Experimental results for drive applications using instantaneous torque control and conventional sinusoidal current control are evaluated and compared.. Such control schemes produce torqu
Trang 1Strategy for the instantaneous torque control of
K.J Tseng, BEng
T.H Lee, MSc, PhD, BA
K.W Lim, BEng, DPhil
K.S Lock, BSc, PhD, CEng, MlEE
Indexing terms: Torque, Control systems, Brushless DC drives
Abstract: The paper describes an instantaneous
torque control for a permanent magnet motor
driven in a brushless direct current drive configu-
ration The motor has high torque capabilities,
which makes it suitable for direct drive applica-
tions, but unfortunately it suffers from torque pul-
sations when controlled by a conventional
sinusoidal current controller Instantaneous
torque control is aimed at eliminating such torque
pulsation, thereby improving speed and position
control The approach adopted is to design an
instantaneous torque control algorithm based on
a variable structure strategy in the dq rotating ref-
erence frame The switching commands for the
inverter are generated by the digital controller
directly The required instantaneous torque feed-
back information is estimated from knowledge of
the motor parameters and measurements of
instantaneous currents and rotor position The
performance of the proposed controller design and
torque feedback technique are investigated in
computer simulation studies and experimental
implementations Experimental results for drive
applications using instantaneous torque control
and conventional sinusoidal current control are
evaluated and compared
List of symbols
a, b, c
U = control variable
8 = electrical angle
0, = mechanical angle
0 = angular velocity
a = angular acceleration
T, = developed electromagnetic torque
7; = load torque
Ter = torque reference
= inverter vector elements
S = switching function of variable structure system
Paper 7493B ( P l ) , first received 27th November 1989 and in revised
form 1 lth June 1989
Dr Low, Mr Tseng, Dr Lee and Dr Lock are with the Department of
Electrical Engineering, National University of Singapore, 10 Kent
Ridge Crescent, Singapore 051 1, Republic of Singapore
Dr Lim is with the Department of Electncal Power Engineering,
University of New South Wales, Kensington, New South Wales 2033,
Australia
i, , i, , i, = phase currents
J = moment of inertia
D = viscosity coefficient
A- = flux linkage
R = winding resistance
1 = inductance
L ,
M,
E ,
Lij,
= self inductance xth harmonic coefficient
= mutual inductance xth harmonic coefficient
= rotor to stator inductance xth harmonic coeffi-
= dq-transformed inductance xth harmonic coef- cient
ficient
1 I n t r o d u c t i o n
High torque PM motors operated in brushless DC (BLDC) drive configuration are suitable for the direct
drive of industrial servo systems and robots [ l 21 A
cascade control structure is usually adopted for BLDC
drive applications (Fig l), consisting of an outer loop
inverter
controller controller
posltion feedback
Fig 1 Cascade BLDC drive rontrol sfrurfure
that generates the reference torque command to achieve the desired speed or position and an inner loop that con- trols the switching of the inverter so as to cause the
motor to produce the desired torque [3, 41 The inner loop, commonly known as the torque controller or
current controller, also ensures synchronism between the stator feed currents and the rotor flux This function is known as electronic commutation and has been com- pared to that of the commutator and brushes of conven- tional brush-type DC motor
Several inner loop configurations have been in use, or
have been proposed, in an effort to achieve the twin objectives of good torque control and the implementa- tion of electronic commutation Most of these methods rely on analogue current controllers to produce sinus- oidal phase currents, as shown in Fig 2 The controller consists of three independent current control loops, which may be based on the current hysteresis controlled
PWM method, or the subharmonic PWM method [ 5 ]
Trang 2Such control schemes produce torque pulsation when the
