Utafiti huu unalinganisha katika mazingira ya MATLAB/Simulink moduli ya upana wa mpigo wa sinusoidal ya mzunguko wazi (Sinusoidal Pulse Width Modulation, SPWM), udhibiti wa PI wa mizunguko miwili iliyofungwa na udhibiti wa PID wa mizunguko miwili iliyofungwa ili kuboresha ubora wa volteji ya pato ya inverter ya awamu moja ya daraja kamili inayotegemea chanzo cha volteji. Inverter ya awamu moja ya daraja kamili ni topolojia ya power electronics inayobadilisha chanzo cha DC kuwa volteji ya AC kupitia H-bridge yenye vipengele vinne vya switching. Kipimo kikuu cha utendaji wa utafiti ni total harmonic distortion (Total Harmonic Distortion, THD); THD ni kiashiria cha spectral kinachoeleza kiwango ambacho vipengele vya harmoniki vilivyo nje ya frequency ya msingi vinaharibu umbo la wimbi la pato.

Katika modeli ya simulation, zinatumika input ya 400 V DC, output fundamental frequency ya 50 Hz, switching frequency ya 10 kHz, inductance ya filter ya 2 mH, capacitance ya filter ya 20 μF na resistive load ya 50 Ω. Katika SPWM ya open-loop bila LC filter, THD ya output voltage imepatikana kuwa %52,82. LC low-pass filter inapoongezwa kwenye mfumo huohuo wa open-loop, THD hushuka hadi %6,52. Matokeo haya yanaonyesha kwamba passive filter ina jukumu la msingi katika kukandamiza high-frequency harmonics zilizo karibu na switching frequency.

Closed-loop feedback inapoongezwa, harmonic performance huboreka zaidi. Katika double closed-loop PI control yenye LC filter, THD hufikia thamani ya chini kabisa ya utafiti ya %0,26, huku double closed-loop PID control ikipata %1,15 THD. Chanzo kinapendekeza kwamba PID inaweza kutoa faida katika transient response kutokana na derivative term yake, lakini amplification ya high-frequency feedback noise kupitia derivative operation inaweza kusababisha upungufu fulani wa spectral purity katika steady state.

Hata hivyo, utafiti unategemea kikamilifu simulations za MATLAB/Simulink na Simscape Electrical. Hakuna prototype halisi ya inverter, DSP control system au hardware measurement. Aidha, kwa sababu final PI/PID gains, critical Ziegler–Nichols parameters na precise discrete simulation time step hazijachapishwa, maelezo ya ziada yanahitajika ili kuzalisha upya matokeo hayo kwa usahihi uleule.

Kwa nini inverter ya awamu moja ya daraja kamili inatumika?

Inverters za awamu moja za daraja kamili hutumika sana katika matumizi ya ubadilishaji wa nishati ya nguvu ndogo na ya kati kama distributed photovoltaic systems, home energy storage systems na uninterruptible power supplies. Kwa sababu muundo wa H-bridge unaweza kubadilisha polarity ya DC input mara kwa mara kwenye load kwa kutumia power switches nne, huruhusu matumizi ya juu ya DC bus.

Katika modeli ya chanzo, Insulated Gate Bipolar Transistor (IGBT) switches nne zinatumika. Wakati jozi za diagonal switches zinaendeshwa pamoja, upper na lower switches kwenye bridge leg ileile lazima zifanye kazi kwa namna inayokamilishana.

Mchakato huu wa switching hubadilisha 400 V DC bus voltage kuwa high-frequency SPWM pulses. LC low-pass filter kwenye output inalenga kukandamiza high-frequency components zilizo karibu na switching frequency na kuunda kwenye load sinusoidal AC voltage iliyo karibu na 50 Hz.

Sinusoidal Output Inaundwaje kwa SPWM?

Katika mfumo wa chanzo, SPWM switching signals huundwa kwa kulinganisha kwa amplitude sinusoidal reference wave ya 50 Hz na triangular carrier wave ya 10 kHz. Hali za power switches huamuliwa kulingana na kama reference ni kubwa au ndogo kuliko carrier; hivyo usambazaji wa pulse widths kwa muda hufuata sinusoidal envelope, na LC filter hukandamiza high-frequency carrier harmonics ili fundamental component ya 50 Hz iwe dominant kwenye load.

Vigezo vikuu vya mzunguko

Jukumu la LC filter

Matokeo ya SPWM switching hayatoi pure sine moja kwa moja upande wa load. Bridge output ina fundamental component pamoja na 10 kHz carrier na high-frequency harmonics zinazoizunguka.

