Teaching Modelica for Mathematicians and Engineers Modelica Educational Workshop Berlin
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1 Teching Modelic for Mthemticins nd Modelic Eductionl Workshop Berlin Bernhrd Bchmnn University of Applied Sciences Bielefeld
2 Outline Pst Teching Experience Mthemticins precognition, course objectives Course Detils theoreticl content, tools, exercises ] [A I.i I.i I3.i Discussion on Future Teching Options Mthemticins nd mster students hving less mthemticl bckground Tools nd concepts dpttion of previous course ] [A I.i I.i I3.i
3 Pst Teching (999 8) Course ttendees (diplom-study in mthemtics) [c. 5] good mthemticl bckground nlysis nd liner lgebr topics optimiztion (liner, nonliner problems) numericl methods (no ODEs) theory on ordinry differentil equtions fmilir tools:mple, Mtlb (no Simulink) bsic progrmming knowledge (C/C++) bsic engineering bckground simple mthemticl modeling of physicl components mechnics, electricl systems (sttic) Course objectives engineering spects component nd librry development in Modelic mthemticl spects understnd symbolic trnsformtions nd numericl issues 3
4 Pst Teching (999 8) Course detils 4 semester periods per week (3 weeks) theory nd prcticl exercises lerning by doing (smll projects) tools Mtlb-Simulink (st project) Dymol (Modelic projects) exm prcticl projects (development nd explntion) theory mthemticl nd modeling spects 4
5 Pst Teching (999 8) st course: Bsic understnding of the principles using simple electricl system modeling u develop the DAE representtion bstrct mthemticl view understnd numericl integrtion (Euler method) sort the eqution system (find cuslity) i i u u i u 3 u 4 simultion nd implementtion using Mtlb using Simulink using Dymol (flt representtion) u = A sin(π f t + ϕ) u = u i = i u = du C dt + i R i + u, = i,, u 3 u = u = di L dt 3 R i + u, = u 4 4 5
6 Pst Teching (999 8) st course project bsic understnding of the principles using simple mechnicl system modeling develop the DAE representtion understnd numericl integrtion (Euler method) sort the eqution system (find cuslity) simultion nd implementtion using Mtlb using Simulink using Dymol input: u(t) z.b. sin(t) τ = u, c 3 4 c ϕ, τ J ϕ, τ ϕ, τ 3 J ϕ, τ 4 = J τ J 3 ω = τ ω = τ + τ = τ + τ, ω = ϕ 3 = c ( ϕ ϕ ) ω = ϕ 6
7 Pst Teching (999 8) nd course: Benefit of using Modelic Getting strted with Dymol exmples from st course continued modeling drg nd drop librry structure find components simultion compile model experiment setup view nd compre results u i i u u i u 3 u 4 input: u(t) z.b. sin(t) c 3 4 c ϕ, τ J ϕ, τ ϕ, τ 3 J ϕ, τ 4 = 7
8 Pst Teching (999 8) nd course project build up nd simulte different physicl systems exmples from st course drive trin triple pendulum height = 8
9 Pst Teching (999 8) 3rd course: Getting strted with Modelic flt Modelic bsic keywords model, prmeter, eqution, bsic types, der, type ttributes min, mx, units, type clsses librry SIunits hierrchicl Modelic model nd connector clsses connect sttement bsic principles of flow nd potentil vribles 9
10 Pst Teching (999 8) 3rd course project implement nd simulte Pendulum model flt representtion using predifined types (SIunits) hierrchicl representtion (using Multibody librry) nimtion build up simple controller to djust the ngle J ϕ = m g L cos( ϕ) d ϕ + τ
11 Pst Teching (999 8) 4th course: Introduction to bsic control techniques exmples with/without feedbck Lplce-trnsformtion different mthemticl formultions functionl description block digrm Step function response stndrd controller P-, D-, I-, PD-, PI-, PID-controller 4th course project exmple from 3rd course continued try different controller nd compre results
