Block diagram of automatic steering system with conventional autopilot. ... switching to conventional autopilot control ... B = 38 m, D = 20 m) in service between.
An Adaptive Steering System for a Ship Tatsuo Arie, Masanori Itoh, Akira Senoh, Nobuhiko Takahashi, Seizo Fujii, and Naoki Mizuno ABSTRACT: This paper describes an adaptive steering system for ships that was developed by Nippon Kokan K.K. in cooperation with Yokogawa Hokushin Electric Corporation. The purpose of the system is to improve a ship‘s automatic steering performance under a variety of operational and environmental conditions. The techniques of hill climbing and model reference adaptive control are used in the course-keeping and course-changing modes, respectively. The results of related full-scale experiments with ocean-bound bulk camers are presented.
Introduction An autopilot is a ship’s steering controller, which automatically manipulates the rudder to decrease the error between the reference heading angle and the actual heading angle. Conventional autopilots are based on simple PID control. In order to maintain the desired performance of PID-type autopilots, thecontrol parameters must be adjusted in accordance with the variations of both ship dynamics and environmental disturbances. Ship dynamics vary due to operational conditions. The main environmental disturbances are wind, waves! and currents? which also vary according to weather and sea conditions. However, it is a tedious and difficult task to properly adjust the control parameters of an autopilot. The adjustment is therefore only approximate, and a fixed setting is often used during navigation. This may cause inferior steering quality such as propulsive energy losses due to excessive rudder motion or inadequate maneuvering performance. To cope with the problems associated with parameter optimization of autopilots, the authors have developed the Adaptive Steering Presented at the 1985 International Conferenceon IndustrialElectronics,Control, and Instrumentation, San Francisco, CA, November 18-22, 1985. T. Arie, M. Itoh, and A. Senoh are with the Systems and Control Research Center,Nippon Kokan K.K., 1-1,Minami-Watarida-cho,Kawasaki-ku, Kawasaki 210, Japan; N. Takahashi is with Yokogawa Hokushin Electric Corporation, 9-32, Tokyo 180, Nakacho2-chome,Musashino-shi, Japan;and S. Fujii and N. Mizunoarewith the Department of Mechanical Engineering, Nagoya Institute of Technology,Gokisocho,Showa-ku, Nagoya 466, Japan.
System, which uses the techniques of hill climbing and model reference adaptive control (MRAC) [l] in the course-keeping and course-changing modes. Control is implemented using a microcomputer, and is designed tobe easily applied by interfacing signals with existing conventional autopilots. Full-scale experiments camed out with 86,000- and 64,000-DWT (dead weight ton) bulk camers show not only a great economical improvement in the course-keeping mode, but also excellent maneuvering performance in the course-changing mode. This paper presents an outline of the authors’ study. Ship steering characteristics are introduced first, and then problems with conventional autopilots are stated. The control systems for course-keeping and coursechanging, and the results of experiments, are described next: After the completion of this work, three recent references pertaining to ship steering were brought to the authors’ attention, and they are presented here for the readers’ benefit [2]-[4].
Steering Characteristics and Problems Ship Steering Characteristics
Figure 1 shows a block diagram of a common automatic steering system with a conventional autopilot, where e is the heading emor, u , the ordered rudder angle, u the actual rudder angle, y the ship’s heading angle, and y r the reference heading angle. The ordered rudder angle u, (control input) is generated by aPIDcontroller using the e m r between the reference and actual heading angles. The feedback gains and other control parameters must be adjusted manually. Ship steering dynamics, between the actual rudder angle u and the ship’s heading AUTOPILOT #
I
angle y . can be described by the following transfer function, assuming linearity [5], where TI, T2, T3, and K are the parameters representing the ship’s dynamics.
yo-u(s)
K(1
(1
+ T3s)
(1)
+ T,s)(l + T*s)s
In a more practical sense, Eq. (1) is often approximated by the following transfer function, where T = TI + T2 - T3.
you(s)
K
(1
(2)
+ Ts)s
Theship parameters are basically determined by the ship size and shape, and may vary depending upon operational conditions such asshipspeed,draft, trim, and water depth. In this study, the dynamics between the ordered rudder angle u, and the ship’s heading angle y is the plant to be controlled. The plant dynamics and environmental disturbances are assumed to be unknown and varying slowly during navigation. Problems
An autopilot has two major tasks: coursekeeping and course-changing. The former is the steady-state heading regulation used to keep the shipona desired course against environmental disturbances caused by wind, waves, and currents. The latter is the heading control in the transient state that changes the ship’s original course. A different control performance is required in each mode, depending on its purpose.
