A microprocessor-based speed controller for DC motors

A Microprocessor ... based Speed Controller for DC Motors by Prof. E. BertrU1, J. Herranz, L Martinez, J. Miguel and I. Mu nil la College of Engineering and Telecommunicatiorn iU_P 8 ), Barcelona The introduction of microprocessOrs into electric vehicles has opened many interesting possibilities for improving the operation and maintenance of such automotive systems. On the other hand, microcomputer-based motor control systems are playing an ever increasing role in research on applied electronics. In this paper, a microcomputerbased digital dynamic control system (DDC) for a de motor is described. The description includes motor identification and corrector digital implementation, as well as precision analysis of the control system. The influence of poles and corrector gain on the system response is also presented, this allows the choice of appropriate parameters for the design of a lag-lead controller. The application of such a controller with a low power de motor verifies the theoretical approach and reveals the necessary information to analyse the speed control system stability of a chopper-fed de motor using the same controller. lntrodudion .. ....-p r- ------:-:::-~~---:-:;'i" .. -.-::c.c----------, '6 . ' I J s .. >-1 t- -1 I I I J l: 0/A I .0,/0 I I ' I ______ ; ----------------- ---- ---- -- r---1 I rc. l r·~·.-· --~ •&•••-- 0 ...... "" ...... T--~ ...... .. , .. - .. ......... , ... LSI techniques development has caused digital electronic devices to become much smaller, faster and cheaper; consequently, the tleld of automotive electronics has been considerably broadened due to microcomputer utilization. In 1977 the first microprocessor was introduced in the Oldsmobile Toronado as part of the spark ;>lug timing circuit. In these fuel-vehicles the microprocessor is delegated to perform the <!ngine conrrol and provide valuable information to the driver. On the other hand. microcomputer-based control for ~lectric vehicles provides a higher etficiency. allowing speed adjustment or torque control. \famely, both ignition and timing control, as well as cylinder selection. which constitutes the main control tasks in a fuel-vehicle and are replaced by a dosed-loop digital control in the electric vehicle. ~oreover, by changing only the control programme, different services .:an be obtained with the same propulsion system. This versatility also allows to implement different kinds of ~lectric vehicles (vans. cabs, airport trucks) with the same propulsion system. The low cost and feasibility of microprocessors is another significant reason for their use either as chopperfed de motor controllers or as inverter controUers when ac motors ace used. F"~ 1 Function• bloc:tc di8Qnm of the microcompu'lllr ~ comrof svsam As regards the motor selection for ?rotessor E. 13ertran. J. Hemsnz. L. Mart(nez. J. Miguel and I. Munllla are with the Department of Systems Control. The Collage of Engineering and Telecommun'- catfons (U.P.B.l. Jordl Glrona SaiQIIdo, 5/N, Barcelona 34. Spain. an dectric vehicle. it cannot be made by ..:onsidering the motor services only, but must take into account the relationship between motor services and the <!SSOciated electronic control. From [he electronic control point of view. ac motor ..:ontrol is more complex. However. whereas a de motor rarely has a conversion efficiency bigger than 85%. that of an ac motor is approximately 90%. Even allowing for important losses in the control system. the global efficiency of the propulsion system-control benefits by using ac. Finally. energy recovery is simpler for the de motor which constitutes the best alternative when working at low voltages. Digital system This paper discusses a digital system Z2 ELECT .. IC VEHICLE DEVELCPMEN'TS SUMME .. 