EE 438 Automtic Control Systems echnology bortory 5 Control of Seprtely Excited DC Mchine Objective: Apply proportionl controller to n electromechnicl system nd observe the effects tht feedbck control hs on system performnce. Model n electromechnicl system using differentil nd lgebric equtions. Determine the stedy-stte nd dynmic performnce of torque-controlled permnent mgnetic dc motor with different controller prmeters. Observe the effects of feedbck control on motor-genertor system tht is subject to externl disturbnces. Apply proportionlintegrl controller to the motor-genertor system bove nd compre the performnce to proportionl controller. heoreticl Bckground Previous lbs demonstrte tht the response of system is modified by negtive feedbck control. he response speed of the system is incresed s the proportionl gin on the system increses. his ws demonstrted using n electricl nlog for process. his section of the circuit represented first order lg process. his lb introduces commonly used finl control element nd uses it in the proportionl controller designed from the previous experiment. he seprtely excited dc motor is widely used in process industries s n ctutor. his mchine hs liner model ignoring sturtion. Motor speed, torque or power cn be controlled to meet number of industril pplictions. his lb uses smll permnent mgnet dc mchines in motor, speed sensing, nd genertor pplictions. his is equivlent to lrger seprtely excited mchine tht hs constnt field current. he schemtic model of seprtely excited voltge controlled dc mchine is shown in Figure. For rmture voltge control the speed of the motor is proportionl to the rmture voltge ssuming tht there is no sturtion of the field. he electricl prmeters of the circuit re the rmture resistnce R, the rmture inductnce, nd the counter emf, e b. he vlue of e b is proportionl to the speed of the motor for liner opertion. he proportionlity constnt is clled the bck emf constnt, K e. his cn be found from test or in the mnufcturer's dt sheets. Writing KV eqution round the rmture circuit gives the stedy-stte response for the rmture. e e I R ( ) b Fll 206 lb4.doc
Where e ( 2) b K e m d Figure. Seprtely excited dc motor model. he stedy-stte speed of the motor is found by combining Equtions nd 2. e I R m ( 3) Ke he stedy-stte developed motor torque depends on the strength of the mgnetic field flux nd the rmture current. his is lso liner reltionship if no sturtion is ssumed in the mgnetic circuits. Since the motor mgnetic flux is constnt, the motor torque is linerly relted to the rmture current through the proportionlity constnt K. d K I ( 4) For motor speed to remin constnt, the motor lod torque, must be equl to the motor developed torque plus ny rottionl loss torque. Where ( 5) f d d = motor developed torque = mechnicl lod torque f = frictionl torque due to rottionl losses Fll 206 2 lb4.doc
Since the developed torque of the motor is proportionl to the rmture current, equtions 3 nd 4 cn be combined to give n eqution tht reltes the rmture current to the lod torque, K I (6) Since ll prcticl mchines hve non-zero vlues of f, n unloded motor must drw t lest enough current to overcome its rottionl losses. he motor's no-lod speed will depend on the mechnicl prmeters. f he mechnicl prmeters of the dc mchine re the viscous friction of the motor B m nd the rottionl inerti of the motor rmture, J m. he vlue of J m nd the rmture ccelertion determine the inertil torque tht the mchine must overcome while the vlue of B m reltes the dynmic friction to the rmture speed. he dynmic equtions of the mchine re differentil equtions tht relte the electricl inputs to the developed torque nd speed of the motor. When rrnged in the form shown below they re clled stte equtions. Stte eqution formultions re more flexible thn trnsfer function models becuse tht llow non-zero initil conditions