A DSP Based Servo System Using Permanent Magnet
Synchronous Motors PMSM
Longya Xu, Minghua Fu, and Li Zhen
The Ohio State University
Department of Electrical Engineering
2015 Neil Avenue
Columbus, OH 43210
Abstract- A digital servo system using a Digital Signal Pro cessor DSP is presented in this
pap er. A Permanent Magnet Synchronous Motor PMSM with rotor p osition enco der and
Hall sensor is used. The eld oriented vector control technique is employed to achieve robust
p erformance and fast torque resp onse. The system uses p osition and sp eed regulations as the
system outer lo op, and the current regulation with vector control as the inner lo op. A DSP system
using TI's TMS320C240 is develop ed, and the prop osed digital control strategy is implemented
in the DSP.
Key Words: Vector Control, Motion Control, Servo System, Digital Control, Permanent Mag-
net Synchronous Motor PMSM , Digital Signal Pro cessor DSP
I. Intro duction
Precise motion control plays an imp ortant role in various areas such as automation industry,
semiconductor industry, etc. Permanent magnet synchronous motors PMSM are ideal for
advanced motion control systems for their p otentials of high eciency, high torque to current
ratio, and low inertia. Advances in Digital Signal Pro cessors DSP have greatly enhanced the
p otential of PMSM in servo applications. Digital control can b e implemented in the DSP, which
makes it sup erior to analog based stepp er control, since the controller is much more compact,
reliable, and exible. High p erformance of PMSM can be obtained by means of eld oriented
vector control, which is only realizable in a digital based system.
In this pap er a DSP based servo system is presented. A digital servo controller using TI's
TMS320C240 is develop ed. Position and sp eed regulations are develop ed to ensure accurate
p osition control and fast tracking, and current regulation with eld oriented vector control is
implemented to secure fast dynamic resp onse. The system has b een proved to be robust and
e ective with very reasonable cost.
II. Analysis of PMSM Vector Control 1
The mo del of a PMSM is shown in Fig. 1. Di erent reference frames can be used to analyze
the motor, that is, 3-phase frame a-b-c , stationary frame x-y , or rotational frame d-q [1].
From the control p oint of view, the d-q reference frame is convenient and most widely used. Note
that the d-axis of the reference frame is lo cked to that of the p ermanent magnet.
y y
b q q
V
E I Liqq d λ d θ iq λ Lidd O a ,x m O θ a, x id
(b) (a)
c
Figure 1: a Di erent frames of the PMSM. b Flux, Current and Voltage Vectors
The voltage and ux equations for a PMSM in the rotational d-q reference frame can be
expressed as:
d
d
V = R i + ! 1
d s d q
dt
d
q
V = R i + + ! 2
q s q d
dt
= L i + 3
d d d m
= L i 4
q q q
where V ;V and i ;i are voltages and currents in the d-q axis, R is the stator winding resistance,
d q d q s
L ;L are inductances in d-q axis, ; are ux linkages in d-q axis, is the main ux linkage
d q d q m
of the p ermanent magnet, and ! is the angular frequency of the rotor. The transformation
between di erent reference frames can be achieved by[1]
3 2 2 3
i i
a d
7 6 6 7
i i
5 = T
5 4 4 5
b q
abc dq
i 0
c 2
3 2 3 2
i i
a x
7 6 7 6
6 i = T i
5 4 5 4
b abc xy y
i 0
c
" "
i i
x d
7 = T
xy dq
i i
y q
where
3 2
cos cos 2=3 cos +2=3
2
7 6
sin sin 2=3 sin +2=3
T =
5 4
abc dq
3
1=2 1=2 1=2
3 2
1 1=2 1=2
p p
2
7 6
T =
0 3=2 3=2
5 4
abc xy
3
1=2 1=2 1=2
"
cos sin
T =
xy dq
sin cos
and
1
T = T ;
dq abc
abc dq
1
T = T ;
xy abc
abc xy
1
T = T :
dq xy
xy dq
The torque T can b e written as
e
3 P 3 P
T = i i = [ i L L i i ] 8
e d q q d m q q d d q
2 2 2 2
where P is the motor p ole numb ers.
It is apparent that if we can control i to b e zero then the torque is directly prop ortional to
d
i . Hence, vector control is achieved by controlling i to be zero and i to pro duce the required
q d q
torque. Thus, the PMSM has the fastest dynamic resp onse and also op erates in the most ecient
state. The vector control scheme is shown in Fig. 2.
The mechanical equation of the PMSM can be written as
2
d d
T = J + T 9 + B
e L
2
dt dt
where T is the motor torque, J the inertia, the rotor p osition, B the friction constant, and T
e L
the load torque. 3 Va,Vb,Vc Sa,Sb,Sc PWM dq-abc VSI PMSM Generator Inverter Transformation
Vd Vq PI PI Controller Controller i i a b Position i d Encoder abc-dq - + Transformation +- - iq θ
i*=0 i*
d q
Figure 2: Vector Control of the PMSM
III. Servo Control Scheme
A. System Structure
The servo control scheme of the PMSM is illustrated in Fig. 3. As shown in Fig. 3, the
controller has an inner lo op of current regulation using vector control, and an outer lo op of
hybrid sp eed and p osition regulation. This dual-lo op structure ensures the fast torque resp onse
by using the vector control, high p osition accuracy with the p osition controller, and fast tracking
p erformance with the hybrid sp eed and p osition control. The structure is also imp ortant to
secure the stability of the system.
