Delta Power Electronics Center Basic Control for Power Electronics --1-- • Andrew Zhang • Dr. Jianping Ying DPEC Shanghai 2003-06-06 Basic Control for Power Electronics Delta Power Electronics Center Basic Control for Power Electronics --2-- Contents 1) Basic concepts and classifications � State Space Method � PWM Switching Method � CCM � DCM 2) Design methods � Voltage loop � Peak current � Average current Delta Power Electronics Center Basic Control for Power Electronics --3-- Benefits of modeling technology � help to catch on the inherent essence. � help to guide the design of close-loop. Delta Power Electronics Center Basic Control for Power Electronics --4-- Basic Model of Power Electronics System sL sC 1 V0 I0 i ∆ DTs v ∆ v i Little ripple approximation 0 0 0 I i I i I I << ∆ ≅ ∆ + = V D D V D V ⋅ = ⋅ − + ⋅ = 0 ) 1( 0 0 0 V v V v V V << ∆ ≅ ∆ + = Weighting & Averaging I D D I D I ⋅ − = ⋅ + ⋅ − = ) 1( 0 ) 1( Inductor and Capacitor determine the n-order. CCM CCM Delta Power Electronics Center Basic Control for Power Electronics --5-- 1. SSM(State State--Space Method) Space Method): commonly and widely used. Classifications of Modeling 3. SIM SIM(Switch Inductor Model): (Switch Inductor Model): can be implemented us can be implemented using ing Pspice Pspice.(ignored here) .(ignored here) 4. HFNM(High Frequency Network Method): High Frequency Network Method): can be implemented us can be implemented using ing Pspice Pspice.(ignored here) .(ignored here) 5. Others 2. PWM Switch PWM Switch: Suits for : Suits for Pspice Pspice simulation directly. simulation directly. Delta Power Electronics Center Basic Control for Power Electronics --6-- ?? How to model the topology of PE Weighting & Averagingare the right ways to implement. Causes: � the PE topologies generally belong to non-linear system. � hard to model that kinds of topologies. � linear extension at ONE point is ok. D V Delta Power Electronics Center Basic Control for Power Electronics --7-- 1) Basic SSM(State State--Space Method) Space Method) Overview: There are two groups of state equations in CCM mode. u B x A x 1 1 + = & u B x A x 2 2 + = & Weighting Averaging d 1-d u B x A x * * + = & 2 1 * ) 1( A d dA A − + = 2 1 * ) 1( B d dB B − + = Where: Step 1 Delta Power Electronics Center Basic Control for Power Electronics --8-- X x x + = ˆ D d d + = ˆ U u u + = ˆ Add the disturbances at steady state. ¶ Ignore the high order. 0 = + BU AX d U B B X A A u B x A x s ˆ ] ) ( ) [( ˆ ˆ ˆ 2 1 2 1 − + − + + = [ ] U B B X A A A sI d x u ) ( ) ( ) ( ˆ ˆ 2 1 2 1 1 0 ˆ − + − − = − = steady equations: Output to Duty: B A sI u x d 1 0 ˆ ) ( ˆ ˆ − = − = Output to Input: ¶ partial difference. AC transfer functions: 2 1 ) 1( A D DA A − + = 2 1 ) 1( B D DB B − + = where: Step 2 1) Basic SSM(State State--Space Method) (cont.) Space Method) (cont.) Delta Power Electronics Center Basic Control for Power Electronics --9-- We use Buck for example. L C R M D Vin L C R Vin L C R Vin 0<=d<=Don Don> Delta Power Electronics Center Basic Control for Power Electronics --30-- Summary of Basic topology -Transfer