Ukufundisa uLawulo lwe-PID kumaQela eeRobhothi aseZikolweni eziPhakamileyo Ngaphandle kokusebenzisa i-Calculus
Awuzidingi ii-equation ezingunobangela (differential equations) ukuze ufundise ulawulo lwe-PID; udinga kuphela iingcamango ezintathu ezilula: ukuba ukude kangakanani kwithagethi, lixesha elingakanani ungayifumani, kwaye ukhawuleza kangakanani ukuyisondela.
Awuyidingi ikalkhulasi (calculus) ukuze ufundise ulawulo lwe-PID kubafundi basezikolweni zamabanga aphakamileyo. Isilawuli se-PID yifomyula nje egqiba ukuba imoto yombane (motor) ifanele ityhale ngamandla angakanani ngokusekelwe kwimibuzo emithathu elula: Sikude kangakanani kanye ngoku? Lixesha elingakanani sibambeke ngaphandle kwethagethi? Kwaye sikhawuleza kangakanani ukusondela kuyo?
Xa amaqela e-FIRST Tech Challenge (FTC) okanye abafundi beerobhothi basesekondari bedibana nolawulo lwe-PID kumaxwebhu, badla ngokujongana neempawu ze-integral kunye ne-derivative ezidida nabani na ongekagqibi izibalo eziphakamileyo zasezikolweni. Enyanisweni, ikhowudi esebenza kwirobhothi ayisombululi ii-differential equations eziqhubekayo. Yenza izibalo ezisisiseko kanye qho kwii-millisecond ezimbalwa. Zakuba iingcamango zomsebenzi wokwenyani we-P, I, kunye no-D ziqondakele kubafundi, bangabhala, balungelelanise (tune), baze balungise iimpazamo (debug) kwii-control loop ngokuthembekileyo.
Ingcamango Engundoqo: Impazamo (Error)
Yonke i-control loop ikho ngenjongo yokunciphisa inani elinye: impazamo (error).
Impazamo yile kuphela: Target - Current Position. Ukuba ingalo yerobhothi ikuma-degrees angama-20 kwaye kufuneka ibe kuma-90 degrees, impazamo ngu-+70. Ukuba i-flywheel kufuneka ijikeleze nge-2,000 RPM kodwa ijikeleza nge-2,100 RPM, impazamo ngu--100. Igama ngalinye kwi-PID lithatha eli xabiso lempazamo lize liliguqule libe ngamandla emoto yombane.
1. Elinganayo (Proportional - P): Okwangoku
Igama elithi Proportional lisebenza njenge-raba elolukayo (rubber band). Okukhona ukude kwithagethi yakho, kokukhona litsala ngamandla.
Ukuba uqhuba imoto uze uphume ngeemitha ezintlanu ngasekhohlo ukusuka embindini wendlela yakho, wenza ulungiso olukhulu lwesiteringi ukuya ngasekunene. Ukuba uphume ngeesentimitha ezimbini kuphela, wenza intshukumo encinci kakhulu. Ngokwezibalo kwikhowudi, oku kumane kungu-kP * error.
Apho i-P isilela khona xa iyodwa:
- Ukugqitha ithagethi nokungcangcazela: Ukuba i-
kPiphezulu kakhulu, irobhothi ikhawuleza kakhulu ukuya kwithagethi kangangokuba amandla entshukumo (momentum) ayigqithisa ngaphaya komgca. Emva koko itsala ngamandla ibuyela umva, iphinde igqithe kwakhona, ize ingcangcazele ngamandla. - Impazamo engapheliyo (Steady-state error): Ukuba i-
kPiphantsi kakhulu, amandla emoto ancipha kakhulu njengoko impazamo isiya incipha kangangokuba ayikwazi ukoyisa ukukhuhlana (friction) okanye umxhuzulane (gravity). Indlela yokunyusa (elevator) ephakamisa uzipho lwe-500-gram iya kuma nje kwiisentimitha ezimbalwa ngezantsi kwethagethi ngenxa yokuba amandla emoto alingana nomxhuzulane ize ime apho.
2. Ephuma Kwenye (Derivative - D): Ikamva (Izithuli-zantshukumo)
Igama elithi Derivative lijonga indlela impazamo etshintsha ngokukhawuleza ngayo ukusuka kumjikelo omnye we-loop ukuya komlandelayo. Umsebenzi walo kukusebenza njengesithomalalisi sentshukumo (shock absorber) okanye ibhuleki.
Khawufanise nokupaka imoto egaraji. Ukuba udonga lukumgama ozimitha ezilishumi, ucofa i-accelerator. Kodwa ukuba ubona udonga lusondela ngokukhawuleza, awulindi de ibhampa ibe yisentimitha enye ukusuka kwisitena ukuze ubambe iibhuleki—ubhuleka ngokusekelwe kwisantya osondela ngaso.
Kwikhowudi, derivative = (current_error - previous_error) / time_elapsed. Xa irobhothi ibaleka isiya kwithagethi yayo, impazamo iyancipha ngokukhawuleza, nto leyo eyenza igama le-derivative libe nguthabatha (negative), lithobe amandla kwimoto yombane ngaphambi kokuba igqithe ithagethi. I-D ithomalalisa ukungcangcazela kwaye ikuvumela ukuba usebenzise i-P gain ephezulu ngaphandle kokudiliza irobhothi ngokungcangcazela.