motor flux distribution differs significantly from the ideal
sinusoid and it is well-known that nonsinusoidal flux dis-
processing of signals such as position, velocity and current, which contain information on disturbances and parameter variations, the switching patterns can be opti-
rotor
_ _ _ _ _
C
e
feedback
Fig 2 Conventional current controller
torque estimator
torque producer
and load
torque
referencc
I
1
I
I
L -_
currents position
I information information
r - - - 7
Fig 3
control
Block diagram illustrating the concept of instantaneous torque
tribution is a characteristic of high torque PM motors
16, 71
In a direct drive system, the load is directly coupled to
the shaft of the brushless motor This eliminates the
backlash and high friction inherent in a conventional
geared drive [8, 91 However, the absence of a high gear
ratio requires the motor to operate at low speeds, where
torque pulsation becomes highly undesirable At high
speeds, these ripples are usually filtered out by the system
inertia For low speed operations, there is obviously a
need for instantaneous torque control to minimise the
torque pulsation so as to achieve excellent transient and
steady-state responses Instantaneous torque control
would also permit the fastest possible response for speed
or position control [lo] It is to be noted here that the
desired torque trajectory must be determined by the
outer loop controller
In recent years, research efforts have been directed at
the direct digital control of inverters, in which the switch-
ing signals for the inverter are generated directly by
microprocessors This type of control has been made
feasible only in recent years owing to the advent of high
performance digital signal processors (DSP) A great
advantage of direct digital control is that it has made
possible new control algorithms that are not easy to
implement using conventional analogue current control-
lers It is also easy to modify or upgrade the control
program Another important advantage is that since the
on-off patterns for switching devices are generated by the
mised On the other hand, such optimising algorithms cannot be easily implemented on analogue current con- trollers [ll-151
The direct digital control of an inverter provides the possibility of designing an instantaneous torque control-
ler The concept is illustrated in Fig 3 The combination
of the inverter and PM motor is regarded as a torque- producing unit controlled by a three-bit digital command from the torque controller The instantaneous torque feedback signal can be estimated from knowledge of the instantaneous currents and the rotor position Thus, by designating an appropriate control algorithm, it is pos- sible to eliminate torque pulsation by direct digital control of the inverters
This paper describes the instantaneous torque control
of a BLDC drive, with the objectives of minimisation of
torque ripples and improvement of the transient and steady-state responses of speed and position control The focus is on the digital approach to torque control, whereby the switching signals for the inverter are gener- ated directly by a microprocessor The problem of obtaining a reliable and accurate instantaneous torque feedback is examined The performances of the proposed controller design and torque feedback technique are investigated in computer simulation studies and experi- mental implementations
2 P M motor modelling
The motor is modelled as two interconnected subsystems One is the electromagnetic subsystem, which converts the effects of electrical currents into developed torque (airgap torque), and the other is the mechanical subsystem, which governs mechanical responses to the torque
The mechanical dynamics can be summarised in a motor dynamic equation:
The electromagnetic behaviour of a three-phase synchro- nous machine is modelled as consisting of a field winding
f and three stator windings a, b and c This model is the
abc-model For a PM motor, the rotor may be modelled
as a fictitious winding with a constant current source i, The voltage equation for each of the stator windings can
