ECEN5807. Modeling and Control of Power Electronic Systems

Transcription

1 Modelng and Control of Power Eletron Systems Instrutor: Dragan Maksmo Offe: OT346, , Offe hours Monday 2-4 pm Class blog aalable for questons and omments related to HW assgnments and ourse materals Emal questons wll be answered wthn 48 hours (workng days). Please use 5807 n the subjet lne Course web ste: Announements, ourse materals, assgnments, lnks to blog and D2L Textbook: Erkson and Maksmo, Fundamentals of Power Eletrons, 2 nd edton, Sprnger 2000 On-lne ourse letures: Aessble through CAETE (aete.olorado.edu)

2 blog Lnked on the ourse webste You wll reee an ntaton to ontrbute to the blog a e-mal to your olorado.edu address Use the blog to post questons or omments related to HW assgnments or ourse materals

3 Requred Software Spe smulator free LTspe s a reommended Spe smulator MATLAB/Smulnk Control Systems Toolbox Student erson s suffent Software s aalable to on-ampus students on Power Lab and Cruts Lab omputers The ourse webste nludes more detals and LTspe and MATLAB/Smulnk materals

4 Assgnments Weekly homeworks (3 total), 52% of the grade HW wll be assgned on Frday ths week Mdterm exam (open book/notes, take-home), 6% of the grade Fnal exam (open book/notes, take-home), 32% of the grade HW assgnments and due dates posted on the ourse web ste Desre2Learn (D2L) on-lne system All work must be uploaded a D2L. Hand-wrtten work must be sanned and uploaded as a sngle, easly readable pdf fle HW and exam sores, as well as solutons wll be posted on D2L Due dates/tmes are the same for all students are enfored eletronally by the D2L system 4

5 Power Eletrons Program at CU Boulder ECEN5797 Introduton to Power Eletrons Fall semesters Modelng and Control of PE Systems Alternate Sprng semesters (203) ECEN587 Resonant and Soft-Swthng Tehnques n PE Alternate Sprng semesters (204) ECEN557 Power Eletrons Lab Sprng semesters Professonal Certfate n Power Eletrons ECEN507 Pwr El for El. Dre Vehles ECEN5737 Adjustable Speed AC Dres Graduate Certfate n Eletr Dretran Tehnology 5

6 ECEN 5807 tops.introduton to onerter modelng and smulaton usng MATLAB/Smulnk (notes) 2.Aeraged-swth modelng and smulaton (Seton 7.4 and Appendx B) 3.Tehnques of desgn-orented analyss wth swthng onerter applatons Mddlebrook s extra-element and feedbak theorem tehnques (Appendx C and notes) Input flter desgn (Chapter 0) Wrtng omplex onerter transfer funtons by nspeton (notes) Mddlebrook s feedbak theorem (notes) 4.Dynam modelng of onerters n dsontnuous onduton mode Aeraged swth modelng (Chapter and Appendx B) Introduton to sampled-data modelng (notes) 6

7 ECEN 5807 tops 5. Current-mode ontrol Aeraged modelng of peak urrent-mode ontrol (Chapter 2) More aurate models based on sampled-data modelng (notes) Aeraged urrent-mode ontrol (notes) 6. Modern retfers Power and harmons n nonsnusodal systems (Chapter 6) Pulse-wdth modulated low-harmon (.e. power-fator orreton, or PFC) retfers (Chapter 8) System modelng Current ontrol tehnques Voltage ontrol tehnques 7. Introduton to dgtal ontrol of swth-mode power onerters (notes) Dgtal realzaton of the bas ontrol loop Dsrete-tme modelng Dsrete-tme ompensator desgn examples 7

8 Introduton to Swthed-Mode Conerter Modelng usng MATLAB/Smulnk MATLAB: programmng and srptng enronment Smulnk: blok-dagram modelng enronment nsde MATLAB Motaton: Powerful enronment for system modelng and smulaton More sophstated ontroller models, analyss and desgn tools But*: Blok-dagram based Smulnk models, undretonal sgnals Not a tradtonal rut smulator; spealzed physs-based Spe dee models or omponent lbrares are not readly aalable *Varous add-ons to Smulnk are aalable to allow tradtonal rut dagram entry and rut smulatons (e.g. SmPowerSystems, PLECS), or to embed Spe wthn MATLAB/Smulnk enronment. These add-ons are not requred and wll not be used n. 8

9 Introduton through an example g Synhronous buk onerter R on L _ Load L R L R esr g dt s T s PWM V M R on2 C C _ out _ Magntude (db) Bode Dagram From: To: SynBuk/out Phase (deg) Frequeny (Hz) Swthng model Aeraged model 5 Vg g Small-sgnal lnearzaton and frequeny responses 0.36 V out out See MATLAB/Smulnk page on the ourse webste ( Materals page) for omplete step-bystep detals, and to download the example fles 0 Load Load g g Sope SynBuk Smulnk model: synbuk_ol.mdl 9

