IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 52, NO.

3, JUNE 2003 785

Advanced Precision Linear Stage for

Industrial Automation Applications
Kay-Soon Low, Senior Member, IEEE, and Meng-Teck Keck

Abstract—In the area of factory automation, accurate posi-

tioning systems are increasingly required in various industries to
improve the productivity and to lower the manufacturing cost. In
this paper, we present a prototype precision linear stage. It has
a positioning accuracy of 1 m and a peak speed above 1 m/s. A
permanent magnet dc linear motor has been used in the system
as the actuator to eliminate the need for mechanical transmission
from the rotary to linear motion. To achieve a fast and accurate
closed loop response, we develop a state space predictive controller
and a dynamic friction compensation system for the precision
stage. The system has been optimally tuned using the genetic
algorithm. Some experimental results are presented.
Index Terms—Friction compensation, genetic algorithm, preci-
sion linear stage, predictive control. Fig. 1. Experimental vision inspection system.

I. INTRODUCTION that is able to describe complex friction behavior, such as the

stick-slip motion, presliding displacement, Dahl and Stribeck
W ITH the advancement of technology, many applications
require precision linear stage or xy-tables for accurate
positioning of equipment less than a ten micrometers, such as
effects, etc., in our system.
The effectiveness of the prototype system has been evaluated.
those in the microelectronics industry, precision laser cutting The experimental results have demonstrated that the system has
and engraving applications, optical fiber grating processes, in- performed well.
tegrated circuit leads inspection systems, coordinate measuring
machines, etc. [1]–[3].
Traditionally, a rotary type brushless dc motor is often used II. SYSTEM SETUP
as the actuator in the linear stage. To obtain the required linear
Fig. 1 shows the photograph of our prototype system whose
motion, lead screw or other mechanical means are needed. For
primary application is integrated circuit leads inspection. The
very high precision applications that require movement of few
purpose is to ensure that the lead forms of the integrated cir-
micrometers, such arrangements have limited performance and
cuits meet the PCB assembly requirements. This type of ap-
are often not suitable. In this paper, we describe our prototype
plication is being increasingly used in factory automation due
system that uses a permanent magnet dc linear motor. This al-
to the continuing increase in the lead count and tighter lead
lows us to obtain a smooth direct linear thrust due to the lack
pitches of the integrated circuits. In this experimental system,
of mechanical transmission devices. To obtain a robust and fast
the linear motor has a short moving coil secondary containing a
closed loop system, we design an advanced state space predic-
three-phase winding known as the slider. It is positioned in the
tive controller to control the linear stage. The gains of the control
airgap between a U-shaped stationary permanent magnet pri-
system are optimally tuned using the genetic algorithm (GA).
mary, i.e., the magnet way. The travel length of the magnet way
In the experimental system, the friction has detrimental ef-
is 0.33 m. The slider (also known as the forcer) is attached to
fect on the system response especially for short distance move
a platform that is supported by two low friction linear guides
(less than 500 m). Thus, the friction model of the system has
placed at two sides of the magnet way.
been experimentally determined and the instantaneous friction
In the setup, the linear motor is driven by a three-phase
is estimated and used for the feedforward compensation. Dif-
voltage source PWM inverter. To facilitate position measure-
ferent from most friction compensation schemes which use only
ment and to provide the commutation logic, a linear optical
the static friction-speed map, we use a dynamic friction model
encoder with a resolution of 1 m has been used. Though a
10- m resolution is sufficient for the present vision inspection
Manuscript received December 13, 2000; revised January 20, 2003. applications, a higher resolution encoder is used in the setup to
K.-S. Low is with the School of Electrical and Electronic Engineering, provide the flexibility for reconfiguring the system for other
Nanyang Technological University, Singapore. future work. In the system, a 32-bit floating-point digital signal
M.-T. Keck is with the School of Information and Communications Tech-
nology, Ngee Ann Polytechnic, Singapore. processor (TMS320C31) with a sampling period of 2 ms has
Digital Object Identifier 10.1109/TIM.2003.814355 been used.
0018-9456/03$17.00 © 2003 IEEE
786 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 52, NO. 3, JUNE 2003

Fig. 2. System modeling of the linear drive.

Fig. 3. Overall system block diagram. Fig. 4. Experimental friction-speed curve.

III. DYNAMIC MODEL OF THE LINEAR STAGE IV. DESIGN OF THE CONTROL SYSTEM
The linear drive of the stage uses a typical cascaded loop con- In developing the precision stage, a predictive controller that
trol structure. For the inner current control loops, two PI con- incorporates the future reference information has been used for
trollers have been used based on the well known vector con- the system design. Since the task in our present integrated cir-
trol concept. Fig. 2 shows the simplified block diagram of the cuit’s leads inspection application is repetitive and the desired
system. In the figure, and are the motor winding resistance motion profile can be predetermined, it is advantageous to in-
and inductance. is the viscous coefficient. is the mass corporate them into the controller as it improves the tracking
of the moving coil secondary plus the nominal weight of the performance and reduces the actuator requirements. The con-
camera system. , are the force constant and back emf trol law is formulated as
constant.
To model the precision stage, we define the following vectors: (8)