3. Ehlanganisiweyo (Integral - I): Ixesha Eladlulayo (Inkumbulo)
Igama elithi Integral lidibanisa impazamo eqhubekayo ekuhambeni kwexesha. Ukuba irobhothi ibikhe yahlala kancinci ngaphandle kwethagethi kangangemizuzwana emininzi, isambuku se-integral siyakhula de sinike iimoto zombane ukutyhala okongeziweyo okwaneleyo ukoyisa ukukhuhlana okanye umxhuzulane.
Khawufanise nokutyhala itroli enyukela endulini. Uyatyhala (P), kodwa umxhuzulane ukumisa kancinci ngaphambi kwencopho. Ukuba ume apho imizuzwana emihlanu ungenakufikelela phezulu, igama elithi Integral ngokufanelekileyo lithi, "Kudala sibambeke apha; yongeza amandla angakumbi de siwele incopho."
Ingxaki ekhoyo: I-Integral iyingozi xa ingalawulwa kakuhle. Ukuba ingalo iyabambeka ngokwasenyameni, isambuku se-integral siya kukhula siye kutsho kunaphakade (isimo esibizwa ngokuba yi-"integral windup"). Xa ingalo ikhululeka kwingxaki, imoto iya kutshayisa ngamandla amakhulu kwizithinteli ezilukhuni. Kwi-FTC nakwezoorobhothi zezikolo, i-Integral kufuneka ibe nomlinganiselo ophezulu (accumulator limit), okanye isetyenziswe kuphela ngaphakathi kwi-error window emxinwa.
Inkqubo Yamanyathelo Amane Yokulungelelanisa Kwiworkshop
Musa ukuqagela onke amanani amathathu ngaxeshanye. Yenza abafundi bakho balandele ukulandelelana kokulungelelanisa okunokuphindwa kwibhetri egcweleyo ngokupheleleyo (utshintsho lwe-voltage lutshintsha indlela imoto esabela ngayo):
| Inyathelo | Isenzo | Indlela Yokuziphatha Ekujoliswe Kuyo | Iimpawu Zokuba Ayilunganga |
|---|---|---|---|
| 1. Cwangcisa zonke ii-gain ku-0 | kP = 0, kI = 0, kD = 0 | Iimoto azenzi nto. | — |
| 2. Nyusa i-kP | Nyusa i-kP kancinci kancinci de indlela yokusebenza ifikelele kwithagethi ngokukhawuleza. | Ifikelela kwithagethi ngokutsiba-tsiba okuncinci nokuzinzileyo okanye ukungcangcazela kufutshane ne-setpoint. | Ukungcangcazela ngamandla kuthetha ukuba i-kP iphezulu kakhulu; ukungashukumi kuthetha ukuba iphantsi kakhulu. |
| 3. Faka i-kD | Nyusa i-kD ngokuthe ngcembe de ukutsiba kuphele. | Indlela yokusebenza ingena ngokukhawuleza kwindawo yayo ize ime ngokufanelekileyo ngaphandle kokungcangcazela. | Ingxolo ekhawulezayo okanye ukudidizela kuthetha ukuba i-kD iphezulu kakhulu (ikhulisa ingxolo ye-sensor). |
| 4. Faka i-kI (Kuphela xa ifuneka) | Faka i-kI encinci kakhulu ukuba indlela yokusebenza ima ngo-1–2 mm ngaphambi kwethagethi ngenxa yokukhuhlana. | Impazamo yokugqibela yokuphela kokushukuma yehlela ku-zero. | Ukungcangcazela okucothayo okuza njengamaza (hunting) kuthetha ukuba i-kI iphezulu kakhulu. |
Iingxaki Eziqhelekileyo Kwiirobhothi Zabafundi
- Ingxolo ye-Sensor (Sensor Noise): Ii-optical encoder kwii-drivetrain ze-FTC zihlala zicocekile, kodwa ukukhululeka kweenxalenye zomatshini (backlash) kuya kudida igama le-derivative. Ukuba i-gearbox inokhexo, u-D uya kusabela kuloo ntshukumo yobuxoki yomatshini endaweni yentshukumo yokwenyani.
- Ukutshintsha-tshintsha KweXesha Le-Loop: Ukuba ikhowudi yeqela lakho isebenzisa i-vision processing ngasemva kwi-thread enye, ixesha le-loop lisenokutsiba lisuke kwi-10ms liye kwi-80ms ngendlela engalindelekanga, lonakalise izibalo eziqhelekileyo ze-PID. Zigcine ii-control loop zohluliwe kwaye zilula.
- Ii-Flywheel vs Iingalo: Ulawulo lwesantya (ii-flywheel) lusebenza ngendlela eyahlukileyo kulawulo lwendawo (iingalo). Ii-loop zesantya azifane zifune u-D ngenxa yokuba amandla entshukumo yenkqubo sele esebenza njenge-low-pass filter; zisebenza kakuhle kakhulu ngegama elisisiseko le-feedforward (kV) kunye ne-P no-I ephakathi.
Kumaqela alungiselela ukhuphiswano lwengingqi, ukwazi ulawulo lwe-closed-loop yinto eyahlula iindlela zokusebenza ezingazinzanga kwiinkqubo ezizimeleyo ezifumana amanqaku rhoqo kumdlalo ngamnye. Ukuba iqela lakho lilungiselela ukhuphiswano lwasekhaya kwaye lifuna isikhokelo sobugcisa esilungelelanisiweyo malunga ne-drivetrain kinematics kunye nokudityaniswa kwee-sensor, jonga iinkqubo ze-FTC robotics zethu ukuze ufumane izikhokelo zoqeqesho olusebenzayo.