Course-keeping During navigation onthe -ocean, the course-keeping mode is nearly always used. When there are no traffic obstacles in the vicinity,themajor concern of merchant ships is minimization of propulsive losses due to steering without harmful yawing. Thus, course-keeping control is de-
POWER UNIT GEAR STEERING
SHIP
U L
I
Fig. 1. Block diagram of automatic steering system with conventional autopilot. 0272-1708:86/1000-0003 $01.OO 0 1986 IEEE
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signed from the viewpoint of energy-saving in this study. When navigating in confined waters,accurate course-keeping-rather than energysaving-is most important. Of course, accurate course-keeping requires some steering. In such a case, the ship’s officers will choose the steering qualities: accurate course-keeping or energy-saving. Accurate course-keeping can be easily achieved by switching to conventional autopilot control with fixed high feedback gains.
Course-changing When changing course, a steady and consistent turning rate is usually desired. This is because the track and acceleration acting on the ship can be predicted at the beginning of the turn by using the ship speed and turning position, which givesa great advantage in the safe handling of the ship.
Course-keeping Control Structure of Controller
An on-line parameter optimization procedure, based on the hill-climbing technique, is used in the course-keeping mode to minimize propulsive energy losses due to steering. Figure 2 shows a block diagram of the course-keeping control system. The basic structure is a combination of a PIDcontroller with a parameter optimizer, which isdistinctly different from a conventional autopilot (where the blocks between u, and y are the same as those in Fig. 1). A quadratic performance index composed of heading error e and rudder angle u is introduced into the parameter optimizer, i.e., the feedback gains of the PID controller are optimized by minimizing the performance index. Equations ( 3 ) and (4) present the PID controller and performance index, respectively, where e(k) is the heading error. u,(k) the ordered rudder angle, k,,. k,, and kd the proportional, integral, and derivative feedback gains. respectivelk-. z - ’ the backward shifi operator, u(k) the actual rudder angle. X the weighting coefficient. and n the number of samples.
+ k, + k,) - (kp + 2kd)?-’ + kdz-:]
U,(k) = [(k,
[I
- z1-I
(3)
e(k)
AU’OPILOT
x
d
TIME
(a) Time Chart
of
U
Parameter Oscillation
(b) Map of Performance Index
Fig. 3 . Parameter optimization scheme (course-keeping control).
J = When an appropriate value for the weighting coefficient is used, the performance index J represents the propulsive energy losses due to steering. The weighting coefficient has been discussed previously by Koyama [ 6 ] , Norrbin [ 7 ] , and others, independently. In general, thelarger value of X should be given to the smaller ships. The proportional and derivative feedback gains, k,, and k d , are designed to be adjustable because they have a great affect on course-keeping qualities. A constant value is given to the integral feedback gain kj because, given stable conditions, simulation tests prove that the course-keeping qualities are influenced only slightly by ki. Figure 3 shows how the control parameters are adjusted. Programmed square oscillations are given to the adjustableparameters kp and k d . Then the value of the performance index is measured in each section, which is divided into four according to the oscillation phases ( J , , J 2 . J3, and J4). Furthermore, the bias level of each parameter is corrected by comparing the values of the performance index measured during parameter increases and decreases. i.e.. kph is updated by comparing ( J , + J:) to (J3 + J,) and kdb by ( J , + J 3 ) to (J2 T J;). The strategy previously mentioned can be achieved by the following parameter optimization law,, where k,,(n) is the bias of kp in the nth trial. kdb(n) is the bias of kd in the nth trial, J j ( n ) is the measured performance index in the ith section in the nth trial, and G, and Gd are positive gains.