B. Initial Position Identi cation
Incremental enco ders can only give displacements from the initial p osition and cannot provide
absolute p osition. Hence to achieve vector control usually initial p osition alignmenttoa known
p osition is required. However in some circumstances such alignment is not desired and needs
avoided.
By means of Hall sensors the rotor initial p osition can be identi ed, and further corrected
when the rotor starts rotating. Assuming the Hall sensors are lo cated at each phase, as shown
in Fig. 4. The output signals of the Hall sensors are illustrated in Fig. 5. It can be seen that
o
the resolution of the Hall sensor signals are 60 electrical degree . Table 1 shows the p ossible
combinations corresp onding to di erent p ositions.
From Fig. 5 and Table 1, given a sp eci c Hall sensor output combination, the rotor must
o
reside in certain region with a range of 60 . The initial p osition is determined as follows. When
a group of output signals are obtained, for example, 101 , we can nd which region the rotor is
o
in region 1 in this example . We can set the initial p osition at the center of the region 30 in
o
this example . It can b e seen that the maximum error of the initial p osition is 30 , which o ccurs 4 Va,Vb,Vc Sa,Sb,Sc PWM dq-abc VSI PMSM Generator Inverter Transformation
Vd Vq PI PI Controller Controller i i a b Position i d Encoder abc-dq - + Transformation +- - iq θ
PI i*=0 i* d q Controller +- - + + θref n - d/dt Kv + d/dt n
ref
Figure 3: Servo Control Scheme of the PMSM
Ha=1
N
S
Hb=0 Hc=0
Figure 4: Hall Sensor Lo cations
o
when the rotor is at the edge of two regions. However, even with 30 error, the motor will still
be able to pro duce sucient torque to start the motor.
Once the motor starts rotating, the p osition can be readily corrected when the rotor moves
out of the initial region and enters the next region. This p osition is accurate. In the previous
example, when the motor starts rotating in the p ositive direction from region 1, the rotor p osition
o
can be corrected when the p osition =60 . 5 60 60 60 60 60 60 60 60 60 60 60
Ha
Hb
Hc 0 60 120180 240 300 360 420 480 540 (0) (60) (120) (180)
(Electrical Degrees)
Figure 5: Hall Sensor Output Signals
Region H H H Position
a b c
1 1 0 1 0-60
2 1 0 0 60-120
3 1 1 0 120-180
4 0 1 0 180-240
5 0 1 1 240-300
6 0 0 1 300-360
Table 1: Combinations of Hall Sensor Output Signals
C. Anti-Hunt Processing
When the motor reaches to the required p osition and needs to pro duce torque at standstill,
sp ecial attention needs paid since the rotor will very likely oscillate hunting . A variable gain
anti-hunt algorithm is develop ed.
As shown in Fig. 6, the PI gains of the sp eed and p osition regulators are kept normal when
the p osition error is large. When the p osition error is small enough in region 1 or 3 , the gains
should be gradually reduced. Once the rotor enters the anti-hunt window region 2 , the gains
are reset to zero. This approach has e ectively avoided the rotor oscillation at the standstill
p osition.
IV. Hardware Setup 6 12 3
P, I Gains
X
Position
Figure 6: Variable Gains for Anti-Hunt
The DSP based servo system is shown in Fig. 7. The system is comp osed of the DSP controller,
power circuit, PMSM with enco der/Hall sensor, and development to ols emulator and host PC .
SCI Input/Output
External Display Memory D/A Converter JTAG TMS320F240 Emulator DSP A/D Converter
Host Driver Circuit Computer Current Sensor
Power Circuit
PMSM Encoder
/Hall Sensor
Figure 7: Servo System Structure
Fig. 8 shows the picture of the DSP servo controller. Main comp onents in the controller
include DSP TMS320F240 , FPGA, memories, DAC, etc. The controller directly outputs PWM
signals for the power circuit, and accepts analog signals motor currents, analog commands,
etc. and p osition information enco der and Hall sensor signals . The controller also has RS232
interface for on-line tuning. A new version of the controller, which is under development using
TMS320F243, will also include Control Area Network CAN bus interface.
V. Conclusions 7
Figure 8: The DSP Servo Controller
A TMS320F240 based DSP servo controller has b een develop ed. The system has reached
compact size and high reliability. Highly complicated digital control algorithms, including vector
control, current regulation, and sp eed/p osition regulations have b een implemented in the DSP.
To avoid initial rotor alignment, initial p osition identi cation using the Hall sensor signals are
implemented. Anti-hunt technique using anti-hunt window and variable controller gains are also
develop ed. The system has b een proven to be highly e ecticve and ecient with relatively low
cost.
VI. References
[1] Paul C. Krause, Oleg Wasynczuk, and Scott D. Sudho , \Analysis of electric machinery,"
McGraw Hill, 1986.
[2] P. Pillay and P. Freere, \Literatre survey of p ermanent magnet AC motors and drives."
IEEE-IAS Annual Meeting, 1989, pp. 74-84.
[3] D. W. Novotny and T. A. Lip o, Vector Control and Dynamics of AC Drives. Oxford University
Press, 1997. 8