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242 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 25, NO. 2, APRIL 2000

written as

(1)

(2)

where is the control input (shaft torque). However, can be

measured by using a laser-Doppler velocimeter (LDV) system, aparticle image velocimeter (PIV) system, or an acoustic Dopplervelocimeter system for instance. In this paper, a state observerfor reconstruction of will be designed, that is, is treatedas an unmeasured state.

Healey et al.[12] have modified the models (1) and (2) todescribe overshoots in thrust which are typical in experimentaldata. Based on the results of Cody [6] and McLean [21], Healeyand co-workers propose a two-state model

(3)

(4)

(5)

(6)

Here is the shaft speed, is the axial flow velocity in thepropeller disc, and is the forward speed of the vehicle. Thiswas done by modeling a control volume of water around thepropeller as a mass-damper system. The mass-damper of thecontrol volume interacts with the vehicle speed dynamics whichalso represents a mass-dampersystem.

Originally, Healey et al.[12] considered a voltage-controlledmotor. However, as shown in Appendix A, the model represen-tation (3) can be used to describe:

motor (armature) voltage control; motor (armature) current control; motor torque control.

The different dc-motor control strategies are obtained bychoosing and according to Table II in Appendix A. Ex-perimental verifications of the one-state and two-state modelsare found in Whitcomb and Yoerger [28].

A more general model is the three-state propeller shaft speedmodel of Blanke et al. [3]:

(7)

(8)

(9)

(10)

(11)

where damping in surge is modeled as the sum of linearlaminar skin friction (see [8]) and nonlinear quadratic

drag (see [7]). Similarly, linear dampingis included in the axial flow model since quadratic damping

alone would give an unrealistic response at lowspeeds (zero quadratic damping at zero speed). However, thelinear skin friction gives exponential convergence to zero atlow speeds.

The ambient water velocity in (8) is computed by using

the steady-state condition

(12)

where is the wake fraction number(see [15]).In the following, the unmeasured state will be recon-

structed by using a nonlinear state observer. The objectiveis that propeller thrust and torque can becomputed for a time-varying , resulting in a more accurateand robust control scheme than conventional shaft speedcontrollers where this effect is neglected.

A. Propeller Losses

When designing a UUV control system, commanded forcesand moments must be realized by a propeller control systemusing a mapping from thrust demand to propeller revolution.This is a nontrivial task since a propeller in water suffers severalphenomena that cause thrust losses. The primary phenomenonaare the following.

Axial Water Inflow: Propeller losses caused by axial waterinflow, that is, the speed of the water going into the propeller.The axial flow velocity will in general differ from the speed ofthe vehicle. The dynamics of the propeller axial flow is usuallyneglected when designing the propeller shaft speed controller.This leads to thrust degradation since the computed thruster

force is a function of both the propeller shaft speed and axialflow. The magnitude of the axial flow velocity will strongly in-fluence the thrust at high speed so it is crucial for the propellerperformance.

Other effects that will reduce the propeller thrust were de-scribed by Srensen et al.[25] and references therein. Some ofthese effects are the following.

Cross-Coupling Drag: Water inflow perpendicular to thepropeller axis caused by current, vessel speed or jets from otherthrusters. This will introduce a force in the direction of theinflow due to deflection of the propeller race.

Air Suction: For heavily loaded propellers, ventilation (airsuction) caused by decreasing pressure on the propeller blades

may occur, especially when the submergence of the propellerbecomes small due to the vessel's wave frequency motion.In-and-Out-of-Water Effects: For extreme conditions with

large vessel motions, the in-and-out-of water effects will resultin a sudden drop of thrust and torque following a hysteresispattern.

ThrusterHull Interaction: Thrust reduction and changeof thrust direction may occur due to thrusterhull interactioncaused by frictional losses and pressure effects when thethruster race sweeps along the hull. The latter is the Coandaeffect (see [7, pp. 270272]).

ThrusterThruster Interaction: Thrusterthruster interac-tion caused by influence from the propeller race from one
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FOSSEN AND BLANKE: NONLINEAR OUTPUT FEEDBACK CONTROL OF UNDERWATER VEHICLE PROPELLERS 243

thruster on neighboring thrusters may lead to significant thrustreduction.

