Utafiti huu unalinganisha mbinu tatu tofauti za udhibiti kwenye Twin-Rotor Multi-Input Multi-Output System (TRMS), mfumo unaotumika katika mazingira ya maabara kuwakilisha baadhi ya matatizo ya udhibiti usio wa mstari katika helikopta na vyombo vya anga vinavyopaa na kutua wima. Kwa sababu rotor kuu na rotor ya mkia ya TRMS huathiriana kiaerodinamiki, mwendo wa pitch na yaw haujitegemei; msuguano, mvutano wa kebo, disturbance za aerodynamics na kutolingana kikamilifu kwa mfumo halisi na modeli ya kihisabati huifanya changamoto ya udhibiti kuwa ngumu zaidi.

Watafiti kwanza walitumia Backstepping ya kawaida inayotegemea modeli kama mbinu ya msingi. Ingawa controller huyo huyo alitoa tracking error ndogo sana katika simulation bora ya kihisabati, alikosa uthabiti kwenye kifaa halisi cha TRMS hasa katika mhimili wa yaw. Thamani ya majaribio ya yaw RMSE ilifikia 2.5624 rad na oscillations zinazoongezeka zilionekana katika mwendo wa yaw. Matokeo haya yanaonyesha moja kwa moja tatizo kuu la utafiti la “tofauti kati ya modeli na mfumo halisi”.

Ili kushinda kushindwa huku, mbinu mbili zililinganishwa. Katika ya kwanza, gain za Backstepping zinarekebishwa online kwa kutumia Rate-Constrained Sequential Quantum Black Hole Optimization (RS-QBHO) iliyoundwa upya ili kufanya kazi katika real time. Katika ya pili, term ya Sliding Mode Control inaongezwa kwenye muundo wa Backstepping na kuunda Hybrid Backstepping–Sliding Mode Control (BSMC). RS-QBHO ilirejesha uthabiti katika mfumo halisi na kupunguza pitch na yaw RMSE hadi 0.0799 rad na 0.2305 rad mtawalia. Hybrid BSMC ilipata tracking error ndogo zaidi katika ulinganisho huo huo wa majaribio, ikiwa na 0.0682 rad pitch RMSE na 0.1858 rad yaw RMSE.

Jambo muhimu ni kwamba Hybrid BSMC haionekani kuwa bora kuliko Backstepping ya kawaida katika simulation. Modeli bora inapotumika, mbinu zote mbili hutoa thamani sawa za RMSE na ITAE. Kwa tafsiri ya watafiti, sababu ni kwamba term ya Sliding Mode haiamiliki wakati hakuna disturbance ambayo haijamodeliwa, na controller mseto hujikaribisha kwa tabia ya Backstepping katika hali nominal. Hardware halisi inapoingia kazini, athari za aerodynamics ambazo hazijamodeliwa huonyesha uwezo wa kimuundo wa disturbance rejection unaotolewa na sehemu ya Sliding Mode.

Mbinu ya RS-QBHO pia ilitoa matokeo muhimu: iliweza ku-stabilize mfumo halisi usio thabiti kwa kurekebisha gain katika real time bila kubadilisha architecture ya control. Kwa gharama hiyo, algorithm huingia katika awamu ya stochastic exploration katika takriban sekunde 10 za kwanza, ikijaribu candidate gains tofauti, na kipindi hiki huongeza kipimo cha jumla cha error. Kwa kuwa Hybrid BSMC haihitaji learning/search process kama hiyo, ilijibu moja kwa moja zaidi kwa mabadiliko ya haraka ya aerodynamics ambayo hayajamodeliwa.

Hata hivyo, utafiti si flight test ya chombo halisi cha anga. TRMS iliyotumika ni kifaa halisi cha maabara na majaribio yalifanywa chini ya mazingira tulivu. Watafiti wanaeleza wazi kwamba time-varying parametric disturbances na structured external disturbances zinapaswa kujaribiwa tofauti katika kazi zijazo.