nd produce the time function solutions directly when solved by computer. Where di R dt dm K dt J m K i e B i J m m m e m J m () (b) ( 7) R = the motor rmture resistnce = the motor rmture inductnce e = the motor rmture voltge m = the motor speed (rd/sec) B m = the totl motor/lod viscous friction coefficient (N-m-s/rd) J m = the totl motor/lod rottionl inerti (N-m-s 2 /rd) K e = bck emf constnt (V-s/rd) K = torque constnt (N-m/A) = motor lod torque (N-m) In this formultion of the motors dynmic response the vribles i nd m re clled stte vribles. he inputs to the system re the rmture voltge, e nd the motor lod torque,. Eqution 7 describes the electricl dynmics of the motor nd eqution 7b the mechnicl dynmics. Solving these equtions using pproprite computer routines will give plots of the responses of the motor speed nd rmture current. hese vribles completely describe the response of the motor. Fll 206 3 lb4.doc
Armture-Controlled Dc Mchines In the stte eqution model of dc motor bove, the motor speed is controlled by chnging the rmture voltge. Figure 2 shows the schemtic for n rmturecontrolled dc motor. his method of control requires vrible dc voltge source nd ssumes constnt field flux. Permnent mgnet dc motors hve constnt field flux. his lb ctivity will use this type of motor. R Vrible Dc Source e i e b + Mechnicl od J B B m J m Figure 2. Armture-Controlled Dc Motor Model. In Figure 2 schemtic, vrible dc voltge source supplies voltge to the motor rmture. Eqution 7 describes the electricl response of the motor to chnge in the vrible input voltge, e. his eqution writes e b in terms of the motor speed nd the bck EMF constnt. Eqution 8 below resttes eqution 7b s torque blnce t the rmture. J m dm B dt m he terms on the left-hnd side of the eqution represent the inertil torque, the viscous friction torque, nd the motor lod torque. hese torques must equl the developed rmture torque to mintin constnt motor speed. he rmture voltge, the motor constnts nd the viscous friction coefficient determine the speed of the rmture-controlled dc motor. At equilibrium there is no ccelertion nd not chnge in current so the derivtives in equtions 8 nd 7 re zero. Combining these equtions gives the reltionship for speed s function of the rmture voltge. Note tht the in stedy-stte f =B m m. m K i ( 8) K E R ( ) f m ( 9) K K e Fll 206 4 lb4.doc
Where m = motor rmture speed. (rd/sec) K = motor torque constnt (N-m/A). Ke = motor EMF constnt (V-sec/rd) = lod torque (N-m) f = frictionl torque If the motor is unloded then is zero nd the vlue of f limits the motor speed to the no-lod vlue. he motor rmture voltge, E, must be set to vlue tht will produce t lest the friction torque or the motor will not strt spinning. Incresing the vlue of E bove the no-lod voltge will cuse the rmture to ccelerte until it reches new stedy-stte speed. Additionl mechnicl lod cn then be pplied until f + = K I. In stedy-stte, rmture voltge reltes to rmture current through the following expression: Where: E K R e m I m = motor stedy-stte speed (0) If more torque is required by the motor but the rmture voltge remins fixed then the rmture current cnnot increse limiting the torque nd the motor will stll. he rmture current must increse to meet the torque demnd plced on the motor. his mens tht the rmture voltge must increse s well to produce more current. he block digrm show in Figure 3 shows how the rmture current nd lod torque ct s inputs to the mechnicl system comprised of the motor rmture nd its lod. I (s) d (s) - K + J s m B m m (s) Figure 3. Block Digrm of Current Driven Dc Motor with n Externl od. he direct-coupled motor/lod combintion is first order lg process with time constnt tht is given by J m /B m. he totl rottionl inerti is J m nd totl viscous friction is B m. Fll 206 5 lb4.doc