B. Contributions

The main contributions of the paper are a global exponentialstable (GES) nonlinear observer for estimation of axial flow ve-locity usingvessel speedand propeller revolution measurements(Theorem 1). In addition, a nonlinear output feedback propellershaft speed controller using feedback from the estimate of theaxial flow velocity (Theorem 2) is proven to be GES. This is,however, done under the weak assumption that the propellerrevolution and axial flow velocity have the same signs. If thisassumption is removed, the overall system will be semi-globalexponential stable.

The nonlinear shaft speed controller compensates for thrustlosses due to time variations in axial flow velocity and it isshown to provide superior thrust quality compared to conven-tional designs. Stability is provenin theframework of Lyapunovstability theory. The proposed output feedback controller is a

step towards the design of more sophisticated output feedbackshaft speed propeller controllers minimizing some of the pro-peller losses listed in the previous section.

C. Outline

The paper is outlined as follows. Section II briefly reviewsthe theory of propeller thrust and torque modeling. Section IIIdescribes the modeling of the underwater vehicle dynamics andthe axial flow dynamics of the propeller. In Section IV, a non-linear observer for axial flow velocity is proposed while SectionV contains a nonlinear output feedback controller for propellershaft speed using the observer. Section VI extends the results ofSection V to integral control. Section VII contains a case studywith a UUV driven by a single propeller and Section VIII con-tains concluding remarks.

II. PROPELLER THRUST AND TORQUE MODELLING

For a fixed pitch propeller, the shaft torque and force(thrust) depend on the forward speed of the vessel, theadvance speed (ambient water speed), and the propellerrate (see Fig. 1). In addition, other dynamic effects due tounsteady flows will influence the propeller thrust and torque.According to Newman [22], Breslin and Andersen [4], andCarlton [5], the following unsteady flow effects are significant:

air suction; cavitation; in-and-out-of-water effects (Wagner's effect); wave-influenced boundary layer effect; Kuessner effect (gust).

In this paper, we are considering a deeply submerged vesselimplying that the first four effects above can be neglected. TheKuessner effect, which is caused by a propeller in gust, will ap-pear as a rapidly oscillating thrust component. These fluctua-tions are usually small compared to the total thrust in a dynam-ical situation. In this paper, we will hence assume that this effectcanbe neglectedas well. We canthus approximate thethrust andtorque models with a quasi-steady representation. As a result,

Fig. 1. Definitions of axial flow velocity u , advance speed u , and vehiclespeed u .

we limit our discussion to quasi-steady thrust and torque mod-eling while a dynamic model for shaft speed , advance speed

, and surge velocity will be presentedUnsteady modeling is, however, an important topic for fu-

ture research since unsteady flow effects are significant in manypractical situations, in particular, for surface vessels. A more de-tailed discussion on the accuracy of unsteady and quasi-steadymodeling is found in [4, pp. 374386].

A. Quasi-Steady Thrust and Torque

Quasi-steady modeling of thrust and torque are usually donein terms ofliftand drag curves which are transformed to thrustand torque by using the angle of incidence. This approach hasbeen used by Healey et al. [12] and Whitcomb and Yoerger [28].

The lift and drag are usually represented as nondimensionalthrust and torque coefficients computed from self-propulsiontests (see [9] or [15]). The nondimensional thrust and torque

coefficients and are computed by measuring and. Moreover,

(13)

where is the propeller diameter, is the water density, and

(14)

is the advance ratio. The numerical expressions for andare found by open water tests, usually performed in a cavitationtunnel or a towing tank. These tests neglect the unsteady floweffects since steady-state values of and are used.

The nondimensional thrust and torque coefficients can alsobe described by the following parameters (see [24]):

(15)

(16)

where is the pitch ratio, is the expanded-area ratio,is the number of blades, is the Reynolds number, is
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ambient water velocity and vehicle speed in the steady state is(see [15])

(30)

where (typically 0.10.4) is denoted as the wake fractionnumber (see also [25]).

A. Determination of the UUV Model Parameters

The UUV model parameters can be found by using systemidentification (SI) methods (see [31]), for instance, hydrody-namic computation programs, semi-empirical methods, or en-gineering judgement. For a slender body, a first guess could be(see [9])

(31)

The damping coefficients can be found as

(32)

where is a design parameter(time constant insurge),is the drag coefficient, and is the cross-sectional area

in surge as defined by Morrison's equation (see [15]). Alter-natively, and can be found by performing a freedecay test (see [7]).