Tathmini kwa mtazamo wa Uturuki: Matokeo yanaweza kuwa mfano muhimu wa majaribio kwa maabara za udhibiti, mekatroniki, anga na UAV nchini Uturuki, kwa kuwa yanaonyesha kuwa control law inayofanikiwa katika simulation inaweza kushindwa inapohamishwa kwenye mfumo halisi kwa sababu ya model mismatch. Hata hivyo, thamani za RMSE za TRMS haziwezi kuhamishwa moja kwa moja kwa helikopta halisi, UAV au platform ya VTOL. Kwa matumizi ya flight halisi nchini Uturuki, aerodynamic model, actuator limits, sensor noise, external disturbances, real flight envelope na safety conditions lazima zithibitishwe tofauti.

Kwa nini TRMS ni tatizo gumu la udhibiti?

Twin-Rotor MIMO System ni mfumo halisi wa maabara wenye propeller mbili na mihimili miwili mikuu ya mzunguko. Rotor kuu hudhibiti hasa mwendo wa pitch katika plane ya wima, huku rotor ya mkia ikidhibiti yaw katika plane ya usawa. Hata hivyo, rotor hizi mbili hazijitegemei. Aerodynamic force au reactive torque inayotengenezwa na rotor moja inaweza kubadilisha tabia ya mhimili mwingine.

Kwa hiyo mfumo ni Multi-Input Multi-Output, yaani una input nyingi na output nyingi. Motor voltages mbili ndizo input za mfumo, huku pitch na yaw positions zikiwa outputs kuu za control. Mfumo pia una nonlinearity kubwa, aerodynamic cross-coupling, gyroscopic effects na nonlinear friction.

State vector iliyotumika katika utafiti ni:

\[ x= [x_1,x_2,x_3,x_4,x_5,x_6]^T = [\psi,\dot{\psi},\tau_1,\phi,\dot{\phi},\tau_2]^T \]

.

• \(x_1=\psi\): pitch angle,
• \(x_2=\dot{\psi}\): pitch angular velocity,
• \(x_3=\tau_1\): aerodynamic torque ya rotor kuu,
• \(x_4=\phi\): yaw angle,
• \(x_5=\dot{\phi}\): yaw angular velocity,
• \(x_6=\tau_2\): aerodynamic torque ya rotor ya mkia.

Control inputs ni:

\[ u=[U_1,U_2]^T \]

ambazo ni DC voltages zinazotumika kwa motor za rotor kuu na rotor ya mkia.

Kwa nini tofauti kati ya modeli na mfumo halisi ni muhimu?

Katika mbinu za nonlinear control zinazotegemea modeli kama Backstepping, controller hujaribu kusawazisha au kufuta terms fulani za system dynamics kihisabati. Mbinu hii ni yenye nguvu sana modeli ikiwa sahihi. Lakini ikiwa mfumo halisi una friction, aerodynamic drag, high-frequency turbulence, mechanical cable tension au parameter deviation ambazo hazimo kwenye modeli, cancellation haiwezi kuwa kamili.

Ulinganisho wa simulation na hardware katika utafiti unaonyesha jambo hili wazi. Conventional Backstepping ilikuwa stable na accurate kwenye pitch na yaw katika modeli bora, lakini kwenye TRMS halisi mhimili wa yaw uliingia kwenye oscillations zinazoongezeka.

Conventional Backstepping ilitumikaje?

Katika control design, TRMS iligawanywa katika subsystems mbili: pitch na yaw. Aerodynamic cross-coupling terms zilichukuliwa kama bounded external disturbances. Backstepping hufafanua tracking error hatua kwa hatua na katika kila hatua huunda virtual control variable ili kufanya derivative ya Lyapunov function iwe hasi.

Kwa mhimili wa pitch, error ya kwanza ilifafanuliwa:

\[ z_1=x_1-x_{1d} \]

. Virtual control ya kwanza ni:

\[ \alpha_1=-c_1z_1+\dot{x}_{1d} \]

. Lyapunov candidate ya kwanza:

\[ V_1=\frac{1}{2}z_1^2 \]

ilichaguliwa ili error dynamics zikielekee sifuri. Kisha error variables za ziada kama \(z_2\) na \(z_3\) hufafanuliwa na control law hutolewa nyuma hadi kufikia motor voltage halisi.

Katika yaw, muundo huohuo hujengwa kupitia error variables \(z_4\), \(z_5\) na \(z_6\).

