Ukufundisa Amathimba Amarobhothi Ezikole Zamabanga Aphakeme Ukulawula Nge-PID Ngaphandle Kokusebenzisa i-Calculus
Awuzidingi izibalo zokuhlukanisa (differential equations) ukuze ufundise ukulawula nge-PID; udinga kuphela imiqondo emithathu ecacile: ukuthi ukude kangakanani lapho uya khona, sesinesikhathi esingakanani uphuthelwa, nokuthi usondela ngesivinini esingakanani.
Awuyidingi i-calculus ukuze ufundise abafundi bezikole zamabanga aphakeme ukulawula nge-PID (PID control). Isilawuli se-PID simane siyifomula enquma ukuthi imotho kufanele iphuse ngamandla angakanani ngokusekelwe emibuzweni emithathu eqondakalayo: Kumanje sikude kangakanani lapho kufanele siye khona? Sesinesikhathi esingakanani siphambene nendawo okuyiwa kuyo? Futhi sisondela ngesivinini esingakanani?
Lapho amathimba e-FIRST Tech Challenge (FTC) noma abafundi bamarobhothi ezikoleni zamabanga aphakeme behlangana nokulawula nge-PID emibhalweni yokufunda, bavame ukubhekana nezimpawu ze-integral kanye ne-derivative ezisabisa noma ngubani ongakayiqedi izibalo ezithuthukile (advanced mathematics). Eqinisweni, ikhodi esebenza erobhothini ayixazululi izibalo zokuhlukanisa eziqhubekayo (continuous differential equations). Yenza izibalo eziyisisekelo kanye njalo ngemva kwamamilisekondi ambalwa. Lapho abafundi sebeziqonda izindima ezibonakalayo zika-P, I, no-D, bangabhala, balungise (tune), futhi balungise amaphutha ezihibe zokulawula (control loops) ngokwethembeka.
Umqondo Osemqoka: Iphutha (Error)
Zonke izihibe zokulawula zenzelwe ukunciphisa inombolo eyodwa: iphutha (error).
Iphutha limane liwuku: Target - Current Position. Uma ingalo yerobhothi iku-20 degrees futhi idinga ukuba ku-90 degrees, iphutha ngu-+70. Uma i-flywheel idinga ukuzungeza ngo-2,000 RPM kodwa izungeza ngo-2,100 RPM, iphutha ngu--100. Igama ngalinye ku-PID lithatha leli nani lephutha bese liliguqulela emandleni emotho.
1. I-Proportional (P): Isikhathi Samanje
Ingxenye ye-Proportional isebenza njengerabha elilula. Lapho ukude kakhulu nalapho uya khona, idonsa ngamandla kakhulu.
Uma ushayela imoto bese uphuma ngamamitha amahlanu kwesokunxele ukusuka phakathi nomzila wakho, wenza ukulungisa okukhulu kwesiteringi ukuya kwesokudla. Uma uphume ngamasentimitha amabili kuphela, wenza ukunyakaza okuncane kakhulu. Ngokwezibalo ekhodini, lokhu kumane kungu-kP * error.
Lapho u-P ehluleka khona eyedwa:
- Ukuqhubekela phambili ngokweqile nokungcangcaza (Overshoot and oscillation): Uma i-
kPiphezulu kakhulu, irobhothi lisheshisa kakhulu libheke kulokho okuhlosiwe kangangokuthi amandla omfutho alidlulisa ngalé komaka. Bese lidonsa ngamandla libuyela emuva, lidlule futhi lapho kumiwe khona, bese lingcangcaza ngamandla amakhulu. - Iphutha lesimo esizinzile (Steady-state error): Uma i-
kPiphansi kakhulu, amandla emotho aba mancane kakhulu njengoba iphutha lincipha kangangokuthi ahluleka ukunqoba ukukhuhlana okungokwemvelo (friction) noma amandla adonsela phansi (gravity). Umshini oyilifti ophakamisa uzipho olungu-500-gram uzomane ume ngamasentimitha ambalwa ngaphansi kwalapho obekuhlosiwe ngoba amandla emotho alingana namandla adonsela phansi bese eyama lapho.
2. I-Derivative (D): Isikhathi Esizayo (Amabhuleki)
Ingxenye ye-Derivative ibheka ukuthi iphutha lishintsha ngokushesha okungakanani ukusuka kumjikelezo owodwa wesihibe ukuya kolandelayo. Umsebenzi wayo ukusebenza njenge-shock absorber noma ibhuleki.
Cabanga ngokupaka imoto egaraji. Uma udonga luqhele ngamamitha ayishumi, ucindezela i-accelerator. Kodwa uma ubona udonga lusondela ngokushesha, awulindi kuze kube yilapho ibhampa isisentimitha elilodwa ukusuka ezitladini ukuze unyathelise amabhuleki—ubhuleka ngokusekelwe ejivinini yakho yokusondela.
Ekhodini, derivative = (current_error - previous_error) / time_elapsed. Lapho irobhothi lijahe lapho lilibangise khona, iphutha liyancipha ngokushesha, okwenza ingxenye ye-derivative ibe yinombolo engaphansi kukaziro (negative), idonse amandla emothweni ngaphambi kokuba lidlulele ngalé kokuhlosiwe. U-D udambisa ukungcangcaza futhi ukuvumela ukuthi usebenzise i-P gain ephezulu ngaphandle kokuxegisa nokuhlaphaza irobhothi.