Passive LC network iliyotumika katika chanzo, yenye inductance ya 2 mH na capacitor ya 20 μF, hupunguza high-frequency components hizi na kufanya fundamental component ya 50 Hz iwe dominant.

LC Filter Inapunguza THD kwa Kiasi Gani?

Katika open-loop SPWM system bila LC filter, THD ni %52,82; LC filter yenye thamani za 2 mH na 20 μF inapoongezwa kwenye mfumo huohuo, THD hushuka hadi %6,52. Hivyo katika simulation ya chanzo, kuongeza passive filter pekee kumepunguza harmonic distortion takriban mara nane, lakini bila closed-loop control haijafikiwa performance ya kiwango cha %0,26–%1,15.

Open-loop SPWM bila filter

Figure 5 kwenye ukurasa wa 7 wa PDF inaonyesha open-loop SPWM output bila filter. Katika time domain, voltage huwa katika mfumo wa pulse train inayoswitch kwa kasi kati ya positive na negative DC bus levels.

Katika FFT analysis:

THD = %52,82

imeripotiwa.

Chanzo kinahusisha harmonic content hii ya juu hasa na 10 kHz switching carrier na harmonics zilizo karibu nayo.

Open-loop SPWM yenye LC filter

Katika Figure 6, baada ya LC filter kuongezwa, load voltage inaonekana kuwa sinusoidal kwa uwazi.

FFT result:

THD = %6,52

imetolewa.

Ulinganisho huu unaonyesha moja kwa moja umuhimu wa LC filter katika system performance.

Kwa Nini Double Closed-Loop Control Inatumika?

Katika muundo wa double closed-loop, outer voltage loop hulinganisha load voltage na sinusoidal reference na kupunguza steady-state voltage error, huku inner current loop ikirekebisha kwa kasi filter inductor current kulingana na reference inayotolewa na outer loop. Uwezo wa inner loop kutoa current control ya haraka zaidi na outer loop kusimamia voltage accuracy huongeza kwenye mfumo feedback correction ambayo open-loop SPWM haina dhidi ya load variations.

Outer voltage loop

Outer loop hupima actual load output voltage na kuilinganisha na ideal sinusoidal reference. Error inayotokea huchakatwa kupitia controller na kutengeneza reference kwa inner current loop.

Kulingana na chanzo, lengo kuu la loop hii ni kupunguza steady-state voltage error na kuhakikisha stability ya output voltage.

Inner current loop

Inner loop hupima LC filter inductor current na kujaribu kufuatilia reference inayotoka kwenye outer voltage loop.

Chanzo kinaeleza kwamba inner current loop inaweza kusaidia kutekeleza overcurrent limits pamoja na kutoa dynamic response ya haraka zaidi.

Tofauti Kuu Kati ya PI na PID ni Nini?

PI controller hutumia proportional na integral terms kurekebisha instantaneous error na accumulated steady-state error, huku PID controller ikiongeza derivative term inayotumia rate of change ya error. Katika utafiti huu derivative term hii inahusishwa na potential ya transient response ya haraka zaidi, wakati uwezekano wa term hiyo kukuza high-frequency switching noise unatafsiriwa kama sababu inayowezekana ya steady-state THD ya PID kuwa juu kuliko ya PI.

PI control

PI control ina components mbili:

• P — proportional: hujibu current error.
• I — integral: huchakata accumulation ya error kwa muda ili kupunguza permanent offset.

PID control

PID huongeza:

• D — derivative: rate of change ya error

kwenye hizo.

Chanzo kinaeleza kwamba D term hii inaweza kutoa response ya haraka zaidi katika abrupt changes.

Mbinu na Matokeo ya Utafiti

MATLAB/Simulink na Simscape Electrical

Mifumo mitatu tofauti imeundwa katika MATLAB/Simulink na Simscape Electrical:

1. Open-loop SPWM model.
2. Double closed-loop PI model.
3. Double closed-loop PID model.

Figures 2–4 kwenye kurasa za 4–5 za PDF zinaonyesha Simulink models hizi tatu.

Simulation solver

Chanzo kinaeleza kwamba fixed-step discrete solver imetumika. Lengo ni kukamata 10 kHz switching pulses kwa time resolution ya kutosha na kupunguza numerical problems kama aliasing katika FFT analysis.

Total simulation time:

0,5 s

imetolewa.