Hybrid BSMC inaongeza nini?

Hybrid Backstepping–Sliding Mode Control huhifadhi muundo wa model-based Backstepping lakini katika hatua ya mwisho huongeza Sliding Mode reaching term. Kwa pitch, sliding surface ilichaguliwa:

\[ S_1=z_3 \]

na reaching law katika chanzo ni:

\[ \dot{S}_1=-k_{s1}\operatorname{sign}(\varepsilon S_1)-c_3S_1 \]

.

Kwa yaw vivyo hivyo:

\[ S_2=z_6 \]

na:

\[ \dot{S}_2=-k_{s2}\operatorname{sign}(\varepsilon S_2)-c_6S_2 \]

zilitumika.

Lengo la term hii ni kuilazimisha system kuelekea sliding surface wakati aerodynamic disturbances zisizowakilishwa kikamilifu na modeli zinapotokea, hivyo kuzuia tracking error. Katika Lyapunov derivation kwa pitch:

\[ \dot{V}_3= -c_1z_1^2-c_2z_2^2-c_3S_1^2 -S_1k_{s1}\operatorname{sign}(\varepsilon S_1) \]

na negative terms zinazofanana hupatikana kwa yaw.

Tatizo la sign(εS) katika chanzo

Hapa kuna sehemu ya chanzo inayohitaji kutenganishwa kwa uangalifu. Katika mjadala wa majaribio ya hardware, paper inasema thamani ndogo ya \(\varepsilon\) hulainisha ideal discontinuous behavior ya signum function kwa kuunda boundary layer na kupunguza chattering.

Lakini mathematical expression iliyochapishwa ni moja kwa moja \(\operatorname{sign}(\varepsilon S)\). Ikiwa \(\varepsilon>0\):

\[ \operatorname{sign}(\varepsilon S)=\operatorname{sign}(S) \]

. Kwa hiyo kuzidisha argument kwa positive constant pekee hakufanyi signum function iwe continuous. Chanzo hakionyeshi wazi kama saturation, tanh au continuous boundary-layer function nyingine ilitumika katika physical implementation. Kwa hiyo low mechanical vibration iliyozingatiwa inaweza kuripotiwa kama matokeo; lakini haiwezekani kuhitimisha moja kwa moja kutoka equation iliyochapishwa kwamba “ε mathematically smooths the sign function”.

RS-QBHO ni nini?

Suluhisho la pili hu-tune Backstepping gains online badala ya kubadilisha structure ya control law. Watafiti walibadilisha Quantum Black Hole Optimization kwa real-time physical control na kupendekeza muundo waliouita Rate-Constrained Sequential QBHO.

Katika standard population-based metaheuristic optimization, candidates wengi lazima watathminiwe katika iteration moja. Physical TRMS hufanya kazi kwenye control loop ya 10 ms, yaani 100 Hz. Kwa hiyo badala ya kutathmini population yote kwa wakati mmoja, candidates husambazwa kwa muda.

Kwa nini pitch na yaw zina-optimize tofauti?

Badala ya ku-optimize gains sita kwa wakati mmoja, tatizo limegawanywa kuwa subproblems mbili za dimensions tatu:

\[ \Theta_\psi=[k_1,k_2,k_3]^T \]

kwa pitch na:

\[ \Theta_\phi=[k_4,k_5,k_6]^T \]

kwa yaw.

RS-QBHO instances mbili hufanya kazi parallel. Kila moja hu-optimize gains zake kutokana na tracking error ya mhimili husika.

Logic ya real-time ya RS-QBHO

Kila optimizer hutumia population ya N=30 particles. Kila candidate gain set hujaribiwa kwa samples 50, yaani sekunde 0,5. Performance metric ni ITAE, integral ya absolute error iliyowekwa uzito kwa muda:

\[ J_{\text{perf}} = \int_{t_0}^{t_0+T_w} \tau |e_{\text{sub}}(\tau)|\,d\tau \]

. Subsystem inaweza kuwa pitch au yaw.

Algorithm ina phases mbili:

1. Exploration/Test: Gains za candidate particle zinajaribiwa kwenye mfumo halisi.
2. Exploitation/Settle: System inarudishwa kwenye best current “Black Hole” gains na kuruhusiwa kutulia kabla ya candidate inayofuata.