chogenertor Model he speed of dc mchine cn be mesured with dc tchometer. A dc tchometer is permnent mgnet dc genertor tht is connected to the sme shft s the drive motor. he output voltge of the dc genertor under constnt lod is proportionl to the genertor shft speed. he time domin nd plce equtions for this device re: where v k t V (s) k t t t m m (s) k t = the tchogenertor constnt (V-s/rd) v t = the tchogenertor output voltge (V) m = motor rmture speed (rd/sec) It my be necessry to scle the output of tchometer to reduce the spn of its output. OP AMP scling circuits, similr to those in b, cn scle the tchometer's output to ny prcticl rnge. () Vrible Dc Using Pulse-Width Modultion Pulse-Width Modultion PWM cn produce controllble dc output tht hs high voltge nd current.. PWM produces vrible dc voltge by switching dc source on/off for frction of pulse duty cycle. An idel PWM circuit hs liner reltionship between duty cycle nd output voltge. his modultor compres reference level to tringle wve nd produces n output squre wve with vrible duty cycle. his output signl cn control higher voltge nd current source producing n djustble dc level. +Vf V f V in +Vf V f V in -Vf t (sec) -Vf t (sec) t on t on V omx Vo f t (sec) Vo f t (sec) Figure 4. Pulse-Width Modultion Output for Vrying Input Voltge. Fll 206 6 lb4.doc
Figure 4 shows the wveforms for typicl PWM output. In this reliztion, the output voltge pulse width increses s the control voltge, V c, decreses Incresing the pulse width increse the verge dc output voltge linerly with the on time, t on. Mximum output occurs when t on = f, where f is the period of the tringle wve used to modulte the output. he duty cycle cn vry from 0%-90% in prcticl reliztions of PWM. he following eqution describes the reltionship. between duty cycle nd output voltge. Where: V t V on o mx o (2) f V o =modultor output voltge V omx = mximum supply voltge t on = pulse on time (sec) f = tringle wve period (sec) he slope of the tringle wve ffects the sensitivity of the output voltge to the modultor input voltge, V in. Using the concept of similr tringles on Figure 4 gives the following reltionship between the control voltge V in nd the pulse on-time, t on. t Vf mx Vin For - Vfmx Vin Vf mx f on 2 V (3) f mx his eqution is vlid for tringle wves input to non-inverting comprtor's negtive input nd control voltge pplied to the positive terminl. his lso ssumes finl switching device connect so it conducts when the comprtor output is high. Combining Equtions (2) nd (3) reltes the input voltge of the PWM to the dc output. V o Vf mx Vin Vo mx 2 V (4) f mx PWM Drive Circuit Using Anlog Devices Figure 5 shows PWM circuit for delivering vrible voltge to smll permnent mgnet dc motor. he circuit uses common ICs to produce tringle wve nd compre it to reference voltge. he dc motor directly couples to tchogenertor nd smll genertor for this lb ctivity. his lb fixture is vilble for the lb instructor. he ICs U, U2 nd U3 form the tringle wve genertor. he IC U is 555 timer configured to operte s n stble multivibrtor. In this configurtion, the time produces squre wve output tht hs widely vrible duty cycle nd frequency set by resistors R, R2 nd cpcitor C. Fll 206 7 lb4.doc
2V R6 2.2k U UA555 R 4k Gnd rg Out Rst Vcc Dis hr Ctl R2 4k D N45 20V Vt R3 3.3k C4 uf R4 0k C2 0.0uF C 0.0uF 0.033uF C3 0k 2V R7 + U2 F35-2V R5 0k 2V + R8 56k U3 F35-2V 2V R3 0k 2V U4 P3-2V R4 0k R0 2.2k D2 N4004 R9 4.7k M Q IRF50 ch M2 M3 V Genertor R2 0k 0% -2V Figure 5. ypicl Dc motor Current Dive Circuit Using unity Gin Follower Fll 206 lb4.doc