B. Determination of the Axial Flow Parameters

The mass and quadratic damping coefficientof the control volume can be treated as design parameters. Aguideline could be to choose (see [12] and [3])

(33)

where is the density of water, is the cross-sectional area ofthe thruster, is the length of the duct, and is an em-pirically determined added mass coefficient. For conventionalvehicles, .

Furthermore, the thrust deduction and wake fraction numbersare chosen as

typically

typically

while the linear damping coefficient is treated as adesign parameter

(34)

where is the time constant corresponding to the linearpart of the axial flow dynamics.

C. Resulting Model for Vehicle Speed and Propeller Axial

Flow Dynamics

When designing the nonlinear observer, the followingassumption for the nonlinear term is needed.

Assumption A1: Under normal operation of the vehicle, it isassumed that axial flow velocity and propeller revolution

have the same signs. This implies that.

Under Assumption A1, (25) and (28)(30) can be combinedto give

(35)

(36)

The measurement equation is

(37)

This can be written in state-space form according to

(38)

(39)

where , and

IV. NONLINEAR OBSERVER FOR ESTIMATION OF PROPELLERAXIAL VELOCITY

A nonlinear observer for shaft speed estimation and fault de-tection hasbeen proposed by Blanke et al. [2] under theassump-tion that the effect of the propeller axial inlet flow can be ne-glected. They have proven semi-global asymptotic and (local)exponential stability for the case with quadratic damping.

Nonlinear observers for underwater vehicles can also be de-signed by using contraction analysis as described by Lohmiller[17, pp. 3842] and Lohmiller and Slotine [18], [19]. This canbe related to the work of Lewis [16] where it is shown that theRiemann metric can be used as a tool for contraction analysisof nonautonomous nonlinear systems. Furthermore, combina-tion properties of contracting systems canbe exploited to designglobally convergent observer-controllers for shaft speed output
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Fig. 3. Block diagram showing the two control loops.

The two control loops are shown in Fig. 3, indicating how anonlinear shaft speed propeller controller together with a con-ventional UUV speed controller should exploit the estimate ofthe propeller axial flow velocity . It is also seen that this is anonlinear output feedback control problem. One solution to thiscontrol problem is to apply observer backstepping (see [14]).This will be discussed in the next section.

Experiments with different shaft speed control strategiesand position control of underwater vehicles are reported byTsukamoto et al. [26] and Whitcomb and Yoerger [29].

VI. NONLINEAR OUTPUT FEEDBACK CONTROL DESIGNIn this section, we will design a nonlinear output feedback

propeller controller using only surge speed measurements andpropeller revolution measurements . The axial flow velocity

will be estimated by the state estimator (40) and (41) whichwas proven to be GES under Assumption A1 (Theorem 1). Thedesign goal is to render the closed-loop error dynamics of theobserver-controller GES.

A. Nonlinear Model for Propeller Shaft Speed Control

Consider the unified dc-motor model (Appendix A)

(80)

which canbe used to describe motor voltage, current, andtorquecontrolled propellers. Substitutingtheexpression for given by(27) into (80) yields the third-order model

(81)

(82)

(83)

B. Lyapunov Analysis

The observer (40) is used to generate an estimate of .Consider the control Lyapunov function candidate

(84)

(85)

where is the tracking error. Substituting (81) into(85) yields

(86)

The expression for suggests that the control law shouldbe chosen to include three parts: 1) a nonlinear P-controller,

; 2) a nonlinear feedforward term based onthe measured propeller revolution and the desired propellerrevolution ; and 3) a nonlinear cross-termcompensating for the axial flow into the propeller. This is themain result of the paper.

Theorem 2 (GES Observer-Controller Error Dy-

namics): Consider the nonlinear shaft speed controller

(87)

with

(88)

Let the estimate be generated by using the nonlinear ob-server (40) and (41) with in Lemma 1 implying that
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must satisfy . Hence, the equilibriumpoint of the observer-controller error dy-namics

(89)

where and

is GES.Proof: Substituting (87) into (86) yields

(90)

Using the fact that

the cross term in (90) can be replaced by

(91)

implying that

(92)

Hence, according to Lyapunov stability theory, the equilibriumpoint of the observer-controller error dy-namics (89) is GES if and

.

