Auv Controllability With Control Plane Faults

7/29/2019 Auv Controllability With Control Plane Faults

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Royal Institution of Naval Architects

International Journal of Maritime Engineering

AUV CONTROLLABILITY WITH CONTROL PLANE FAULTS

D Perrault, DRDC-Atlantic, Canada, N Bose and S O'Young, Memorial University, Canada, andD Williams, Institute for Marine Dynamics, Canada.

SUMMARY

It may be important to be able to operate an autonomous underwater vehicle (AUV) when it has reduced controlauthority due to a control plane fault, such as a jammed or a missing control plane. Knowledge of how the vehiclebehaves under these conditions will allow the mission planner to make critical decisions about the viability of themission or about certain specific subtasks. Knowledge of vehicle behaviours under fault conditions can also facilitate theuse of operational envelopes in restricted waters; i.e. a healthy AUV may be restricted in the magnitude of control plane

deflections, so that it can maintain a safe trajectory even if a control plane fails. A systematic study was made involvingsimulations of the vehicle under fault conditions to identify the vehicle behaviours typical of such fault conditions. Thesimulation tool used is a linear model developed from a fully nonlinear model of the Canadian Self-Contained Off-the-shelf Underwater Testbed (C-SCOUT), and the manoeuvres used were those most likely to be desired during normaloperation: holding course, a controlled dive, and a turn in the horizontal plane.

The fault condition simulations provide useful information, especially concerning safe operating envelopes for the C-SCOUT for particular mission requirements. The information can also be used to enable the vehicle to perform self-diagnosis procedures under some conditions.

NOMENCLATURE

x , y , z Vehicle position co-ordinates with respect

to an Earth-fixed reference system.

, , Vehicle orientation angles roll, pitch, yaw

respectively.x& , y& , z& Vehicle translational velocity (surge, sway,

heave respectively) described in the Earth-fixed reference frame.

& , & , & Vehicle rotational velocity (roll, pitch, yaw

respectively) described in the Earth-fixedreference frame.

u, v, w Vehicle translational velocity (surge, sway,

heave respectively) described in the(vehicle) body-fixed reference frame.

p, q, r Vehicle rotational velocity (roll, pitch, yawrespectively) described in the (vehicle)

body-fixed reference frame.CB Center of buoyancy.

CE Center of effort (point of application of hulllift and drag).

CG Center of gravity (a.k.a. CM center of mass).

CP Center of pressure (point of application of control plane lift and drag).

ak , e

k , rk Gains of the roll controllers using all control

planes, elevators (horizontal planes), and

rudders (vertical planes) respectively.

zk Gain for depth controller.

1 INTRODUCTIONAutonomous underwater vehicles (AUV) are rapidlybecoming useful and versatile tools for offshoreengineering. In order for AUV to be firmly established asa viable, mature technology there are several issues that

need to be addressed, not the least of which is reliability.

It may not always be economically or physically possibleto abort the mission and recover the vehicle when a faultoccurs, and, in most cases, it would be better to be able toaccomplish at least some subset of the mission

objectives. It is also useful to have a means ofdetermining the nature of the fault.

Since it may be necessary to operate the vehicle when ithas reduced control authority due to a control plane fault,such as a jammed or a missing control plane, knowledge

of how the vehicle behaves under these conditions isimportant. It will allow the mission planner to makecritical decisions about the viability of the mission orabout certain specific subtasks. Knowledge of vehiclebehaviours under fault conditions can also facilitate theuse of operational envelopes in restricted waters; i.e. ahealthy AUV may be restricted in the magnitude of

control plane deflections, so that it can maintain a safetrajectory even if a control plane fails.

This paper describes the effects of actuator faultconditions on vehicle behaviour. A systematic study wasmade involving simulations of the vehicle under fault

conditions to identify the vehicle behaviours typical ofsuch fault conditions. The simulation tool used is a linearmodel of the C-SCOUT, and the manoeuvres used were


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those most likely to be desired during normal operation:

holding course, a controlled dive, and a turn in thehorizontal plane.