Mabadiliko ya ghafla ya gain yanazuiwaje?

Ili kulinda physical rotors dhidi ya gain changes za ghafla, first-order transition filter inatumika:

\[ \Theta(k)= \Theta(k-1)+ \lambda[\Theta_{\text{target}}-\Theta(k-1)] \]

. Katika utafiti:

\[ \lambda=0.1 \]

ilichaguliwa. Watafiti wanasema values ndogo hupunguza kasi ya transition, huku values kubwa zikiongeza risk ya gain jitter.

Fitness function pia inaadhibu parameter jumps kubwa:

\[ f_i= -\left( J_{\text{perf}}+ \beta\|\Theta_i-\Theta_{\text{prev}}\|^2 \right) \]

na:

\[ \beta=0.01 \]

ilitumika. Chanzo kinasema range ya 0.005–0.05 kwa \(\beta\) ilitoa stable behavior katika mfumo halisi.

“Black Hole” update inafanyikaje?

Ikiwa particle iliyojaribiwa ni bora kuliko current best solution, inakubaliwa kama new global best. Particles nyingine zina-update kuelekea nafasi ya Black Hole kwa quantum attraction rule:

\[ X_j(t+1)= X_j(t)+ \rho[X_{BH}(t)-X_j(t)] \]

. \(\rho\) inawakilisha stochastic quantum uncertainty.

Mpangilio wa simulation

Control strategies zote tatu zilitathminiwa kwanza katika MATLAB/Simulink R2014a. Fixed-step ode1 (Euler) solver ilitumika na simulation sampling time:

\[ T_s=1\ \text{ms} \]

iliwekwa. Kila experiment ilidumu sekunde 100, sinusoidal pitch na yaw references zilezile zilitumika, na motor voltages ziliwekewa kikomo cha ±2,5 V ili kuendana na physical TRMS.

Matokeo kwenye ideal model

Katika ideal conditions, Conventional Backstepping na Hybrid BSMC zilitoa performance values zinazofanana kabisa. Watafiti wanatafsiri hili kama design property muhimu ya Hybrid BSMC: ikiwa hakuna model error, hakuna haja ya additional intervention ya Sliding Mode disturbance-rejection term na hybrid controller hukaribia nominal Backstepping behavior.

RS-QBHO ilitoa error kubwa kidogo chini ya perfect-model condition. Sababu ni kwamba metaheuristic algorithm hufanya search katika gain space, wakati nominal Backstepping imetolewa mahsusi kwa modeli inayotumika.

Kwa nini hardware halisi ilifanya tofauti?

Katika physical TRMS, athari ambazo hazikuwepo katika ideal simulation zilijitokeza, kama nonlinear friction, mechanical cable effects na high-frequency aerodynamic variations. Hivyo tofauti ilitokea kati ya mathematical model na real system ambayo controller ilipaswa ku-compensate.

Conventional Backstepping ilionyesha limited tracking kwenye pitch lakini haikuweza kubaki stable kwenye yaw. Yaw angle iliingia kwenye oscillations zinazoongezeka na experimental yaw RMSE ikaripotiwa kuwa 2.5624 rad.

RS-QBHO ili-stabilize mfumo halisi vipi?

Online optimizer ilijaribu gain sets tofauti na ku-compensate model mismatch katika mfumo halisi kupitia gain tuning. Katika takriban sekunde 10 za kwanza, gain zilionyesha stochastic changes nyingi, kisha parameters zika-converge kwenye eneo jembamba zaidi.

Hasa, gains \(k_1\) na \(k_4\) zilifikia upper bound iliyowekwa ya 5.0, na hii ilitafsiriwa kwamba algorithm ilichagua maximum allowed loop gain ili kupunguza tracking error.

Kwa matokeo hayo mfumo halisi uli-stabilize kwenye pitch na yaw.

Kwa nini Hybrid BSMC ilitoa RMSE ndogo?

RS-QBHO lazima ijaribu candidates kwa muda ili kupata gains mpya zinazofaa. Hybrid BSMC inalenga kukandamiza disturbance ambayo haijamodeliwa kupitia structural Sliding Mode term ya control law bila kupitia gain-search process.