function 2 2 1 1 / 1 ˆ ˆ ) ( o o zc o s s Q s s Vin d v s Gvd ω ω + + + = = 2 2 2 1 1 / 1 ˆ ˆ ) ( o o z o s s Q s s R Vin d i s Gid ω ω + + + = = 2 2 1 1 / 1 ˆ ˆ ) ( o o zc in o s s Q s s D v v s Gvv ω ω + + + = = 2 2 1 1 ) / 1( ˆ ˆ ) ( o o zc o o s s Q s s sL i v s Zo ω ω + + + = = 2 2 2 2 / 1 1 1 ˆ ˆ ) ( z o o o in s s s s Q D R i v s Zin + + + = = ω ω C zc CR s 1 = ) ( 1 2 C z R R C s + = LC R R LC R C o 1 ) ( ≈ + = ω R L R L CR Q o C o 1 1 1 1 ω ω ≈ + = 1 D L C R d Ic ˆ d D VD ˆ RC aiˆ ciˆ invˆ ovˆ Buck-type converter Delta Power Electronics Center Basic Control for Power Electronics --31-- Summary of Basic topology -Transfer function(cont.) 2 2 2 1 1 ) / 1 )( / 1( ' ˆ ˆ ) ( o o zRHP zc o s s Q s s s s D Vin d v s Gvd ω ω + + − + = = 2 2 3 2 1 1 / 1 ' 2 ˆ ˆ ) ( o o Z O o s s Q s s RD V d i s Gid ω ω + + + = = 2 2 1 1 / 1 ' 1 ˆ ˆ ) ( o o zc in o s s Q s s D v v s Gvv ω ω + + + = = 2 2 1 1 ) / 1( ˆ ˆ ) ( o o zc o o s s Q s s sL i v s Zo ω ω + + + = = 3 2 2 2 / 1 1 1 ' ˆ ˆ ) ( p o o o in s s s s Q RD i v s Zin + + + = = ω ω C zc CR s 1 = L R D szRHP 2' = LC D R R LC R D C o ' ) ( '2 ≈ + = ω CR R R C Q o C o ω ω 1 ) ( 1 ≈ + = Boost-type converter ) ( 1 3 R R C s C P + = CR sZ 2 3 = L C R RC d Iinˆ d D VD ˆ − in vˆ ovˆ D 1 Delta Power Electronics Center Basic Control for Power Electronics --32-- 3) DCM PWM Switch (cont.) Vin L C R Buck a c p ia ip Active Passive ac V cp V ai pi + − + − d 1 d Common dTs d1Ts d2Ts L V V o in − L V o − in V in V o V Vcp Vac ip ia o in V V − Delta Power Electronics Center Basic Control for Power Electronics --33-- 3) DCM PWM Switch (cont.) ac s a v Lf d i 2 2 = p ac s cp i v Lf d v 2 2 2 = d i i pk a 2 = 1 2 d i i pk p = p a i d d i 1 = s pk ac dT i L v = s pk cp T d i L v 1 = ac cp v d d v 1 = s ac pk dT L v i = 1 2 d i i p pk = ac p s v i d Lf d 2 1 = dTs d1Ts d2Ts L V V o in − L V o − in V in V o V Vcp Vac ip ia o in V V − Active Passive ac V cp V ai pi + − + − d 1 d Common Delta Power Electronics Center Basic Control for Power Electronics --34-- 3) DCM PWM Switch (cont.) ac s a v Lf d i 2 2 = p ac s cp i v Lf d v 2 2 2 = e s a ac R d Lf i v = = 2 2 e e ac p cp P R v i v = = 2 + − + − e R eP ac V cp V ai pi Loss-Free Resistor (LFR) Active Passive ac V cp V ai pi + − + − d 1 d Common Delta Power Electronics Center Basic Control for Power Electronics --35-- ac s a v Lf d i 2 2 = p ac s cp i v Lf d v 2 2 2 = 3) DCM PWM Switch (cont.) p p p cp cp cp ac ac ac a a a i I i v V v v V v i I i d D d ˆ ˆ ˆ ˆ ˆ + = + = + = + = + = ac s a V Lf D I 2 2 = d k v g i i ac i a ˆ ˆ ˆ + = p ac s cp I V Lf D V 2 2 2 = cp o o ac f p v g d k v g i ˆ ˆ ˆ ˆ − + = ac a s i V I Lf D g = = 2 2 D I Lf DV k a s ac i 2 = = ac p cp s ac f V I V Lf V D g 2 1 2 = = D I V Lf DV k p cp s ac o 2 1 2 = = cp p o V I g = Delta Power Electronics Center Basic Control for Power Electronics --36-- 3) DCM PWM Switch (cont.) – BUCK d k v g i i ac i a ˆ ˆ ˆ + = cp o o ac f p v g d k v g i ˆ ˆ ˆ ˆ − + = Active Passive ap vˆ cp vˆ Common ig d ki ˆ + − + − o g ac fv g ˆ d ko ˆ piˆ Delta Power Electronics Center Basic Control for Power Electronics --37-- Vin L C R buck a c p ia ic 3) DCM PWM Switch (cont.) – BUCK Active Passive ap vˆ cp vˆ Common ig d kiˆ + − + − og ac fv g ˆ d koˆ piˆ A Passive cp vˆ C ig d ki ˆ + − og ac fv g ˆ d koˆ piˆ L C R invˆ + Rc Rc Delta Power Electronics Center Basic Control for Power Electronics --38-- A ig d ki ˆ og ac fv g ˆ d koˆ L C R invˆ + P C 3) DCM PWM Switch (cont.) – BUCK ) 1( 2 M R M V V I V I g o in in ac a i − = − = = DR M V D I D I k o in a i 2 2 2 = = = R M V V I I V I g o in in o ac p f 2 ) ( 2 2 = − − = = DR M V D I I D I k o in o p o ) 1( 2 ) ( 2 2 − = − = = R M V I I V I g o in o cp p o − = − = = 1 o in in o I I V V M = = in a I I = o in ac V V V − = M K M D − = 1 R Lf K s 2 = Rc Delta Power Electronics Center Basic Control for Power Electronics --39-- A ig d ki ˆ og ac fv g ˆ d koˆ L C R invˆ + P C 3) DCM PWM Switch (cont.) – BUCK r f o i g g g r + + = 1 L C R Rc Rc d Kd ˆ o i d k k k + = C L L C L C L L d vd Z R Z Z R Z R Z r K s G || || )] || ( || [ ) ( + + = Delta Power Electronics Center Basic Control for Power Electronics --40-- 3) DCM PWM Switch (cont.) – BUCK ) 1 )( 1( 1 ) ( 2 1 p p zc vd vd s s s K s G ω ω ω + + + = π π ω ω π ω ω ω s p p s p p c zc f f M L R M M RC C R ≥ = ≥ − = − − = = 2 1 ) 1( 1 2 1 1 2 2 2 1 fp1 fzc fp2 fp2>> fp1 Therefore, DCM is similar to single-pole system. Delta Power Electronics Center Basic Control for Power Electronics --41-- Summary 1. The Steady equations and AC transferring functions can be deduced by SSM & PWM Switching Method. 2. SSM can be used in DC/DC, PFC and so on to analyze. 3 . SSM deduction is lightly complicated and boring. 4. SSM can be deduced by MATHEMATICA MATHEMATICA software(symbol calculation). 5. PWM Switching Method can be integrated into Pspice-like simulations. Delta Power Electronics Center Basic Control for Power Electronics --42-- Any comments & suggestions? Delta Power Electronics Center Basic Control for Power Electronics --43-- Voltage Loop Design Delta Power Electronics Center Basic Control for Power Electronics --44-- Voltage Loop Design ) ( ) ( ) ( ) ( s F s G H s G s G M C dv L ⋅ ⋅ ⋅ = Gdv(s) GC(s) H ) ( ˆ s vo _ + ) ( ˆ s vref FM(s) ) ( ˆ s vi ) ( ˆ s vG dˆ GL(s) eˆ Gdv(s): transfer function H : voltage divider FM(s) : saw-wave gain. GC(s) : added compensation. Delta Power Electronics Center Basic Control for Power Electronics --45-- K e ∆ K Ts e Ts d = ∆ ⋅ ∆ Voltage Loop Design –parameters Fm(s) ) ( ) ( ) ( ) ( s F s G H s G s G M C dv L ⋅ ⋅ ⋅ = For saw-waveform K e d s FM 1 ) ( = ∆ ∆ = dTs ∆ e ∆ dTs ∆ Delta Power Electronics Center Basic Control for Power Electronics --46-- Basic regulators - + Z2 Z1 IN OUT ) (1 ) ( 2 ) ( s Z s Z s F − = ) ( : ) ( lg 20 ) ( : ) ( ) ( ) ( ϖ ϕ ϖ ϖ ϖ ϖ ϖ ϕ Phase A j L Amplitude e A j F j = = Voltage Loop Design –parameters Gc(s) Delta Power Electronics Center Basic Control for Power Electronics --47-- - + R2 R1 IN OUT - + R1 IN OUT - + R1 IN OUT C1 C1 P I D 1 2 ) ( R R s GC − = 1 1 1 ) ( C sR s GC − = 1 1 ) ( C sR s GC − = 20lgK1 w L(w)/dB w P(w) 0 0 -20db/dec w L(w)/dB w P(w) 0 0 -90 0 20db/dec w L(w)/dB w P(w) 90 0 P I D