How to get real and imaginary terms from an expression?

I am trying to get real and imaginary terms from the following expression TF. But real(), imag() is not able to give me any solution.

syms s real
ws = 2 * pi * 85000 ;
Lp = 27.13e-6 ;
Cpp = 129.23e-9 ;
Zp = s * Lp + ws * Lp * 1i ;
Zpp = 1 / ( s * Cpp + ws * Cpp * 1i ) ; 

TF = Zpp * Zp / ( Zp + Zpp ) ;

These two commands give me following answers.

TFreal = real(TF)

TFreal = 

TFimag = imag(TF)

TFimag = 

You can observe that the answers have real, imag commands in them instead of answers.

[Paul]

Hi Aditya,

Normally, a transfer function, which I assume is what TF means, is defined as a function of s, which is a complex variable, and all other terms in the tansfer function are all real. But here, we have s defined as real, and other terms in the TF are complex. Can you clarify exactly what this code is intened for?

[Aditya Zade]

Hey Paul,

Only 's' is a variable which I have defined as a real number.

Answer 1

[Walter Roberson]

syms s real
ws = 2 * pi * 85000 ;
Lp = 27.13e-6 ;
Cpp = 129.23e-9 ;
Zp = s * Lp + ws * Lp * 1i ;
Zpp = 1 / ( s * Cpp + ws * Cpp * 1i ) ; 

TF = Zpp * Zp / ( Zp + Zpp ) ;
TFreal = real(TF)

TFreal = 

TFimag = imag(TF)

TFimag = 

simplify(TFreal)

ans = 

simplify(TFimag)

ans = 

[Aditya Zade]

Hi Walter,

Thanks for the comment.

I have more complex expressions where simplify command is not helping me. Can you help me with that?

Id = 2.1467 - 51.0287i ;
Req = 17.5865 ;
Vm = 277 * sqrt(6) ;

ws = 2 * pi * 85000 ;

Lp = 27.13e-6 ;
Cpp = 129.23e-9 ;
Cps = 175.29e-9 ;
Ll = 34.69e-6 ;
Lm = 782.76e-6 ;

syms s real

Zp = s * Lp + ws * Lp * 1i ;
Zpp = 1 / ( s * Cpp + ws * Cpp * 1i ) ; 
Zps = 1 / ( s * Cps + ws * Cps * 1i ) ; 
Zl = s * Ll + ws * Ll * 1i ; 
Zm = s * Lm + ws * Lm * 1i ; 

Kp1 = ( Req * ( 1 + ( ( Zps + Zl ) / Zm ) ) ) + Zps + Zl ;
Kp2 = 1 + ( Zp / Zpp ) + ( Zp / ( Zps + Zl ) ) ;
Kp3 = Zp / ( Zps + Zl ) ;

H_mi_idcap = ( 2 * sqrt(3) / pi ) * Vm / ( ( Kp1 * Kp2 ) - ( Req * Kp3 ) ) ;

H_mi_idenvcap = ( simplify( real( H_mi_idcap ) ) * ( real ( Id ) ) + simplify( imag( H_mi_idcap ) ) * ( imag( Id ) ) ) / ( abs( Id ) ) ;

This gives me the following answer where you can see imag and real commands instead of a proper solution. Everything is a function of 's' which I have defined as a real number :

