
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55. Coffee Break
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56. Practice makes perfect
Assignments
Practice makes perfect

57. Assignments Teaching assistants: Thomas Klostermann Martijn Schouten
Tim Broenink
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58. Assignments Two sets of assignments, A and B Found on:
Or here.
Make one set now

59. Practice makes perfect
Vrimibo
Practice makes perfect