11113 which uses a Rockwell Aim-65 micro· .:ompu ter to control the speed of a de 5ervomotor. For this application. the Rockwell Aim-65 microcomputer is used to implement the sampled-data feedback .:ontrol. and the micro- ..:omputer speed control system is shown in Fig. I. The actual speed is obtained by means of a tachogenerator. Its output is compared to the reference input and the error is then compen· sated by the microprocessor whose output provides the corrected control signal to the preamplifier. The servoamplifier is driven by the preamplifier and provides the output signal to the motor. OC motor model An important element in the analysis and design of a speed control system is the choice of model for the ~ .... ~ - ;. ,. _ . -. .. . -. - ~~ "l'ltlt1UX' ~ ·s ~D ·--- msrs: 1-"'- ... - ~ ,.,.. I 'MS ~C:A.I.. .t "Dc:.DDaq. I I ~ ~ -,- ~~ 0 l I lz. s "' S' .. ,. o~ la 1! .AtiOfllltS .4A/~c!> . . ~ DINT f. I• ... :1 iS~ w;! 0 ' 11 ~ ~ CJ.Oeo<... lb.rr CVIA) Fig. 2 Functional sc:hame of the analog in111rfac:e u..ci in the experiment power actuator. Correct motor identification is the result of measuring the mechanical time constant as well as the static gain. Mechanical time constant A step input voltage is applied to the motor armature and the exponential rise of the motor speed is measured on an oscilloscope. Thus. b)' generating a low frequency pulse train in the D/A converter output. the corresponding tachometer output can be obtained bemg the time constant 7>.~ the time required for the tachometer voltage to rise to 63 . ~<::; of its final vaiue. Static eain The~ motor static gain K0 can be obtained by generating a signal in the D/A converter outout and readinc the corresponding tachometer outpu-t by means of the AID converter. Motor transfer function ~otor transfer function can be written: w0 (s 1 = V(s) where K0 <Y 205 rad.sec1 /volt. and Tc ""' 0.::!5 secs for the motor used in the experiment. A/D Conversion Assembler Programme Figure 2 shows the functional scheme of the analog interface for the Rockwell Aim-65 microcomputer system which has been developed in the Department of Systems Control (ETSIT. Barcelona). The design is easily adaptable to any -other computer. lt uses eight multiplexed inputs and one output, and has been designed to control low-power devices. LDA *DF The microcomputer controls the analog input through the so-called VIA ia set of programmable input/output ports) by using an Aim-65 system. Bv means of the usuarv subroutine the main programme in ·Basic makes the following sequence oi assembler instructions for the A/D conversion: . DEFISE VIA'S OPERATIOS MODE STA LDA STA LDA STA \OP NOP LDA STA LEVl . LDA SEC SBC BNE JMP A003 : 3F A0Cb1 . ~- :::z:: _, : A00l =i= 27 A00 AOOl #07 LEV 1 C0D 1 . SELECT ANALOG 1!\'PL ~ T . HOLD :END OF CONVERSIOJ'\'~ RETURN TO BASIC Corrector Digital Implementation By using the bilinear transformation a Jag-lead controller has been programmed in the microcomputer. its transfer funcnon being: G (s) = K L!:..C. c s+p The corresponding Basic programme is given below: ELECTRIC VEHICLE DEVELOPMENTS SUMMER 1983 23 ' .., 5 7 10 15 18 20 22 DlM X<4> DIM Y<4> INPUT "TRNS. Z= l" ; FR IF FR:::ol GO TO 300 INPUT "SAMPLING PERIOD" ; T INPUT "DELAY" ; Z INPUT "C" = ; C 24 INPUT "P'' = ; P 26 INPUT "K" = ; K 28 INPUT "DER=l, BlLIN.