be written as
d l
v = R i + -
dt
Trang 3The flux-current relationships can be given as
where I,, is the self inductance of coil x and I,, is the
mutual inductance between coils x and y
The effects of saliency are included by expressing the
stator self and mutual inductances as Fourier functions of
the electrical rotor position 0, which is defined as the
angle between the rotor direct axis and stator phase a
axis [7, 161
The torque developed by the motor can be derived by
using the energy method, which is based on the principle
of the conservation of energy [17] It can be shown that
the developed torque is therefore given by
where P is the number of poles
This abc-model has been studied using the SIMNON
simulation package [18] The parameters for the motor
model are determined experimentally The motor used
has the back EMF waveform shown in Fig 4 The wave-
r
Fig 4 Back EMF waveform
form differs significantly from the ideal sinusoid The
variations in the self and mutual inductances of the
motor phase windings with respect to rotor position are
shown in Figs 5 and 6 , respectively They too differ from
the perfect sinusoid
Fig 5 Variation ofwinding selfinductance with position
While the abc-model is useful for simulation studies, it
does not lend itself to easy manipulation when designing
a controller for the inner loop The dq-axis model has
proved useful in this respect [l5] The model is obtained
by using the dq-transformation, which can be represented mathematically in terms of the electrical angle 0 [17]
Fig 6 Variation of winding mutual inductance with p o s i t m
By applying the transformation rule to the flux- current relationships of eqn 3, the following expressions for the direct and quadrature axis fluxes are obtained
I d = Id, id + Id, i, + ld, i, ( 5 )
I , = I,, i, + id + I,, i, ( 6 )
where the transformed inductances can be written as
id, = L d d o + L d d 6 COS 60 + L d d l 2 cos 120 f ' '
'dq =
Id, = L d f o + L d f 6 COS 60 + L d / l z cos 120 + ' ' '
I,, = L,,o + Lqq6 COS 60 4- L,,,, COS 128 +
(7)
Ldq6 sin 60 + LdqlZ sin 120 + (8)
(9) (10)
L,,, sin 60 + L,,,, sin 120 +
L,,, sin 60 + Lqf12 sin 120 +
(11) (12) The transformed inductances contain harmonics that are multiples of six By transforming the voltage equations from the abc-domain, the direct and quadrature axis volt- ages are obtained:
lqd =
d l d
dt
ud = Rid + - - wi,
d l
dt
where w = dQ/dt is the rotor electrical angular velocity The torque equation is obtained as
3 Torque control
The torque control design is based on the variable struc- ture strategy (VSS), in which the switching signals for the inverter are determined directly by the digital controller There is no need for the analogue PWM hardware associated with conventional current controllers In vari- able structure strategy systems, the control is allowed to change its structure [19]
A hierarchical method is adopted for the design of the VSS systems The design sequence for the ith hyper-
surface begins with the selection of a switching surface
s(x, t ) = 0 This will determine the desired characteristic
of the system in the sliding mode The parameters of the discontinuous control are then determined from the con- ditions that cause sliding mode to exist This ensures that
Trang 4the control action will steer the state to the sliding
surface After reaching the sliding surface, the state will
be forced to remain (slide) on this plane Then the system
is said to be in the sliding mode, which is a special phe-
nomenon of VSS
The sufficient condition for the sliding mode to exist
on the ith hypersurface is given by the following inequal-
ity:
S,-O
This is known as the existence condition for a sliding
mode This sliding mode can also be shown to be stable
The developed torque of a PM motor modelled using
the dq transformation is seen to be a function of the
values of direct axis current id and quadrature axis
current i, Therefore, the states are selected as id and i,
To select the switching surfaces, the following objec-
tives are considered:
