Microprocessor-Based Position-Servo System of Permanent Magnetic Synchronous Motor with Sliding Mode Control

Copyngth ~ IFAC Mouon Control for Intelligent Automation Perugla. Italy. Oc:tober 27·29. 1992

MICROPROCESSOR-BASED POSITION-SERVO SYSTEM OF PERMANENT MAGNETIC SYNCHRONOUS MOTOR WITH SLIDING MODE CONTROL. M.X. CHEN·

and HJ. HUANG ••

• Shanghai Jiao Tong University. Oeparunent of Automatic Control. Shanghai 200030. P. R. China •• China Textile University. Department of Automation, Shanghai 200051. P. R China

AINtr_L

A Do"1 poa.ltioD .... ~ .,..tcm of penaaDnl malllctle ,,.Dcbrollo., motor (PNSN) wltb .Udllll mode coatrol

CSMC) baKd

011

mlcroprocnaor le praeated III the paP£I . la tbe

.".IaD, we cmploy Ilkllal mode coDtrol of V,, (Variable

Stnll:tlln Syltem. ) with a .pcc:i&1 uaumDI Imootb method a. eoDtrol lira tee. tbe Ilrate",1I rub_d by a maopr_.or 1091 aad a PWM -MOSFET IlIftrter .. bleb powan a lOO. PMSM. Tbe eaperlCDCDW f •• lla 1110. that tbe lIo.cl_"o .,stem

... three achaDta.e. onr tbe re,lIlar PlO CODtrOiled

IC"O

1"ltem . (I) With SMC aDd acearate m eaallf la&. lower Oftraboot ud

mlCDllblUt" to the .. nallon of IYltem parameters can be .aLlled . (2) CombLllcd with a PWM-M05f"J!T IDftrtcr lluecI OD a mlcroprOOUlOr . OIe PMSM call OJ)Crate .ader tile patterD of nctor-eoatroL 0) With tbe calatalec of SMC .. tilflcd . a IlArabolD 1 .. IICh-IiDt, DClOomplllicd by rcat-Umt SMC ,ain decrcuc, alinlate. the clIattcrlll, Iltar ori.illal poillt.

1. INTRODUCTION

Recently, high performance leno Iy.tema are increasingly demanded in motion drive Iyltema such as robot •. The relearch on lervo .ystema becomes one hot topic.Many papen on the top· ic can be seen in some leading journals, and lome companies have produced practical products. Through surveying, we can draw three conclulions on the trend, of motion drive 'YItems. 0) DC motor ia gradually replaced by AC motor including lynchronoul moton. a) High-level microprocellon and new power electronic devicel are applied. (3) Modern control theory is properly adopted. Howe"er, mOlt papers are mainly concentrated on one or two topiea mentioned aboyc (2.,3,4) • lil this paper, we try to Iyn the.ize an three propertiel. AI we know, .ynchronoul motor is a kind of AC motor which pOtlelle. accurate and ttable rotor frequency under a proper control. The PM SM il the lynchroDoul motor with perma· nent rotor magnet. The PMSM is the promilin& plant iD pOlition-.ervo 'Yltem not only be· CUle of ita relatively limple Itncture and fealible operation, but alto becaule of itl practical Y"ector-control combined with digital control·

led inverter . A 200w PMSM i. uled in the IYltem.

.1

the piaut

With the development of microcomputcra and power electronic devicel, high-level procellora can latiafactorily perform .tate feedback con· trol and accurate calculationl. Power electronic devicel such as IGBT and MOSFET can make the inverter achieve a high qualified power con· veraion. In the IYltem, microprocellor 8098 and power MOSFET are uled. The low-level oYCuhoot and the robultnell to IYltem parameter Ihiftinl are the mOlt impor· tant characteriatiea in pOlition-.erYo Iylteml. &MC of VSS theory can allure IYlteml of thele propertiel. We aclopt SMC al the control IUat· egy of the 'Yltem. III lection 2, we delcribe the control.traten. In .ection 3, we IiYe itl realization. Some e~pcri­ mcntal relulll are Ihowed in lection4.

