3 Phse-controlled DC motor drives 3.1 Introduction Two types of speed control: rmture control nd field control
3.2 Principles of DC motors speed Control The induced voltge is dependent on the field flux nd speed e Kφ f ω m The flux is proportionl to the field current φ f i f The speed is expressed s ω m e φ f e i f (v i i f R ) The rotor speed is dependent on the pplied voltge nd field current.
In field control, the pplied rmture voltge v is mintined constnt. Then the speed is represented s 1 ωm i f In rmture control, the field current is mintined constnt. Then the speed is derived s ω m ( v ir )
Hence, vrying the pplied voltge chnges speed. Reversing the pplied voltge chnges the direction of rottion of the motor. The dvntge: the field time constnt is t lest 10 to 100 times greter thn the rmture time constnt. Armture control is ide for speeds lower thn rted speed; field control is suitble bove for speeds greter thn the rted speed.
Fig. 3.1
By combining rmture nd field control, wide rnge of speed control is possible. The reltionship between rmture current nd torque T e Kφ f i The rted torque T er Kφ fr i r The normlized version T en T T e er Kφ Kφ f fr i i r φ ( φ f fr i )( i r ) φ fn i n, p.u.(per unit)
Similrly, the ir gp power is P n e n i n, p.u. where e n is the normlized induced emf. As i n is set to 1 p.u., the normlized ir gp power becomes P n e n, p.u. The stedy-stte power output is kept from exceeding its rted design vlue, which is 1 p.u.
The ir gp power constrins the induced emf nd flux field s P n 1 p.u. e n i n φ fn ω mn i n If i n is equl to 1 p.u., then φ fn ω mn 1 φ fn 1/ω mn Hence, the normlized induced emf is e n 1 In the field weken region, the power output nd induced emf re mintined t their rted vlues by progrmming the field flux to be inversely proportionl to the rotor speed.
3.2.5 Four-qudrnt opertion During stedy speed of ω m, stoping mchine need to slow down t zero speed first. Four-qudrnt dc motor drive chrcteristic function Qudrnt Speed Torque Power FM I + + + FR IV + - - RM III - - + RR II - + -
Fig. 3.4 shows four-qudrnt torque-speed chrcteristics
Fig. 3.5 illustrtes the speed nd torque vrition.
Converter requirements: The voltge nd current requires four qudrnt opertion. The reltionship between rmture voltge nd rmture current Opertion Speed Torque Voltge Current Power Output FM + + + + + FR + - + - - RM - - - - + RR - + - + -
Two bsic methods by using sttic converter The First method: using phse-controller converter to converter the c source voltge directly into vrible dc voltge. The second method: Ac source voltge fixed dc voltge vrible dc voltge. Thyristor devices: SCR, Trnsistors, GTOs, MOSFETs, ect.
3.3 Phse-controlled converter Fig 3.6 is single-phse controlled-bridge converter (positive verge vlue).
The bridge conduction is delyed in ltter beyond positive zero crossing. The dely ngle is mesured from the zero crossing of voltge wveform nd is generlly termed α. Thus, this voltge is quntified s V dc 1 π α+π α V m sin( ω s t)d( ω s t) 2V π m cosα
Fig. 3.7 is the controlled-converter opertion with negtive verge voltge (α > 90º).
In the cse tht the lod current is discontinuous, the verge output is V dc 1 π α+γ α V m sin( ω s t)d( ω s [cos( α) cos( α + where γ is the current conduction ngle. For certin vlue of γ, the output voltge for discontinuous conduction cn be greter thn tht for continuous conduction. For exmple, let α+γπ, nd α 30 V V dc dc (dis) (con) t) V π Vm Vm [cosα cos( α + γ)] 1.866 π π 2Vm 2Vm 1.732 1.732V cosα π π 2 π m m γ)]
The source inductnce cn be introduced to reduce the rte of rise of current in the thyristors. If the source inductnce is L ls, the voltge lost due to it is 1 α+µ V V V sin( t)d( t) m x m ωs ωs [cosα cos( α + µ )] π α π where, the overlp conduction period is µ cos 1 [cosα πωsl V ls m I dc ] α
Fig. 3.10 is three-phse thyristor-controlled converter.
The thyristor requires smll rectors in series to limit the rte of current rise, nd snubbers, which re resistors in series with cpcitors cross the devices, to limit the rte of voltge rise. The trnsfer chrcteristic of the three-phse controlled rectifier is derived s V dc 1 π / 3 2π / 3+α π / 3+ α Vm sin( ωst)d( ωs cosα The chrcteristic is nonliner (s shown in Fig. 3.13). t) 3 V π m
A control technique to overcome this nonliner chrcteristic is tht the control input to determine the dely ngle is modified to be α cos v ( V 1 c 1 cm ) cos (v cn ) where v c is the control input nd V cm is the mximum of the bsolute vlue. Then the dc output voltge is 3 3 1 3 3 Vm V dc Vm cosα Vm cos(cos vcn ) [ Vm ]vcn vc π π π V π cn K r v c
Fig. 3.14 is schemtic of generic implementtion. The mximum dely ngle is usully set in the rnge from 150 to 155 degree.