(i) The instantaneous torque response sould he as fast
as possible for optimum transient response of the mecha-
nical outputs
(ii) The desired torque is to be achieved with the
minimum input current This is to minimise ohmic losses,
thereby ensuring maximum efficiency
c41
(iii) Electronic commutation must be maintained
(iv) There should be no steady-state error
(v) The torque loop must be robust and stable
Since the direct axis is always aligned with the rotor
flux axis, the contribution to torque from id (reluctance
effect) is much smaller than that from i, Therefore, by
keeping id close to zero at all times, the total torque is
where K is the torque parameter, which can be assumed
to be constant during the small switching interval at
Objective (ii) is thus achieved This is equivalent to
keeping the torque angle at 90" By regulating the level of
i, to track the torque demand, objective (i) is also
achieved As id and i, are imaginary quantities that rotate
with the rotor, electronic commutation is maintained,
thereby satisfying objective (iii) Objectives (iv) and (v) are
guaranteed if the control inputs satisfy the existence con-
dition of the sliding mode at all times
The switching surfaces are therefore selected as
where id,,, = 0 and T,,, is the torque reference, as deter-
mined by the outer loop controller
The VSS control functions are selected as
1 s ; > o
- 1 s ; < o
sgn (si) =
These selections are based on the concept of vector
control The controller determines the control inputs U,
and U,, which are in the rotating dq-domain, by consider-
ing the positions of the state trajectories in the switching
plane These control inputs are then mapped into the abc
voltage vectors of the inverter
It is necessary to determine V, and V, so that the exis- tence condition of sliding mode (eqn 16) is satisfied Determination of V,:
From eqn 13,
d
U, = Rid + - ( I , ) - 01,
dt
= Rid + - d (I,, i, + I,, i, + I d , if)
dt
- a i, + I,, id + I,, i,)
S, = id
If we multiply eqn 24 by s, and substitute in eqn 20, the
following equation is obtained:
d
' d d ' [ dt
s, S, = A Rid + - (I,, i, + I,, i,)
ld + 1,, i, + I,, id + I,, i,
A sufficient condition for V, to satisfy eqn 16 is therefore
d
By repeating the above exercise for V,, we find that a sufficient condition for V, to satisfy the existence condi- tion for sliding mode is
There are four possible combinations of U, and U, Their
effects can be classified as in Table 1 The forms of the
control functions have been selected so that the mapping
to the actual inverter vectors is simple yet effective The PM motor is driven by a three-phase voltage-fed inverter bridge The inverter consists of three pairs of power MOSFETS Each pair operates in a toggle
Table 1 : Control inputs and actions
Control inputs Control actions
vd = + V d , vq = + V , Increase i d , increase i o
vd = +V, vq = - V , Increase i d , decrease i,
v d = - V d , v q = + V , Decrease i d , increase i q
vd = - V d , vq = - V , Decrease i d , decrease i ,
Trang 5manner and is controlled by a single bit digital signal
The three-bit control signal is known as a vector There
are eight different vectors possible Table 2 lists the
vectors and line voltages in terms of the DC link voltage
Table 2 : Vectors and line voltages
Vector Line voltages
' a b ' b c
0 0 1 0 -vdc +v,,
0 1 0 -v,= +v,, 0
0 1 1 -v,, 0 +v,,
1 0 0 +v,, 0 -vdc
1 0 1 +v,, -vdc 0
1 1 0 0 +VdC -vdc
K c Vectors 0 and 7 are null vectors as they caused a
short circuit to either the positive or the negative termin-
als of the DC link The remaining six combinations are
active vectors These vectors can be illustrated in a vector
diagram, as in Fig 7
Pictorial representation of inverfer networks
Fig 7
To map the control in the dq-plane to the actual
inverter vector, the electrical rotor cycle is divided into 12
regions Depending on which of the 12 regions the rotor
angle is in, the closest inverter vector to each of the four
control inputs is selected It is shown that as long as the
DC link voltage is large enough that eqns 26 and 27 are
satisfied, the existence condition for sliding mode is not