H_mi_idenvcap =

(172683135000208604551535223026586347005871322726587908178108096625276636501114880000000*imag(1/((260655775425866130589094142874939721854279679342140669722801980358790866066735104000000000000*((4003681333757921*s)/147573952589676412928 + (pi*46121i)/10000))/(3199587759584921875*s + pi*543929919129436693725184i + 3484491437270409865864955980101306485309440000/(6622268966257761*s + 3536760160863479398400i)) + (((2441085682324977*s + 1303712463883813781504i)*(2502300833598700625*s + pi*425391141711779115040768i) + (160693804425899027554196209234116260252220299378279283530137600000000*((4003681333757921*s)/147573952589676412928 + (pi*46121i)/10000))/(3199587759584921875*s + pi*543929919129436693725184i + 3484491437270409865864955980101306485309440000/(6622268966257761*s + 3536760160863479398400i)) + 1742245718635204932932477990050653242654720000)*(s*(4619058782255093538217914766794407636638949233813262172160000 - 21168034995631362998836147051869896922367328720757068922880000i) + pi*(78011169021401466968879757554262818755122444066860299426830745600 + 1854409792978907913925284668047915815504542811708541297105253171200i) + pi*s*(6944434942837917949164811082012024629727852242338660690690048 - 146068978425098581708069587328360702057061537084478402330624i) - pi*s^2*6501418518427872464610362653183025793653342863217393664i - s^2*(20247246437114752669473895744275033930756435040419840000 + 40849617310811283933296436264138582256579234682880000000i) - 38243638343693369198375882169918233116530201328125*s^3 + (5388772738081004572469698920051915105680717877468455087175106560000 - 3358895989106063476910444219158740309232214042176845740119162880000i)))/(11952676787541737523111330423471*s^2 + s*12767150139401286081539645192745910272i - 3409280732243783574557653655779097234636800))))/1437601757967713 - (7264420886176792199257085734292880601658091595116561440468289605814950758973440000000*real(1/((260655775425866130589094142874939721854279679342140669722801980358790866066735104000000000000*((4003681333757921*s)/147573952589676412928 + (pi*46121i)/10000))/(3199587759584921875*s + pi*543929919129436693725184i + 3484491437270409865864955980101306485309440000/(6622268966257761*s + 3536760160863479398400i)) + (((2441085682324977*s + 1303712463883813781504i)*(2502300833598700625*s + pi*425391141711779115040768i) + (160693804425899027554196209234116260252220299378279283530137600000000*((4003681333757921*s)/147573952589676412928 + (pi*46121i)/10000))/(3199587759584921875*s + pi*543929919129436693725184i + 3484491437270409865864955980101306485309440000/(6622268966257761*s + 3536760160863479398400i)) + 1742245718635204932932477990050653242654720000)*(s*(4619058782255093538217914766794407636638949233813262172160000 - 21168034995631362998836147051869896922367328720757068922880000i) + pi*(78011169021401466968879757554262818755122444066860299426830745600 + 1854409792978907913925284668047915815504542811708541297105253171200i) + pi*s*(6944434942837917949164811082012024629727852242338660690690048 - 146068978425098581708069587328360702057061537084478402330624i) - pi*s^2*6501418518427872464610362653183025793653342863217393664i - s^2*(20247246437114752669473895744275033930756435040419840000 + 40849617310811283933296436264138582256579234682880000000i) - 38243638343693369198375882169918233116530201328125*s^3 + (5388772738081004572469698920051915105680717877468455087175106560000 - 3358895989106063476910444219158740309232214042176845740119162880000i)))/(11952676787541737523111330423471*s^2 + s*12767150139401286081539645192745910272i - 3409280732243783574557653655779097234636800))))/1437601757967713

[Walter Roberson]

vm is not defined.

[Aditya Zade]

You can take

Vm = 277 * sqrt(6) ;

[Aditya Zade]

Check the code again, I have added Vm.

[Walter Roberson]

Id = 2.1467 - 51.0287i ;
Req = 17.5865 ;
Vm = 277 * sqrt(6) ;

ws = 2 * pi * 85000 ;

Lp = 27.13e-6 ;
Cpp = 129.23e-9 ;
Cps = 175.29e-9 ;
Ll = 34.69e-6 ;
Lm = 782.76e-6 ;

syms s real

Zp = s * Lp + ws * Lp * 1i ;
Zpp = 1 / ( s * Cpp + ws * Cpp * 1i ) ; 
Zps = 1 / ( s * Cps + ws * Cps * 1i ) ; 
Zl = s * Ll + ws * Ll * 1i ; 
Zm = s * Lm + ws * Lm * 1i ; 