2. SYSTE.M CONTR.OL STRA TEGY 2.1. Control of PMSM Fed by PWM-MOSFET inycrter baled on the microproccllor, the .ynchronoul motor can

n - 123

:HE.."· r-:.x .. HCA."\G HJ

run under the lelf-controlled pattern. Since PMSM has constant rotor magnet, by meas· uring the rotor position of PM SM. we can get vector-control. The main principle is as follows .

where. M is the Torque, K'..,is a parameter, Il is the vector of StEltor curren 1. (2-1-1) can be rewritten 88

Fig. 2-1-1 and fig . 2-1-2 give the block dia · grams of motor structure and PM SM system .

d is shown in fig . 2-1-3 . We know that : ill .. 1, x COl (cut +«1 ) i lb - 1, x cos (cu t +d+ 120· )

T'-------------- . .; S. M. I

Cv"

~:=:===

~

odt t .~ . . :I.MJ

--- -- ---\Jf

(] ) ft

PMSM

I

•••••. (2-1- 2)

ilC "'" lax cos (O)t+d-120· ) Where, lJ is the angle between stator axis and rotor allis. ill' i,b' ilC are three phase currents. If, 1, is given, we measure i", i. b• and make

I

L ____ - - - - - _______ .J

i..... -I, x sin (cut) iI b - l , x lin(Q)t+60· i,t'" -( ill + i,b)

Fig. 2-1-1 Structure of motor

•••••• (2-1-3)

Where, cut ... , ... The position of rotor , we can keep 1.1.. ~ , or lJ ... 90 Then, (2-1-1) turns to be

MOSF£T

D

M -= K. 'm X IJJ x I, x sind -= K. m X 1,

•

••.•.. (2-1-4)

As K.., and III are both constant, M is lolely determined by I •. Vector-control i. got.

Fig. 2-1-2 Diagram of PMSM Iystem Becaule of the rare-earth material and the Ipecial .tructure in PM SM, the magnet-resistance il greater, the armature relponle is lower. Consequently, the vector of rotor magnet ha. nearly the aame direction aa the alli. of rotorpoai· tion. Fiji. 2-1-3 gives eq uivalent vector diagram. where, ~ .tands for rotor nUll, A atands for .tatol nis. and I C O)t, 0) is the motonpeed.

-

We allume that I, be the output of SMC. Be· caule the time-delaying between the ou tpu t of SMC and the output of digital PWM -M OSFET inverter accounts for a very am all part of the whole system time-delaying, we alao allume that it be omitted. Here, the whole .ystem include. PM SM. in verter. and microprocessor etc.

2.2. SM C Strategy Fig. 2-2-1 and fig. 2-2-2 prelent. the hard· ware and the dynamic block diagram of the aya· tem respectively.

l~

Fig. 2-1-3 Vector diagram of PMSM Obyioualy, we haye:

J

I

-.l

....

....

M - K.'III x.xI •

Fig. 2-2-1 Hardware of the .yltem .--•• (2-1-1)

n - 124

,\{]C'ROPROCESSOR · BASED

posmo~ -SER VO SYSTE."1

OF PER"1A.'"E'\I MAG!\TIlC SLIDr-;G MODE CO:'\lROL

SY~CHROSOt..:S

MOTOR

\I,Trn

-_~------------------r---X.

Fig. 2-2-3 Conventional SMC switch lines

Fig. 2-2-2 Dynamic block diagram To design a SMC, the electromechanical equa· tion of the PMSM system can be described as M = Km X I. (from 2-1-4) M-M L= J X dO) I dt + BO) O)o::dB/dt where,M

••.••• (2-2-1)

= load torque

= inertia coefficient B = frictional coefficient

J

0)

B

-

mechanical rotor speed

= angle of rotar.

However, because of the high moving speed of RP (repreaentation point) near original point, it is quite possible for RP to slide over to other quadrants and to cause chattering. In order to alleviate chattering, real-time changes to other switch lines that have a gentle slope are re· Quired, which is shown in fig. 2-2-4 (6) .Tak· ing account of effective alleviation of the chat· tering in SM C and convenient digital realiza· tion, we put forward a novel strategy as shown in fig. 2-2-5, in which, the switch-line S3 i. represented as (2-2-4).

(2-2-1) is rewritten in terms of the poaition er· ror and its derivative as state variables.

•..••. (2-2-4)

X I -= B·-B

~2=

X,

=-dBI dt = - 0 ) •••••• (2-2-2) X 2 =-dO)I dt = [ML-M +BO)] / J

and

Fig. 2-2-4 R.egular adaptin SM C switch line or

x-

AX +bU + Dn

_ •••• (2-2-3)

In (2-2-3), U stands for I., diaturbance n stands for ML.Actually, the parameters A, b, D are time-varing. The aim of applying SM C is to keep the system insensitive to these varia· tions al well aa to maintain z:ero overahoot. For second-order time-varing Iysteml, there arc more than one way of using SMC. Fig. 2-2-3 il a connntional SM C, in which, all Iwitch curves arc .traight lines. Sliding along L.e linel, the .,stem can reach the aim.