2 C-SCOUT: THE REAL AND THE VIRTUALThe Institute for Marine Dynamics (IMD) of the NationalResearch Council (NRC) Canada and the OceanEngineering Research Centre (OERC) of MemorialUniversity of Newfoundland (MUN) began acollaborative effort in September of 1998 to design astreamlined autonomous underwater vehicle (AUV), the

Canadian Self-Contained Off-the-shelf UnderwaterTestbed (C-SCOUT). The construction of the vehiclewas greatly aided by the Instrumentation, Control andAutomation Centre (INCA) at MUN.

2.1 THE PHYSICAL VEHICLEThe C-SCOUT vehicle was designed and built bygraduate students at Memorial University ofNewfoundland, by work term students employed by IMDand OERC, and by IMD and MUN technical personnel[1]. The AUV is part of the Natural Sciences and

Engineering Research Council (NSERC) StrategicProject: Offshore Environmental Engineering usingAutonomous Underwater Vehicles which involves anumber of research and industrial partners includingMUN, IMD, C-CORE, the University of Victoria, Petro-Canada, International Submarine Engineering (ISE) Ltd.,and Geo-Resources [2].

C-SCOUT is typical of many vehicles active in the worldtoday; it is a hydrodynamically streamlined, axi-symmetric1, slender body using control planes fordirectional control. It is atypical in that the after controlplanes are mounted on the parallel mid-body rather than

on the tail section. This allows greater variation of theconfiguration of the vehicle, i.e. different tail sectionsand main propulsors may be used without redesigningthe control plane section. The elliptical nose and cubicspline tail section (designed to increase the inflow to thepropulsor) are also somewhat distinctive.

To date, the first vehicle (see Figure 1) has been built andis currently undergoing systems validation. A second hullhas been fabricated [3] for full-scale hydrodynamicexperiments. The second hull has already been used fortesting a novel propulsion scheme (a cyclic-pitch

propeller) for low speed directional control withoutcontrol planes or through-body thrusters [4]. It has alsobeen used to test flow conditions for through-bodythrusters [5].

1The vehicle is axi-symmetric in terms of geometry (and

thus in terms if volume of water displaced), but it is notasi-symmetric in terms of mass distribution. This hassignificant effects on the vehicles stability and motion.

y

z

xCGCB

CE

CP

Figure 1. Base Configuration C-SCOUT AUV withReference Axes

2.2 THE VIRTUAL VEHICLEIn conjunction with the physical vehicle, a computermodel was developed to test ideas and algorithms beforecommitting them to hardware. The nonlinear computermodel and the linearized model formulated from it were

developed in MatlabTM

/SimulinkTM

[6].

2.2.1 The Nonlinear ModelThe nonlinear model of the C-SCOUT is based on

Newton-Euler equations of motion, which equates thechanges in linear and angular momentum to the

externally applied forces and moments on the body. On

the assumption that the vehicle behaves as a perfectlyrigid body, the quantities defining the rate of change ofmomentum in each degree of freedom (DOF) can be

determined exactly, algebraically. The external forcesand moments, however, by their nature are somewhat

uncertain. They include the following types of forces(and the associated moments):

F= FS + FI + FR+ FC + FE

where

FS - Static (hydrostatic) forces - weight and buoyancy

FI- Ideal fluid forces Added MassFR- Real fluid forces DampingFC - Control forcesFE - Environmental forces - waves, current, etc .

For the present the environmental forces, FE, are assumed

to be zero, since the preliminary testing of C-SCOUTwill be in calm water.

Each set of forces and moments may be analyzedseparately, and the results superimposed. Buoyancy andgravity can be solved at each instant of time by purely

analytical means. The added mass values used in the

nonlinear model are assumed to be constant (therefore,the vehicle is assumed to be deeply submerged), and


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are determined off-line by a separate computer program -

Estimate Submarine Added Masses (ESAM) developedby George Watt of Canada's Defence ResearchEstablishment Atlantic (DREA) [7]. The excitationforces due to viscous effects are formulated in terms of

lift and drag equations applied to each of the components

of the vehicle, i.e. to the hull and the control planes. Theresulting forces and moments are summed together toprovide the forcing function applied to the vehicle. Thismethod is called the body build-up technique [8] or thecomponent build-up method [9]. The advantage here isthat these forces can, for the most part, be determinedanalytically, and therefore provide a quick answer

without excessive computational effort.