Kp1 = ( Req * ( 1 + ( ( Zps + Zl ) / Zm ) ) ) + Zps + Zl ;
Kp2 = 1 + ( Zp / Zpp ) + ( Zp / ( Zps + Zl ) ) ;
Kp3 = Zp / ( Zps + Zl ) ;

H_mi_idcap = ( 2 * sqrt(3) / pi ) * Vm / ( ( Kp1 * Kp2 ) - ( Req * Kp3 ) ) ;

H_mi_idenvcap = ( ( real( H_mi_idcap ) ) * ( real ( Id ) ) + ( imag( H_mi_idcap ) ) * ( imag( Id ) ) ) / ( abs( Id ) ) 

H_mi_idenvcap = 

[N, D] = numden(H_mi_idenvcap);
H_mi_idenvcap = collect(simplify(N), s) / simplify(D)

H_mi_idenvcap = 

[Aditya Zade]

Thank you very much. Btw how do you arrange the answer so nicely? Is there any tool for that.

[Aditya Zade]

Also, I need to use this 'H_mi_idenvcap' to generate a step response. So, I need it as a transfer function with s = tf('s'). Do you know how can I do that?

TF = tf(N, D) ;

is giving me an error.

[Walter Roberson]

format long g
Id = 2.1467 - 51.0287i ;
Req = 17.5865 ;
Vm = 277 * sqrt(6) ;

ws = 2 * pi * 85000 ;

Lp = 27.13e-6 ;
Cpp = 129.23e-9 ;
Cps = 175.29e-9 ;
Ll = 34.69e-6 ;
Lm = 782.76e-6 ;

syms s real

Zp = s * Lp + ws * Lp * 1i ;
Zpp = 1 / ( s * Cpp + ws * Cpp * 1i ) ; 
Zps = 1 / ( s * Cps + ws * Cps * 1i ) ; 
Zl = s * Ll + ws * Ll * 1i ; 
Zm = s * Lm + ws * Lm * 1i ; 

Kp1 = ( Req * ( 1 + ( ( Zps + Zl ) / Zm ) ) ) + Zps + Zl ;
Kp2 = 1 + ( Zp / Zpp ) + ( Zp / ( Zps + Zl ) ) ;
Kp3 = Zp / ( Zps + Zl ) ;

H_mi_idcap = ( 2 * sqrt(3) / pi ) * Vm / ( ( Kp1 * Kp2 ) - ( Req * Kp3 ) ) ;

H_mi_idenvcap = ( ( real( H_mi_idcap ) ) * ( real ( Id ) ) + ( imag( H_mi_idcap ) ) * ( imag( Id ) ) ) / ( abs( Id ) );
[N, D] = numden(H_mi_idenvcap)

N = 

D = 

19758232616516474986477649920000

N = collect(simplify(N), s);
[N1, D1] = numden(N);
c1 = sym2poly(N1);
c2 = sym2poly(D1);
D = simplify(D);
H_mi_idenvcap = tf(c1./double(D), c2)

H_mi_idenvcap =
 
                         2.205e188 s^7 + 8.513e195 s^6 + 3.049e201 s^5 + 5.943e207 s^4 + 1.696e213 s^3 + 1.181e219 s^2 + 2.349e224 s + 5.088e229
  ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
  8.527e170 s^10 + 9.029e176 s^9 + 2.602e183 s^8 + 1.91e189 s^7 + 2.231e195 s^6 + 1.11e201 s^5 + 6.483e206 s^4 + 2.105e212 s^3 + 6.002e217 s^2 + 9.105e222 s + 9.863e227
 
Continuous-time transfer function.

[Aditya Zade]

Thanks for your help.

[Aditya Zade]

One of my transfer function is mentioned below. The problem is matlab is considering it as inf/inf which is giving me NaN in TF. How can I reduce the accuracy of each cofficients such that matlab doesn't consider numerator and denominator as inf.

