2002中華民國自動控研討會
Anti-windup Speed Control of an AC Servo Drive
Ming-Shyan Wang*, Houang-Wen Laio**, Wang-Cheng Chen**, and Hong-Zgi Chen*
王明賢*,廖鴻文**,陳旺承**,陳鴻志*
*Department of Electronic Engineering, Southern Taiwan University of Technology
1,Nan-Tai St.Yung Kang City, Tainan Hsien, Taiwan, 710
TEL:(06)2533131 ext.3125
E-mail:mswang@mail.stut.edu.tw
** Eternity Electronics Industry Co., Ltd.
TEL:(06)2797611
Abstract
of functions, and generality of used components, etc.
In the paper, the anti-windup PI control is
Some guidelines are provided for interpretation of
studied for the commercial AC servo motor drive.
AC/DC drive speed performance specifications from
The self-conditioned algorithm is used. In the
a drive system’s application perspective in [5].
experimental
test,
control
loop
bandwidth,
The windup problem in controllers is an adverse
per-normal (PN) inertia, and noise sensitivity are
effect that occurs in the integral action of PID control,
considered. And the load shock recovery is also
when nonlinearities exist between the controller
tested.
output and the plant input [6-9]. It has been found
Keywords: Anti-windup PI control, AC servo motor
that this phenomenon may be overcome by some
drive, self-conditioned algorithm.
anti-windup
摘要
anti-windup (CAW), Hanus conditioned controller,
本文針對工業用 AC 伺服馬達驅動器之速度
general
控制，以自我條件法則探討重置捲起的問題。實
schemes,
conditioning
such
as
technique
conventional
(GCT),
and
observer-based anti-windup, and so forth.
驗上，將速度迴路頻寬、單位正規慣量、雜訊靈
In the paper, the HO series drives, designed under
敏度與負載干擾恢復時間等規格皆列入討論。
the cooperation between teachers and students with
關鍵字:反重置捲起比例積分控制,交流伺服馬達
the department of electronic engineering of STUT
驅動器,自我條件法則.
and the manager Fu-Sun Hsu of EEI, for AC servo
1. Introduction
motors (PMSM type) of Sinano company are
It is well-known that the permanent-magnet
considered. The proportional-integral-anti-windup
synchronous motor (PMSM) has the advantages of
algorithm is tested in the velocity loop control. And
higher torque-to-inertia ratio and power density when
the guidelines in [5] are used for HO drives.
compared to the induction motor or the wound-rotor
This paper is organized as follows. Section 1 is the
synchronous motor [1-4]. So, a PMSM is often used
introduction. In section 2, the single phase model and
for the commercial AC servo drive. Then, the
the dq-transform model of HO drives are investigated.
research and manufacture of AC servo drives become
Section3 describes the windup problem in the control
more popular and competitive. However, except for
system, and the conditioned PI controller. In section
the most important specification performance, there
4, the experimental results are shown, and the
are
analysis of the guidelines in [5] is given. Finally,
some
realistic
terms
considered
in
the
commercial AC servo drive, such as cost, complexity
some conclusions are made.
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2002中華民國自動控研討會
2. PMSM and its drive
Although, the calculation of (2a) and (2b) can be
The model of a PMSM is given by [10,11]
 vu   Ra  pLa
0
0   iu   eu 
  


Ra  pLa
0   iv    ev 
 vv    0
vw   0
0
Ra  pLa  iw  ew 


where v j , i j and e j ,
replaced with lookup table. It would need a while
time for a non-DSP type, general micro-controller,
( 1 )
for example, 16-bit M16C/62 group. And the
dq-model is not available for the brushless DC motor
(BLDCM). So, for uniform design algorithm of
j  u, v, w , represent the
drives of PMSM and BLDCM, the single phase
phase-j voltage , current and back emf, respectively ,
and
model (1) is adopted in HO series drives even the
p  d dt . The following linear transformation
necessary compensation for e j in the control loop.
