Exercise 1 Principles of Computer Aided Modeling and Simulation
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1 Gdans Universiy o Technology, Faculy o Ocean Engineering and Ship Technology Modeling and Conrol o Dynaic Syses, Laboraory, M. H. Ghaei Eercise Principles o Copuer Aided Modeling and Siulaion OBJECTIVE The objecive o his eercise is geing sared wih MATLAB and SIMULINK as a powerul pacage or odeling, siulaion and analysis o dynaic syses and heir conrols. The irs eercise is a war up aciviy o ae you ailiar wih he principles o dynaic syse odeling and conrol syse. You ae your own odel and eaine he open loop responses. The inluence o syse paraeers on is dynaic behavior will be esed, oo. REQUIREMENTS A. Prerequisie nowledge: Beore saring he eercise you are epeced o now he ollowing opics:. Maing a aheaical odel using he second Newon s and Lagrange s laws.. Tie response o eleenary pars o conrol syses, paricularly sep and ipulse responses 3. The eaning and usage o qualiy crieria o conrol syses: rise ie, seling ie, overshoo, bandwidh, seady sae error, ie o irs pea, ec. 4. Nuerical ehods or solving he ordinary dierenial equaions ODEs. B. MATLAB/SIMULINK You should be ailiar wih he ollowing MATLAB/SIMULINK aspecs:. Variables scalars, arices and vecors. Principle aheaical operaions, 3. MATLAB iles generaion and ipleenaion, as well as I/O iles, 4. Fundaenals o ploing and graphical presenaion, 5. Siple odel generaion and siulaion using SIMULINK. LAYOUT Par A: Geing sared wih MATLAB/SIMULINK. Review and es he os iporan eaures, coands and uncions o MATLAB he lecurers will inroduce you he a lab... Wrie one. ile using uncion or ploing he requency characerisics only Nyquis and Bode diagras o he syse you received ro he lecurer. 3. Open hero ile in MATLAB coand window and ry o undersand he srucure o he syse. Wrie he aheaical equaions boh algebraic and ODE o his syse. Par B: For your own dynaic syse, delivered by he lecurer, ollow he ne seps:. Mae he aheaical odel o he syse and wrie he syse equaions.. Lis he iniial condiions, assupions and analye he syse. 3. Pu he odel in MATLAB using hree dieren ehods: sae space ehod, ranser uncion and ZPK Zero-Pole-Gain or. 4. Using. ile wrie a uncion, which describes he syse equaions. 5. Chec uni ipulse and sep responses o he odel as he objecive o conrol syse open loop response. For his case use sep and ipulse. 6. Use lsi, ode3 and ode45 o siulae he uni responses and hen plo and copare he resuls in one igure. 7. Try o change he paraeers o ODE solvers and repea poin 6 o achieve he adequae resul. 5
2 Gdans Universiy o Technology, Faculy o Ocean Engineering and Ship Technology Modeling and Conrol o Dynaic Syses, Laboraory, M. H. Ghaei 8. Repea poin 6 or a sinusoid inpu signal, e.g. sin. 9. Plo he requency response o he syse using nyquis and bode or alernaively ha uncion which you wroe in Par A, Poin.. Mae he odel o your syse in SIMULINK.. Mae siulaion o open loop syse in SIMULINK. Repea your siulaion using sep uncion, consan value and sine uncion as inpu and plo all hree responses in one igure.. Try o change he siulaion paraeers and solving ehods, hen repea your siulaions. 3. Invesigae he inluence o syse paraeers on uni sep response. Mae he relaed plos o es he eec o paraeers changing. MATLAB/SIMULINK MATLAB/SIMULINK is a prograing language and daa visualiaion soware pacage which is especially eecive in siulaion and syse analysis. Inoraion abou MATLAB/SIMULINK can be ound a he web page o he vendor The MahWors, Inc. whose URL is hp:// The ollowing MATLAB coands and ah uncions are necessary o be undersood and applied in his eercises: abs ais bode cos den ep igure or uncion grid help ipulse linspace load log log logspace looor lsi liview nu nyquis ode3 ode45 prin save sign sin sqr sep subplo ile label ylabel Please ry o ype >>help coand/uncion or each case o ge deails. 6