In other words, how can I make this expression into a TF to generate bode plots.

H_mi_idenvecap = (3198609293274692543065653067624214930931010880602439324145398125122373719207088478979647504147912365379393279754941675512836511355487782993690473574523041631084160518721751172162257705176739868804951103644988270056301183639951764002961292649184871320805158132898539453590562021769463423670681600*s^10 + 528394964584010682783572570459412119664515594164049190345558269437867459470515176667326104615180103456012477355413596835172119921200079260151617877500088502992749340415451742149406277381474643891231659256544455164436234396533126019809440535921033867151082644616021673572586341975274322902549476147200*s^9 + 3364815264139209882761251038034730020362043044801573317888318745671317862412400497423209337541418420521260443952869134388981445799336993041335421299405549089717062472469931053659028441787475552139751801731258711488308627072509140489498330224609031510667147325022465839409185515146370263699813850219632656384*s^8 + 563685908110931596054975975789145169901513780980290358304128472564818439113945323667367115971977027594918152558869188644661828289297726904892093313231476094308350368709481298326017516778957422345680859263591644269304648598798995637702553858174358334141567592255906469564947805207135557231654360809390637347504128*s^7 + 1490257685171315468981773939159767624935105379546903549767553901546757666260988184536138242660525137524427599600907269172197568037353264870592893757184448550843993106896014192025989160859007053395078824566748256700430184559758347451096212214570755769067612673807213370221663874574993990956271545381513459363454956601344*s^6 + 224411121359031406238956529185520395250362431900419601379549724354175300141779807782002787175390937335420258029478904711464033857382032746518758309250170139544602989872581677894407504342046674752426946975585667274279454218538522463096065609371083080593692625877514805336214723108899068335933784036977289350835195383669325824*s^5 + 313435614540771365005472378788015656763925845027971206036651498864090340592352682307018010940557769472344445076584267523825439903337732769841322691195467198038852610063857978387582140881350878878314891681041745284058278276910429225911095101311401498430011153223268796705288141506966312381716632816295470628030364360123375283077120*s^4 + 33052372310506629010656599121147115620859961521559341305146351113127420214834631202990344435993579760702170846892190791973857746526095679537107762472443219962883772363971249591309331211286424393764376285694816602968673940014673553192267278248106274456921340775937053409889209132481984880619358508372583085903071902984276537872895442944*s^3 + 10554849876610050019218981278396688996628674897403163356241700611846899932472970866934831849299194775963827696479104585836123032305509546783003015154442878237125239205963612543055962962608195786274300100491480333594963695160464423230708118733213297370805489181822237410178521006221240286568706063689875376392244199192804233754948767114592256*s^2 + 753392467992893717086282360117150962316839153406675455633706582201238077981189206904259370759701924447550938546700321591834810653022526799241547416036382680758251634390626464710218582595943371303498239715517551074690452253677797215333441705005554261781839683641360100743141925156332627926700008050827621415436588867603559400388725106077190848512*s + 40393566359665865213299995369702801378786875218724874851168023401021269156066673958605743192955287230615526894469312967897474790091218367504457257709499999902912836650529949891815535967261169141147611466577851052777443496008708518428106932969186262475588373778567341855852815573620320080624013993765045842114972784171785710233396747569200139998330880)/(8796093022208*(1736567701589301145136648268745070267169586006463452702588095291310545287345936191207231693796554822487658048259058768341620886269302733511008839672446368759925297181964446329483562182298316297460367920025475136735375318177318220152446938927265225*s^16 + 717181706990849576639378846143604344747449411096706760755432781269930354932423747033964722181786892343713490722151365999943109079738204766382874076277599763531511760836188464560773573023546208271499106196789947712108879925411040105198246484299810406400*s^15 + 8474902337396137452537172814758191980658242868146989657851391747578894251875032832065877742822364594666025855664179609126663161480336968740345550831115764290784755921679756769231426450016836146980279285273763923555792818972379443730261637462558119995610497024*s^14 + 3060326629338539947795355844711670424230830104533914727180539407962588796854615013646350523884347125794176122078030819700072795725888050006338552712785006937280184063404052729170190527501487957786817505885405810768143497607256181752489430834429438245071731940130816*s^13 + 15335444336168058219053185629448334708949063277544031136997077132483020621337637079802757161722640630404872281753614633056555568331414532672223094357966529046772826765042453467781257350997846896530993396891805695459960227266764332535793736164051751621607630139917288341504*s^12 + 4711858733362574057644866067860734266890167073692817480732992906997138035715344442510025574475777812882693974120674123611995382178060815482516053616266140291523815161417712375969402534241363378219168042007415040048566795665071810311976396545823703304132119454866433941966946304*s^11 + 12461014205963250065638676548329519983986852678656821442028223071451986862953854290657145129348903622243955644402794979315564378889686689969794544728780606414037860400637500820387005456202310836355975107206149920656892865375979089113148380105538910212977991189672316595043017557016576*s^10 + 3153610764893990481124174423558310705947546643632994209428020901123162737494351255973870435414198228754915355165434369521635012685859083006757509655278714956660143488334593307926704075313537591188840386118802653628117669854992826061562111167065459384377864567395435560227329653331202146304*s^9 + 4196412284794922572702360089303675577340283804488759850189612200368294017368398595914096366806020918778693395129234114128153062192604212478313975760328409295684988085937308175782203157955672589220365686768906199996621051328446913656225084261462685321058494326091046314623083166983844470867361792*s^8 + 839696424033259323305277259210900820320478003816838709480281015945809199296634999150590387829225143482425327884290937963213529918958215499963010050257883261661116698672089983062272555691561771948624741135615136402177972155830430074599923524875698012649853320313826785826359259368579738843006040539136*s^7 + 341072015811716244581240425181942419448756068895024422843527961260011128604733215760197603405155010453702864279995268573154131226786824324708691134950163294295325223338672708909939254713696078247686589394867848835471068071716381633979836751951857567203826189555176612717339907046903740670679827717512232960*s^6 + 51476173533824520781908853124919012872558430328391461780218775183986801463554817939279579606358525500680300575053075911956606069305313326101015765941389705874779285216218534083105540702681692717458081833490789076288368074605827448462551175726017448688748586848426830311404300308080734687142200861235996885254144*s^5 + 9228963476387818526423807612115148970316248169275808385076365503267308598269819401998734036439982463217524876484624976388723299159343094174914050928582387570266303834881596621229787172099209884856109159135095077583516660315341853942084463079767357281710097403352648761070698296853785890788932711840594861082305101824*s^4 + 911043127300211915454447709952136661126629354017481583423569852460766841727455715209418097330189535279221498687673228467765980464696556517614401815146230080830691482821416104568196921957378920491489758562441974400120279545914620076777651283757517630045507906342397020857506949542233013765663031850658377453871364193648640*s^3 + 75868678050389397096199117807278223110751098365028855498075829798267143867014386665936900343279698677835660735344427396694303631098532043960596038629673009001621357014913910492452492780815641595686087435829590661675243076354379570729851910901126879665446131462508434640539917488307446180193941439583412905434367223985904549888*s^2 + 3174513831849780742601338555460290943793994469034596358746253922613510616605561379821305476696010693727089813475729119325248586731428000109372903713452154026995530738937814787974412887244775242394586804120936971001141865477711946150235680311292016446655479884972049090441497967508802274262026411582423828562014806418492161112670208*s + 85101763546936457815360949157574484179847571907787276421705398659175650996907399114220574701462894693638387449557772198429740759814194738572525547329802602231403046298633131911713278866661938182354784531853129097941253657184023638815783627856915654844607628228041193047656641242417683444772761706726371526915906514106247461005512671232))