degraded by this simple mapping The results of the
mapping are tabulated in Table 3
The sampling frequency should be high, at least
10 kHz, so that the chattering of the currents is small
Also, the computation delay should be kept to a
minimum Therefore, the control algorithm requires a
Table 3: Mapping t o inverter vectors
Rotor angle Inverter vectors
345"-15"
1 5 " 4 5 "
450-75"
75"-105"
105"-135"
135"-165
165"-195"
195"-225"
225"-255"
255"-285"
285"-315"
31 5"-345"
V d = +v,
v u = +vu
1 1 0
1 1 0
0 1 0
0 1 0
0 1 1
0 1 1
0 0 1
0 0 1
1 0 1
1 0 1
1 0 0
1 0 0
v,= -v,
vo = +v,
0 1 0
0 1 1
0 1 1
0 0 1
0 0 1
1 0 1
1 0 1
1 0 0
1 0 0
1 1 0
1 1 0
0 1 0
Vd = -v, Vd = +v,
vo = -v, vq = -vo
0 0 1 1 0 1
0 0 1 1 0 0
1 0 1 1 0 0
1 0 1 1 1 0
1 0 0 1 1 0
1 0 0 0 1 0
1 1 0 0 1 0
1 1 0 0 1 1
0 1 0 0 1 1
0 1 0 0 0 1
0 1 1 0 0 1
0 1 1 1 0 1
digital signal processor for its realisation Fig 8 shows the block diagram of the torque controller
m
I
Id I I I U U l e
loop controller
tronsformat ion
from outer controller loop
tronsformat ion
torque est i motor
to outer loop controller
Fig 8 Block diagram of torque controller
3.2 Simulation results
The direct digital torque controller, the inverter and the
PM motor have been simulated using SIMNON The controller sampling period is 100 p s The simulated torque from the motor model is used as the feedback torque signal, i.e the feedback is ideal Therefore, the simulated performance of the controller depends solely
on the control algorithm and is not degraded by any nonideal feedback
Simulation results are shown in Figs 9a-9 The steady state instantaneous torque is constant and contains no torque fluctuation This shows that the control algorithm
is effective as an instantaneous torque control scheme as long as an accurate torque feedback signal can be obtained The transient response is almost immediate As the developed torque is constant, the shaft velocity is also constant
The phase current is not sinusoidal Harmonics are present in the waveform to neutralise the harmonics in the flux distribution Thus, the controller is able to elimi- nate the torque ripples The direct axis current id has been kept close to zero, which is one of the objectives of the controller The entire torque is thus contributed by the quadrature axis current i, The quadrature axis current waveform shows ripples caused by the control action in keeping the instantaneous torque constant Figs 9f and g show the nature of the switching control inputs ud and U,,:
The results indicate that the digital torque control algorithm can have a very good performance if an accu- rate instantaneous torque signal can be obtained to provide the feedback
4 Torque feedback
A prerequisite for the proper functioning of the proposed torque control is the torque feedback information If instantaneous torque control is desired, then the torque feedback must accurately reflect the developed instanta- neous torque It can be directly measured by torque transducers, such as strain gauges [20], however these
Trang 6are impractical for servo control applications as slip rings are required to transmit the measured signal They are also susceptible to noise Thus, alternative means of obtaining the torque information must be sought The method proposed here is to estimate the torque from knowledge of the motor parameters and measurements of instantaneous currents and rotor position
4.1 Torque estimation
In the torque control scheme, the direct axis current i, is controlled at zero at all times Therefore, by assuming
i, = 0, the torque equation, eqn 15, becomes
dl
01
b
C
0
-1
I :
'
;
,
- 1 0
e
10r
10
-10
-101
9
Fig 9
(I Torque.Nrn
h Speed radls
< Phase current, A
d Direcl-axis current A
Quadrature-are current A
f Direct-axis voltage, V
g Quadralure-axis vollage, V
Simulation results oJrorque control with ideal torque feedback
The estimated torque can be either the average or instan- staneous torque, depending on the degree of simplifica- tion of eqn 28
To estimate the average torque, only the fundamental components of the variation in machine inductances with rotor position are included The transformed inductances become