3 Gdans Universiy o Technology, Faculy o Ocean Engineering and Ship Technology Modeling and Conrol o Dynaic Syses, Laboraory, M. H. Ghaei REPORT a. Plo he requency characerisics o your syse. b. Deliver he aheaical equaions o hero syse. c. Describe he physical eaning o your dynaic syse. Deine he objecive o he syse, inroduce all consrains, boundary and iniial condiions. d. Deliver all plos enioned in LAYOUT par. Inerpre he physical eaning o he plos or each inpu. e. Read he ain paraeers o he syse response ro your plos gain, ie consans, rise ie, seling ie, overshoo, ie o irs pea and bandwidh o he syse. Discuss on inluence o: solving ehods, siulaion paraeers, and syse paraeers on dynaic behavior o he syse. Model or Eercise : Car Suspension Syse Phoo: Couresy o The Car Bible Hoe. hp:// Here we invesigae he suspension syse o a car. One wheel can be used o sipliy he proble o a one diensional ass-spring-daper syse, see he ollowing diagra. The physical odel o car suspension syse. : ass o car body : ass o suspension syse : spring consan o suspension syse : spring consan o wheel including ire : daping consan o suspension syse 7
4 8 Gdans Universiy o Technology, Faculy o Ocean Engineering and Ship Technology Modeling and Conrol o Dynaic Syses, Laboraory, M. H. Ghaei : daping consan o wheel including ire : eernal orce conrol inpu : absolue displaceen o : absolue displaceen o Equaions o oion: Use Lagrange equaion or second Newon s law o wrie he oion equaion o he syse. The resul can be presened or eaple in his or: Eaple Consider he ollowing ass-spring-daper proble: The dierenial equaion o syse oion is as ollows: This aheaical odel can be represened in sae space irsly by deining he sae variables: The inpu signal and oupu signals are: u and y As a resul [] [ ] [ ] [ ][ ] u y u For g, N/, 5 N//s and N, he syse can be coded as ollows:» a[ ; - -.5];» b[ ;.];» c[ ];» d;» sysssa,b,c,d; Then ipulse and sep response can be ploed:» ipulsesys;grid
5 Gdans Universiy o Technology, Faculy o Ocean Engineering and Ship Technology Modeling and Conrol o Dynaic Syses, Laboraory, M. H. Ghaei 6-3 Ipulse Response Apliude » sepsys;grid Tie sec. Sep Response Apliude Tie sec. Now we can epress he ranser uncion o he syse:» [nu,den]ssa,b,c,d; gnu,den Transer uncion: s^.5 s I is possible o use lsi o ind he syse sep response:» :.:5;» u:5;» [Y,T,X] lsisys,u,,[ ];» plot,y; which is he sae as previous igure. We can plo he sae variables and copare he wih sep response:» hold on» plot,x:,,'r'» plot,x:,,'b'» label'tie [s]'» ylabel 'Apliude' 9
6 Gdans Universiy o Technology, Faculy o Ocean Engineering and Ship Technology Modeling and Conrol o Dynaic Syses, Laboraory, M. H. Ghaei» ile'sep Response'» grid» legend'', '' Sep Response 4 Apliude Tie [s] We can also wrie a uncion:» uncion pri,» doeros,;» u;» do;» do.*u-.5*-*;» prido; and hen use ode3 or ode45 o solve he proble:» [,y]ode45,[ 5],[ ];» plo,y:,; grid This produces he sae plo as presened above. To ae siulaion using SIMULINK, irsly draw he bloc diagra o he syse, which can be presened, or eaple, as ollows: - The adequae SIMULINK odel can be ade now based on his bloc diagra:
7 Gdans Universiy o Technology, Faculy o Ocean Engineering and Ship Technology Modeling and Conrol o Dynaic Syses, Laboraory, M. H. Ghaei Noe ha here a sep uncion has been seleced as inpu signal and he oupu is ransied o scope. By wriing he values o, and under MATLAB Coand Window:» ;5;; we will be able o deine he syse paraeers. Then siulaion can be eecued o achieve he sae resuls as beore. Reeber ha he presened bloc diagra and SIMULINK odel are no unique. For N, he syse response will be analogically he sae, bu he apliude will be uliplied by. Finally, ry o use liview GUI Graphic User Inerace o es LTI Linear, Tie- Invarian syses you have already enered o worspace. Try o ae dieren plos o undersand he characerisics o your syses. * * *
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