Tofauti hii inaonekana hasa kwenye yaw katika experimental results. BSMC ilitoa tracking error ndogo zaidi dhidi ya unmodeled reactive effects zinazotokana na rotor kuu kwenye mhimili wa mkia.

Matokeo muhimu zaidi ya utafiti ni nini?

Utafiti unaonyesha jambo muhimu zaidi kuliko swali la “controller gani ni bora katika simulation?” Ingawa Conventional Backstepping na Hybrid BSMC zilitenda sawa kwenye ideal model, behavior zao zilitofautiana sana kwenye physical hardware. Kwa hiyo nominal simulation success pekee haihakikishi robustness dhidi ya unmodeled physical dynamics.

Mbinu zote mbili za suluhisho zili-stabilize mfumo halisi:

• RS-QBHO: hujifunza/ku-optimize control parameters online ili ku-adapt model mismatch.
• Hybrid BSMC: huongeza robust disturbance-rejection structure moja kwa moja kwenye control law.

Katika physical TRMS results za chanzo, mbinu ya pili ilitoa pitch na yaw RMSE ndogo zaidi.

Mbinu na Matokeo ya Utafiti

Physical HIL experimental setup

Control algorithms ziliendeshwa kwenye Simulink Desktop Real-Time kernel. Sampling frequency ya physical control loop ilikuwa:

\[ f_s=100\ \text{Hz} \]

na sampling period:

\[ T_s=0.01\ \text{s} \]

.

Advantech PCI-1711 data-acquisition card ilitumika kati ya computer na TRMS. 12-bit DAC channels za card zilitoa motor voltages, huku quadrature optical encoder pulses zikitumika kupima system position. Encoder resolution iliripotiwa kuwa 2000 pulse/revolution.

Ili kulinda physical motors, control commands zote ziliwekewa kikomo:

\[ -2.5\ \text{V}\le U_1,U_2\le +2.5\ \text{V} \]

.

Real-time experimental results

Ujumbe muhimu wa jedwali: Paper ya chanzo ime-bold performance values zote nne za Hybrid BSMC na kusema mbinu hiyo ndiyo “ya chini zaidi katika metrics zote zilizorekodiwa”. Lakini namba za pitch ITAE haziungi mkono dai hilo: Conventional Backstepping ina 1990.24 rad·s, Hybrid BSMC ina 2733.71 rad·s. Kwa hiyo kwa namba za jedwali lenyewe Hybrid BSMC si ya chini zaidi kwa pitch ITAE. Contradiction hii imehifadhiwa wazi bila kusahihishwa.

Pia, baseline experiment plot inaonyesha takriban sekunde 40 kwa sababu ya instability, wakati experiments za proposed controllers zinaonyeshwa kwa plots za sekunde 100. Kwa kuwa ITAE ni metric inayojikusanya kwa muda, chanzo hakielezi wazi tofauti hizi za duration zilishughulikiwaje katika Table 3. Kwa hiyo methodological uncertainty hii inapaswa kuzingatiwa hasa wakati wa kutafsiri ITAE values.

Matokeo ya Conventional Backstepping

Katika physical experiment, pitch RMSE ilipimwa kuwa 0.2571 rad, wakati yaw RMSE ilipanda hadi 2.5624 rad. Reference sinusoidal motion haikufuatiliwa kwenye yaw plot na oscillations zinazoongezeka zilitokea. Watafiti wanaeleza tabia hii kwa kusema aerodynamic drag na friction ambazo hazipo kwenye nominal model zilivuruga model-based cancellation mechanism ya Backstepping.

Matokeo ya Online RS-QBHO

RS-QBHO ilirejesha stability ya physical system. Pitch RMSE ilikuwa 0.0799 rad na yaw RMSE 0.2305 rad.

Katika takriban sekunde 10 za kwanza, exploration transitions zinaonekana kwa sababu optimizer inajaribu gain candidates tofauti. Watafiti wanahusisha sehemu kubwa ya ITAE ya juu na initial exploration cost hii.

Matokeo ya Hybrid BSMC

Hybrid BSMC ilipata 0.0682 rad RMSE kwa pitch na 0.1858 rad kwa yaw katika physical experiment. Hizi ndizo RMSE values za chini zaidi kati ya mbinu tatu katika Table 3.