4'7 = L,,o
r,, = o
I,, = 0
I,, = L * f O
The torque equation simplifies to the following familiar form :
which is termed the estimated average torque
For a motor with sinusoidal rotor flux distribution, this estimated torque is also the instantaneous torque However, if the machine has a nonsinusoidal flux dis- tribution, the equation only gives the average torque For
a constant torque command, the control action would be
to maintain a constant i, This is equivalent to injecting purely sinusoidal phase currents Hence, using the esti- mated average torque for torque control is, in principle, equivalent to the conventional sinusoidal current control
To estimate the instantaneous torque, it is necessary
to take into account all the significant harmonic com- ponents of the variations in inductances with rotor angle Generally, for a high-torque PM motor, the contribu- tions to torque by the stator winding self and mutual inductances are much smaller than that of the rotor PM
flux [7] If this is coupled with the fact that the harmonic components decrease progressively with frequency, it is sufficient to consider only the fundamental components
of the stator winding self and mutual inductances There- fore,
I 44 = L W O
I,, = 0
For the rotor flux, all the significant higher harmonic terms must be considered:
I,, = L,,, sin 68 + L,,l sin 128 +
Therefore, the torque equation can be approximated by
3 P
T = - - [L,,, i, + (6L,,, + Ldf6)i, cos 68
+ (12LqfI2 + L,,,,)i, cos 128 +
3 P
2 2
i,
- - -
- [ K O + K , cos 68 + K , , cos 120 + ' .]i, ( 3 0 )
which i is a multiple of six The estimated instantaneous
torque is found from eqn 30 To take into account any saturation effect, some form of torque harmonic param- eter estimation scheme must be devised, which is beyond the scope of this paper
Trang 74.2 Simulation results
The torque controller has been simulated with estimated
average torque feedback to produce sinusoidal currents
The results are given in Figs loa-c The phase current is
microcomputer
- ' b L 0 2 O L 0 0 6 0 8 IO
DC input
0 5 1
01
b
1
C
Fig 10
torque feedback
a Torque, Nrn
h Speed, rad/s
sinusoidal The developed torque contains torque ripples
because of the interaction of the sinusoidal phase current
with the nonsinusoidal rotor flux Fig 10b shows that the
torque pulsation causes speed ripples in the shaft veloc-
ity The torque waveform also shows that the dominant
torque ripple harmonic is six times that of the phase
current frequency
Figs 1 la-c show the results obtained using estimated
instantaneous torque feedback The torque pulsation has
been eliminated Therefore, the shaft velocity shows little
fluctuation The phase current is no longer sinusoidal
The simulation results show that using torque control
with estimated average torque feedback is equivalent to
sinusoidal current control It causes torque pulsation if
the rotor flux distribution is nonsinusoidal The results
Simulation results of torque control with average estlmated
c Phase currenl, A
0
0 2
C
Fig 11
feedback
o Torque Nm c Phase currenl, A
h Speed rad/s
Simulation results of torque control with instantaneous torque
also show that the combination of VSS torque control and estimated instantaneous torque feedback form a viable instantaneous torque controller
5 Implementation of controllers
5.1 DSP-based experimental setup
A DSP-based experimental control system setup has been
constructed to investigate the performance of the pro- posed instantaneous torque controller The block diagram of the experimental setup is shown in Fig 12
( t o osci I loscope)
II 1 /-
digital signal processor
I ;h2 ( t o oscilloscope)
ch 1
Fig 12 DSP-based experimental setup
CT = Hall-etTecl current transducer
The mechanical arrangement consists of an experimental
PM motor coupled to an absolute rotary optical encoder
at one end of the rotor shaft with the other end coupled
to a load via a shaft-torque detector
A voltage-fed three-phase inverter bridge is used to