(1) where , are the controller gains and is the estimate

of . In (8), , are the position reference vector and speed
(2)
reference vector, respectively. The lengths of the vectors depend
where and are the mechanical position and speed, respec- on the prediction horizons used in the design. In this paper, the
tively, and is the output of the integrator. Let be the sam- prediction horizon is set as 10 after trading off between the per-
pling time of the system and the state variables as formance and computation time. Fig. 3 shows the overall system
block diagram.
(3) To obtain well tuned controller gains, the genetic algorithm
(GA) is employed as the optimization tool. GAs are global, par-
where is the difference operator such that allel search techniques which emulate natural genetic operations
(4) [6]. As compared to other optimization techniques, such as the
traditional gradient type optimization, GA obtains its optima
then the discrete time state space model of the precision stage by evolving from generation to generation without the needs of
[3] can be expressed as stringent mathematical formulation. The underlying basis of GA
(5) comprises a set of individual elements and a set of biologically
inspired operators defined over the population itself. The poten-
(6) tial solution is represented by a string, which is known as the
where and are the system and input matrices which are chromosome. In this application, the chromosomes are repre-
functions of the motor’s parameters, the output matrix is a sented in floating point number to encode the control parameters
constant matrix defined as due to its ease in encoding and decoding the chromosomes. The
chromosome is defined as shown in the equation at the bottom
(7) of the next page.
To begin the optimization, the GA starts with a random ini-
With this state space model, we can now proceed to design the tial population. The chromosomes then undergo three basic ge-
control system. This is discussed in the next section. netic operations: reproduction, crossover, and mutation. When
LOW AND KECK: ADVANCED PRECISION LINEAR STAGE 787

a new organizm is to be created, two parents are chosen from

the current population. Organizms that have high fitness scores
are given a higher probability to be chosen as parents.
In this paper, the fitness function to be minimized by the ge-
netic algorithm is defined as

Fitness

(9)

where is the desired move time for the linear stage to

reach the final position. In (9), , , and are the weighting
factors. To achieve a smooth motion, the position reference tra-
jectory is computed as s-curve profile.
With the system model (5) and (6), the control law (8), the
fitness function (9), and the experimentally identified friction
model to be discussed in the next section, the genetic algorithm
can proceed its evolutionary process to optimize the system con-
troller. The GA optimization is terminated after the average fit-
ness and the best fitness converges to the same value over the
iterated generations. From the study, it is found that this occurs Fig. 5. Position responses for 30-cm move.
around 1000 generations.

V. FRICTION MODELING AND COMPENSATION SYSTEM

For a relatively short move that is less than 1mm, the distur-
bance caused by the friction becomes significant in the system
response. This leads to deterioration in the performance. Thus,
the friction is modeled in our system and the estimated value is
used for the compensation. To model the friction accurately, we
use the LuGre friction model [4], [5] instead of the commonly
used static friction-speed map. Let , be the frictional force
and the speed, respectively, then the friction dynamics is mod-
eled as

(10)

where is a nonmeasurable state and the function is

(11)

where is the Coulomb friction, is the Stribeck velocity and

is the static friction. With the internal state defined Fig. 6. Motion profiles for 30-cm move.
in (10), the dynamic friction is obtained as

where is the viscous friction coefficient, the parameter is

(12) the stiffness coefficient and is the damping coefficient.
788 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 52, NO. 3, JUNE 2003

Fig. 7. Position response of 2-cm move.

Fig. 8. Motor current response for 2-cm move.

With constant speed and , the steady-state fric-

tion characteristics can be derived by substituting (10) and (11)
into (12) which yields

(13)

From (10)–(13), it is clear that the complete friction model

is characterized by the four static parameters , , , and
, and the two dynamic parameters , . In our system, the
four static friction parameters are determined by constructing
the friction-speed map. The experimental friction map shown
in Fig. 4 is obtained through moving the forcer with a series
of extremely low and constant speed tests. GA is then used to
search the optimal static parameters such that (13) fits the exper-
imental data. The two dynamic parameters are determined indi-
rectly by matching the simulated and experimental current com-
mand curves through tuning the dynamic friction parameters.
With a sufficiently accurate friction model, the estimated fric-
tional force is added into the current command as Fig. 9. Position response for 500-m setpoint without friction compensation.

