Scintillas System Dynamics Tutorial Tim Broenink

Planning Introduction Lecture on SysDyn Break Exercises/Practice 11/19/2018

Introduction Why this lecture? Extra instructions, extra practice. Based on test 1 Promote understanding www.scintilla.utwente.nl/docs/cursus/SysDyn 11/19/2018

Student Panel A new (exiting and fun) way Evaluate understanding Promote questions 3-5 people Hopefully different next time. 11/19/2018

On the nature of dynamics Lecture 1 On the nature of dynamics 11/19/2018

Contents Why SysDyn? Energy Units Generalizations Elements Storage Transformations BondGraphs

Why SysDyn Generalization of domain into a universal system. Use Electrical knowledge for other domains. Cross domain interactions. 11/19/2018

Energy Two universal units: Time [s] Energy [J] Power [J/s] Basis for all dynamical systems. 11/19/2018

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] 11/19/2018

Energy The basis for all domain 1 quantity for energy/X Effort 1 quantity for X/time Flow 11/19/2018

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] 11/19/2018

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 11/19/2018

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. 11/19/2018

Elements Different groups 1-port Sources Dissipative Storage 2-port Transformation 11/19/2018

Elements Sources Can Source or Sink infinite power Hard to create in real life. Model approximation. Two options Effort Flow 11/19/2018

Elements Effort Sources Constant Variable Electrical Rotation Translation Hydraulics 𝑉 𝐼 𝑇 𝜔 𝐹 𝑣 𝑝 𝜙 11/19/2018

Elements Flow Sources Constant Variable Electrical Rotation Translation Hydraulics 𝐼 𝑉 𝜔 𝑇 𝑣 𝐹 𝜙 𝑝 11/19/2018

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. 11/19/2018

Elements Resistance Equation Electrical 𝑉=𝑅∗𝐼 Rotation Translation Hydraulics 𝑉=𝑅∗𝐼 T=𝑅∗𝜔 𝐹=𝑅∗𝑣 p=𝑅∗ϕ 11/19/2018

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? 11/19/2018

Elements Storage Storage of energy into an internal state Intergrate over time [J/s] -> [J] Required for dynamic behaviour. Store two things Effort Flow 11/19/2018

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 = 1 2 𝑞 2 𝐶 11/19/2018

Elements Storage- Different types Store either Effort -> p-type Generalized momentum Flow -> q-type Generalized displacement Same behaviour, different equations 11/19/2018

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 11/19/2018

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 11/19/2018

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? 11/19/2018

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 11/19/2018

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 11/19/2018

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 11/19/2018

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 11/19/2018

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 11/19/2018

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. 11/19/2018

Bondgraphs Graph, BondGraph 11/19/2018

Bondgraphs Why Bondgraphs Bondgraph Elements Junctions (0, 1) Causality

Why bondgraphs Dynamic systems based on energy. Keep energy flows together, A bond: Energy Effort Flow Direction 11/19/2018

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 11/19/2018

Why bondgraphs Direction Bondgraphs signify power flow. Direction defines positive power direction: Resistor consumes power: Resistor generates power: Negative power is generated 11/19/2018

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 11/19/2018

Elements Resistor Icon: R Parameter: R Element equation: 𝑒=𝑓∗𝑅 11/19/2018

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 11/19/2018

Question Can you answer this? Give equations for the following systems: 11/19/2018

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 11/19/2018

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 11/19/2018

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 11/19/2018

Question Can you answer this? Equivalent electrical system for these bondgraphs: 11/19/2018

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. 11/19/2018

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. 11/19/2018

Question Can you answer this What causality must a source of effort have? And a source of flow? 11/19/2018

Causality Prefered causality The causality of sources elements is fixed Can be determined from the equations. 11/19/2018

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 11/19/2018

Causality Dependant causality Transformers and gyrators have a causality that depends on the other port: 11/19/2018

Causality Dependant causality Junctions have a dependant causality Only one bond can determine effort 1 junction Only one bond can determine flow 11/19/2018

Causality assignment Start with: Fixed causality Fill in all dependant causalities Next, prefered causality Next, pick one. 11/19/2018

Question Can you answer this Assign causality to the following schematics 11/19/2018

Coffee Break 11/19/2018

Practice makes perfect Assignments Practice makes perfect

Assignments Teaching assistants: Thomas Klostermann Martijn Schouten Tim Broenink 11/19/2018

Assignments Two sets of assignments, A and B Found on: www.scintilla.utwente.nl/docs/cursus/SysDyn Or here. Make one set now

Practice makes perfect Vrimibo Practice makes perfect