10 Synhronous Buk Conerter g R on L _ Load L R L R esr g R on2 C C _ out _ dt s T s PWM V M Inputs: g, Load, Outputs: out, g State arables:, 0

11 Conerter state equatons g R on L _ Load L R L R esr g R on2 C C _ out _ dt s T s PWM V M State equatons Output equatons L d L dt g Ron RL out ( ) R R ( 0) on2 L out g ( ) 0 ( 0) d C dt C Load out R esr Load

12 Smulnk model 5 Vg SynBuk subsystem blok g 0.36 V out out 0 Load Load SynBuk g g Sope g 2 3 Load PWM u u CCMbuk y y d /dt d/dt s apator ntegrator s ndutor ntegrator 2 SynBuk subsystem blok nternals CCM buk out 3 out g 4 g 2

13 Synhronous buk (SynBuk) subsystem Inputs g 2 3 Load PWM subsystem PWM u u CCMbuk y y d /dt d/dt Integraton of state arables s apator ntegrator s ndutor ntegrator 2 Outputs CCM buk Conerter state equatons out g 3 out 4 g 3

14 PWM operaton and model Add Comparator PWM ramp Smulnk PWM model 4

15 Conerter state equatons: embedded MATLAB srpt g 2 3 Load PWM u u u CCMbuk y CCM buk y Conerter state equatons y d /dt d/dt out g s apator ntegrator s ndutor ntegrator 2 3 out 4 g u = nputs = [g Load ] y = outputs = [/C L/L out g] out g R esr ( ) 0 ( 0) Load d C dt C Load L d L dt g Ron RL out ( ) R R ( 0) on2 L out 5

16 Numeral example g R on L L _ R L R esr Load Swthng frequeny: f s = MHz g dt s T s PWM V M R on2 C C _ out _ I out = 0 V g = 5 V L = H R L = 0 m R on = R on2 = 20 m 5 Vg g C = 200 F 0.36 R esr = 0.8 m V 0 Load Load SynBuk out g out g Sope PWM ramp ampltude V M = V V = 0.36, D = 0.36 Smulnk model: synbuk_ol.mdl 6

17 Numeral example: synhronous buk onerter model 5 g Vg 0.36 V out out 0 Load Load SynBuk g g Sope Maskng a Smulnk subsystem allows parameterzaton Same subsystem model an be re-used Models and MATLAB srpts an be olleted n a lbrary 7

18 Swthng smulaton: open-loop start-up transent out g 20 s/d Zoom n, s/d 8

19 d L L Ts dt d C C Ts dt d g out L T T s s d g L dt d C dt ( ) 0 ( 0) C Load T s T s T T s R esr T T s s Load Load Aeraged model Ron RL out ( ) R R ( 0) on2 g R out esr Load L T T s s out Swthng model State-spae aeragng (reew Textbook Setons ) R R d R R s d g T on L T out on s s T 2 s Large-sgnal aeraged model L T s out T s 9

20 Conerter aeraged state equatons: MATLAB The MATLAB funton stays exatly the same, exept d (duty-yle) replaes (swth ontrol) 20

21 Synhronous buk (SynBuk) subsystem: swthng or aeraged model 2 Inputs Aeraged model of the PWM /VM PWM PWM Gan g sw onstant d 3 Load Swth d u CCMbuk y u CCM buk Conerter state equatons y d /dt d/dt out g Integraton of state arables s apator ntegrator s ndutor ntegrator 2 3 out 4 g Outputs 2

22 Start-up transent smulatons Swthng model Aeraged model out g 22

23 Lnearzaton of the large-sgnal aeraged model Large-sgnal (nonlnear) aeraged model Lnearzaton at an operatng pont V g d R L L L g D L D g I o d R esr C R Small-sgnal aeraged model The small-sgnal model an be soled for all mportant onerter transfer funtons: G d ˆ ( s) dˆ G g ( s) ˆ ˆ g Z out ˆ ( s) ˆ Control-to-output Lne-to-output Output mpedane load 23

24 Reew textbook Chapter 8 Synhronous buk onerter example Buk SSM V g d g D L D g I o d dˆ R L G d (s) L L R esr C R G d ( s) G d V g ( s) ˆ o dˆ s s Q o esr s o 2 Par of poles: f o khz 2 CL Low-frequeny gan: G do 5V 4dBV L / C R Qloss db Q load 5 R R L / C Q Q loss esr L QlossQload Qload db Q Q loss load f ESR zero: esr 2CR esr MHz 24

25 Magntude and phase Bode plots of G d 80dB 60dB (/V M )G d (s) 40dB 20dB G do ( / V M ) 5 4dB Q dB 0dB f o khz 40dB/de -20dB 0 / 2Q f o 0 o f esr MHz 20dB/de -90 o 0 / 2Q f o /0 f esr 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz -80 o 25

26 Lnearzaton and frequeny responses n MATLAB/Smulnk 5 g g. Set transfer funton nput and output ponts Vg 0.36 V out out 0 Load Load Load SynBuk 2. MATLAB srpt (BodePlotter_srpt.m) omputes DC operatng pont, lnearzes the model, omputes and plots the transfer funton magntude and phase responses g g Sope 26