is used to obtain dq-axis representation [10,11]
 vu 
vd 
2  cos re cos( re  2 3) cos( re  2 3)   
v   
 vv
3  sin  re  sin(  re  2 3)  sin(  re  2 3)  
 q
vw 
where
 re
Fig.1 shows that there are three closed-loops,
current control, velocity control, and position control,
in the servo control system. And, Fig.2 shows the
( 2 a )
block diagram of the drive hardware. The 16-bit
is the electric angle between the stator
M16C micro-controller provides sufficient ROM for
and the rotor, and its inverse transformation is
program instructions, multifunctional 16-bit timers to
 vu 
 sin  re
 cos re

2
 
 v d 
 vv   3 cos( re  2 3)  sin(  re  2 3) v 
q
v w 
cos( re  2 3)  sin(  re  2 3)  
generate 3-phase PWM signals, 25 internal and 8
( 2 b )
and 62.5ns the shortest instruction execution time at
external interrupt sources, serial I/O for RS232C and
RS485, 10 bits * 8 channels ADC, 8 bits * 2 channels
DAC, one watchdog timer, some programmable I/Os,
By using (2a), we have
vd   Ra  pLa
v   
 q    re La
where
and
fin=16MHz, etc. The I/O interface and encoder
interface are designed in the CPLD. The intelligent
  re La  id   0 
     (3)
Ra  pLa  iq  eq 
power unit (IPM) is the main chip of the inverter of
the drive. IPM provides some protections, such as
Ra ( La ) is armature resistance (inductance),
 re
over-current,
is the electric velocity. The electric torque
where
load
short-circuit,
and
under-voltage detections. There are three kinds of
of the motor is
Te  k t i q
overheat,
drives in HO series on their maximum collector
currents, 15A, 20A, and 30A, respectively.
( 4 )
The PI control is applied to the velocity control
k t is the torque constant .
loop of the drive to get the zero steady-state error.
If the model (3) is used, we know that the control
And, the proportional gain constant k p and integral
of (3) is easier than that of (1). The output torque of
gain constant
the motor is only determined by i q . And, it has
k I are adjustable according to the
load. However, the windup problem and load
id  0 , and works
magnetic field weakening for negative i d . However,
higher efficiency on power for
disturbance have to be considered in the adjust
procedure.
it’s necessary to use the linear transformation (2a)
3. Anti-windup design
and inverse transformation (2b) in the control loop.
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2002中華民國自動控研討會
In a linear control system, if there is an integral
If a PI controller is considered, the conditioned
action in its controller and a limiter in the plant, it
structure is shown in Fig.6, and yields:
will integrate the error signal such that the integral
v r (t )  v r (t  1)  k I [u r (t  1)  v r (t  1)] / k p (9a)
term may become very large if integration lasts for a
u(t )  v r (t )  k p [w(t )  y(t )]
(9b)
long time and saturation occurs. It is true because all
4. Experimental results
physical systems are subject to actuator saturation or
limitation. This is called windup problem.
The experimental arrangement is 6CC401 PMSM
However, the windup problem in the integrator
whose parameters are shown in Table 1, driven by
part of the controller is only a special case of a
H15 drive with a 3.45 Kgcm2 dummy load. Fig.7
general problem. The general windup problem is
shows
described in Fig 3. There exists a non-linearity
k p  0.625 and torque limit
the
3000
rpm
step
responses
for
TLMT  TR with
linear controller output u (t ) and plant
ant-windup control and without anti-windup control,
u (t ) [6-9] . And, the lack of consistency in
respectively; and their corresponding waveforms of
the controller states may give rise to a deterioration
current command and i u . Fig.8 shows the results for
of control performance.