Yaw ITAE pia ilikuwa 8624.69 rad·s, chini ya 10,268.60 rad·s ya RS-QBHO na 21,281.99 rad·s ya unstable baseline.

Tofauti kuu kati ya simulation na physical experiment

Model-equation inconsistency katika chanzo

Kuna tofauti ya wazi ya kihisabati kati ya full TRMS model na decoupled models zilizotumika katika control derivation. Katika full model, friction term kwenye pitch ni:

\[ -B_{2\psi}\operatorname{sgn}(x_2) \]

na kwenye yaw:

\[ -B_{2\phi}\operatorname{sgn}(x_5) \]

. Lakini kwenye decoupled subsystems za Hybrid BSMC derivation, terms zinazolingana zimetolewa:

\[ -B_{2\psi}x_1 \]

na:

\[ -B_{2\phi}x_4 \]

. Chanzo hakielezi kama mabadiliko haya ni remodeling, approximation au typographical error. Kwa hiyo hapa equation moja haijachukuliwa kimya kimya kuwa “sahihi” kuliko nyingine.

Validation boundary ya RS-QBHO

Abstract ya utafiti inasema mbinu zote mbili zilizopendekezwa zimefanyiwa formal validation kwa Lyapunov analysis. Lakini detailed sections zinaonyesha explicit Lyapunov functions na negative derivative conditions kwa Hybrid BSMC, huku hakuna comparable closed-loop adaptive stability derivation inayoonyeshwa kwa RS-QBHO. Sehemu ya RS-QBHO inategemea algorithm, fitness, rate constraint na experimental stability.

Kwa hiyo strong experimental RS-QBHO result inayotolewa na utafiti haipaswi kuchukuliwa kuwa sawa na independent formal adaptive stability proof.

Utafiti unaunga mkono nini?

• Unaonyesha kwa majaribio kwamba Conventional Backstepping inayofanikiwa kwenye ideal model inaweza kushindwa kwenye physical TRMS kwa sababu ya unmodeled dynamics.
• Unaonyesha online RS-QBHO gain tuning inaweza ku-stabilize physical TRMS iliyokuwa unstable.
• Unaonyesha Hybrid BSMC inatoa pitch na yaw RMSE ndogo zaidi kati ya mbinu tatu katika mazingira yale yale ya physical experiment.
• Unaonyesha Sliding Mode-based structural robustness inaweza kutoa RMSE ndogo zaidi kuliko online metaheuristic search mbele ya fast unmodeled aerodynamic effects.
• Unatoa direct laboratory comparison inayoonyesha simulation performance pekee si ushahidi wa real-hardware robustness.

Utafiti hauthibitishi nini?

• Hauthibitishi Hybrid BSMC ni control method bora katika MIMO systems zote au aircraft zote.
• Matokeo si flight test ya helikopta, UAV au VTOL halisi.
• Haijaonyeshwa controllers zitaendelea na performance ileile chini ya time-varying parametric uncertainties na strong structured external disturbances.
• Haijaonyeshwa RS-QBHO ni bora kuliko optimization methods zote.
• Haijaonyeshwa expression iliyochapishwa ya sign(εS) inatengeneza mathematically continuous boundary layer.
• Dai la Table 3 kwamba mbinu ni “ya chini zaidi katika metrics zote” haliungwi mkono na namba zake za pitch ITAE.

Mwelekeo wa baadaye uliopendekezwa na watafiti

Katika conclusion, watafiti wanapendekeza baadaye kuunganisha neural-network-based observers zinazokadiria actively unmodeled dynamics na structural Sliding Mode robustness. Pia wanapanga majaribio katika disturbance-rich na flight-like scenarios zenye ukali zaidi.

Dokezo la Chanzo na Mbinu

Jina kamili la kazi asilia: Robust Control of Twin-Rotor MIMO Systems Under Unmodeled Dynamics: Comparative Experimental Validation of Hybrid BSMC and Online QBHO Strategies

Waandishi na mpangilio: Abderrahmane Kacimi; Azeddine Beloufa; Souaad Tahraoui; Abderrahmane Senoussaoui; Mehdi Houari Zaid; Abdelbasset Azzouz; Jun-Jiat Tiang.