he diode D bypsses R2 forming wide rnge duty cycle circuit. he following design equtions will find vlues of R nd R2 given vlue of C duty cycle nd frequency. he design shown is set for 5000 Hz nd 50% duty cycle. f 0.67(R R2) C R DC R R2 (5) he output of the timer couples to the OP AMP integrtor circuit through high pss filter formed by C4 nd R3. his circuit removes the dc component of the squre wve nd centers it bout ground. he high pss filter hs cut-off frequency of 50 Hz. he OP AMP U2 is n integrtor circuit with cut-off frequency of 500 Hz nd dc gin of. Design this circuit be selecting frequency well below the timer output, usully fctor of /0 is sufficient, selecting vlue of input resistnce R4 nd computing vlue of C3. he ICs U2 nd U3 re high slew rted JFE input OP AMPs the cn ccurtely reproduce higher frequency signls. he circuit implemented using U3 is simply n inverting OP AMP with gin set by resistors R5 nd R8. his circuit hs dc gin of 5.6 nd inverts the output with respect to the input signl. he IC U4 is non-inverting voltge comprtor tht cts s the pulse width modultor. he tringle wve enter the device on the inverting input nd the control voltge, V c, enters on the non-inverting terminl. he selected device hs n open collector output tht cn be connected to seprte voltge source. Vrying the vlue of Vc chnges the duty cycle of the comprtor output s shown in Figure 4. he output of the comprtor drives MOSFE device tht is in series with the permnent mgnet dc motor. MOSFE devices re voltge controlled devices tht drw negligible current. he resistors R9 nd R0 form the bis network of the MOSFE. When the output of U4 is high the MOSFE cts s closed switch nd the full motor supply voltge ppers cross its terminls. Mesuring the voltge cross the MOSFE will show zero volts indicting tht the source voltge ppers cross the motor rmture. When the comprtor output is low the MOSFE cts s n open switch nd the source dc voltge ppers cross the MOSFE. No voltge ppers cross the motor rmture. he schemtic shows diode D2 connected cross the motor rmture so it is reverse bised. his diode suppress inductive voltge spike tht pper when the rmture current is switched off. his diode should hve voltge rting of severl hundred volts nd current rting similr to the full lod current of the motor. Fll 206 lb4.doc
he resistors nd potentiometer R2, R3 nd R4 form voltge divider network tht provides control voltge for testing this circuit. Remove these components nd connect this comprtor input to the controller output. Seprtely Excited Dc Genertor Model Figure 6. Seprtely Excited Dc Genertor Model. Figure 5 shows the schemtic of seprtely excited dc genertor. A permnent mgnet dc motor cts s seprtely excited dc genertor if it is coupled to source of mechnicl power. he source of mechnicl power is clled the prime mover of the genertor. When the genertor is not connected to n electricl lod the prime mover supplies enough power to overcome the rottionl losses of the genertor. If the genertor is driven t constnt speed then the rottionl power losses cn be expressed s frictionl torque just s in the motor cse. As electricl lod is pplied to the mchine dditionl torque must be supplied by the prime mover or the speed of the system will decrese. he stedy-stte power blnce t the rmture of the genertor is given s: where d n E I ( 6) 30 d = the torque developed t the rmture (N-m) n = rmture speed (RPM) E = induced rmture voltge (V) I = rmture current (A) he left-hnd side of the eqution is the mechnicl power input nd the right-hnd side is the totl electricl power output. he power trnsferred to the lod is the rmture power given in Eqution 2 minus the power losses of the rmture resistnce. Fll 206 0 lb4.doc