k p  4.375 and TLMT  TR . Fig. 9 depicts the
between
input
r
Consider a linear and discrete controller [7],
waveforms for k p  0.625 and TLMT  3TR ,
v(t  1)  A(t )v(t )  B(t ) w(t )  E (t ) y (t ) (5a)
and Fig.10 depicts the results for k p  4.375 and
u (t )  C (t )v(t )  D(t ) w(t )  F (t ) y (t ) (5b)
TLMT  3TR . Replacing the dummy load with the
where the matrices A(t ), B(t ), C (t ), D(t ), E (t )
other PMSM, the results are shown in Figs.11 and 12
and F (t ) have the appropriate dimensions , D(t )
for 4 cases: TLMT  TR and i g  2 A (generator
is invertible , v (t ) is controller state vector , w(t )
output
is reference input vector , and y (t ) is output vector .
k p  0.625 , and k p  4.375 ,
The
corresponding
unconditioned
discrete-time
where T and
T (q, t )  C (t )[ Iq  A( y )]
B(t )  D(t )
S (q, t )  C (t )[ Iq  A(t )] 1 E (t )  F (t )
(6)
response of smaller overshoot, and needs less current
to drive the motor, for lower proportional gain
(7a)
k p .For higher k p , the responses of two control
(7b)
systems are almost same. These situations also
and q is the forward shift operator,
q  x(t )  x(t  1)
happen on load disturbance applied to system.
(8)
However, the anti-windup control system has longer
The self-conditioned controller shown in Fig.5 is
rise time.
given by [7].
Assuming the system natural frequency/loop
vr(t+1)=[A(t)-B(t)D-1(t)C(t)] *vr(t)+B(t)D-1(t)ur(t)
bandwidth=10 and PN Noise=0.001, we have other
+[B(t) D-1(t)F(t)-E(t)] *y(t)
parameters, torque loop bandwidth=4500 rad/s and
u(t)=D(t){w(t)-T-1(q,t)*S(q,t)y(t)+[D-1(t)- T-1(q,t)]
speed sample time=0.2 ms. By [1], the procedure to
*u(t)}
input w
r
find the maximum speed loop bandwidth is:
v (t ) , obtained with auxiliary
Step 1:
K max  15,
to cancel the effects of the nonlinearities,
Step 2:
J  7.15ms (PN inertia),
where state vector
respectively.
controlled by anti-windup algorithm has better speed
S are square matrices and given by
1
and i g  5 A ,
From Figs.7-12, we know that the system
controller shown in Fig.4 fulfills the equation:
u (t )  T (q, t ) w(t )  S (q, t ) y (t )
current), TLMT  3TR
r
are necessarily adequate .
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2002中華民國自動控研討會
Step 3: theoretical
BWmax  2000rad / s ,
Step 4: constrained
BW max  900rad / s ,
Step 5: final
velocity
command
current
command
motor
BW max  900rad / s .
position
command
position
control
+-
velocity
control
+-
current
control
+-
It is known that the performance of the speed loop
power
inverter
+
current loop
velocity
+ sensor
velocity loop
was constrained by the drive technology. This
+ position
sensor
position loop
constraint is caused by the current loop bandwidth,
due to the non-specific DSP motor control chip,
Fig.1 Block diagram of a drive
MC16, and the delay time of the power IC in the
CN3
CN4
CN1
inverter. And, from Figs. 11 and 12, we find that the
I/O Interface
shock recovery time is very short.
Keys&
Display
cpu
CPLD/FPGA
5. Conclusions
CN2
The speed control is studied in the commercial
AC servo motor drive. Self-conditioned PI control
Pow er unit
Motor
Encoder
algorithm is researched for further discussion. It is
TB1
shown that the response under self-conditioned PI
control has the smaller overshoot and damping, but
Fig.2 Hardware architecture of a drive
longer rise time. The specifications of control loop
w(t)
bandwidth, PN inertia, noise sensitivity, and load
controller
u(t)
N.L
ur(t)
Plant
y(t)
shock recovery time are discussed. However, the
torque-speed response on self-conditioned PI control
has not tested yet. Further, although the performance
of speed loop bandwidth is constrained by torque
Fig.3 Classical unconditioned control loop
loop bandwidth, HO drives still have about 900 rad/s
speed loop bandwidth by using non-specific DSP
+
W(t)
Plant
motor control chip for other considerations.