POaE? UNIT GEAR STEERI%G
Figure 4 shows the exteriorof an Adaptive Steering System installed onto the right side of a conventional autopilot stand. The system consists of a 16-bit microcomputer, and the course-changing control (which will be mentioned below) is included in the same hardware system. E?rperiments
Experiments have been camed out with this system over a six-month period onboard an 86.000-DWT bulk camer ( L = 230 m, B = 38 m, D = 20 m) in service between Japan and Australia, and Japan and Canada. The difference in performance between the
SHIP
OPTIMIZE?
Fig. 2. Block diagram of course-keeping control system.
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Fig. 4. Exterior of adaptive steering system.
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adaptive and conventional controls was evaluated by experimental results. For the onboard experiments, the adaptive and conventional controls were exchanged every four hours, and the heading error, rudder angle, ship speed, shaft horsepower, and other important data were collected. The Computer-Aided Navigational System,developed by Nippon Kokan K.K., provides navigational information to the ship operators, and is employed as an automatic data collector. Figure 5 shows the difference in the value of the performance index between adaptive and conventional controls. For this experiment, the initial values of the adjustable feedback gains for adaptive control were set at the same value as the fixed gains for conventional control. In the figure, the scale is adjusted so the average level of the performance index for conventional control is 100 percent. The value of the performance index with adaptive control gradually decreases to a level lower than the conventional autopilot. This suggests that the control parameters were adjusted successfully. Figure 6 shows the difference in coursekeeping performance between the adaptive and conventional controls.Ruddermotion, which causes propulsive energy losses, was considerably decreased by using the adaptive system. The slight increase in ship heading error was not a serious operational problem. The relationship between the ship’s speed
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(x1031 9’5
r
9.0
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FULL-LOAD CONDITION 0 ADAPTIVE x CONVENTIONAL
- 12 U
-11
5 Bw
v)
U
?
5 - IO viP
1 - 9
26
27
28
30
29
V, SHIP SPEED (kwh)
Fig. 7. Relationship between ship speed and shaft horsepower (fullload condition).
V and shaft horsepower P during navigation was investigated in order to quantitatively evaluate the system’s economical steering performance. Considering that the shaft horsepower ofthe main engine is proportional to the ship’s speed cubed [Eq. ( 6 ) ] , the proportional coefficient “C” was identified as a direct indicator of required propulsive energy, where P is shaft horsepower, I/ ship speed, and C a proportional coefficient.
n
FULL-LOAD CONDITION
ao -
P =
cv3
(6)
The difference between the adaptive and conventional controls in the relationship V vs. P is shown in Figs. 7 and 8 for the fullload and ballast conditions, respectively, with an average of 20 minutes plotted for adaptive; X , conventional). each point (5, The measured shaft horsepower P is compensated by eliminating the added resistance directly caused by waves and wind. So, the influence of weather and sea conditions is nullified. The graphs in each figure are cubic curve-fitted lines based on the identified “C.” With full-load conditions (Fig. 7), coefficient C with adaptive control was reduced by as much as 3.5 percent from conventional control. Under ballast conditions (Fig. 8), energy-saving is decreased, but almost 1.0 percent energy-saving is still possible.
Course-changingControl Structure of Controller L”
0
3
6
9
12
I8
15
21
TIME[C!
Fig. 5. Measured performance index (adaptive and conventional). RUDDER ANGLE(deg)
+5
I
- J
COURSE ERROR(deg!
-0 +5
O
-
-
ADAPTIVE 1
CONVENTIONAL,
2
3
4
TIME(h!
Fig. 6. Course-keeping performance (adaptive and conventional).
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The technique of model reference adaptive control (MRAC) improves the ship’s maneuverability, making it possible to assign the desired transient characteristics with a reference model. Figure 9 presents the structure of the course-changing control system. The controller consists of three major parts: a linear model following (LMF) controller,an adaptation mechanism, and a reference model. The ship’s steering dynamics, located between the ordered rudder angle u, and the ship’s heading angle y , is the controlled plant. When using MRAC, thecontrolled
5
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-
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-
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a.0
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3
7.0
d 6.5
-
6.0
-
Yo
- I
-
7.5
fn
1'
-
a
B
1'
CONVENTIONAL
TIME - 1
yo : Original Course y,
e J
-!
P = 0.346 V'
.