Voltage Loop Design –parameters Gc(s)(cont.) Delta Power Electronics Center Basic Control for Power Electronics --48-- - + R2 IN OUT Cz R1 Cp ) 1 ( 1 ) ( 2 1 1 + + = τ τ s s s K s F ) ( 1 2 1 Z P C C R K + = where Z C R 1 1 1 = τ e C R 1 2 1 = τ p z p z e C C C C C + = common regulator Voltage Loop Design –parameters Gc(s)(cont.) Delta Power Electronics Center Basic Control for Power Electronics --49-- - + R2 IN OUT Cz R1 Cp When Cp >> Cz (10 times is enough) Z e C C ≅ s K s s s K s F 1 ) 1 ( 1 ) ( 1 2 1 1 ≅ + + = τ τ The regulator equals Integration regulator. - + R2 IN OUT Cp I 2 1 τ τ = Voltage Loop Design –parameters Gc(s)(cont.) Delta Power Electronics Center Basic Control for Power Electronics --50-- When Cp << Cz (10 times is enough) p e C C ≅ ) 1 ( 1 ) ( 2 1 1 + + = τ τ s s s K s F Z C R 1 1 1 = τ p C R 1 2 1 = τ Zero Pole Properties: � Zero is determined by Cz & R1, independent on Cp & R2. � Pole is determined by Cp & R1, independent on Cz & R2. � Gain K1 is determined by Cz & Cp & R2, independent on R1. Lead-Lag - + R2 IN OUT Cz R1 Cp Voltage Loop Design –parameters Gc(s)(cont.) Delta Power Electronics Center Basic Control for Power Electronics --51-- ) 1 ( 1 ) ( 2 1 1 + + = τ τ s s s K s F Voltage Loop Design –parameters Gc(s)(cont.) 1 1 τ 2 1 τ -900 -1 -1 ) (ω M ) (ω Φ ω ω Delta Power Electronics Center Basic Control for Power Electronics --52-- Voltage Loop Design –compensation consideration Gdv(s) GC(s) H ) ( ˆ s vo _ + 0 ) ( ˆ = s v ref FM(s) dˆ GL(s) eˆ [ ] ) ( ) ( ) ( ) ( s G s F H s G s G C M dv L ⋅ ⋅ ⋅ = Initial system compensation ) ( ) ( ) ( ' s G s G s G C dv L ⋅ = ) ( ) ( ) ( ' s F H s G s G M dv dv ⋅ ⋅ = Delta Power Electronics Center Basic Control for Power Electronics --53-- How to judge the stability of the system? How to judge the stability of the system? - frequency domain analysis • Hurwitz Criterion • Nyquist Criterion • Bode plot • Nichols Chart Delta Power Electronics Center Basic Control for Power Electronics --54-- Hurwitz Hurwitz Criterion Criterion Standard format: 0 a s a ... s a s a s a n 1 n 2 n 2 1 n 1 n 0 = + + + + + − − − Conditions: 0 ... 0 0 0 a n 2 1 0 > > > > ∆ ∆ ∆ system is stable n 3 4 5 6 7 1 2 3 4 5 0 1 2 3 0 1 n a 0 0 0 0 0 ... ... ... ... ... ... ... a a a a a ... a a a a a ... 0 a a a a ... 0 0 0 a a = ∆ Delta Power Electronics Center Basic Control for Power Electronics --55-- -1 X jY γ g K 1 Stability margins: Stability margins: γ : 450 ~ 600 g K > 6 dB Bode Plot Nyquist Criterion ω ω GH lg 20 ) (ω ϕ -900 -1800 0dB γ g K 1 Nichols Chart ) (ω ϕ GH lg 20 -1800 -900 -2700 0 + - γ g K 1 "s" domain Criterions Criterions Delta Power Electronics Center Basic Control for Power Electronics --56-- The requirements of system stability: 1. In order to keep the stability of system, p(w) must be left about 60degree when M(w)=0. 2. Sometimes the system is steady, However, for some other characteristics, Such as FAST, ANTI-Disturbance etc, the regulator has to be added. 