2.2.2 THE LINEAR MODELA linear model can be developed from the nonlinearmodel by perturbing the nonlinear model by a small

amount, , from some given equilibrium state, X , suchthat the rate of change of force (or moment) with respectto the parameter perturbed may be determined, e.g.,

-u

X XXX

=

This process was followed to obtain the velocitydependent derivatives for the linear model of C-SCOUT.The added masses from ESAM were used for theacceleration dependent derivatives.

The standard form for a state-space model is:

x=Ax+Bu

y=Cx+Du

&

In order to achieve this format, the gravity-buoyancyeffects (FS) must be included in the A matrix, since theyare vital to the correct solution. In order to include themthe state vector is augmented

x = [u v w p q r]T

and the dynamic equations are augmented by two

kinematic equations to keep the A matrix square,facilitating linear analysis.

The equilibrium condition used is straight and level flightat 3 m/s. All the simulations were performed for thisspeed.

3 VEHICLE RESPONSE WITH CONTROLPLANE FAULTS

3.1 CONTROL AUTHORITYStability and manoeuvreability are conflicting

requirements for any vehicle. For a vehicle to hold a

stable course, it must be able to reject any kind of force

that would cause it to deviate from that course. On theother hand, for a vehicle to be manoeuvreable, it must beable to change course quickly. One of the key elementsof control plane design (size, shape, and location) is to

find an applicable balance between these two

requirements. The measure of the ability of the controlplanes to affect change in the vehicle direction is referredto as the control authority of the control plane. The finstaken together (with the propulsor) form the total controlauthority for the base configuration of C-SCOUT. If theability of one or more of the control planes to take up thecommanded deflection angle is impaired, the process of

diving or turning may be adversely affected. The controlauthority of that fin, and indeed the vehicle, is reduced.

3.2 SCOPE OF THE STUDY3.2.1 Types of FaultsFault conditions that can occur in operation run frompower loss to programming errors to mechanicaldifficulties. This study is focused on hardware rather thansoftware problems, though there is much overlap in theeffects of various fault conditions. Hardware faultsinclude such things as degradation or loss of propulsion,

which would have major impact on the motion ofvehicles like the C-SCOUT, since these types of vehiclesare entirely dependent on the propulsor not only forattaining motion, but for facilitating directional control aswell. Other major faults involve the jamming of controlplanes, which may occur due to an electrical or

mechanical defect, or due to operational hazards such asbeing fouled with seaweed, etc. It is even possible to losea control plane if it gets snagged, or is involved with animpact with some other body. There are many othertypes of fault conditions possible during the course ofoperation of an AUV, but this study was limited to

jammed and missing control planes. Further it waslimited to single-point failures that represent a reductionin, but not a loss of, the vehicles control authority.Specifically, two types of faults were investigated:

One control plane missing; and

One control plane jammed.

3.2.2 General Simulation ProcedureThe series of simulations included three basicmanoeuvres common to AUV missions: holding course,diving (in this case a 100 m descent), and turning (here astarboard turn through 180). To understand the effects of

control plane fault conditions, it is necessary to reviewthe behaviour of the vehicle in its nominal, healthystate. Then the vehicle behaviour in the presence ofjammed control plane conditions, and its behaviour in theabsence of a control plane can be examined with some

context.


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3.2.3 Symmetry of Manoeuvres and Symmetry ofFault Conditions

Both dives and holding course (holding both heading and

depth) are manoeuvres in the x-z plane of the inertial

reference frame. Assuming the vehicle starts (and ends)the manoeuvre in straight and level flight (i.e., the body-fixed heave axis is parallel to the inertial z-axis), thisplane is also the plane of symmetry of a vehicle like C-SCOUT. Vehicle response reflects this symmetry. Sincethe vehicle is not symmetric about the x-y plane of thebody-fixed reference axes2 (even when the body-fixed

heave axis is parallel to the inertial z-axis), the vehicleresponse is not expected be symmetric in the horizontalplane. The fault condition simulations show that, forholding course and diving manoeuvres, the following aretrue:

Symmetry condition 1: vehicle response with ajammed starboard control plane is similar tovehicle response with a jammed port control plane

for any given angle of jam, the major differencebeing the direction of heading error induced;

Symmetry condition 2: vehicle response with theupper (or lower) control plane jammed at apositive deflection angle is similar to vehicleresponse with the upper (or lower) control planejammed at the same magnitude of negativedeflection angle, with the direction of inducedheading error again the major difference;

Asymmetry condition 1: vehicle response with ajammed upper control plane is not necessarily

similar to vehicle response with a jammed lowercontrol plane for comparable angles of jam

3; and

Asymmetry condition 2: vehicle response with thestarboard (or port) control plane jammed at apositive deflection angle is not necessarily similarto vehicle response with the starboard (or port)control plane jammed at the same magnitude ofnegative deflection angle.