12 Pst Teching (999 8) 5th course: Build Librries in Modelic pckge concept exmple using simple electricl component modifier concept build librries in Dymol icon lyer, digrm lyer coordinte system connector view prmeter settings 5th course project build up librry motor (including control scheme) ger box (including friction elements) djust control prmeter for suitble test cses
13 Pst Teching (999 8) 6th course: Build Librries in Modelic generl connection concept energy flow, domin specific potentil nd flow vribles discuss prcticl issues (rottionl) multidisciplinry modeling prmeter propgtion modifictions GUI in Dymol 6th course project continue 5th course project 3
14 4 Pst Teching (999 8) 7th course: Advnced Modelic clss types type, model, block, function, pckge, connector lgorithm versus equtions dditionl keywords input, output, protected mtrices definition, element ccess, opertions, inline functions exmple of generl trnsfer function 7th course project still continue 5th course project u b b b b b b b b b y u + = + = x x x
15 Pst Teching (999 8) 8th course: Symbolic trnsformtion lgorithm mthemticl DAE representtion regulr (index ) problems mtching lgorithm sorting (Trjn lgorithm) BLT representtion of djcence mtrix 8th course project implement the BLT lgorithm for rndom mtrices f f f 3 f 4 f 5 z z z 3 z 4 z 5 5
16 Pst Teching (999 8) 9th course: Higher Index problems exmples (mechnicl, electricl) mthemticl DAE representtion definition of the structurl nd differentil index detect singulr set of equtions Pntelides lgorithm dummy derivtive method stte selection mechnism initiliztion of models 9th course project continue 8th course project f f f 3 f 4 f 5 z z z 3 z 4 z 5 6
17 Pst Teching (999 8) th course: Advnced Modelic rrys of component for-loop, vrible number of connect sttements exmple trnsmission line model introduce bsic het flow librry th course project simulte the temperture distribution of n isolted br p R R=R C=C C R R=R C=C ground C R3 R=R C=C C3 R4 R=R n R R[] R[] Rn n=3 C[] C[] C[3] 7
18 Pst Teching (999 8) th course: Model discontinuities Modelic Stndrd librry digitl controller electricl switch or diode (not idel) clutch nd brke model Modelic lnguge elements if-then-else, when, noevent, smooth, reinit, pre, symbolic trnsformtion synchronous eqution i u th course project implement exmples hysteresis function pulse width modultion block u u i i 3 8
19 th course: Model Discontinuities numericl issues stiffness ( not idel switch) time versus stte events rounding errors event itertions Pst Teching (999 8) u i u u i i 3 th course project implement further exmples bouncing bll Sw itch.v [V] Sw itch.i [A]
20 th course: Model Discontinuities numericl issues stiffness ( not idel switch) time versus stte events rounding errors event itertions Pst Teching (999 8) g h th course project implement further exmples bouncing bll h
21 3th course: Model Discontinuities vrying higher index problems exmples mechnicl, electricl symbolic trnsformtion nlyse singulrity dummy derivtive method Pst Teching (999 8) u i i u u u 3th course project run nd nlyse exmples introduce dummy derivtive terms in brnches
22 3th course: Model Discontinuities vrying higher index problems exmples mechnicl, electricl symbolic trnsformtion nlyse singulrity dummy derivtive method Pst Teching (999 8). u i i u u u 3th course project run nd nlyse exmples introduce dummy derivtive terms in brnches
23 Discussion on Future Teching Options Course ttendees mster-study in Optimiztion nd Simultion mthemticins nd engineers mechnicl, electricl, mechtronics, heterogeneous bckground in mthemtics nd engineering Course objectives engineering spects component nd librry development in Modelic mthemticl spects understnd symbolic trnsformtions nd numericl issues Tools licencing issues OpenModelic (SimForge), Dymol, MpleSim, MthModelic Applictions / Projects 3
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