drive the motor It consists of three pairs of power MOSFETs and their gate-drive circuitry These MOSFETs are capable of switching speeds of above
100 kHz The DC link voltage is adjustable The switch- ing signals to the bridge are sent directly by the digital controller Phase current feedback signals are produced
by Hall-effect current transducers As the stator windings
are star-connected, only two of the currents have to be measured
The heart of the digital control system is a DSP32 digital signal processor [21] This is supported by a microcomputer that serves as a host development system during development of the control application programs and provides input/output (I/O) facilities during real time testing of the programs The DSP32 controller has been physically constructed on a prototyping card mounted in the microcomputer
5.2 Torque control
The flowchart of the torque control program is given in
Fig 13 Both instantaneous torque control and the con-
ventional sinsuoidal current control methods have been
Trang 8implemented Instantaneous torque control is obtained
by coupling the controller with estimated instantaneous
torque feedback By using the estimated average torque
feedback, sinusoidal current is obtained A torque refer-
ence of 1 Nm is set and the load was adjusted so that the
motor speed is about 10 rev/min
I mapping look up table I
output vector
ri
I wait for next sample - 1
Fig 13 Flowchart of torque control program
Fig 15 shows the torque and phase current produced
by the sinusoidal current control There is torque pulsa-
tion with a frequency six times that of the current fre-
quency Fig 14 shows the torque and phase current
obtained using the instantaneous torque control The
torque ripples have been greatly reduced The phase
current waveform is no longer sinusoidal The experiment
Fig 14
control (T,,, = 1 N m )
Torque: 0.5 Nm/div
Phase current: 1.0 A/div
Torque and phase current produced with instantaneous torque
Time: I 0 0 ms/div
are shown in Figs 16 and 17 The results again show a
great reduction in torque ripples Thus, the instantaneous torque control implemented is effective in eliminating torque pulsations
Fig 15
control (T,,, = 1 Nm) Torque: 0.5 Nm/div Phase current: 1.0 A/div
Torque and phase current produced with sinusoidal current
Time: 100 msldiv
Fig 16
control IT,,, = 2 N m )
Torque: 0.5 Nm/div Phase current: 1.0 A/div
Torque and phase current produced with instantaneous torque
Time, 100 ms/div
Fig 17
control IT,,, = 2 N m )
Torque: 0.5 Nm/div Phase current' 1.0 A/drv
Torque and phase current produced with sinusoidal current
Time: 100 ms/dw
Trang 95.3 Speed control
A PI speed control algorithm is implemented on the DSP
controller together with the inner loop controller Both
the sinusoidal current control and the instantaneous
torque control are tested with the speed controller
The time response of the system for a step speed
command for the two different combinations of speed
and inner loop control schemes are shown in Figs 18a
and b The results show that speed ripples are negligible
for speed control with instantaneous torque control
Large variations in speed occur for speed control using
sinusoidal current control at very low speed From the
oscillograms, it is clear that the instantaneous torque
control has improved the dynamic response to speed
control
b Fig 18
U With mslanianeous torque control
h Wilh sinusoidal current conlrol
I rev/min/div, 5Ml ms/div
Experimental results for speed control
6 Conclusions
To overcome the problem of torque pulsation in the
operation of brushless DC drives, an instantaneous
torque control scheme has been designed and simulated
The torque control algorithm is based on a variable
structure strategy and the switching patterns for the
inverter are generated directly by the digital controller
The torque feedback information is derived from know-
ledge of machine parameters, instantaneous currents and
the rotor angle Simulation results have shown the
scheme to be viable
An experimental controller centred on a high per-
formance digital signal processor has been constructed to