3. I-Integral (I): Isikhathi Esedlule (Inkumbulo)
Ingxenye ye-Integral ihlanganisa iphutha eliqhubekayo ngokuhamba kwesikhathi. Uma irobhothi lilokhu limi kancane ngaphandle kwendawo okuhlosiwe kuyo imizuzwana embalwa, isamba se-integral siyakhula size sinikeze izimotho amandla engeziwe anele okunqoba ukukhuhlana noma amandla adonsela phansi.
Cabanga uphusha inqola yokuthenga (trolley) endaweni ekhuphukayo. Uyaphusha (P), kodwa amandla adonsela phansi ayakumisa ngaphambi nje kokuba ufike esiqongweni. Uma uma lapho imizuzwana emihlanu uhluleka ukufinyelela phezulu, ingxenye ye-Integral empeleni ithi, "Sesinesikhathi eside kakhulu sibambeke lapha; yengeza amandla amaningi size seqe lesi siqongo."
Inselele: I-Integral iyingozi uma ingaphathwanga kahle. Uma ingalo ibhajwa ngokomzimba, isamba se-integral sizokhula ngokweqile siye kokungapheliyo (isenzeko esibizwa ngokuthi yi-"integral windup"). Lapho lokho okubambile kusuka, imotho izoshaya ngamandla amakhulu ezindaweni zokuma eziqinile. Ku-FTC nasemarobhothini ezikole, i-Integral kufanele ibekelwe umkhawulo (accumulator limit), noma isetshenziswe kuphela ngaphakathi kwebanga elincane lephutha.
Uhlelo Lwezinyathelo Ezi-4 Lokulungisa E-workshop
Ungaziqageli zonke izinombolo ezintathu ngesikhathi esisodwa. Yenza abafundi bakho balandele ukulandelana kokulungisa okuphindekayo ebhethrini eligcwele ngokuphelele (izinguquko ze-voltage zishintsha ukusabela kwemotho):
| Isinyathelo | Isenzo | Ukuziphatha Okuhlosiwe | Izimpawu Zokuthi Akulungile |
|---|---|---|---|
| 1. Setha wonke ama-gain abe ngu-0 | kP = 0, kI = 0, kD = 0 | Izimotho azenzi lutho. | — |
| 2. Khulisa i-kP | Khuphula i-kP kancane kancane kuze kube yilapho umshini ufika lapho kuhlosiwe khona ngokushesha. | Ufinyelela lapho kuhlosiwe khona ngokubhaxabula okuncane nokungaguquki noma ngokungcangcaza eduze kwephoyinti elimisiwe. | Ukungcangcaza ngamandla kusho ukuthi i-kP iphezulu kakhulu; ukwehluleka ukunyakaza kusho ukuthi iphansi kakhulu. |
| 3. Faka i-kD | Khulisa i-kD kancane kancane kuze kuphele lokho kubhaxabula. | Umshini ungena ngokushesha endaweni yawo futhi ume kahle ngaphandle kokungcangcaza. | Ukunyakaza okusheshayo nokukhencezayo noma umsindo wokuduma kusho ukuthi i-kD iphezulu kakhulu (ikhulisa umsindo wenzwa). |
| 4. Faka i-kI (Kuphela uma kudingeka) | Faka i-kI encane kakhulu uma umshini uma nge-1–2 mm ngaphambi kwalapho kuhlosiwe ngenxa yokukhuhlana. | Iphutha lokugcina lokuma kancane lyehla lifike kuziro. | Ukungcangcaza okunensayo, okunjengamagagasi (hunting) kusho ukuthi i-kI iphezulu kakhulu. |
Izinkinga Ezivamile Amarobhothi Abafundi Abahlangabezana Nazo
- Umsindo Wenzwa (Sensor Noise): Ama-optical encoder ezinhlelweni zokushayela ze-FTC (drivetrains) ngokuvamile ahlanzekile, kodwa ukuxega komshini (mechanical backlash) kuzodida ingxenye ye-derivative. Uma i-gearbox inokuxega, u-D uzosabela ekuxegeni komshini kunokuba asabele ekunyakazeni kwangempela.
- Ukushintshashintsha Kwesikhathi Sesihibe (Loop Time Variability): Uma ikhodi yethimba lakho isebenzisa ukucutshungulwa kwemibono (vision processing) ngasemuva kuxhano olulodwa (single thread), isikhathi sesihibe singagxuma sisuke ku-10ms siye ku-80ms ngendlela engalindelekile, sonakalise izibalo ezijwayelekile ze-PID. Gcina izihibe zokulawula zihlukanisiwe futhi zizacile.
- Ama-Flywheel uma eqhathaniswa Nezingalo (Flywheels vs Arms): Ukulawulwa kwesivinini (ama-flywheel) kuziphatha ngendlela ehlukile kunokulawulwa kwendawo (izingalo). Izihibe zesivinini azivamile ukudinga u-D ngoba umfutho wesistimu usuvele usebenza njengesihlungi (low-pass filter); zichuma kakhulu engxenyeni eyisisekelo ye-feedforward (kV) kanye no-P no-I abalingene.
Emaqenjini alungiselela imincintiswano yesifunda, ukwazi kahle ukulawulwa kwe-closed-loop yikho okuhlukanisa imishini engazinzile nezinhlelo ezizimele (autonomous routines) ezithola amaphuzu ngokungaguquki kuwo wonke umdlalo. Uma ithimba lakho lilungiselela umjikelezo wemincintiswano yendawo futhi lidinga isiqondiso sobuchwepheshe esihlelekile mayelana ne-kinematics ye-drivetrain nokuhlanganiswa kwezinzwa, hlola izinhlelo zethu zamarobhothi ze-FTC ukuze uthole izinhlaka zokuqeqesha ezisebenzayo.