~"; FT 3(J IF FT=l GO TO 38 32 o 1 = <K•c•T -2•K>t<2+P*T> 34 01 = <2•K+K*C•T>/<2+P*T> 36 Q3 = <P*T -2>/<P*T+D 38 FOR I =~TO 4 ~ X<D=0 -4-2 Y<D=0 44 ~EXT I Motor responses to a 5 volts-step in the set-point have been obtained for different values of p (figure 3) and K (figure 4). Being the corrector gain a constant, the overshoot and damping frequency of the output will decrease if the corrector pole becomes more negative, as it can be seen in figure 3. On the contrary, a great increase of K makes the damping frequency component bigger when p and c are fixed (fig. 4 ). Stability Analysis Figure 5 shows the system block diagram where the microcomputer computation lag has been modelled by means of a delay block of T seconds. Choosing c=4 its transfer function can be obtained, from the system block diagram as follows: (100+10p}z3 + (1 Op-IOO+l5.J8K)z1 + 30.76Kz + !5.J8z = 0 If the system is stable all the roots Zi of this equation will lie inside the unit circle, or I Zi I< I. Chopper-fed DC Motor Figure 6 shows the functional block diagram of a de motor which is fed by a c hopper. Differences between this scheme and that in figure 1 can easily be established. Thus. p reamplifier and s ervoamplifier a re replaced here by pulse g enerator and c hopper . From the point of vi ew of sta bility it me:ms that a new block diagram must be anaJ ys ed. In which case. the c hopper transf er f un c tion is d etermined by its duty cycle: V(s) = E IJ(s) 211' where E represents the battery voltage. ~8 POKE 40962. 255 5(J X <a>= X <I> 52 X<I>=X<2> 53 X <~=X<3> 54 X <3> = X <4> 55 y <0> = y < 1 > 56 y <1> = y <2> 57 y <2>= y <3> 58 Y<3>=Y<4> 60 POKE 04 . ~ e-Ts ( l - e·Ts ) K s + c Km ' S'T'P TniS'-:n H(s) = 65 POKE 05. 12 I + K K + e·Ts ( l - e-T s) K ~ A S s + p Km 1"TT1S + I 70 W=USR<R> 75 U =PEEK <40959> = e·Ts ( l - e·Ts ) K.820 85 X <4> = <U-!2T> • 08 88 IF FR =I GO TO 350 s1 + sp + e-Ts ( 1 - e ·Ts ) K.l 5. 38 89 IF FT= l GO TO 250 91 Y<4>=X<J>*Ql+X<4> And its pulse transfer function: ~~ 102 104 110 120 • Q2 -y <3> • Q3 FOR L=0 TO Z H(z) = 820K (zl + 2z + I) (lOO+ 10p)z3 +(lOp100 + 1538K)zl + 30.76Kz + 1538K 150 254' 252 255 300 310 32~ 350 3 51 360 370 380 40(.1 G = 3 • 5 ~EXTL 0 = <Y <4>. 13.5> + 127 POKE 40960 . 0 GO TO 5~ F or particular values of K. p and c, the stability of such a system can be determined from the loca ti on of t he roots of the characteristic equation y <4> = Y <J> + K•X<4>-K*X<3>+K*C•T•X<4> y <4> = Y <4> I <1 + P•T> GO TO LOO INPUT Nl.JM. COEFFICIENTS IN DECREASING ORDER: A0. Al. A2, A3. A4. INPUT DEN . COEFFICIENTS :00. Bl, B2, B3, B4 GO TO 38 Y <4> = X<4>* A<0>+X<J>• AI +X<D* A2 Y <4> = Y<4>•X<I>•AJ+X<4>*A4 Y <4> = Y<4>-Y<J>•BJ-Y<2>*B2-Y<I>•BJ-Y<0>*84. Y <4>= Y<4> /80 GO TO 100 END Different tasks in this programme are explained as follows: 10-28 300-310 60-85 32-58 91 110-120 250-252 310-380 100-104 Input parameters Sample error signal Compute y(t} Output to Dl A converter Correct the computation of y(t) by means of the bilinear transformation Find y(t) by means of the z-transfonn Delay introduced by the usuary to experiment the influence of the sampling period. Options: -Direct computation (22, 24, 26). - Computation by means of z-transfonn ( 1 fl. 3119, 31 t) -Modify sampling time (29). ELECTRIC VEHICU DEVELOPMENTS SUMMER 1113 Moreover, an important class of pulse generators can be modeUed as a zeroorder-hold circuit I l I whose transfer function can be written as follows: I - e-Ts G(s) = G0 (....:....- 5 ~-1 where T is the microprocessor sampling time. By i ntroducing both chopper and pulse gener ator tran sf er iunc tions (fig. 5) , the system char acte ristic e qua tion can be obtained, in order to verify the stability of the system. Conclusion The application of a personal computer on a de motor control has b een descri bed. Th e s tudy shows that the co ntr ol can be used sa ti sfactorily in servomo tor applicati ons a nd as a speed control. As for its utilization in e lecoic vehicles. the sa me c on c ept :1 pplies. In this case, the p ower is s upplied to t he motor t hrough a c hopper {SCR or transistor), this be ing t