27 Magntude and phase Bode plots of G d 40 Bode Dagram From: To: SynBuk/out 20 Magntude (db) Phase (deg) Frequeny (Hz) 27

28 Reew Textbook Chapter 9 Closed-loop (oltage-mode) ontrol L (t) I out L V g C R o Dead-tme ontrol f s = MHz PWM duty-yle ommand Compensator error _ /V M G (s) V ref =.8 V Pont-of-Load (POL) Synhronous Buk Regulator 28

29 Reew Textbook Chapter 9 Closed-loop SMPS blok dagram Control objetes: tght output oltage regulaton Stat or dynam dsturbanes Input (lne) oltage g Load urrent load Component toleranes 29

30 Small-sgnal model: loop gan T T(s) Loop gan: T(s) = H(s)G (s)(/v M )G d (s) 30

31 Small-sgnal model: losed-loop responses T(s) 3

32 Feedbak loop desgn objetes T(s) To meet the ontrol objetes, desgn T as large as possble n as wde frequeny range as possble,.e. wth as hgh f as possble Lmtaton: stablty and qualty of losed-loop responses 32

33 Unompensated loop gan T u L (t) I out L V g C R o _ G d (s) _ f s = MHz Dead-tme ontrol PWM duty-yle ommand Compensator error _ H sense = (n ths example) /V M G (s) = V ref T u (s) = H sense (/V M )G d (s) Plot magntude and phase responses of T u (s) to plan how to desgn G (s) 33

34 Magntude and phase Bode plots of T u 80dB 60dB T u (s) = H sense (/V M )G d (s) 40dB 20dB T uo G do ( / V ) H 5 4dB M sense Q dB 0dB -20dB f o khz 0 / 2Q f o 40dB/de T uo f f o 2 0 o target f 20dB/de f esr MHz -90 o 0 / 2Q f o /0 f esr 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz -80 o 34

35 Lead (PD) ompensator desgn. Choose: f 00 khz m 53 o 2. Compute: 33 khz 300 khz 3. Fnd G o to poston the rossoer frequeny: T uo f f o 2 G o f f p z G o T uo f f o 2 f f z p db Magntude of T u at f Magntude of G at f 35

36 Lead (PD) ompensator summary G ( s) G o s z s p Lead ompensator s p 2 HF pole f G o 5.45 f z 33 khz 5 db f p 300 khz 00 khz (=/0 of f s ) Hgh-frequeny gan of the lead ompensator: G o f p /f z = 49 (34 db) Added hgh-frequeny pole: f p2 MHz (= f esr = f s n ths example) 36

37 Loop gan wth lead (PD) ompensator 80dB 60dB 40dB T uo G o dB G ( s) G o s z s p s p 2 20dB 0dB f 00 khz -20dB f z 0kHz f z 33kHz f p 300kHz 0 o -90 o 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz m 53 o -80 o 37

38 Add lag (PI) ompensator Integrator at low frequenes Choose 0f L < f so that phase margn stays approxmately the same: f L = 8 khz Keep the same ross-oer frequeny: G G o G m db 38

39 Addng PI Compensator 80dB 60dB 40dB 20dB 0dB f L 8kHz f 00 khz -20dB 0 f L 0 o /0 f L PI ompensator phase -90 o 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz m 53 o -80 o 39

40 Complete PID ompensator: summary G m db f L 8 khz f z 33 khz f p 300 khz f p2 MHz Crossoer frequeny: Phase margn: f 00 khz (=/0 of f s ) m 53o 40

41 Magntude and phase Bode plots of T 80dB 60dB 40dB 20dB 0dB f 00 khz -20dB Phase of unompensated T u 0 o Phase of ompensated T -90 o 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz m 53 o -80 o 4

42 Closed-loop oltage regulator n Smulnk Smulnk model: synbuk_cl.mdl 5 g g Vg x out out Step Load Load SynBuk g g Sope H x y Injeton pont y 5.45 Gm /(2*p*8e3)s /(2*p*8e3)s Inerted zero /(2*p*33e3)s /(2*p*300e3)s PD Compensator /(2*p*e6)s HF pole.8 Vref PID ompensator Input and output lnearzaton ponts for fndng the loop-gan, T = - y / x The output pont (y) should be Open Loop, as shown by an x symbol next to the output arrow 42

43 Loop gan and stablty margns MATLAB srpt BodePlotter_srptT.m (omputes d op, lnearzes, alulates and plots frequeny response and stablty margns) 00 Bode Dagram Gm = Inf db (at Inf Hz), Pm = 5.6 deg (at.05e005 Hz) From: x To: Gm/y Magntude (db) Phase (deg) Frequeny (Hz) 43

44 Closed-loop 0-5 Astep-load transent responses Aeraged model Swthng model out g 5 s/d 5 s/d See MATLAB/Smulnk page on the ourse webste ( Materals page) for omplete step-by-step detals, and to download the example fles 44