implement the control scheme Experimental results show that the instantaneous torque controller has successfully minimised torque pulsation and significantly improved the performance of the speed controller when the latter is coupled with the instantaneous torque controller
7 References
I LOW, T.S., BINNS, KJ., RAHMAN, M.F., and WEE L.B.: ‘A Nd-Fe-B excited permanent-magnet motor - design and per- formance Third International Conference on Electrical Machines and Drives, IEE, London, UK, Nov 16th-18th 1987, pp 246249
2 LOW, T.S ‘Permanent-magnet motors for direct drive applica-
tions’, Autom News, Nov 1987, pp 1 4 1 7
3 RAHMAN, M.F LOW, T.S., and WEE, L.B.: ‘Development of a digitally controlled brushless dc drive system’ Proceedings of the
1986 Conference on Applied Motor Control (CAMC ’86) Minnea-
polis, Minnesota, USA, June 10th-12th 1986, pp 283-288
4 WEE, L.B., LIM, K.W., LOW, T.S., and RAHMAN, M.F : ‘A vari- able structure strategy for motion control’ Proceedings of the 1987 Conference on Industrial Electronics (IECON ’87), Cambridge Massachusetts, USA, November 3rd-6th 1987, pp 167-174
5 HOSHINO, A., KUROMARU, H., and KOBAYASHI, S.: ’AC
ssynchronous servo based on the armature voltage prediction model’ Proceedings of the 1987 Conference on Industrial Elec- tronics (IECON ’87), Cambridge, Massachusetts, USA, Nov 3rd-6th 1987, pp 205-21 1
6 HOANG, L., PERRET, R., and FEUILLET, R ‘Minimization of
torque ripples in brushless dc motor drives’, IEEE Trans., 1986,
IA-22, (4) pp 748-755
7 NG, B.H., LOW,T.S., LIM, K.W., and RAHMAN, M.F:’An mves- tigation into the effects of machine parameters on the torque pulsa- lions in a brushless dc drive’ Proceedings of the 1988 Conference on Industrial Electronics (IECON ’88), Singapore Oct 24th-28th 1988,
8 ASADA, H., KANADE, T., and TAKAYAMA, 1.: ‘Control of a
direct drive arm’, Trans A S M E , 1983,105, pp 136142
9 DAVIES, S., and CHEN, D.: ‘High performance brushless dc
motors for direct drive robot arm’, P C I M , Aug 1985, pp 35-38
IO ILK-SPONG, M., MILLER, T.J.E., MACMIN, S.R., and THORP,
J.S.: ‘Instantaneous toraue control of electric motor drives’ IEEE,
pp 749-754
1987, PE-2, (l), pp 55-6‘1
11 CHAMPENOIS, G., MOLLARD, PH., and ROGNON, J.P ’ ‘ T w o
digital torque control structures for permanent magnets converter fed sinusoidal synchronous machines’ Proceedings of the 1988 Con-
ference on Industrial Electronics (IECON ’W), Singapore, Oct
24th-28th 1988, pp 725-730
12 MATSUI, N., and OHASHI, H ‘DSP-based adaptive control of a brushless motor’ IAS 88, Pittsburgh, Pennsylvania, USA, Oct 2nd-6th 1988, pp 375-380
13 HASHIMOTO, H., KATO, Y., and MIYATA, M: ‘On-off pattern generation based on VSS for dc servo motor’ Proceedings of the
1987 Conference on Industrial Electronics (IECON 27) Cambridge
Massachusetts USA, Nov 3rd-6th 1987, pp 118&11R6
14 HASHIMOTO, H.: ‘Variable structure strategy for motion control systems’ Proceedings of the 1987 Conference on Industrial Elec- tronics (IECON ’87) Cambridge, Massachusetts, USA, Nov 3rd-6th 1987, pp 159-165
15 HASHIMOTO, H., YAMAMOTO, H., YANAGISAWA S., and
HARASHIMA, F.: ‘Brushless servo motor control using variable
structure approach’, IEEE Trans., 1988.24, (I), pp 16&170
16 NG, B.H.: ‘An investigation into the effects of machine parameters
on the torque pulsations in a brushless dc drive’ MEng Thesis
1988, National University of Singapore
17 FITZGERALD, A.E., KINGSLEY, C., and UMANS, S.D.: ‘Electric machinery’ (McGraw-Hill, 1983)
18 SIMNON, ‘User’s guide for MS-DOS computers’ version 1.0,
Department of Automatic Control, Lund Institute of Technology, Aug 1986
19 DeCARLO, R.A., ZAK, S.H., and MATTHEWS, G.P.: ‘Variable structure control of nonlinear multivariable systems: a tutorial’, Proc IEEE, 1988.76, (3) pp 212-232
20 JONES, B.E.: ’Instrumentation, measurement and feedback’ (McGraw-Hill, 1977) pp 55-56
21 ‘WE DSP32 digital signal processor information manual’ (The
AT&T Documentation Management Organization Sept 1986)
22 ‘WE DSP32-SL support software library user manual’ (The AT&T Documentation Management Organization, March 1987)