Hata hivyo, ingawa chanzo kinasema “precise” time step imetumika, hakichapishi actual numerical value ya time step hiyo.

PI na PID Gains Zinatunewaje kwa Ziegler–Nichols?

Katika utafiti, double closed-loop controllers zinatunewa kutoka ndani kwenda nje; kwanza outer voltage loop inazimwa ili kupata critical gain na oscillation period ya inner current loop, kisha wakati tuned inner loop inaendelea kufanya kazi, utaratibu huohuo unatumika kwa outer voltage loop. Ultimate gain \(K_u\) na ultimate period \(P_u\) zilizopatikana huwekwa katika sheria za Ziegler–Nichols na PI au PID coefficients hukokotolewa.

Tuning ya inner current loop

Katika hatua ya kwanza, outer voltage loop inazimwa. Kwa inner loop:

huchukuliwa na \(K_p\) pekee huongezwa kuanzia thamani ndogo.

Proportional gain kwenye mpaka ambapo continuous oscillation yenye constant amplitude hutokea katika inductor current:

\(K_{u1}\)

na oscillation period:

\(P_{u1}\)

hufafanuliwa.

Tuning ya outer voltage loop

Baada ya inner loop kutunewa, outer voltage loop inaunganishwa tena. Katika outer controller, integral na derivative components huwekwa sifuri kwanza na \(K_p\) huongezwa.

Output voltage inapofikia critical oscillation yenye constant amplitude:

\(K_{u2}\) na \(P_{u2}\)

hupatikana.

Ziegler–Nichols formulas

Kwa conversion kwenda parallel PID structure katika MATLAB/Simulink, chanzo kinatoa mahusiano yafuatayo:

Chanzo kinasema raw Ziegler–Nichols parameters zinaweza kusababisha aggressive transient response inayoweza kuzalisha takriban %10–30 overshoot, na kinaeleza kwamba katika matumizi proportional gains zimepunguzwa kwa %10–15.

Hata hivyo, final controller gains hazijachapishwa.

Kwa Nini THD ya PI Control ni Ndogo Kuliko ya PID?

Kulingana na tafsiri ya chanzo, derivative term katika PID inaweza kukuza si tu mabadiliko ya haraka katika error signal bali pia high-frequency switching ripple na noise inayobaki kwenye feedback path; kurudisha small high-frequency components kwenye modulation command kunaweza kuchangia steady-state THD ya PID ya %1,15 kuwa juu kuliko thamani ya PI ya %0,26. Hata hivyo, utafiti hauhakiki moja kwa moja mechanism hii kwa noise spectrum au D-term ablation test.

Matokeo ya double closed-loop PI

Figure 7 kwenye ukurasa wa 8 wa PDF inaonyesha initial na steady-state output voltage ya mfumo unaodhibitiwa na PI. Chanzo kinaeleza kwamba baada ya initial transition, mfumo hufikia sinusoidal tracking ndani ya muda mfupi.

FFT result katika Figure 8:

THD = %0,26

imetolewa.

Hii ndiyo harmonic distortion value ya chini kabisa katika utafiti huu.

Matokeo ya double closed-loop PID

Figure 9 kwenye ukurasa wa 9 wa PDF inaonyesha transient na steady-state voltages za PID-controlled system, huku Figure 10 ikionyesha FFT spectrum.

FFT result:

THD = %1,15

imeripotiwa.

Chanzo kinadai kwamba PID inaweza kujibu kwa haraka zaidi abrupt system changes kutokana na derivative term. Hata hivyo, hakuna numerical rise time, settling time au overshoot results zilizotolewa kwa transient performance.

Ulinganisho wa mikakati yote

Je, %0,26 THD Inaweza Kupatikana Pia Katika Inverter Halisi?

Utafiti huu hauonyeshi hilo. Matokeo ya %0,26 THD yamepatikana kutoka double closed-loop PI model katika mazingira ya MATLAB/Simulink na Simscape Electrical; actual IGBT switching delays, dead-time, sensor noise, parasitic elements, temperature variations, DSP computation delay na physical LC component tolerances hazijathibitishwa kwenye hardware prototype.

Matokeo yanayoungwa mkono moja kwa moja na utafiti

• Katika open-loop SPWM model bila LC filter, THD ni %52,82.
• Kuongeza LC filter hupunguza open-loop THD hadi %6,52.
• Katika double closed-loop PI + LC filter model, THD ni %0,26.
• Katika double closed-loop PID + LC filter model, THD ni %1,15.
• Katika simulation conditions zilizochunguzwa, lowest steady-state THD imepatikana katika PI control.
• Double-loop structure hutumia pamoja output voltage feedback na filter current feedback.
• Ziegler–Nichols method imetumika kwa initial tuning ya controllers.