20lgK 1/t1 1/t2 -180 0 -90 0 0 0 Voltage Loop Design –purpose ω ω ) (ω M ) ( c P ω ) (ω Φ Delta Power Electronics Center Basic Control for Power Electronics --57-- Voltage Loop Design –purpose(cont.) Delta Power Electronics Center Basic Control for Power Electronics --58-- Voltage Loop Design –compensation consideration ) ( ' s Gdv -900 -1800 -2 -00 -2700 Critical Zone: 1) Phase changes 0o ~ -180o o ω c ω ω ω ) (ω M ) (ω Φ Delta Power Electronics Center Basic Control for Power Electronics --59-- Voltage Loop Design –compensation consideration (cont.) fo is high enough -900 -1800 -00 -2700 -2 -3 -1 -1 o ω c ω ω ω ) ( c P ω ) (ω M ) (ω Φ ) ( 0 180 ω M Delta Power Electronics Center Basic Control for Power Electronics --60-- Voltage Loop Design –compensation consideration (cont.) fo is NOT high enough -900 -1800 -00 -2700 -1 -2 -1 -1 -3 900 ) ( c P ω o ω c ω ) (ω M ω ω ) (ω Φ Delta Power Electronics Center Basic Control for Power Electronics --61-- Delta Power Electronics Center Basic Control for Power Electronics --62-- Ggv(s) Gdv(s) GC(s) H ) ( ˆ s vo _ + 0 ) ( ˆ = s v ref FM(s) 0 ) ( ˆ = s vi ) ( ˆ s vG dˆ GL(s) eˆ ) ( ˆ ) ( ) ( ˆ ) ( ˆ ) ( ) ( ˆ ) ( ˆ s v s F s G H d s G d s G s v s v o M C dv gv G o ⋅ ⋅ ⋅ = ⋅ − ⋅ = ) ( ˆ ) ( ) ( ) ( ˆ ) ( ˆ s v s G s G s v s v o L gv G o ⋅ − ⋅ = ) ( 1 ) ( ) ( s G s G s G L gv T gv + = Voltage Loop Design – Others } Audio susceptibility ) ( ) ( ) ( ) ( s G s F s G H s G dv M C L ⋅ ⋅ ⋅ = Delta Power Electronics Center Basic Control for Power Electronics --63-- L C R ovˆ oiˆ Voltage Loop Design – Others Output impendence ) ( 1 ) ( ) ( s G s Z s Z L o T o + = R 1/sc sL 1+GL(s) Zo(s) ) (s Z T o ) (s Zo Delta Power Electronics Center Basic Control for Power Electronics --64-- Voltage Loop Design – by matlab Ltiview Delta Power Electronics Center Basic Control for Power Electronics --65-- Voltage Loop Design – by matlab Using Rltool and Ltiview tools to simulate. % output Vo=12V Ro=12V/60A=0.2 Ro=12V/0.1A=120 Vin=40;Lo=60e-6; Co=2000e-6; Resr=0.1; % light load Ro=120; szc=1/Co/Resr; sz2=1/Co/(Ro+Resr); wo=sqrt(Ro/Lo/Co/(Ro+Resr)); Q=1/wo/(Co*Resr+Lo/Ro); num=Vin*[1/szc 1]; den=[1/wo/wo 1/Q/wo 1];%s^2 s 1 Gvd1=tf(num,den); close1=feedback(Gvd1,1); % heavy load Ro=0.2; szc=1/Co/Resr; sz2=1/Co/(Ro+Resr); wo=sqrt(Ro/Lo/Co/(Ro+Resr)); Q=1/wo/(Co*Resr+Lo/Ro); num=Vin*[1/szc 1]; den=[1/wo/wo 1/Q/wo 1];%s^2 s 1 Gvd2=tf(num,den); close2=feedback(Gvd2,1); figure(1); step(Gvd1);hold on; step(Gvd2); figure(2); step(close1);hold on; step(close2); Ro=120 Ro=0.2 Delta Power Electronics Center Basic Control for Power Electronics --66-- Voltage Loop Design – by matlab rltool Delta Power Electronics Center Basic Control for Power Electronics --67-- Ro=120 Ro=0.2 Voltage Loop Design – by matlab Unit feedback with Gcv Delta Power Electronics Center Basic Control for Power Electronics --68-- Summary 1) GL is important to design. 