Fig.10.
27
28
29
Fig. 8. Relationship between ship speed and shaft horsepower (ballast condition). plant is treated as alinearsystem. In this case, E q . (7) can be used as an approximate plant model, assuming that the dead zone in the power unit is small, the rate limiter b in the steering gear is large, and the time constants T' and T, are small when compared to the ship's time constant T. The rudder angle limiter c in the steering gear is discussed below [see Eq. (12)].
z-dB(z-l)u,(k)
+ alz-1 + .
&-I)
= 1
B(z-1)
= bo
*
a
+ ud
+ a,z-"
+ b,z-l + . . *
+ b,Z--"
(bo f 0)
where y*(k + d ) is the output of the reference model, which has the desired characteristics.
~ * ( k+ d )
u m
1
POWER STEERING UNIT
-~
( +k d ) = 0
=
(y*(k
+ d)
(9)
- P;60(k))/bo
-
l),
u,(k - m - d ?(it), =
..
(PI,
*
.
*
* * .
,
+ l),
, y(k - n
u,(k)
=
u m ,
lu;(k)l
5
=
R sgn ( 4 ( k ) ) ,
lu,Xk)l
>R (12)
The parameters for the LMF controller [see Eq. (911, such as a),Pi, 7,and bo, are available when the plant parameters are known. In this implementation, the plant parameters are all unknown and the parameters for the LMF controller must be replaced by the estimates h,( k ) , &(k), +(k), and bo@).The estimates are updated by the following adaptation mechanism [ 11:
P(k)
=
P(k - 1)
( y ( k ) - PT(k - 1) 6 ( k
+
,Pnr+d-lr
R
F(k - I) d ( k - d ) + 1 + QT(k X - d ) F(k - 1) 6 ( k - d )
where &(k) = (u,(k
When considering the limiter c in the steering gear, Eq. (12) is used instead of Eq. (9) [8].Equation (12) prevents the actual rudder angle u from reaching the limit c, where u;(k) is equal to the right-hand side of Eq. (9) and c 2 R > 0.
(8)
Figure 10 presents the characteristics of the reference model, which generates a ramp signal in response to a step input or a request for a course change. The ship's turning rate can be regulated as a constant by following the reference. The objective defined by E q . (8) is achieved by the LMF controller described by Eq. (9) [ll.
(7)
Here y(k) is the ship heading angle at time k , u,(k) is the ordered rudder angle at time k , d the time delay, and z-' the backward shift operator. The constant component of disturbance ud, which is caused mainly by wind, is taken into account. It is assumed ) all within the unit that the zeros of ~ ( z - l are circle, n, m, and d are known, and a,, bj, and ud are unknown. The objective of the control is to match the reference output as described by Eq. (8),
AUTOPILOT
Reference model (input-output).
30
V, SHIP SPEED (kmJh)
=
: New Course
1
26
A(Z-')Y(k)
c
l), 1) al, '
a
(10)
with
,
F(k) = - F(k - 1)
- d)}
(13)
'[
x1 ffn,
Y)
GEAR
(1 1)
SHIP
ADAPTATION
MECHANISM
Fig. 9. Block diagram of course-changing control system.
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IEEE Control Systems Magozine
I),
-
d
+ 1):
Experiments
The feasibility of the above-mentioned control technique was first evaluated by simulation tests, followed by full-scale experiments. In the simulation tests, the order of the polynomials A(:-’) and B(z-’) and the length of the time delay d were evaluated. Low-order models. such as the “autoregressive (AR) model with plant dead time’‘ [8] can be employed as a ship steering model. The time delay d should be 3-6, using a proper length of the sampling interval, which must be determined according to the ship‘s approximate time constant T. A series of experiments with a 6 4 , O O O DWT bulk camer ( L = 214 m, B = 32 m, D = 18 m) has been camed out. Typical results of the experiments are shown in Figs.