Matokeo ambayo utafiti peke yake hauungi mkono

• Haijaonyeshwa kwamba %0,26 THD imepatikana katika physical inverter halisi.
• Transient response superiority ya PID haijathibitishwa kwa numerical rise-time au settling-time measurements.
• Haijaonyeshwa kwamba PID ni ya haraka kuliko PI katika operating conditions zote.
• Haijaonyeshwa kwamba PI ndiyo solution bora kwa load types zote.
• Haijaonyeshwa kwamba THD values hizo hizo zitadumishwa chini ya nonlinear au strongly inductive loads.
• Experimental compliance na specific international power quality standard haijathibitishwa.

Nguvu za utafiti

Nguvu kubwa zaidi ya utafiti ni uwezo wa kutenganisha athari za LC filter na active feedback kwa kulinganisha open-loop, passive filtering na closed-loop controllers mbili tofauti kwenye basic inverter structure ileile.

Nguvu ya pili ni matumizi ya FFT-based THD values kama quantitative comparison metric badala ya kuangalia tu visual smoothness ya time-domain waveforms.

Nguvu ya tatu ni kwamba main circuit parameters zimeelezwa wazi kama 400 V, 50 Hz, 10 kHz, 2 mH, 20 μF na 50 Ω.

Mapungufu makuu

Final values za controller gains hazijatolewa. Hili ni tatizo muhimu la reproducibility, hasa katika PI na PID comparison, kwa sababu performance inategemea moja kwa moja controller settings.

Exact fixed simulation time step pia haijaripotiwa.

Transient performance difference kati ya PI na PID haijaonyeshwa kwa numerical metrics.

Utafiti unategemea basic simulation katika context ya resistive nominal load pekee; nonlinear na strongly inductive step loads zimeachwa kama future work.

Physical prototype validation pia imetajwa kama future work.

Maelezo ya Chanzo na Mbinu

• Kichwa asili: Simulation Research on PID Control of Single-Phase Full-Bridge Inverter Based on MATLAB/Simulink
• Mwandishi: Zerui Su
• Taasisi: Portland Institute, Nanjing University of Posts and Telecommunications, Nanjing, China
• DOI: 10.54254/2755-2721/2026.34397
• Uchapishaji: Proceedings of the 4th International Conference on Mechatronics and Smart Systems
• Mwaka: 2026
• Kurasa: 86–96
• Aina ya chanzo: Utafiti wa power electronics simulation unaotegemea MATLAB/Simulink na Simscape Electrical
• Leseni: Creative Commons Attribution 4.0 International (CC BY 4.0)

Vigezo vya main circuit na simulation

• DC input: 400 V.
• Output fundamental frequency: 50 Hz.
• Switching frequency: 10 kHz.
• Filter inductance: 2 mH.
• Filter capacitance: 20 μF.
• Nominal load: 50 Ω.
• Simulation time: 0,5 s.
• Solver: fixed-step discrete solver.
• Simulation platform: MATLAB/Simulink + Simscape Electrical.
• Harmonic analysis: FFT.
• Control tuning: Ziegler–Nichols ultimate sensitivity method + %10–15 Kp fine tuning.

Dokezo la reproducibility

Chanzo kinaeleza basic values za circuit elements lakini hakichapishi exact discrete solver time step, Ku/Pu values wala final PI/PID control gains. Kwa hiyo model ya ziada au Simulink file inahitajika kwa exact independent reproduction ya THD results katika makala.

Kazi ya baadaye

Mwandishi anapendekeza kupima mfumo chini ya nonlinear na strongly inductive step loads; kuchunguza advanced control methods kama adaptive gain scheduling, Model Predictive Control (MPC) na Sliding Mode Control (SMC), na kufanya experimental validation kwenye physical DSP-controlled inverter prototype.

Kikomo cha tafsiri ya kisayansi

THD values za %0,26, %1,15, %6,52 na %52,82 katika utafiti huu ni simulation results zilizopatikana kutoka MATLAB/Simulink models maalum. Haiwezi kuhakikishwa kwa msingi wa utafiti huu pekee kwamba matokeo yaleyale yatapatikana katika real power electronics hardware.