The turning manoeuvre, on the other hand is not in theplane of symmetry, and while the asymmetry conditionshold, the two symmetry conditions do not necessarilyapply; there may be significant differences in response

2 The body-fixed reference axis has its origin at thecenter of gravity (CG; a.k.a. center of mass), which is

below the center of buoyancy (CB); the latter centerbeing on the axis of symmetry of the vehicle.

3 The distance from the center of mass (CG) to the centerof pressure of the upper control plane is greater than the

distance from the center of mass to the center of pressureof the lower control plane, due to the CG being below theCB.

between the port and starboard jam conditions. In thecase investigated here (a 180 turn to starboard), thestarboard fin is inboard, while the port fin is outboard.The reverse occurs for a turn to port, and the responses

outlined below for each of these fins would be reversed;

i.e. the responses for a jammed starboard fin during aturn to starboard should be similar to the vehicleresponse when the port control plane is jammed (at thesame angle) during a turn to port, since each is theinboard control plane in their respective manoeuvres.The same asymmetry is applicable to the sign of upper orlower control plane deflection angles. For example, the

vehicle response in a turn to a particular side at a givenrudder deflection angle, for a positive angle of jam on theupper control plane will not be similar to the response ina turn to the same side when the upper control plane isjammed at an equivalent (in magnitude) negativedeflection angle. However, the response to the upper fin

positive-deflection-angle jam during a turn to starboardshould be similar to the equivalent upper fin negative-deflection-angle jam during a turn to port.

3.2.4 Specifics of the Simulation ProcedureA series of simulations that included various faultconditions were performed. The vehicle was assumed tobe in the fault condition at the start of the simulation, andthe dive and turn manoeuvres were initiated well after thestart of the run. Note that in all the plots that follow, thestarting position of the vehicle is (0,0) in both thehorizontal (x-y) and vertical (x-z) planes. All the

simulations used the linear model of the C-SCOUT withthe dynamics corresponding to straight and level flight at3 m/s.

3.2.4.1 Roll Compensation And Depth Control Gain.The simulations were performed using closed-loop(proportional) control for the heading, depth, and roll.The individual control plane deflections (after starboard,after port, after upper, and after lower, respectively) werecommanded as follows:

( ) ( )

( ) ( )

( ) ( )

( ) ( )

int int

int int

int int

int int

a

a

a

a

as z setpo actual e setpo actual

ap z setpo actual e setpo actual

au setpo actual r setpo actual

al setpo actual r setpo actual

k z z k k

k z z k k

k k k

k k k

= +

=

=

= +

(Equations 1)

For the horizontal control planes a positive deflectionmeans trailing edge down, while for the vertical controlplanes, a positive deflection means trailing edge to port.In either case, a positive deflection of the control planepair will result in a negative moment on the vehicle -

negative pitch (nose down) for the horizontal pair, andnegative yaw (nose to port) for the vertical pair.


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3.2.5 Role of RollRoll dynamics are (theoretically) only relevant formanoeuvres in the horizontal plane; motion purely in thevertical plane should not induce any roll because of the

symmetry of the vehicle about the x-z (vertical) plane

(both the center of buoyancy, CB, and the center ofgravity, CG, are in the vertical centerplane of the vehicle,but only the center of buoyancy is in the horizontalcenterplane see Figure 2). The horizontal fins(actuators for control in the vertical plane) can be used tocause roll or to compensate for roll caused by some othereffect. Since roll is usually undesirable, the horizontal

control planes are more apt to be used to compensate forroll than to cause it. The vertical fins (actuators forcontrol in the horizontal plane) can also be used to causeroll or to compensate for roll induced by other forcesacting on the AUV. Although roll is not desirable, whenthe vertical fins are used, they tend to cause a roll

moment because of the asymmetry about the horizontal(x-y) plane, i.e. the distance from the center of mass tothe center of pressure of the upper control plane isgreater than the distance from the center of mass to thecenter of pressure of the lower control plane. When aturn is the desired manoeuvre, the hydrodynamic forces

in the horizontal plane induce a roll moment on thevehicle, leading to a pitch and depth excursion.