VII. EXTENSIONS TO INTEGRAL CONTROL

When implementing the shaft speed propeller controller, it isimportant to include integral action in order to compensate fornonzero slowly-varying disturbances and unmodeled dynamics.

This can be done by augmenting a constant bias term to (80)according to

(93)

(94)

Choosing the nonlinear control law of PI-type with referencefeedforward and axial flow compensation, that is,

(95)

(96)

implies that (89) takes the form

(97)

(98)

with , and

(99)

(100)

(101)

where we have used that . The error dynamics(97) and (98) are a nonlinear nonautonomous system compli-cating the Lyapunov stability analysis since is onlynegative semi-definite. Hence, LaSalleKrazovskii's theoremfor invariant manifolds cannot be used (see [13]) to prove

uniformly globally asymptotic stability (UGAS). However,UGAS and uniformly locally exponentially stability (ULES)of the equilibrium point of the errordynamics (97) and (98) can be proven by applying the mainresult of Loria et al. [20] which is a theorem for backsteppingwith integral action (see also [11]).1

VIII. CASE STUDY

In the simulation study, the following two controllers werecompared.

1The interested reader is recommended to consult [11]and [20] for the tech-nicalities regarding the proof.
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TABLE IMODEL PARAMETERS

Nonlinear output feedback integral control where the non-linear observer (Theorem 1) was simulated by using thefollowing gains:

while the control gains in (Theorem 2) were chosen as

When simulating the observer-controller, it is noticed thatperformance improvements can be obtained by reducingthe controller gains, particularly if the measurements arenoisy. It is well known that the gain requirements imposedby the Lyapunov analysis are rather conservative. More-over, the closed-loop system can be exponential stable formuch smaller gains than those given by Theorem 2. Infact,we noticed that theperformancewas significantly im-

proved when was reduced by a factor of 10 and thisdid not affect the stability of the closed-loop system.

Conventional shaft speed control of PI-type:

(102)

with

For both controllers, the torque-controlled representation ofthe dc-motor (118) was used.

A. Model ParametersThe model parameters are given in Table I. The propeller

characteristics were taken from an experiment with a full-scalepropeller (see Fig. 4).

A least-squares curve fitting of and gave the fol-lowing results (straight lines in Fig. 4):

(103)

(104)

Even though this overall linear approximation is crude, in par-ticular, for reverse conditions , the observer is able to

Fig. 4. Experimental results for K and 1 0 K versus J (circles) andleast-squares fits to a straight line (solid lines).

cope with the model inaccuracies and give a useful estimate of.For simulation convenience, the values for and

were chosen equal to and which again were com-puted from the and mappings.

B. Discussion of Simulation Results

The control laws were simulated by commanding a referencethrust of (N) which was shifted to (N)

at (s) (see Fig. 6). The results form the simulation studycan be summarized according to the following.

Estimation of Axial Flow Velocity: Fig. 5 shows the perfor-mance of the nonlinear observer. Both estimation errors

and (upper plots) are zero mean whitenoise processes. Even thoughthe surge measurement andshaftspeed measurement are corrupted with white noise with am-plitudes 0.1 (m/s) and 0.1 (rps), and standard deviations of

in the simulation study, excellent convergence ofis obtained (lower left plot). The estimate is, however,

more noisy than its true value . This can be further improvedby tuning the observer gains. In addition, we see that we obtaingood filtering of the noisy signal (lower right plot).

Thrust Tracking Capabilities: From Fig. 6, it is seen that theoutput feedback integral controller has excellent thrust trackingcapabilities (lower plots) while an offset in thrustis observed for the PI-controller (see Fig. 7). The desired thrust

(N) is transformed to shaft speed reference signalsand by using (74) and (75). The offset in thrust for the

PI-controller is due to variations in axial flow velocity . Thisis seen by plotting the components

(105)

(106)

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(a)

(b)

Fig. 5. (a) Estimation errors ~u and ~u versus time. (b) Actual axial flow velocity u and measured surge speed u together with their estimates ^u and ^u versustime.