If I nd V t re mesured nd the vlue of rmture resistnce, R is known, the developed torque is given by Eqution 3. 2 30 V I I R d ( 7) n his reltionship shows tht if speed is held constnt then the torque developed in the prime mover must increse. Increses in lod occur when more resistors re connected in prllel cross the genertor terminls. his cuses n increse in I which lso increses the losses due to rmture resistnce. he induced voltge is proportionl to the rmture speed for seprtely excited genertor. he emf constnt of the genertor gives the reltionship between the prime mover speed nd the induced voltge. E K e n he dynmic equtions for the seprtely excited genertor re shown in stte vrible form. hese equtions ssume tht the prime mover is seprtely excited dc motor. dg K dt J di R dt v R g i i R m B J i g g K g J g K e g g i (b) (c) () ( 8) where g = genertor rmture speed (rd/sec) i m = motor rmture current (A) i = genertor rmture current (A) R = genertor rmture resistnce ( = genertor rmture inductnce (H) R = lod resistnce ( K e = genertor emf constnt (V-s/rd) K = motor torque constnt (N-m/A) J g = genertor rottionl inerti (N-m-s 2 /rd) B g = genertor viscous friction coefficient (N-m-s/rd) v = lod terminl voltge Eqution 4 describes the mechnicl dynmics of the genertor. he prime mover rmture current is considered n input to the system. his set of equtions cn be combined with the model for the current driven dc motor to give n overll response of the system. Eqution 4b represents the electricl dynmics of the genertor rmture Fll 206 lb4.doc
circuit. he lod is considered to be fixed resistnce. Eqution 4c is the output eqution tht reltes the stte vribles g nd i to the output. Design Project I Proportionl Control of Dc Motor-Genertor System.) Construct the PWM Driver circuit shown in Figure 5 using the vlues shown in the schemtic. he IRP50 power MOSFE should be mounted on het sink. Use two power supplies to derive the voltge sources for the circuit. One supply will provide the 20 Vdc for the motor nd MOSFE only. he other supply will provide the voltges for the controller nd current converter circuits. Set the OP AMP supply for 2 Vdc. 2.) est the circuit by connecting it to the motor-genertor test setup provided. It consists of 3 identicl permnent mgnet motors with coupled shfts. he mchine prmeters re: K e = 0.06398 V-sec/rd K = 0.06426 N-m/A R = 22.6 ohms = 0.044 H B m = 0.745x0-6 N-m-s/rd J m = 3.39x0-6 N-m-s 2 /rd Assume tht ll three mchines re identicl so the bove prmeters describe ll mchines mounted on the test setup. One of the mchines will be driven by the PWM driver circuit while nother mchine will function s dc tchometer to mesure the speed of the motor. he lst mchine will be connected s dc genertor. Initilly the genertor will operte with no-lod. he functionl block digrm of the desired system is shown in Figure 7. V sp + - V e Proportionl Controller V c PWM Vrible Voltge circuit VI Voltge-fed PM dc motor m PM dc Genertor V V bis V m Voltge scling V t cho genertor Figure 7. Block Digrm of the Motor-Genertor Control System. est the combintion of the PWM driver nd motor-genertor-tchometer system by pplying different vlues of input voltge, V c, to the comprtor U4 using the Fll 206 2 lb4.doc
potentiometer R2. Record the vlues of motor rmture current I, tchometer output voltge V t, Q drin-to-source voltge, V DS nd the genertor output voltge. Mke the mesurements for the following vlues of V c shown in ble -A. Determine the vlue of V c tht just cuses the rmture to turn (between 60 nd80 ma of rmture current) when there is no-lod connected to the genertor. Record this dt in ble -B. 3.) Modify the difference mplifier nd proportionl controller from the Experiment 2 so tht bis voltge produces V c tht just cuses the motor rmture to spin. he feedbck signl to the difference mplifier nd the set-point voltge signls should be disconnected nd both inputs to the difference mplifier grounded when testing this circuit modifiction. Grounding the inputs is equivlent of hving zero error. 