4

If roll can be eliminated, or at least, minimized, thereshould be a forced decoupling between horizontal andvertical manoeuvres, such that there is no change indepth when the desired motion is a turn. Further, since a

fault condition on any single control plane is likely toinduce a roll motion, controlling the roll motion may bekey to ensuring reliable motion characteristics even whensuch faults occur.

For each of the three manoeuvres a simulation was

performed for four modes of roll compensation:

1. No active roll compensation (i.e. only the passiveroll stability effects). Passive roll stability isprovided by the vertical distance between the

4

The asymmetry about the horizontal (x-y) planesuggests that it may be possible to pre-compensate (aform of feed-forward) for this roll effect by using theratio of moment arms to the upper and lower fin centersof pressure to allocate the rudder deflections. Howeverwhen this kind of compensation is implemented, thevehicle responded with a greater depth excursion in aturn; i.e. the roll is prevented but there is a greater change

in depth. To negate the roll induced by the asymmetry ofthe vertical control planes about the surge axis (the x-axisof the body-fixed reference frame), a greater lift force isrequired on the lower control plane, which has theshorter moment arm. The increase in depth excursion is a

result of the increased drag force on the lower controlplane as it deflects more in order to produce a greater liftforce.

Buoyant Force Buoyant Force

Weight Weight

Righting

Moment

CB

CG

CB

CG

z

y

z

y

Figure 2. Passive Stability

center of buoyancy (the buoyant force acting

through the center of the volume from which

water is displaced see Figure 2) and the center ofmass (or gravity, where the weight of the vehicleacts). When the vehicle is upright, the forces of

buoyancy and weight have a common line ofaction, but opposite directions, and for a neutrallybuoyant vehicle, they cancel each other. When thevehicle rolls, the lines of action of these two forcesare no longer collinear, and a righting moment isproduced which will tend to return the vehicleback to the upright position (see Figure 2). The

lack of active roll compensation was implemented

by settinga

k to zero in Equations 1).

2. Active roll compensation via elevators (starboardand port horizontal control planes). Here adifferential deflection of the horizontal controlplanes will actively force the vehicle back to the

upright position; e.g., a positive deflection of theport plane and a negative deflection of the starboardplane will generate a positive roll moment on thevehicle. This form of active roll compensation was

accomplished by settinga

k to unity and rk to zero

in Equations 1).

3. Active roll compensation via rudders (upper andlower vertical control planes). This type of activeroll compensation was implemented

by settinga

k to unity and ek to zero in Equations

1).

4. Active roll compensation via all control planes. Herethe roll compensation was performed by setting both

rk and ek to unity in Equations 1).

In each case wherea

k , rk and ek were not being

used as a filter mechanism (i.e. set to unity or zero), thegain value was the same, 0.0148.


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In addition, each of these cases was further simulated at

two values of depth controller gain. In the vertical plane,the gravity-buoyancy couple acts as a restoring moment,making the vehicle response very similar to a first-ordersystem, where the magnitude of the controller gain can

cause the system to exhibit an overdamped (no

overshoots) response or an underdamped (overshootspresent) response in depth. The former response wasachieved by setting the depth controller gain to kz = 0.01,while the latter response was accomplished with a depthcontroller gain of 0.07.

The need for two values of proportional gain for the

depth controller was made apparent by the vehiclesimulation results. The vehicle motion characteristics(with jammed fins) were much better with theunderdamped controller (higher gain), as might beexpected. However, the vehicle response was unstablewith the higher gain when the vehicle was missing a

control plane; the response could be made stable by usingthe lower control gain. As a consequence, all thesimulations of jammed control plane conditions wereperformed with kz = 0.07, and all the simulationsinvolving missing fins were performed with kz = 0.01.