Control modeling The gin of the linerized controller-bsed converter is K r 1.35V V cm, The converter is smpled-dt system. The smpling intervl gives n indiction of its time dely. The dely my be treted s one hlf of this intervl 60 / 2 1 T r (time period of one cycle) 360 12 1 f s
The converter is then modeled with G r (s) K r e T s r The bove eqution cn lso be pproximted by s G r (s) K r (1 + st r ) For the cse tht the trnsfer chrcteristic is nonliner, the gin of the converter is obtined s smll-signl gin by K r δv δ dc {1.35V cosα} 1.35sin α δα δα
Fig. 3.15 is current source converter.
Fig. 3.16 current source opertion.
Fig. 3.17 is hlf-controlled converter.
Fig. 3.18 is the converter with freewheeling diode.
Fig. 3.20 shows the converter configurtion for four-qudrnt dc motor drive.
3.4 Stedy-stte nlysis... Averge vlues: The stedy-stte performnce is developed by ssuming tht the verge vlues only re considered. The rmture voltge eqution v R i + e Termed by verge vlues V R I + KΦ f ω mv Averge electromgnetic torque is T v KΦ f I KΦ f V { KΦ R f ω mv } KΦ f 1.35V cos { α KΦ R f ω mv }
The normlized electromgnetic torque T en T en T T v er T KΦ [1.35V v fr I r f {1.35V cosα KΦ KΦ I R Positive nd motoring torque is produced when cosα > en KΦ cosα Φ R n Φfnω 1.35V mn n fn ω mn fr ] Φ fn r, p.u. f ω mv } [1.35V cosα KΦ I R r f ω mv ] Φ fn
Stedy-stte solution including hrmonics ccurtely predict its electromgnetic torque The speed of the mchine nd the field current re ssumed to be constnt. Then di R i + L + Kbωm dt v where v V m sin(ω s t+π/3+α), 0<ω s t<π/3 The induced emf is constnt under the ssumption of constnt speed, hence its solution is i V (t) ( Z m ){sin( ω s t + π / 3 + α β) sin( π / 3 + α β)e t / T } ( E R )(1 e t / T ) + i i e t / T
where ω s 2πf s, β tn -1 (ω s L /R ) mchine impednce ngle, T L /R rmture time constnt, i i initil vlue of current t time t 0, Z R +jω s L motor electricl impednce. Criticl triggering ngle α c : when the rmture current is brely continuous (ii 0). α c β + cos 1 (E / V { c 1 m ) 1 (1 e cosβ ( π / 3tnβ) )} When the current becomes discontinuous, the voltge cross the mchine the is the induced emf itself. π 3 + θ 1
The stedy stte is x s s t t 0, V E dt di L i R ω < < ω + + 3 / t t 0, i s x s π < < ω ω x s s s m t t 0 ), 3 / t sin( V V ω < < ω + α + π ω 3 / t t, E s x s π < < ω ω
Fig 3.24
3.5 Two-Qudrnt three-phse convertercontrolled DC motor drive Fig. 3.26 is speed-controlled two-qudrnt dc motor drive
3.6 Trnsfer functions of the subsystems Fig. 3.27 is DC motor nd current-control loop.
Fig. 3.28 is step-by-step derivtion of dc mchine trnsfer function.
Converter (fter lineriztion) G r V V c (s) (s) K r 1+ st r The current nd speed controllers of proportionl-integrl type re G G c s K (s) K (s) c s (1 + stc ) stc (1 + sts ) st s The gin of current feedbck is H c. The trnsfer function of the speed feedbck filter is Kω G ω (s) 1+ st ω
3.7 Design of controllers Fig 3.29 is the block digrm of the motor drive
Fig 3.30 is current-control loop.
Speed controller: Fig. 3.32 is the representtion of the outer speed loop in the dc motor drive.
The closed-loop trnsfer function of the speed to its commnd is ω ω * r m (s) (s) 1 H ω 1+ 4T s [ 4 2 2 1+ 4T s + 8T s 4 4 + 8T 3 4 s 3 ]
3.8 Two-qudrnt DC motor drive with field wekening Fig. 3.38 is its schemtic.
3.9 Four-qudrnt Dc motor drive Fig. 3.39 is its schemtic.