Corresponding author: Jun-Jiat Tiang.

Equal contribution/co-first author: Hakuna tamko la equal contribution katika chanzo.

Taasisi: Department of Instrumentation Maintenance, Institute of Maintenance and Industrial Safety, University of Oran 2; Laboratory of Electrical Engineering and Renewable Energies, Hassiba Benbouali University; Signals, Systems and Artificial Intelligence Laboratory, Hassiba Benbouali University; Electrical Department, University of Mascara Mustapha Stambouli; Laboratoire AVCIS, University of Science and Technology of Oran; Laboratory of Electronics, Advanced Signal Processing, and Microwave, Saida University; Centre for Wireless Technology, CoE for Intelligent Network, Faculty of Artificial Intelligence and Engineering, Multimedia University.

Journal: Actuators.

Publisher: MDPI, Basel, Switzerland.

Publication identity: Actuators 2026, 15, 236.

DOI: 10.3390/act15050236.

Official publication link: https://doi.org/10.3390/act15050236

Publication process: Received 20 March 2026; revised 21 April 2026; accepted 23 April 2026; published 28 April 2026.

Source type na peer-review status: Peer-reviewed research article. Utafiti wa experimental control engineering unaochanganya numerical simulation na physical hardware-in-the-loop TRMS experiment.

License: Creative Commons Attribution (CC BY).

Academic editors: Xiaoxiong Liu na Yu Li.

Funding: Article Processing Charge (APC) ilifadhiliwa na Multimedia University (MMU), Malaysia.

Ethics committee: Haitumiki.

Informed consent: Haitumiki.

Data availability: Chanzo kinasema original contributions ziko ndani ya article na maswali ya ziada yanaweza kuelekezwa kwa corresponding author.

Conflict of interest: Waandishi hawakuripoti conflict of interest.

Author contributions: Conceptualization A.B. na A.K.; methodology A.B. na A.K.; software A.B.; validation A.B., A.K., S.T., A.S., A.A. na M.H.Z.; formal analysis A.K. na S.T.; investigation A.B. na M.H.Z.; resources A.S. na J.-J.T.; data curation A.B. na M.H.Z.; original draft A.B.; review/editing A.K., S.T., A.S., A.A. na J.-J.T.; visualization A.B.; supervision A.K. na A.S.; project administration na funding acquisition J.-J.T.

Technical inconsistencies ndani ya chanzo: Dry-friction terms katika full TRMS model hazifanani na corresponding terms katika decoupled model iliyotumika kwenye Hybrid BSMC derivation, na mabadiliko haya hayajaelezwa. Expression iliyochapishwa ya sign(εS) kwa positive ε huhifadhi mathematically sign behavior ileile ya sign(S), lakini maandishi yanaieleza kama continuous boundary-layer smoothing. Abstract inasema mbinu zote mbili zimefanyiwa formal validation kupitia Lyapunov analysis, lakini kwa RS-QBHO hakuna separate Lyapunov closed-loop derivation kama ilivyo kwa Hybrid BSMC. Table 3 inasema Hybrid BSMC ndiyo ya chini zaidi katika metrics zote, lakini pitch ITAE yake ni 2733.71 rad·s, juu ya 1990.24 rad·s ya Conventional Backstepping. Pia, kwa kuwa baseline inaonekana takriban sekunde 40 na proposed methods sekunde 100 kwenye experiment plots, haiko wazi katika chanzo kama time-accumulating ITAE values zilihesabiwa kwa durations sawa.

Methodological interpretation boundary: Experiment ilifanywa kwenye physical TRMS laboratory setup; hakuna flight validation iliyofanywa kwenye helikopta, UAV au VTOL inayoruka kweli. Experimental conditions zilikuwa steady na time-varying parametric disturbances pamoja na stronger external-disturbance scenarios ziliachwa kwa future work.

Scientific method, equations, parameters, experimental setup, performance values na results katika maudhui haya ya Verianla zinategemea tu source study iliyochunguzwa. External sources zilitumika tu kuthibitisha bibliographic identity na publication status; hakuna experimental finding mpya iliyoongezwa kwenye utafiti.