(a)

(b)

Fig. 6. (a) Thrust T and (b) torque Q for the nonlinear output feedback controller versus time.

together with the total thrust and torque. The PI-controller tracks (the term is

not available since is unknown when using a PI-controller)while the nonlinear output feedback integral controller uses the

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(a)

(b)

Fig. 7. (a) Thrust T and (b) torque Q for the PI-controller versus time. Notice the steady-state offset in thrust.

estimate to track the total thrust . Anotherbenefit of using the nonlinear observer in conjunction with anoutput feedback integral controller is that the estimate can beused to compute a more accurate shaft speed reference from

. This is seen from (74) where is needed.RPM Tracking Capabilities and Motor Torque Com-

mands: Figs. 8 and 9 show the shaft speed tracking perfor-mance for the two controllers and the corresponding motortorque commands (control inputs). Since the PI-controllerdoes not use model information, a high gain is needed inorder to obtain good shaft speed tracking capabilities. Thisresults in more noisy motor torque control signals than for themodel-based nonlinear output feedback integral controller. Itis also seen that the tracking performance for the nonlinearcontroller is better than the PI-controller mainly due to thecompensation of axial flow velocity effects.

IX. CONCLUSION

A high-performance nonlinear output feedback integral con-troller for propeller shaft speed was presented in this paper. Thecontrol law was designed by first designing a nonlinear observerfor the propeller axial flow velocity and next using observerbackstepping to produce a globally exponentially stable con-troller. The control law was also modified to include integralaction resulting in a uniformly globally asymptotically and uni-formly locally exponentially stable integral controller. The pro-posed output feedback controller was shown to be robust fordisturbances in propeller revolution and torque.

The case study was an unmanned underwater vehiclepropulsed with a single main propeller. The propeller wasassumed driven by a dc motor and a simulation study was usedto demonstrate the tracking capabilities of the observer and

controller. The observer was capable of producing accurateestimates of the advance speed. Hence, this estimate could beused to compensate the effect of axial flow velocity on the pro-peller thrust and torque. The estimate of the axial flow velocitycould also be used to compute more accurate set-points for thevehicle speed controller since the thrust commands could bemore accurately mapped to propeller revolution commands.

APPENDIX ADC-MOTOR DYNAMICS

Consider a dc motor (see [9])

(107)

(108)

where is the armature voltage, is the armature current,is the propeller revolution, and is the load from the propeller.In addition, is the armature inductance, is the armatureresistance, is the motor torque constant, and is the rotormoment of inertia.

Since the electrical time constant is small com-pared to the mechanical time constant, time scale separation
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(a) (b)

(c)

Fig. 8. Actual n and desired n (a) propeller revolutions, (b) tracking errors n 0 n , and (c) motor torque Q commands the nonlinear output feedback controllerversus time.

(a) (b)

(c)

Fig. 9. Actual n and desired n (a) propeller revolutions, (b) tracking errors n 0 n , and (c) motor torque Q commands for the PI-controller versus time.

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suggests

(109)

Hence, the shaft speed dynamics are given by

(110)

(111)

A. Motor Current Control

The motor current can be controlled by using a -controller

(112)

where is the desired motor current. From (110), we obtain

(113)

The motor dynamics (111) for the current controlled motortherefore take the form

(114)

If a high gain controller is used, this expressionsimplifies to

(115)

B. Motor Torque Control

For a dc motor, the motor torque will be proportional withthe motor current. Hence, the desired motor torque can bewritten as

(116)

From (114), we see that this yields the following dynamics fora torque controlled motor:

(117)

which reduces to

(118)

for .

C. Motor Voltage Control

Motor voltage control is obtained by combining (110) and(111) to yield

(119)

TABLE IIDC-MOTOR CONTROL MODEL

D. Unified DC-Motor Control Model

Based on the three models presented above, a unified controlmodel for the dc-motor shaft speed dynamics can be written as

(120)

where motor voltage, current, and torque control are obtainedby choosing the control input and linear damping coefficient

according to Table II.

ACKNOWLEDGMENT

The authors are grateful to Prof. K. Minsaas and Prof. A.J. Srensen at the Department of Marine Hydrodynamics, theNorwegian University of Science and Technology (NTNU), foruseful discussions on steady and unsteady flow effects for pro-pellers. In addition, K. Petter Lindegaard at the Department ofEngineering Cybernetics, NTNU, should be thanked for his dis-cussions on propeller modeling. Parts of this work were per-

formed while one of the authors, T. I. Fossen, visited the De-partment of Automatic Control, Aalborg University, Denmarkin the period JanuaryMarch 1999.