3.3 VEHICLE MOTION SIMULATIONRESULTS

3.3.1 Hold CourseTo hold course, the vehicle must maintain depth and

heading in the face of any environmental disturbance.This is a regulator problem. Any controller that is robust

to actuator faults such as jams and control plane lossesmust be able to hold course even when the faults are

present. There should be no roll in this type of motionunless there is a disturbance. For the vehicle to hold itscourse (and speed), all rates except the surge velocity(i.e., forward speed) should be zero. In terms of the

velocity parameters described in the body frame, thismeans

v w p q r 0= = = = =

and u is a constant. In terms of the velocity parametersdescribed in the inertial frame, it means

0z z = = = = =& & &&

The values ofx& and y& are constant, therefore x and y

will vary linearly with time, however the heading angle,

, will be constant. There may be some small angle of

roll () and/or pitch () to balance some external forceor moment, but these angles should not result in changesto the heading or depth.

3.3.1.1 Nominal (no-fault) Behaviour for HoldingCourse

The vehicle response under all modes of rollcompensation is identical since no roll was induced on

the vehicle. In all cases the vehicle proceeded with no

heading error and negligible depth error.

3.3.1.2 Holding Course with Jammed Control PlanesA control plane that is jammed at some non-zero anglewill tend to cause the vehicle to roll. When the oppositecontrol plane is used as the sole means of compensating

for the induced roll, there is a limit to the amount of jamangle that can be compensated for. At large angles (e.g. -

25), the opposite fin will have to match the angle thejammed fin is at in order to compensate for the inducedroll, but it will then be required to be active in depth orheading control. It will have insufficient control authority

to accomplish both functions at the same time. Forexample, when the operational port control plane is usedby itself to compensate for the starboard control plane

jammed at -25, the port plane is unable to providesatisfactory roll compensation while at the same time

maintaining good depth control (see Figure 3, where thetop graph shows the projection of the vehicle track ontothe x-y plane the horizontal plane motion; and thebottom graph shows the projection of the vehicle track

onto the x-z plane the vertical plane motion). When theoperational pair of control planes is used either alone or

in conjunction with the functional opposite fin (i.e. allavailable control planes are used), the vehicle response is

more acceptable, since the control authority requirementsare more easily met (see Figure 4, where the deflection inradians of each control plane is shown as a time series).Simulations show, however, that for this manoeuvre,

vehicle response with active roll compensationimplemented is at best only marginally better than theresponse without it (see Figure 3).

Roll compensation can, in some circumstances, haveadverse effects on the vehicle behaviour. When holding

course, the vehicle response is severely degraded, evenwhen roll compensation via all the control planes is used,if the lower control plane is jammed at large deflection

angles (see Figure 5, where it can be seen that the bestvehicle response is achieved when no active roll

compensation is used). At lower angles of jam, however,the vehicle response for the lower plane jams and theupper plane jams, is similar.

3.3.1.3 Holding Course with Missing Control PlanesFor the cases of missing control planes, active rollcompensation does not significantly improve the vehicleresponse for holding course. When either the upper or thelower control plane is missing, there is no induced rolland the vehicle has the same response while holding

course with or without active roll compensation. Thevehicle response is very similar to that of the nominal


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(healthy) vehicle. This result assumes that whatever the

cause of the missing control plane, the vehicle remainssymmetrical about the x-z plane. This is somewhatunlikely in the context of a real loss of the control plane.When either the port or starboard control plane is

missing, the errors in heading and depth are small even

when no active roll compensation is used (see Figure 6).The only real problem during this manoeuvre is theunequal drag due to the missing fin, but the fin drag issmall in comparison with hull drag, so the vehicle is wellable to maintain its depth and heading.

3.3.2 DIVEDiving is a manoeuvre in the x-z plane of the vehicle.Since the vehicle is symmetric about this plane, there isno cross-coupling into other DOF; i.e., no induced roll,yaw, or sway. The motions involved are surge, heave andpitch only. At the end of the dive manoeuvre, the depth,

z, should have a new, constant value (z0 +100 m),otherwise the vehicle velocity and position variablesshould be as described under Hold (Course). In thesimulations, z0 is zero even though the vehicle isassumed to be deeply submerged even at the start, thoughstrictly speaking, the 100 m dive represents a z from the

nominal depth, z0 0.Because of the different response expected in thehorizontal plane (i.e. no deviation in course) and in the

vertical plane (i.e. a controlled change in depth), it ispractical to talk about the effects of a jammed or missinghorizontal control plane separately from the effects of ajammed or missing vertical plane.