-
15
1 l(a) and 11(b). In each experiment, the ship‘s course was changed twice: 0 to 12 degrees and 12 to 0 degrees. A ramp signal with a rate of about 0.07 deglsec was used as the transient reference. The sampling interval was 3 sec. The restriction on the amplitude of the control input was set at R = 10 deg. According to Figs. ll(a) and ll(b), at the beginning of the first turn (0 to 12 degrees), a small deviation (y* - J ) occurred due to incomplete parameter estimation. However, in the second turn (12to 0 degree),the ship’s heading angle followed the reference and the turning rate was successfully regulated as a constant. With regard to Experiment (b), a time interval that exists between :@)-input and u,(k)-output due to the computation of the algorithm (assumed to be zero in the theory of MRAC) was taken into account by modifying the order of B(z-’) (rn = 0 to nz = 1). The remaining experimental conditions of Experiment (b) are the same as those of Experiment (a). A comparison of results (a) to (b) shows that they are nearly the same in
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2
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5
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7
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P
5 0
0
- 5
n -IO
0
TIME (mm)
(a) AR model with dead time used
(n, m. d) = (3, 0, 5)
W
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0
1
2
3
4
5
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TIME (min) (b) Computationtimeconsidered
(n,m. d ) = (3, 1. 5)
Fig. 11. Course-changing performance.
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the first turn, but in the second turn, in which computation time was taken into account, Experiment (b) is better than Experiment (a).
Conclusion This paper described an adaptive steering system that uses the hill-climbing and model reference adaptive control techniques in the course-keeping and course-changing modes, respectively. Full-scale experiments, with two bulk camers, have been camed out with the following experimental results. Course-keeping mode: Using the Adaptive Steering System, propulsive energy-saving of as much as 1.0-3.5 percent can be realized. Course-changing mode: The Adaptive Steering System improved the maneuvering performance, and a steady and consistent turning rate is achieved when changing course.
References [I] 1. D.Landau qnd R. Lozano, “Unification of Discrete Time Explicit Model Reference AdaptiveControl Designs.” Automricu. vol. 17, no. 4, pp. 593-611, 1981. 121 C. G. Kallstrijm. K. J. Astrom. N. E. Thorell, J. Eriksson.and L. Sten,“Adaptive Autopilots for Tankers,” Automarica, pp. 241-254, May 1979. [3] K. Ohtsu, M. Horigome, and G. Kitagawa, “A New Ship’s Auto Pilot Design Through a Stochastic Model,” Aurotmrica, pp, 255268, May 1979. [4] J. vanAmerongen,“Adaptive Steering of Ships-A Model Reference Approach.” Autonuzrica. pp. 3-14, Jan. 1984. [5] K.Nomotoand K . Taguchi: “On Steering Qualities of Ships (2):’ Journal of the Soc i e e of h’aval Architects ofJapan, vol. 101, pp. 57-66, May 1957. [6] T. Koyama,“On the OptimumAutomatic Steering System of Ships at Sea,” Journal of the Societ); of Naval Architects of Japan, vol.122, pp. 18-35, Dec. 1976. [7] X. H. Norrbin, “On theAddedResistance due to Steering on a Straight Course,” Proc. 13th Inrl. Towing Tank Con$, Berlin/Hamburg, pp. 382-430, 1972. ’ [8] S. Fujiiand N. Mizuno, “Construction of a Discrete MRACS for Plants with the Restriction of Input Amplitude,” Trans. of the Sociee of Instnunent and Control Engineers (Japan), vol. 18, no. 8, pp. 103-105, 1982. [9] S. Fujii and N.Mizuno. “A Discrete Model ReferenceAdaptiveControlUsing an Autoregressive Model with Dead Time of the Plant.” Preprints of 8th IFAC Congress VII, pp.120-125,1981. [lo] K. J. Astromand B. Wittenmark, Computer Controlled Systems Theon. and Design, Prentice-Hall, pp. 221-253: 1984.
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Tatsuo Arie received his
-^-T~
B.E.degree in mechanicalengineering in 1975 fromNagoyaUniversitr, Japan. Since 1975. he has been lvorking for Nippon Kokan K.K.- (NKK);~Japan. His \vork experience
Akira Senoh received his B.E.degree in electrical engineering in 1956 from the University of Tohoku. Sendai. Japan. He worked in shipyards as a design -E% =s =-*--- .- . engineer of electrical and 20 control systems for & ? yean. He is currently en*-- s 2% s5 oaged in research and de:-2 -velopment 2 of control S ~ S ..~ . -. p temsforship.enpine. and ~z =various other plants at Nippon Kokan K.K.. Japan.
