Multi-Domain Modeling

Simulink in barebones form not-well suited for simulating networks/nodal systems◦ 1) No sense of bi-directionality◦ 2) No notion of ‘nodes’◦ 3) Energy conservation has to be maintained via

algebraic constraint blocks in each sub-unit

Can be done….but very messy, difficult to expand

Issue: Simulating Networks In Simulink

Approach◦ Solve network state in one custom block

Pros◦ Better understood on how to get the correct solution

Cons◦ Not well-suited for ‘group’ approach◦ Code interface to solver block could get messy fast◦ Hard to expand to new sub-systems

Option #1: Custom Matrix Solver

Option #2: Simscape Approach

◦ Use Simulink ‘Simscape’ Libraries

Pros◦ Let Simulink do the book-keeping for energy

conservation, flows, network state, time etc◦ Graphical components for building networks

Cons◦ Built-in Hydraulic domain assumes constant temperature◦ New thermo/hydraulic domain (and accompanying

components) have to be written/re-written

A simulink package to model physical domains and networks

Based off of ‘Bond-Graph’ Theory◦ Physical dynamic systems can be abstracted into

networks in which: 1) There exists “Flow” variables 2) There exists “Effort” variables 3) Energy is conserved

What is Simscape?

Example Simscape Network

How to write a domain that couples hydraulic and thermal behavior?◦ Learn the mechanics of ‘Simscape’ Language

(structure, syntax, etc) ◦ Test with a sample, energy conserving networks

How to modify that domain to accurately model our system?◦ Mass flow rate, pressure, enthalpy, momentum,

etc.◦ Build a source, flowing into a simple network of

pipes

Plan of Attack

Writing New Multi-Domain Models

Electro-Hydraulic Servo valve Example

Initial ‘Toy’ Thermal/Hydraulic Domain

2 ‘Effort’ (across) variables◦ Temperature and Pressure drops

2 Corresponding ‘FLOW’ variables Power = Flow*Effort

◦ Energy conserving variables noted◦ Default values assigned (but are over-written in

each model)

Writing Thermo/Hydraulic Components

At,p +

Bt,p -

Component Template

qf qt

“Toy” Thermo-hydraulic Pipe Model

Includes both domains, but not coupled Units matter!!

Constraints, not assignments!

Writing Thermo/Hydraulic Components

Reference node

Example 1: Divider-like loop

Example 2: Addition of External Heat Source

Moving on to the next step… What are our effort variables and units?

What are our flow variables and units?

What are the governing network equations, in nodal form?

What are the domain coupling expressions/constraints between the two domains?