3.3.2.1 Nominal (No-Fault) Behaviour for Diving.Simulations of the fully actuated vehicle responseshowed (as expected) that no roll was induced, thereforethere were no parasitic motions even without active roll

compensation. The vehicle response under all modes ofroll compensation is identical during the diving

manoeuvre.

3.3.2.2 Diving with Jammed Control PlanesVehicle response in terms of heading, in dives with one

of the vertical control planes jammed is similar to thevehicle heading response when attempting to hold coursewith a jammed vertical plane. The active rollcompensation methods implemented tend to make theoverall vehicle response worse. In fact, only thecontroller without active roll compensation results in thevehicle achieving the dive without a large heading error

(see Figure 7). At large angles of jam a jammed lowercontrol plane has a more detrimental effect than ajammed upper fin. When the jam angle is smaller, thevehicle response is similar whether the upper or thelower control plane is jammed. The vehicle responsewhen the jam angle is 0 is like that of the fault-free

vehicle.

None of the compensation methods were effective in the

dive manoeuvre at high negative angles (e.g. 25) of

horizontal control plane jam. The negatively jammedplane will try to cause the vehicle to pitch nose-up andrise, working against the dive command. The dive was

not achieved with or without active roll compensation

(see Figure 8).

At lower jam angles the dive was achieved, except whenthe roll compensation via elevators alone wasimplemented (see Figure 9). Even at a jam angle of 0,the control authority of the one remaining horizontalcontrol plane is insufficient to achieve the commanded

depth change in a reasonable amount of time. Indeed,when the angle of jam is positive 25

, and therefore

aiding the dive, the controller with roll compensation viaelevators alone is unable to stop the descent since theremaining horizontal fin has insufficient controlauthority.

The best overall control in this instance is that using rollcompensation via rudders, but the response is onlyslightly better than that for roll compensation via allplanes, while the vehicle response when no active rollcompensation is used has a small offset in sway. If the

offset can be lived with, active roll compensation wouldbe unnecessary for acceptable vehicle response with ajammed horizontal control plane.

3.3.2.3 Diving with Missing Control PlanesThe vehicle response in dive is very similar to that of the

nominal (healthy) vehicle when either the upper or thelower control plane is missing; there is no induced rolland the vehicle has the same response with or withoutactive roll compensation.

When either of the horizontal planes is missing, roll

compensation via the rudders or all the (remaining)control planes gives better vehicle response in dive thancontrol without active roll compensation, since theyreduce the heading error (sway offset - see Figure 10).Roll compensation via the elevators is, understandably,inadequate.

3.3.3 TurnIt is desired that the turn be accomplished in the

horizontal (x-y) plane. Because of the asymmetry aboutthe x-y plane of the body reference axes, however, theforces that cause the turn also induce a roll angle and apitch angle on the vehicle.

At the end of the turn, the heading, , should have a

new, constant value ( 0 +180). Otherwise the vehicle

velocity and position variables should be as described

under Hold (Course). In the simulations, 0 is zero.


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In general, the vehicle response will be different for

similar faults on each control plane. The effects of a faultto the upper fin can be expected to differ from a similarfault on the lower fin due to the asymmetry of the vehicleabout the horizontal plane. The effects of a fault on the

starboard fin will be different from those of a fault on the

port plane because of the asymmetry of the manoeuvre:one plane (starboard in this case) will be inboard of theturn, while the other (port here) will be outboard.

3.3.3.1 Nominal (No-Fault) Behaviour for TurningIn the starboard turn through 180, a roll angle was

induced on the vehicle and a change in depth occurred.Using the rudders to affect roll compensation did reducethe roll angle, but increased the depth excursion (seeFigure 11 where the vehicle starts off moving in thepositive x-direction then almost immediately turnsthrough 180 and continues on in the negative x-

direction). Roll compensation via the elevators or via allcontrol planes working together reduced both the rollangle and the depth change. However, with no active rollcompensation, the depth excursion is less than 1% of thedistance traveled. Therefore, compensation is not reallyrequired for the healthy vehicle even in turns. The

vehicle response with the underdamped (kz = 0.07) depthcontroller was very similar to the vehicle response withthe overdamped (kz = 0.01) depth controller, except thatthe depth was better controlled (less steady state error),as expected (see Figure 12). Note that the higher gaindoes mean overshoots are present in the transientresponse.