2) Matlab is helpful to design loop. 3) Other disturbance is attenuated by 1/(1+GL). Delta Power Electronics Center Basic Control for Power Electronics --69-- Any comments & suggestions? Delta Power Electronics Center Basic Control for Power Electronics --70-- Current Loop Design � Peak current mode � Average current mode Delta Power Electronics Center Basic Control for Power Electronics --71-- What’s difference between Average & Peak Current? •Worse Noise immunity •Slope compensation •Subharmonic Oscillation •Slower response than the counterpart. •Complicated Disadvantage •Faster response ••Simple control Simple control •Good noise immunity •Anti disturbance Advantage Peak Current Peak Current Average Current Average Current Delta Power Electronics Center Basic Control for Power Electronics --72-- Peak current mode 1) Ramp compensation. 2) Sub-harmonic. Delta Power Electronics Center Basic Control for Power Electronics --73-- Without compensation when Duty>50% 1 2 1 1 2 0 1 ) ( m m I m m I I > ∞ → ∆ → ∆ − = ∆ Peak current mode 0I ∆ 1I ∆ Delta Power Electronics Center Basic Control for Power Electronics --74-- Chaotic phenomenon when Duty>50% W/O Compensation Duty kI ∆ Delta Power Electronics Center Basic Control for Power Electronics --75-- With compensation when Duty>50% ) ( 1 2 0 1 c c m m m m I I + + ∆ − = ∆ Delta Power Electronics Center Basic Control for Power Electronics --76-- Chaotic phenomenon when Duty>50% W/ Compensation Duty kI ∆ Delta Power Electronics Center Basic Control for Power Electronics --77-- Peak current mode M id L F s G Rs s Gi ⋅ ⋅ = ) ( ) ( Gid(s) ) ( ˆ s iL _ + ea vˆ FM dˆ GiL(s) ) ( ˆ s vo Voltage loop Rs Gvd(s) Delta Power Electronics Center Basic Control for Power Electronics --78-- Peak current mode –parameters Fm(s) Fm is CONSTANT. Sn Se S n C S n e M T S m T S S F 1 ) ( 1 = + = Delta Power Electronics Center Basic Control for Power Electronics --79-- ea vˆ ) ( 1 ) ( ) ( 1 ) ( ) ( ' _ s Gi s G F F s G Rs s G F s G L vd M M id vd M ea v + ⋅ = ⋅ ⋅ + ⋅ = Peak current mode - design M id L F s He s G Rs s Ti ⋅ ⋅ ⋅ = ) ( ) ( ) ( Gid(s) ) ( ˆ s io _ + FM dˆ GiL(s) ) ( ˆ s vo Voltage loop Rs Gvd(s) Delta Power Electronics Center Basic Control for Power Electronics --80-- ) ( 1 ) ( ) ( ' _ s Gi s G s G L vd ea v + = Peak current mode - design in o V sL R sC R sC d v + = 1 1 ˆ ˆ sL R sC V d i in o + = 1 ˆ ˆ M id vd M ea v F s G s G F s G ⋅ ⋅ ⋅ = ) ( Re ) ( ) ( ' _ Considering GiL(s)>>1, f < fs/2 1 1 ) || 1 ( 1 ) ( ' _ + = = sCR R Rs R sC Rs s G ea v} Delta Power Electronics Center Basic Control for Power Electronics --81-- Peak current mode - design 1 1 ) || 1 ( 1 ˆ ˆ ) ( ' _ + = = = sCR R Rs R sC Rs v v s G ea o ea v L disappears, Single-pole system. C R Rs vea ˆ RC Delta Power Electronics Center Basic Control for Power Electronics --82-- -900 -1800 -00 -1 -2 -1 -1 Peak current mode - design o ω c ω ω ω ) (ω M ) (ω Φ Delta Power Electronics Center Basic Control for Power Electronics --83-- Summary 1) Ramp compensation is necessary & important when D>50%. 