Output power
PR
400W
Torque
TR
1.274 N．m
Stator Current
IR
3.5A
Speed
NR
3000 rpm
y(t)
S(q,t)
Fig-4. Non-conditioned structure
W(t)
D(t)
+
Torque Constant
KT
0.409 Nm/A
back emf constant
KE
42.8 V/Krpm
-
+
r
u(t)
N.L
u(t)
-1
-1
T(q,t)-D(q,t)
2
0.29 Kg．cm
Stator Resistance
JM
Ra
Stator inductance
La
6.33 mH
inertia
u(t)
T(q,t)
2.81 
-1
T(q,t) S(q,t)
Ta b l e 1 . P a r a me t e r s o f 6 C C 4 0 1 PM SM
Fig. 5 Self-conditioned structure
496
plant
y(t)
2002中華民國自動控研討會
KP
+
W(t)
r
u(t)
u (t)
N,L
-
+
KI
+
1-Z
y(t)
Plant
-1
-
r
V (t)
+
1
-
Kp
Fig. 9(a) anti-windup PI
Fig.6 Self-conditioned PI controller
Fig. 9(b) PI control
The 3000rpm step responses for Kp=0.625 and
TLMT=3TR: speed command, response, iu, and
current command.
Fig. 7(a) anti-windup PI
Fig. 7(b) PI control
The 3000rpm step responses for Kp=0.625 and
Fig. 10(a) anti-windup PI
Fig. 10(b) PI control
TLMT=TR: speed command, response, iu, and current
The 3000rpm step responses for Kp=4.375 and
command.
TLMT=3TR: speed command, response, iu, and
current command
Fig. 11(a) Kp=0.625,
anti-windup
Fig. 8(a) anti-windup PI
Fig. 11(b) Kp=0.625, PI
control
Fig. 8(b) PI control
The 3000rpm step responses for Kp=4.375 and
TLMT=TR: speed command, response, iu, and
Fig. 11(c) Kp=4.375,
current command.
anti-windup
Fig. 11(d) Kp=4.375, PI
control
The speed loop load shock recovery tests for ig=2A
and TLMT=TR: speed response, load shock
497
2002中華民國自動控研討會
Apple., Vol.37 ,No. 4 ,pp.1082-1087 , 2001.
[6]
A.H.
Glattfelder
and
W.
Schaufelberger,
“ Stability Analysis of Single Loop Control
Systems with Saturation and Antireset-windup
Fig. 12(a) Kp=0.625,
anti-windup
Circuits “, IEEE Trans. Automat. Control, Vol. 28,
Fig. 12(b) Kp=0.625, PI
No. 12, pp.1074-1081, 1983.
control
[7] R. Hanus, M. Kinnaert, and J.-L. Henrotte,
“
Conditioning
Technique,
a
General
Anti-windup and Bumpless Transfer Method “ ,
Automatica, Vol. 23 , No.6 , pp.729-739 , 1987.
[8] K.S. Walgama, S. Ronnback, and J.Sternby,
“ Generalisation of Conditioning technique for
Fig. 12(c) Kp=4.375,
Fig. 12(d) Kp=4.375,
Anti-windup Compensators “, IEE Proc.-D, Vol.
PI anti-windup
control
139, No.12, pp.109-118, 1992.
[9] M.V. Kothare, P.J. Campo, M.Morari, and C.N.
The speed loop load shock recovery tests for ig=5A
Nett, “ A Unified Framework for the study of
and TLMT=3TR: speed response, load shock.
Anti-windup Designs “, Automatica, Vol. 30, No.
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to colleagues, Dr. Ten-Chuan Hsiao and Chao-Ming
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Huang
25 , No. 2 , pp.274-279 , 1989.
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Southern
Taiwan
University
of
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