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IEEE/MTS Oceans'95, vol. 2, 1995, pp. 10191028.[28] L. L. Whitcomb and D. Yoerger, Development, comparison, and pre-

liminary experimental validationof nonlineardynamic thruster models,IEEE J. Oceanic Eng., vol. 24, pp. 481494, Oct. 1999.

[29] , Preliminary experiments in model-based thruster control for un-derwater vehicle position control, IEEE J. Oceanic Eng., vol. 24, pp.495506, Oct. 1999.

[30] D.R. Yoerger, J. G.Cooke, andJ.-J. E.Slotine,The influenceof thrusterdynamics on underwater vehicle behavior and their incorporation intocontrol system design, IEEE J. Oceanic Eng., vol. 15, pp. 167178,July 1991.

[31] W. W. Zhou and M. Blanke, Identification of a class of nonlinear state-space models using RPE techniques, IEEE Trans. Automat. Contr., vol.34, pp. 312316, 1989.

Thor I. Fossen (S88M91) was born in 1963 inNorway. He received the M.Sc. degree in naval ar-chitecture and the Ph.D. degree in engineering cyber-netics from the Norwegian University of Science andTechnology (NTNU), Trondheim, Norway, in 1987and 1991, respectively.

In the period 19891990, he pursued postgraduatestudies as a Fulbright Scholar in flight control at theDepartment of Aeronautics and Astronautics, Uni-

versity of Washington, Seattle. In May 1993, he wasappointed as a Professorin Guidance, Navigation andControl with the Department of Engineering Cybernetics at NTNU, where heis currently teaching ship and ROV control systems design, flight control, andnonlinear and adaptive control theory. He is also a Scientific Advisor for ABBIndustri AS, Marine Division and Marintek. In cooperation with ABB, he hasdeveloped a nonlinear dynamic positioning (DP) system for free-floating andmoored ships and a nonlinear and passive state estimator for marine vessels. Hehas also designed software for identification of ship dynamics from sea-trials.The most outstanding achievement is a weather optimal positioning controlfor marine vessels minimizing fuel consumption and emission of Co /NO(Patent NO-19985388). He is the designer of the SeaLaunch trim and heel cor-rection systems. SeaLaunch is a free-floating platform built by Boeing-Energia-Kvrner from which thefirstrocket waslaunced outside Hawaiiin March 1999.He is also the author of the book Guidance and Control of Ocean Vehicles (NewYork: Wiley, 1994) and the co-editor of the book New Directions in NonlinearObserver Design (London, U.K.: Springer-Verlag, 1999). He has authored more

than 100 scientific articles and book chapters on guidance, navigation, and con-trol. He has served as advisor to 11 Ph.D. students and over 80 M.Sc. students.Prof. Fossen is the Chair of the IEEE Oceanic Engineering/Control Systems

Joint Society Chapter of the Norway Section.

Mogens Blanke (S73M77SM85) was born in1947 in Copenhagen, Denmark. He received theM.Sc. and Ph.D. degrees in automatic control fromthe Technical University of Denmark (DTU) in 1974and 1982, respectively.

He was a systems analyst at the European SpaceAgency in the Netherlands during 197576, then As-sistant and later Associate Professor of Control En-gineering at DTU from 1976 to 1985. He was headof the Marine Division of the Automation Company

Sren T. Lyngs A/S from 1985 until 1990, where hismain activities included total ship integrated control and diesel engine control.He has been Professor of Control Systems at Aalborg University, Aalborg, Den-mark, since 1990, where he started the research group in autonomous systemsand fault-tolerant control. The group's most visible achievement was the au-tonomous attitude control system for the first Danish satellite, which has beenin orbit since early 1999. His research interests include identification and con-trol of continuous, nonlinear systems, estimation and fault detection, and de-sign methods for fault-tolerant control. His personal application interests in-clude spacecraft attitude control, automatic steering and rudder-roll dampingfor ships, and control systems for ship propulsion. He is active in the Interna-tional Federation of Automatic Control (IFAC). He initiated the IFAC WorkingGroup on Marine Systems in 1986, chaired this and the later technical commit-tees, and is presently a member of the IFAC Council.

Prof. Blanke received the Radio Parts Award in 1985, the Esso Price in 1986and, jointly with the satellite control team in Aalborg, the Aalborg City Spring-time Award in 1999.

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