3.3.3.2 Turning with Jammed Control PlanesVehicle response in a turn using compensation via

elevators (whether alone or in conjunction with thevertical planes) is unacceptable when the inboard fin

(starboard in this case) is jammed at large angles ( 25);

the vehicle does not achieve the turn. The response forcontrol with compensation via the rudders is best, since itreduces the drift in depth that occurs when no active rollcompensation is used (see Figure 13).

When the outboard (port in this case) control plane is

jammed at large angles ( 25), the best response isprovided by the controller using all planes for rollcompensation, while compensation using the ruddersalone tends to turn the vehicle more than desired and toinduce a drift in depth (compare Figure 13 and Figure14). Control with compensation via the rudders is

unacceptable for large-angle jams on the outboardcontrol plane, while it is preferred for large-angle jamson the inboard control plane.

The vehicle response for jams at zero degrees for eitherhorizontal control plane is similar, as might be expected

since nominally both fins would be near zero deflectionin a turn, anyway.

When either vertical control plane is jammed at -25 , the

vehicle will turn past 180

(see Figure 15). When theupper or lower control plane is jammed at 25 , thevehicle will not achieve 180

. Active roll compensation

via the elevators or all (remaining) control planes will

help the vehicle achieve the correct amount of turn, while

keeping the depth excursion small, if the upper controlplane is the problem. When the lower control plane isjammed, none of the roll compensation methods providesacceptable vehicle behaviour; the turn is not achieved(see Figure 16).

The controller with no active roll compensation gives a

reasonable response if the upper control plane is jammedat zero degrees (see Figure 17). The vehicle responsewith the lower control plane jammed at zero degrees issimilar to that with the upper control plane jammed at

zero. In fact, the responses for jams at 10 are similar

for the upper and lower control planes; it is only at the

higher angles of jam that there are significant differencesin the vehicle response.

3.3.3.3 Turning with Missing Control PlanesThe vehicle response in turns while one of the horizontalcontrol planes was missing was best when roll

compensation via rudders was used, but the response wasonly slightly better (less heading error) than the response

without active roll compensation (see Figure 18). Theresponse with the port plane missing was similar to thatwith the starboard control plane missing.

In the cases of the vertical control planes missing duringturns, the integrator was unable to resolve the model, and

no data is available.

3.4 OPERATIONAL ENVELOPES3.4.1 Safety ContextManned submarines can have two basic hazards:flooding, and depth excursions such as may be caused bya jammed control plane. In both cases, the recoveryprocedure involves ascending.

In the case of an AUV, the risk to human occupants doesnot exist, but it is desirable to be able to recover thevehicle. Vehicles like the C-SCOUT have an EmergencyResponse System (ERS) of one form or another. C-SCOUT's ERS will include a releasable ballast. C-SCOUT is also free-flooding except for the pressurevessel and the control plane actuator motor housings. If

the pressure vessel floods, the electronics will shut downand the ERS will automatically release the ballast,bringing the vehicle to the surface rapidly.

If one of the actuator motor housings floods, the controlplane would most likely jam.


9/15


The baseline C-SCOUT has only one set of horizontal

control planes. Recovery from a jammed horizontal planeshould involve reduction in speed to avoid large depthexcursions. Restrictions on speed and deflection anglesmay also be appropriate.

3.4.2 Performance ContextThe idea of operational envelopes can be utilized forperformance criteria as well as safety considerations.Figure 19 through Figure 24 are graphical displays of theenvelopes of acceptable operation. N refers to the vehicleresponse when no active roll compensation is used and A

refers to the vehicle response when active rollcompensation via all control planes is used. In both casesthe depth controller gain is 0.07 for the example casesshown. The roll compensation method used is indicatedby the letter (N or A) in the upper left corner of thefigure, and the depth controller gain is noted along with

the manoeuvre type above the shaded block. The headingacross the top indicates the angle of jam for the particularcontrol plane. The control planes are listed down the leftside.

The shaded block is a matrix of jammed plane

conditions, and the shade of a particular element of thematrix indicates the acceptability of the vehicle responsein the specified manoeuvre with the particular controlplane jammed at the given angle. The lightest gray andnext lightest gray areas show the response of the vehicle

is acceptable in depth (zerr < 1 m), and heading err

Auv Controllability With Control Plane Faults

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