n - 125

Compared with the conventional adaptive SMC .trategy [61, the nonl one ha. the adun· tage of simple mathematic exprellion which can be feasibly procelled by microcomputers. In the novel .trateIY. the gain nlue of SM C in 5) are real-time decrealed in proportion to the ratio of present XJto X JO . XlOis the entering point of 5). The .implified method can achieve the same effect as normal adaptive controla, but its realization is much more practicable. (2-2-4) actually exprelles a con.tant deceleration of RP movement. If RP llides along the cun-e, the cloler R.P i. to original

point, the lower impulse it posseues· to avoid chattering. r ·.'ioully, the transient response time is prolv.ed in the situation. Since the stability and zero overshoot arc the most im· portant characteristics in position-servo sys· tems, prolonging time is compensated. x~

t ••

--~=-----'---------------r---X. o

The times of pulse edge. s!. .. uld be T 1 4-m x T 1 4 x SIN (Q)t.)

Ton -

Toff= 3T 14 +m x T 14x SIN(wt.) where, m is the ratio of modulation. T is the sampling period. Q)t.is anglc of phase A.Since 8098 can process 16-bit words nnd has HSO (high speed ou tpu t ) port. the varing scope of the frequency is from 0 to 1024 Hz. and the re · solving power reaches 0.03 Hz .

3.2. SM C Gain Values All SM C con trol gains in the system are given in the following table.

Fig. 2-2-5 Novel SM C switch line

Curves ! SI I S2 3.

REALIZA TIO N STRATEGY

OF

(l .

P,

y.

~.

0.75 0.25

-0 .75 -0.25

0.2 0.2

-0 .5 -0.5

(lID

PlO

'YIO

~IO

0.125

-0.125

0.05

-0 .1

CONTROL S)

3.1. PWM-MOSFET Inverter

aiO' PlO' Yio ' ~iO

Fig . 3-1-1 shows the principle of natural sam . pling of sinewave PW M strategy which is ap· plied in analogue control. By microprocessor, wc adopt an approll.imate way clI.prcl8cd in fig .

3-}-2 .

are initial SM C values in S). al'

fJ,. y,.~, are determined by the ratio of X Ito X,o . For ex.ample.

where.

X,o= 10%xe* Choosing full state feedback: strategy. wc have the control U ofSMC.

I1

I

I

I

I I

I

I

I I

I

I

I

I

I

I

I

I

I

I

I1

I

I

,

1I

I

,I

I

I

I

1 I

,

I

I

"

where,

I,

~nnn~~

>0 if S, )( X J < 0

if S. )( X.

i - 1.2,3

Fig. 3-1-1Naturallampling of SPWM

'£I _ I

~

T

-

I I

, ........<

:I '1

\ .

/,

T.-:...!

'I ~ ,

0:

I :

s,~ ,.ut.

I_I

i--reu- . Fig. 3-1-2 Approximate SPWM

.amplinl of

n - 126

~'Y ••

if S. )( X 2> 0

l To

if SI )( X 2

'-.,

<0

..

MlCROPROCESSOR -BASED POSTIlOS-SER vo sysTEM OF PER\1A"Bj MAG~TIlC Syr-;CHROSOCS Mm-OR v,:rrn SLIDIl'IG MODE (x)S1ROL

4. EXPERIMENTAL RESULTS

Fig. 4-1 PWM wave form at HSO port

Fig . 4-2 The switching of SMC output in S.

Fig . 4-4 Po.ition error X,( 8· -= 3600

Fig . 4-3Gain value ofSMC in S3

REFERENCES

0

)

Trans.lnd.Elec. , Vol.lE-n,No.3, 1985, pp . 238-244.

[1] Utlcin, V.1. Variable structure controlsy.· tem with sliding model.IEEE Tran •. Automatic Control, Vol. AC-22, No. 2, 1977, pp. 210-222.

[ 4) Namuduri, C. and Sen, P.C . Variable Itructure control of a lelf-control-Iynchronous motor drive. ibid., pp. 503-509.

[2] Lin, S.C. and Tui, S.l . A microprocellor baled incremental servo-IYltem with variable structure. IEEE Trans. Ind. Elec., Vo1.IE-31, NoA, 1984, pp. 313-316.

[ 5) HUANG, H.J. and Chen, M.X. Strategy and realization of PM SM lervo IYltem with lliding mode control. 1st Chinelc Youth Cone. on Power Electronic, 1990, Beijing, PP. 56-62.

3

Harashima, F. et a1. MOSFET converter-fed position lervo-Iystem with mode control. IEEE sliding

ll-127

[6] Utlcin, V.1. Variable Structure System •.