21. Control Systems. Easy: Incremental Linear: P PI PID Intuitive: Fuzzy Logic. It says to cook your food until burned food!

Transcription

1 21. Cotrol Systems Easy: Icremetal Liear: P PI PID Ituitive: Fuzzy Logic Dad, I hate It says to cook your food util bured food! the ceter is o loger red. Not eough colors of black to describe your cookig. But, ot my strawberry strudel! Doh! J V w 21.1

2 Vo Deutschlad Moaco Espaa 21.2

3 Circuit of the Americas 21.3

4 Accuracy Performace measures Magitude of the Error = Desired Actual Stability No oscillatios Overshoot uderdamped, overdamped) Rigig, slow Respose Time to ew steady state after Chage i desired setpoit Chage i load 21.4

5 Motor speed What to cotrol? Error = Desired speed Actual speed Error = Desired period Actual period Desired + Error U X* Cotroller - X e=x*-x Measured Speed State estimator Sesor Period Measuremet Tachometer Actuator V PWM circuit Actual Speed + - R Plat DC Motor L emf Disturbig forces 21.5

6 Distace to oe wall What to cotrol? Error = Desired distace Actual distace Equal distaces to both walls Error = Left distace Right distace wall d L robot wall d R wall Sesors - Time costat -> f s - Filters Aalog, digital - Sigal/oise ratio - Calibratio accuracy, drift 21.6

7 What to cotrol? Agle to most ope track Error = Desired Actual agle d 1 wall Tur so most ope i frot Avoid makig U-turs d 2 d 3 wall robot wall 21.7

8 Agle to wall What to cotrol? speed is determied by distace,d, to object i frot headig A L C is a fixed agle a L b L C L d robot Track the left wall if a R +b R )>a L +b L ) Wat to make A L = 90 If A L =90, the b L /a L = cos C L x L =100*cosC L is a calibratio costat C a R R a,b are measured distaces from ceter of robot to the wall b R A R Track the right wall if a R +b R )<a L +b L ) Wat to make A R = 90 If A R =90, the b R /a R = cos C R x R =100*cosC R is a calibratio costat error = 100*b R )/a R - x R if error > 0, A R < 90, tur left if error < 0, A R > 90, tur right if mia R,b R )<20, move left-right wall error = 100*b L )/a L - x L if error > 0, A L < 90, tur right if error < 0, A L > 90, tur left if mia L,b L )<20, move right-left 21.8

9 Icremetal Cotroller Periodic iterrupt Faster tha motor Slower tha sesor samplig rate Measured=StateEstimator Error = Desired-Measured Too fast <0 >2 U 2 U=U-1 Error =0 >0 Too slow <249 U =249 U=U

10 Icremetal Cotroller log Xstar; // desired log X; // actual, measured iput log U; // PWM actuator output void Timer0A_Hadlervoid){ log E; E = Xstar-X; // error ife < 0) U--; // too fast else ife > 1) U++; // too slow // close eough ifu < 2) U=2; // Costrai output ifu > 249) U=249; PWM0_DutyU); // output TIMER0_ICR_R = TIMER_ICR_CAECINT; } 21.10

11 Laplace Domai X* G s) H s) + X s) X') - K p m 1 s E) Es) K d s State estimator Period Measuremet K s i X s) X * s) PID Cotroller Actuator U) K PWM p + K i s +K d s Us) circuit Sesor Tachometer Xt) Xs) 1 G s) H G s) H Plat m 1+s s) s) 21.11

12 U t) Geeral Approach to PID K p E t) t K i E ) d 0 de t) Proportioal U p = K p E Itegral U i = U i + K i Et Derivative U d = K d E)-E-1))/t PID U = U p + U i + U d Ru te times faster tha motor Ru slower or equal to sesor samplig rate K d dt 21.12

13 Derivative Term x) with oise x) Time Calculated with oise x) without oise t E E K D dt t de K t D d d 1) ) ) ) ) t E E t E E K D d 2) 1) ) ) 2 1 ) t E E E E K D d 6 3) 2) 3 1) 3 ) ) Aalog filter Digital filter Liear regressio

14 PI Cotroller void Timer0A_Hadlervoid){ E = Xstar-X; P = 105*E)/20; // Kp = 105/20 I = I+101*E)/640; // Kit = 101/640 ifi < -500) I=-500; // ati-reset widup ifi > 4000) I=4000; U = P+I; // PI cotroller ifu < 100) U=100; // Costrai output ifu>19900) U=19900; PWM0_DutyU); // output TIMER0_ICR_R = TIMER_ICR_CAECINT; } 21.14

15 Motor Parameters Ivoke a step, measure respose Time lag, time costat, Plot speed i RPM versus duty cycle Sesitivity m SpeedRPM) Real Theory H s) m 1 s

16 Cotroller tuig Start with just a proportioal term Kp). - proportioal cotroller will geerate a smooth motor speed - choose the sig of the term Kp so the system is stable. - try differet Kp costats util the respose times are fast eough The ext step is to add some itegral term Ki) - a little at a time - to improve the steady state cotroller accuracy - without adversely affectig the respose time. - choose the sig of the term Ki so the system is stable. - Do t chage both Kp ad Ki at oce. The last step is the derivative term Kd) - a little at a time - reduce the overshoots/udershoots i the step respose - choose the sig of the term Kd so the overshoots/udershoots are reduced. Highly oliear -> empirical approach 21.16

17 Chargig battery Drai battery 10 25W resistor or motor) Charge tha 8 hours Sayo 8.4V- 3.8 AH NiMH positive temperature egative red white black gd thumb wheel switch red black +8.4V Test battery across load Measure voltage Measure curret 3.8 Amp-hour red RC battery coector CON-210P RC battery coector CON-210S red striped black plug socket black solid 12V 250mA wall-wart 21.17

18 Uder Battery Power Curret path battery-motor-battery Groud soldered male-male Oe +5V board Sayo 8.4V- 3.8 AH NiMH positive temperature egative red white black gd red RC battery coector CON-210P Floatig groud defied by battery thumb wheel switch black plug red black header +8.4V gd protoboard +8.4 gd +5 gd L Cotrol +5 GND+5V ARM board DC motor DC motor Servo +5V ito ARM board Pig))) IR s Tach s ARM board NOT coected to PC 21.18

19 While debuggig with PC Prevet motor curret from goig to board Two +5V, ot coected soldered male-male Groud board L293 Sayo 8.4V- 3.8 AH NiMH positive temperature egative red white black gd red RC battery coector CON-210P thumb wheel switch black plug red black header +8.4V gd protoboard +8.4 gd Cotrol +5 gd ARM board DC motor DC motor Servo Earth groud defied by PC Pig))) IR s Tach s gd ARM board IS coected to PC PC 21.19

20 Regulator Drop out, V d Calculate power loss, P=8.4-5)*I V i 0.33F 7805 I Out +5V Gd 0.1F V d = 2.5V V i > 7.5V I out <1A 4.7 F 4.7 F 21.20