(14)
by specifying a higher gradient reference trajectory but at the
expense of higher control signal.
Next, we show another set of the experimental results with the
VI. EXPERIMENTAL RESULTS required move distance reduced to 2 cm at a settling time of 0.5
Various experiments have been conducted to evaluate the seconds. The position response and the motor current response
performance of the prototype system. Fig. 5 shows the ex- are shown in Figs. 7 and 8, respectively. It is clear from the
perimental results of a 30-cm position move with a settling results that the tracking performance is good. The inset of Fig. 7
time of one second. We observe from Fig. 5 that the actual shows a close up view of the tracking with a position resolution
position response follows the position reference trajectory of 0.5 mm per division. The current response in Fig. 8 shows that
accurately. Furthermore, it reaches the desired final position there is distortion around 0.15 s due to the changes of friction.
at the specified settling time. The inset of the figure shows To study the problem due to the friction, performance degra-
a close up view of the tracking with a position resolution of dation for a short move of 500 m is presented in Fig. 9. A
2 mm per division. The speed versus position curve in Fig. 6 settling time of 0.2 s is used in this test. The results show that
shows that the actual motion trajectory follows very well with the position response has a long settling time. The stick-slip phe-
the desired motion profile. From both Figs. 5 and 6, we observe nomenon of friction causes the position response to distort when
that the achievable peak speed reaches 1.127 m/s at half the the motor reaches around the final 50- m position and degrades
move time (i.e., 0.5 s). This peak speed can be further increased the system performance. With the friction compensation scheme
LOW AND KECK: ADVANCED PRECISION LINEAR STAGE 789

Fig. 11. Experimental results of linear cycle test.

REFERENCES
Fig. 10. Position response for 500-m setpoint with friction compensation.
[1] A. Hace, K. Jezernik, B. Curk, and M. Terbuc, “Robust motion control
of XY table for laser cutting machine,” in Proc. IECON, vol. 2, 1998,
TABLE I pp. 1097–1102.
SUMMARIZATION OF EXPERIMENTAL RESULTS [2] K. K. Tan, S. N. Huang, and H. L. Seet, “Geometrical error compensation
of precision motion systems using radial basis function,” IEEE Trans.
Instrum. Meas., vol. 49, pp. 984–991, Oct. 2000.
[3] K. S. Low, Y. Z. Deng, M. T. Keck, and C. W. Koh, “A high performance
linear motor drive for integrated circuit’s leads inspection system,” in
Proc. IECON, vol. 3, 1998, pp. 1321–1325.
[4] B. Armstrong-Helouvry, P. Dupont, and C. Canudas de Wit, “A survey
of models, analysis tools and compensation methods for the control of
machines with friction,” Automatica, vol. 30, no. 7, pp. 1083–1138, July
1994.
in place, Fig. 10 shows that the tracking performance is signifi- [5] C. Canudas de Wit and P. Lischinsky, “Adaptive friction compensation
with partially known dynamic friction model: Low velocities,” Int. J.
cantly improved. Moreover, the stick-slip phenomenon is dimin- Adaptive Contr. Signal Processing, vol. 11, no. 1, pp. 65–80, February
ished and the settling time is much reduced. Table I summarizes 1997.
the results of the experiments for Figs. 5–10. In general, large [6] D. E. Goldberg, Genetic Algorithms in Search, Optimization and Ma-
chine Learning. Reading, MA: Addison-Wesley, 1989.
position reference command results in faster average and peak
speeds. This leads to larger tracking errors during the transient.
However, the steady error remains zero due to the integrator in Kay-Soon Low (SM’00) received the B.Eng. degree
the controller. in electrical engineering from the National Univer-
Fig. 11 shows the performance of the linear stage using the sity of Singapore, Singapore, and the Ph.D. degree
in electrical engineering from the University of New
linear step cycle based on the machine calibration standard South Wales, Sydney, Australia.
BS3800. In the figure, there are three forward targets, an He joined the School of Electrical and Electronic
overrun of half target, three reverse targets followed by a final Engineering, Nanyang Technological University,
Singapore, in 1994, as a Lecturer and subsequently
overrun of half target. For each target, the s-shape position became an Associate Professor. During 2001 and
profile of 10- m distance is used. The experimental results 2002, he worked with various technology startup
show that the actual motion follows the reference profile very companies to pioneer the R&D work in high data
rate ultra wide-band (UWB) radio systems and to develop enterprise software.
well. Due to the short distance commanded in this test, the His funded projects are in the area of advanced motion control system, power
quantization step of 1 m of the linear encoder can be clearly electronics, and UWB radio. His research interests are in control of power
observed. A Kalman filter has been implemented in the experi- electronics and drive systems, precision servo, and UWB radio. He has served
as a consultant to many companies and holds several patents.
mentally system (Fig. 3) to provide smooth estimated position Dr. Low is a Committee Member in the Industry Applications Society of the
and speed. The solid line that passes through the discrete steps Singapore Chapter.
in Fig. 11 is the estimated position from the Kalman filter.

Meng-Teck Keck received the B.Eng. and M.S. degrees in electrical engi-
VII. CONCLUSION neering from the Nanyang Technological University of Singapore, Singapore.
He has been a Lecturer at the School of Information and Communications
A precision linear stage has been successfully developed for Technology, Ngee Ann Polytechnic, Singapore, since 2000. He teaches internet
the industrial automation applications. High closed loop perfor- computing, internetworking, systems programming, and wireless technology.
mance has been demonstrated experimentally. The results have He is the author of the book Systems Programming and Internet Computing
(Englwood Cliffs, NJ: Prentice-Hall). His research interests include genetic al-
shown that the system has good tracking and steady state per- gorithm, fuzzy logic, neural network, linear motor drive, and mobile and wire-
formance for both short and long distance moves. less communication systems.