he pulse g enera t or or inte rf ace between the microcomputer and the power stage. Stability analysis is also given when the pulse g enerator is modelled as a zero-order ho l d. Real time control constitutes the most stringent demand on microprocessor based equipment. Computat ion lags, conversion times and operationaJ accuracy acquire a relevant d esign significance. Hence, response s peed problems wiTI arise if the rogramme execution time is large. erefore, maximum controlled motor p Th spee p d will be determined by microrocessor minimum sampling time. Titis period is calculated by considering the AID conversion time the control algorithm computation time and the 0/A conversion time. Finally, programming in Basic revea~ that internal operations can be made with great llccuracy at the expense of reducing processing speed. On the other hand, the use of assembler language improves the speed of response. while operations are made with large errors. Therefore, this trade· off between speed response and algorithm operations accuracy constitutes the first problem to be solved when designing a digital controller. References I Linn. A. K. and Koespel, W. W •• "A microprocessor speed control system". IEEE Trans. lnd. Electron . Contr. lnstrum. Vol. IECI-24, No. 3. August 1977. 2 Cen da gorta -G alar ta. M. and Prats, J .• "Yehiculo eiEctrico con alimentaci6n solar". Proyecto Fin de Carrera, ETSIT de Barcelona. 1980. 3 Modular Servo System MS ISO Book 3 DC. Synchro S. AC, Advanced Experiments". Feedback Instruments Limited. 4 Cadzow . J. A. and Martens. H.R .. "Discrete-time and Compute r Control Systems". Prentice·H aD. INC. En~ewood Cliffs. New Jersey. . ·- ... -" · ~ -· . ~ · -- I · I I · t· ... l · ; I , ,. -. ,- .- -.. ~ ~I - ;' J ~\ I . r . .,. - ... .. ;- .. ' . -I ~ I -h !. -' ; ~ .. ; ; I -- . . \- - l - -- ~ - · ~ -: .. - .. ·· -1-l_ ,. .. . ~- . .. . T ...,. .. .. , ~ I t. ::.:,. I"""" . I .... .. ~ ·- .. . r· ., . . , -i I. h . ... -- • · I ~ ..... ' i ... .... ...:. l,.oo ""' . ~-~ .. . - ·'-- I · -- -.l [/ . -I .. _. · I~ . ... . , . ~ .. -; .. .. ' ' - .. . --</ · -- I- . I . I -~ - l . t/ - '! I I· • • '--- :;o ·- "/ ' ! --.. . I ·+· .. I : I I . . - '.J .. : ' I KoG..( I ! - I i --; · .v · 1 I ; . I ' I ' . I I l '.I I i l · J . ..ift.l I I I • - 116' ; I ' ' I i I I ,. I I . I I I I ' I I i ! I 1 .. ' I i I ... ; I i I I i J ' 1" ; I I '#<,~~ I ' I ' I I I I I --. --·- . Fig. 4 Speed r...-- to 5 vat,.._ (K • 0.07. 0.1, O.SI OI•ITA' co~ArC"WI!! I I ' OILA,. Sloli "'''-Tf. llf~T • -~ ,_.~ 1(.~ ...!!4-l_ ..,T1'0r #I ~ .. , ~5•i.l - I l !(,. I r 1<',. r 7"f.CCJW~ CIVr'I"IIT J Fig. 5 S~m block dievr-m I where nn "'"0.25 secs ' Km""' 205 • KT : 25.l<P I KA : 0.75 T : 0.2 secs. I EVC -Expo .83 Fig. 6 Sp.d con1r01 -vn-m at • chopper ied de motor Washinl!ton. DC ( 19 Julv 1983)- The Electri~ Vehicle Council announced toda~ that 13 organisations are so far committed to exhibit products and services during the Council's Expo "83 Conierence and Showcase. The inter· national event will be held at the Hvatt Re2encv Hotel in Dearborn. M.ichigan from: October 4 to 6. 1983. ' 1!\ioth) . . .. . . . . - , I I I - - .- .. -'-- - ----S.- -- -~'- - --- --- ·- - -- - -- -- · • I I "' ••• , I "--' : 1 • : ' .... •• Exhibitors: General Motors Corporation Ford Motor Company Detroit Edison Company Eaton Corporation Long Island Ughting Company Grumman Allied Industries, lnc Alber Engineering, lnc Energy Development Associates (Gulf+ Western) Lucas Chloride EV Systems Ltd Fiat SpA/IVECO Brown, Boveri, & Cie Tennessee Valley Authority AVERE Information is available from the Fig. 3 Speed ~to 5 vol~ (p • 3, 5. 81 Council, llll-19th Street NW. Washington, DC 20036. ELECTRIC VEHICLE DEVELOPMENTS SUMMER 1983 25