2) Inductor is like one current-source in peak current mode. 3) System is only one single-pole. Delta Power Electronics Center Basic Control for Power Electronics --84-- Any comments & suggestions? Delta Power Electronics Center Basic Control for Power Electronics --85-- Average current mode Delta Power Electronics Center Basic Control for Power Electronics --86-- Gid(s) He(s) ) ( ˆ s io _ + FM dˆ GiL(s) ) ( ˆ s vo Rs ) ( ) ( ) ( ) ( s G F s He s G Rs s Gi ca M id L ⋅ ⋅ ⋅ ⋅ = Gvd(s) GCA Average current mode Voltage loop Delta Power Electronics Center Basic Control for Power Electronics --87-- Average current mode – He(s) 2 2 1 ) ( n Z n s Q s s He ω ω + + ≈ s n T π ω ≈ π 2 − ≈ Z Q 100 1 .10 3 1 .10 4 1 .10 5 100 90 80 70 60 50 40 30 20 10 0 Phase vs frequency 0.9 − 90 − P f ( ) fs 2 fs 200 f 2 . 10 4 4 . 10 4 0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 Magnitude vs frequency 3.922 2.03 10 4 − × M f ( ) fs 2 fs 200 f Delta Power Electronics Center Basic Control for Power Electronics --88-- Average current mode -GEA S e V N M T S S F ) ( 1 + = S e V N M T S S F ) ( 1 + = S S e S e V N M V T S T S S F 1 1 ) ( 1 = ≈ + = P PI Lead-Lag Delta Power Electronics Center Basic Control for Power Electronics --89-- Average current mode –GEA(cont.) M(w) P PI Lead-lag Attenuated Const High gain Lead-Lag No attenuation Const High gain PI No attenuation Const Low gain P High Freq Mid Freq Low Freq Delta Power Electronics Center Basic Control for Power Electronics --90-- 2 2 2 1 1 / 1 ˆ ˆ ) ( o o z o s s Q s s R Vin d i s Gid ω ω + + + = = Average current mode –Gid(s) sL V d i s Gid in o = = ˆ ˆ ) (' Simplified: 1 D L C R d Icˆ d D VD ˆ RC aiˆ ciˆ invˆ ovˆ d V D d D V in in ˆ ˆ = ⋅ Buck -type Delta Power Electronics Center Basic Control for Power Electronics --91-- 2 2 3 2 1 1 / 1 ' 2 ˆ ˆ ) ( o o Z O o s s Q s s RD V d i s Gid ω ω + + + = = Average current mode –Gid(s) 0 1 ≈ B sC @high frequency L C R RC d Iinˆ d D VO ˆ − invˆ ovˆ Liˆ D 1 sL V d i s Gid O o = = ˆ ˆ ) (' Simplified: Boost -type Delta Power Electronics Center Basic Control for Power Electronics --92-- Average current mode –current compensation To avoid sub-harmonic. Sn=Se fs V Gca Rs L Vo S ⋅ = ⋅ ⋅ 1 ) ( = s He S M V F 1 = ) ( ) ( ) ( ) ( s G F s He s G Rs s Gi ca M id L ⋅ ⋅ ⋅ ⋅ = Rs Vo fs V L Gca S ⋅ ⋅ ⋅ = 1 1 1 ) ( = ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = sL V fs V Rs V fs V L V sL V Rs s Gi O in O S S in L 1 2 = ⋅ ⋅ L f V fs V iC O in π LD fs L V fs V f O in iC π π 2 2 = ⋅ ⋅ = BUCK max Cross frequency fic Delta Power Electronics Center Basic Control for Power Electronics --93-- Average current mode –current compensation To avoid sub-harmonic. Sn=Se fs V Gca Rs L Vo S ⋅ = ⋅ ⋅ 1 ) ( = s He S M V F 1 = ) ( ) ( ) ( ) ( s G F s He s G Rs s Gi ca M id L ⋅ ⋅ ⋅ ⋅ = Rs Vo fs V L Gca S ⋅ ⋅ ⋅ = 1 1 1 ) ( = = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = sL fs Rs V fs V L V sL V Rs s Gi O S S O L 1 2 = L f fs iC π L fs fiC π 2 = Cross frequency fic BOOST max Delta Power Electronics Center Basic Control for Power Electronics --94-- Design Summary 1) critical fic is determined. 2) High dc gain Integration is place at zero frequency. 3) Stability One Zero is placed at fic/4. 4) High frequency noise. One Pole is placed at fs/2 to attenuate. Delta Power Electronics Center Basic Control for Power Electronics --95-- Any comments & suggestions? Delta Power Electronics Center Basic Control for Power Electronics --96-- Thanks for your attention!