---_
-
~~
~
~
~
a Research and Development Engineer at XKK's Systems and Control Research Center.
Masanori Itoh received hisB.E.degree in 1970 and his M.E.degree in 1971fromNagoyaUnivenit).Japan.where he majored in mechanical engineering.Since 1972. -.~. he has been workin9for Nippon Kokan K.K. (NKK).Japan.His mork experienceincludes d>namic simulation anal! .;is andcontrolsystemsdesign for ship and engine plants. Currently. he is a Research andDevelopmentEngineer at NKK's Systems and Control Reseaxh Center. ~
Seizo Fujii receivedhis B.E. degree in 1955, and his M.E. andD.E.degrees from NagoyaUniversity. Japan. in 1957 and 1960. respectively. all in mechanical engineerIng.He is current11 Professor of Mechanical Engineering at Nagoya InstituteofTechnology, andProfessorofInformation Science at Nagoya University. His present interests are in the area of adaptive control and it, application.
Nobuhiko Takahashi received his B.S. degree in physics in 1975 from Osaka Universitl . Japan. Since 1975. he has been morkinp for Yokopa\\a Hokushln Electric Corporation. Japan. mhere he is presentl? a Research and Development Engineer. Hi5 work experience includes development of autopilot> and other na\ igational inmumcnt> for ships.
.
'
Naoki Mizuno received his B.E. andM.E.degrees in 1978and 1980. respectively. from Nagoya Institute of Technology. Japan. and his D.E. degree in 1986 from NaF o.p University. .Japan.. Currentl!.he is a k c turer at NagoyaInstitute of Technology.His reaearch interests are in adaptivecontroland its application
-5 @+ ;&J
Conference Calendar New Listings International Workshop on Industrial Applications of Machine Vision and Machine Intelligence, Feb. 2-4, 1987. Roppongi. Tokyo,Japan. General Chairman: Prof. Masao Sakauchi. Institute of Industrial Science. University of Tokyo. 22-1, Roppongi 7-chome, Minato-ku. Tokyo 106. Japan, phone: 03-402-6231. ext: 2644. Fax: 03-402-5078. International Workshop on Industrial Automation Systems, Feb. 4-6, 1987. Roppongi, Tokyo,Japan. General Chairman: Mr. Tatsum Hasegawa. Fuchu Works. Toshiba Corporation, 1, Toshiba-choFuchu-shi,Tokyo, 183. Japan. 1987 IEEE International Conference on Robotics and Automation, March 30-April 3, 1987. Radisson Hotel and Civic Center, Raleigh, North Carolina. Four copies of papers should be sent by October l . 1986 to:
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the Program Chairman. Arthur C. Sanderson, The Robotics Institute. Carnegie-MelIon University. Schenley Park, Pittsburgh, PA 15213.
Third International Symposium on A p plication of Multivariable System Techniques, Apr. 13-15. 1987. Plymouth. United Kingdom. Contact: Rosamund da Gama. Institute of Measurement a n d Control. 87 Gower Street. London WClE 6AA. England, phone: 01 387 1949.
Massachusetts. Five copies of extended summary should be sent by March 30, 1987, to Dr. Victor K. L. Huang, AT&T Information Systems. Room 2K303, Crawford Corners Road. Holmdel. NJ 07733.USA, phone: (201) 949-0069. The General Chairman is Guy 0. Beale. Vanderbilt University, Box 1698, Station B. Nashville, TN 37235, phone: (615) 322-2212.
Conference on Decision and Control First International Conference on Computer Vision, June 8-1 1 . 1987. London. England. Fourcopies of complete drafts should be sent by December 15. 1986. to Cochair Azriel Rosenfeld, Center for Automation Research, University of Maryland. College Park. MD 20742. IECON'87, International Conference on Industrial Electronics Control and Instrumentation, Nov. 2-6. 1987. Cambridge.
: Dec. 9-11. 1987
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Los Angclcs. California General Chairman:
Prof. William Levine Dept. of Electrical Engg. University of Maryland College Park. MD 20742
Continued on pase 14.