4.) Unground the set-point input to the difference mplifier nd connect it to the wiper rm of potentiometer tht gives 0-5 Vdc output. With the motor rmture current set to the vlue found in step 3 by the proportionl controller bis, Adjust the output of the set-point potentiometer nd mesure the voltge output of the tchometer. Adjust the set-point vlue until the tchometer output reds 2.06 Vdc. Using voltge divider circuit nd n OP AMP voltge follower circuit, scle the tchometer output voltge to be equl to 2.5 Vdc. 5.) De-energize the whole system nd set the vlue of Kp to 2. Disconnect the inputs of the difference mplifier from ground nd connect them to the set-point vlue nd the feedbck signl supplied from the scling circuit. Set the set-point voltge to 2.5 Vdc nd energize the whole system. Mesure the motor rmture current I, the controller output V c, the feedbck signl voltge, V m, the error voltge V e, nd the tchometer output voltge V t. For the set-point voltges shown in ble 2-A Estimte the motor speed, n m, by dividing V t by the tchometer constnt, K e =0.0067 V/RPM, nd lso record this in ble 2-A. 6.) Set the set-point vlue to 2.5 V. Connect 000 ohm /2 wtt resistor cross the genertor terminls with the proportionl controller in opertion. Mesure I, V c, V m, V e nd V t gin. Record this dt in ble 2-B. Prllel 000 ohm resistors to get the remining lods in ble 2-B nd record the results for ech vlue of R. 7.) Repet steps 5 nd 6 with vlues of Kp set to0 nd 50. Enter the dt for Kp=0 into bles 3-A nd 3-B. For Kp=50 enter the dt into bles 4-A nd 4-B. Include ll the dt collected from the tests on the system in the report. Also derive closed loop trnsfer function for the system with the set-point voltge s the input nd the genertor terminl s the output using Kp=2 nd R =000 ohms. he block digrms for this system nd the derived equtions re in Appendix A of this hndout. Using the dt in bles 2-A, 3-A, 4-A, produce three plots of the set-point voltge, V sp, (x) vs. the error voltge, V e, (y). In the lbortory report, comment on how incresing the proportionl gin ffects the speed error. Also, produce three plots using the dt in bles 2-B, 3-B, 4-B of the genertor lod resistnce, R, (x) vs. the motor speed, n m, (y). Discuss how the motors speed is ffected by the lod chnge with the controller in opertion. Compre the performnce with n uncontrolled system. Fll 206 3 lb4.doc
Design Project II Proportionl-Integrl Control of Dc Motor-Genertor System Proportionl control gives fst response but requires high gins to chieve smll vlues of stedy-stte error. Applictions tht need more precise control cn employ proportionl-integrl (PI) controller. Figure 7 shows n OP AMP implementtion of PI controller. R 2 5V C R 4 R + 5V R 3 + V e UA74 V c -5V -5V Figure 8. Proportionl-Integrl Controller Using Single OP AMP he trnsfer function of this controller is: V c (s) R2 ( 9 ) Ve (s) R R2Cs Eqution (5) ssumes tht R 3 =R 4. he rtio of R 2 nd R sets the proportionl gin nd the cpcitor nd R 2 set the integrl ction rte. he recipricl of the integrl ction rte is the time required for the integrl mode to mtch the chnge in output produced by the proportionl mode. he proportionl gin is defined in terms of the OP AMP prmeters s R 2 Kp ( 20 ) R K I R C ( 2) 2 Disconnect the proportionl controller from the feedbck loop nd substitute PI controller tht hs the following prmeters: Kp=2 nd K I =23 sec -. et C =0.0F for this clcultion nd find vlues for R, R 2, R 3, nd R 4. Figure 8 shows block digrm of the motor-genertor system with the PI controller dded. Fll 206 4 lb4.doc
V sp + - V e PI Controller V c PWM Vrible Voltge circuit I Voltge-fed PM dc motor m PM dc Genertor V V m Voltge scling V t cho genertor Figure 9. Motor Control Using Proportionl Integrl Controller..) With the controller design from bove instlled in the control loop, vry the setpoint voltge over the rnge shown in ble 5-A, nd mke ll the necessry mesurements to fill the tble. 2.) Adjust the set-point to 2.5 V dc nd dd the genertor lod resistors listed in ble 5-B. Mke ll necessry mesurements to fill the tble. 3.) Set Kp=0 nd mintin K I =23 sec -. Vry the set-point with no lod resistor