NPTEL >> Mechanical Engineering >> Modeling and Control of Dynamic electro-mechanical System Module 3- Lecture 22. Design

Transcription

1 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture Time Dely n Ue of MATLAB in Controller Deign Dr. Bihkh Bhttchry h Profeor, Deprtment of Mechnicl Engineering IIT Knpur Joint Inititive of IIT n IISc - Fune y MHRD

2 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture Thi Lecture Contin The effect of Time Dely Ue of MATLAB Aignment Joint Inititive of IIT n IISc - Fune y MHRD

3 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture Time Dely Time ely lwy reuce the tility of ytem! Importnt to e le to nlyze it effect In the -omin time ely i given y e -l Mot ppliction contin ely mple ytem Root locu nlyi The originl metho oe only hnle polynomil Solution Approximtion Pé of e -l Moifying the root locu metho irect ppliction

4 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture More on Time Dely More on Time Dely Pé pproximnt, Firt pproximtion pp, e 4 3 erie McLuren ! 3! e with T 3 / / T T e T

5 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture Time Dely Implementtion Direct pproch exct clcultion Proce G T e G Notice, e T e T j e jt T Moifie root locu conition T D G e D G 8 D G 8 T However, Mtl oe not upport thi pproch...

6 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture How to uil trnfer function in MATLAB? Suppoe we conier the following eqution: K z Form: G p p Form : G K Kz p p p p k Now, we cn evelop thi trnfer function in MATLAB y the following wy: Form : tf=zpk[z],[p,p],k Form : tf=tf[,k],[,,] You cn rw the root-locu y the imple commn: rlocutf Joint Inititive of IIT n IISc Fune y MHRD 6

7 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture Some more ueful commn For fining the repone of the ytem you cn ue the following commn n when require: For tep repone: teptf For impule repone: impuletf For other repone: limtf,u,t, where T i the time vector n U i the correponing excittion vector. You cn ue nyquittf for otining the nyquit plot of the ytem n freqreptf for otining the frequency repone. Joint Inititive of IIT n IISc Fune y MHRD 7

8 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture Ue of MATLAB for ROOT LOCUS DESIGN num=[.5,.774]; % Define the numertor en=[.739,.9, ]; % Define the enomintor Wn=.9; 9;zet=.5; % Define the frequency n mping rlocu num,en % Root locu plot Commn gri zet,wn %Gri for the Root Locu xi [.55]%Set.5]%Set the xe ize [K, pole]=rlocfin num,en e=.; %Otin the gin n cloe loop pole [numc,enc]=cloop K*num,en, ;%The, cloe loop trnfer function tep e*numc,enc%tep repone of the ytem

9 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture Aignment Conier unity feeck ytem with plnt trnfer function: G Input the trnfer function in MATLAB n ketch the root locu. Fin out the co-orinte of the ominnt pole for mping coefficient.77. Fin the correponing Gin. Fin out the vliity of uming the ytem to e of econ-orer. Joint Inititive of IIT n IISc Fune y MHRD 9

10 NPTEL >> Mechnicl Engineering >> Moeling n Control of Dynmic electro-mechnicl Sytem Moule 3- Lecture Specil Reference for thi lecture Feeck Control of Dynmic Sytem, Frnkline, Powell n Emmi, Peron Control Sytem Engineering Normn S Nie, John Wiley & Son Deign of Feeck Control Sytem Stefni, Shhin, Svnt, Hotetter Oxfor Joint Inititive of IIT n IISc Fune y MHRD