connected nd record the dt in ble 6-A. 4.) Adjust the set-point to 2.5 V dc nd dd the genertor lod resistors listed in ble 6-B. Mke ll necessry mesurements to fill the tble. Using the dt in bles 5-A nd 6-A, produce two plots of the set-point voltge, V sp, (x) vs. the error voltge, V e, (y). In the lbortory report, comment on how incresing the proportionl gin ffects the speed error nd how the integrl ction chnges the system performnce. Also, produce two plots using the dt in bles 6-B, 6-B, of the genertor lod resistnce, R, (x) vs. the motor speed, n m, (y). Discuss how the motors speed is ffected by the lod chnge with the PI controller in opertion. Compre the performnce with n uncontrolled system nd the proportionl only controller. Fll 206 5 lb4.doc
Appendix A Block Digrms for b 5 he block digrm below describes the signl flows of torque-driven dc genertor used in the lb. d (s) + - J m s B m mg (s) E g (s) K e s (R R ) I (s) R V (s) g (s) K g Figure 0. Block digrm of Genertor. he prmeters hve the following definitions: d (s) = mechnicl torque developed by the prime mover g (s) = counter torque developed by the genertor J m = the rottionl inerti of the motor nd genertor B m = the viscous friction of the motor nd genertor K e = genertor emf constnt = genertor rmture inductnce R = genertor rmture resistnce R = lod resistnce K g = genertor torque constnt mg (s)= shft speed of motor-genertor I (s) = genertor lod current V (s)= genertor terminl voltge Fll 206 6 lb4.doc
When the speed feedbck control is dded the following block digrm results: V m (s) K s K t - + K P V c (s) K VI I m (s) K m + - J m s B m d (s) mg (s) K e s (R R ) E g (s) I (s) R V(s) V sp (s) g (s) K g Figure. Overll system block digrm. he prmeters nd signls re defined below. V sp (s) = system control setpoint vlue V c (s) = controller output voltge I m (s) = motor rmture current K t = tchometer voltge constnt K s = voltge scling circuit constnt K VI = voltge-to-current converter gin (h FE /R 2 ) K m = motor torque constnt K P = controller proportionl gin he overll trnsfer function is found using the formul below: V V sp (s) G (s) (s) G (s)g (s)h (s) G (s)g (s)h (s) ( 22 ) 2 2 3 2 With: G (s) KPKVIKm (s) KsKt G (s) 2 Jm 2(s) K H H g s B m G3(s) s (R R ) G KPKVIKmKeR (s) ( s (R R ))(J s B m m ) Fll 206 7 lb4.doc
ble -A V c (Vdc) V DS (Vdc) V t (Vdc) I (ma) 0.0.0.5 2.0 2.5 3.0 3.5 4.0 5.0 6.0 ble -B Strting Current Vlues I (ma) V CE2 (Vdc) V t (Vdc) V c (Vdc) ble 2-A K p =2, R =infinity V sp (Vdc) V t (Vdc) V m (Vdc) V e (Vdc) V C (Vdc) n m (RPM) 0.5.0.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 ble 2-B Kp=2, V sp =2.5 Vdc R () I (ma) V t (Vdc) V m (Vdc) V c (Vdc) V (Vdc) n m (RPM) 000 500 250 25 Fll 206 8 lb4.doc
ble 3-A K p =0, R =infinity V sp (Vdc) V t (Vdc) V m (Vdc) V e (Vdc) V C (Vdc) n m (RPM) 0.5.0.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 ble 3-B Kp=0, V sp =2.5 Vdc R () I (ma) V t (Vdc) V m (Vdc) V c (Vdc) V (Vdc) n m (RPM) 000 500 250 25 ble 4-A K p =50, R =infinity V sp (Vdc) V t (Vdc) V m (Vdc) V e (Vdc) V C (Vdc) n m (RPM) 0.5.0.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 ble 4-B Kp=50, V sp =2.5 Vdc R () I (ma) V t (Vdc) V m (Vdc) V c (Vdc) V (Vdc) n m (RPM) 000 500 250 25 Fll 206 9 lb4.doc
PI Controller Design Dt ble 5-A K p =2, K I =23, R =infinity V sp (Vdc) V t (Vdc) V m (Vdc) V e (Vdc) V C (Vdc) n m (RPM) 0.5.0.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 ble 5-B Kp=2, K I =23, V sp =2.5 Vdc R () I (ma) V t (Vdc) V m (Vdc) V c (Vdc) V (Vdc) n m (RPM) 000 500 250 25 ble 6-A K p =0, K I =23, R =infinity V sp (Vdc) V t (Vdc) V m (Vdc) V e (Vdc) V C (Vdc) n m (RPM) 0.5.0.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Fll 206 20 lb4.doc
ble 6-B Kp=0, K I =23, V sp =2.5 Vdc R () I (ma) V t (Vdc) V m (Vdc) V c (Vdc) V (Vdc) n m (RPM) 000 500 250 25 Fll 206 2 lb4.doc