Visakh Seminar

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AN ACTUATOR FAILURE TOLERANT CONTROL

SCHEME FOR AN UNDERWATER REMOTELY

OPERATED VEHICLE

SEMINAR REPORT

submitted in partial fulfillment of

the requirements for the award of M.Tech Degree in

Electronics and Communication Engineering (Applied Electronics and

Instrumentation)

of the University of Kerala

Submitted by

VISAKH .V

First Semester

M.Tech, Applied Electronics and Instrumentation

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

COLLEGE OF ENGINEERING

TRIVANDRUM

2012



DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

COLLEGE OF ENGINEERING

TRIVANDRUM

CERTIFICATE

This is to certify that this seminar report entitled “An Actuator Failure Tolerant Con-

trol Scheme for an Underwater Remotely Operated Vehicle ” is a bonafide record

of the work done by Visakh V, under my guidance towards partial fulfillment of the re-

quirements for the award of Master of Technology Degree in Electronics and Com-munication Engineering (Applied Electronics and Instrumentation), of the Univer-

sity of Kerala during the year 2012.

Mr. Biji Jacob

Associate Professor

Dept. of ECE

College of Engineering, Trivandrum(Seminar Coordinator)

Mr. Vinod B R

Assistant Professor

Dept. of ECE

College of Engineering, Trivandrum(Guide)

Prof. David J

Head of Department

Dept. of ECE

College of Engineering, Trivandrum



ACKNOWLEDGEMENTS

I would like to express my sincere gratitude and heartful indebtedness to my guide

Mr. Vinod B R, Assistant Professor, Department of Electronics and Communication

Engineering for his valuable guidance and encouragement in pursuing this seminar.

I am thankful to Prof. David J, Head of the Department, Department of Electronics

and Communication Engineering for their help and support.

I also extend my hearty gratitude to Mr. Biji Jacob, Seminar Co-ordinator, Depart-

ment of ECE, College of Engineering Trivandrum for providing necessary facilities and

their sincere co-operation. My sincere thanks are extended to all the teachers of the

department of ECE and to all my friends for their help and support.

Above all I am thankful to the God Almighty.

Visakh .V

ii



ABSTRACT

This paper proposes an actuator fault-tolerant control scheme, composed of the

usual modules performing detection, isolation, accommodation, designed for a class of

nonlinear systems, and then applied to an underwater remotely operated vehicle (ROV)

used for inspection purposes. Detection is in charge of a residual generation module,

while a sliding-mode-based approach has been used both for ROV control and fault

isolation, after the application of an input decoupling nonlinear state transformation

to the ROV model. Finally, control reconfiguration is performed exploiting the inher-

ent redundancy of actuators. An extensive simulation study has been also performed,

supporting the effectiveness of the proposed approach.

iii





LIST OF FIGURES

2.1 ROV operational configuration. . . . . . . . . . . . . . . . . . . . . 2

2.2 ROV propellers system. . . . . . . . . . . . . . . . . . . . . . . . . 3

4.1 Incidence Matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

ii



CHAPTER 1

INTRODUCTION

THE applied research area known as marine robotics is receiving increasing at-

tention both by research institutes and by companies interested in the exploitation of

sea resources. In particular, the development of underwater unmanned vehicles (UV) is

attracting noticeable interest as a cost-effective solution for performing complex tasks

in the underwater environment (e.g., environmental data gathering, transportation of

assembling modules for submarine installations, inspection of underwater structures).

Since the UV is expected to operate in a largely uncertain underwater environment, the

control problem of such vehicles is particularly challenging, also in view of the inher-

ent nonlinearity of the dynamics, the presence of external unmeasurable disturbances,

the high uncertainty level in the model. In such a context, fault tolerance is crucial, to

overcome the possible occurrence of faults in the vehicle actuators , and allow nonethe-

less the vehicle to satisfactorily track the assigned reference, thus fulfilling its mission

objectives.

The actuator failure tolerant control scheme presented in this paper is com-

posed by the usual modules performing detection, isolation, accommodation of faults

by control reconfiguration. Detection is performed by a residual generation module,

developed according to structural analysis issues using the nonlinear model of the ROV.

The fault identification module is based on sliding mode control (SMC). In particu-

lar, an input decoupling nonlinear state transformationhas been applied to the nonlinear

model of the ROV, and three sliding surfaces have been designed for the decoupled non-

linear plant in order to ensure that each sliding surface is affected by a single thruster

only (the redundant actuator can assume arbitrary values within a given range). Such

sliding surfaces have been used both for designing a robust ROV control algorithm en-

suring plant regulation, and for performing fault isolation. Since a decoupled sliding

mode control law is used, any fault occurrence can be associated to a single thruster,

and the faulty actuator is this way isolated. Finally, once the failed actuator has been

identified, control reconfiguration is performed using the redundant healthy actuator.

In other words, the control activity is redistributed among the actuators still working

such that the failed actuator is compensated for, and control performances are this way

preserved.



CHAPTER 2

MATHEMATICAL MODEL OF THE ROV

2.1 ROV Nonlinear Model

The equations describing the ROV dynamics have been obtained from classical me-

chanics. The ROV considered as a rigid body can be fully described with six degrees

of freedom, corresponding to the position and orientation with respect to a given coor-

dinate system.

Figure 2.1: ROV operational configuration.

Being the depth controlled by the surface vessel, the ROV is considered to oper-

ate on surfaces parallel to the XY plane. Accordingly the controllable variables are ,x

,y and the yaw angle φ. It should be noticed that the roll and pitch angles ψ and θ will

not be considered in the dynamic model, their amplitude, in fact, has been proven to be

negligible in a wide range of load conditions, and with different intensities and direc-

tions of the underwater current as well. The ROV model is described by the following

system of differential equations:



Substituting for the various physical parameters of the ROV we get

Figure 2.2: ROV propellers system.

2.2 State Space ROV Model

Introducing the state vectors the following state space nonlinear model is ob-

tained.

3



with the value of the functions given by

2.3 Input Decoupling Transformation and Sliding Mode Control

Design

2.3.1 General Case

In this section, the problem of designing a sliding mode controller on a plant of the

form after the application of an input decoupling transformation will be treated in the

general case. Consider the class of MIMO overactuated second-order systems described

by

Theorem 3: For the uncertain plant under Assumptions 1 and 2, it is always possible

to design a robust sliding mode controller such that the following: âAc the robust reg-

ulation problem is solved, i.e. asymptotically it holds equivalently, the achievement of

a sliding motion is ensured onto a suitable sliding surface;each component of the input

vector affects one and only one component of the dimensional sliding surface. Proof:

If the nonlinear transformation is applied to the original plant , the system is obtained,

or, equivalently.

4



2.3.2 ROV Case Study: The Nonlinear State Transformation

The input decoupling state transformation described in the previous section will be

here applied the ROV under study. To this purpose, consider the th thruster fixed, and

rewrite the model as follows:

Consider the following nonlinear change of coordinates:

Applying transformation , one gets the following model equation,where the sub-

script denotes that the model has been obtained considering fixed the th thruster. Just as

an example, when the case is considered, the transformation matrix and the following

model, corresponding to (27), is obtained:

5



2.3.3 ROV Case Study: Sliding Mode Control Law

The results stated in Theorem 3 will be applied here to the ROV under study. Again,

without loss of generality, the case with will be considered in the following . In partic-

ular, the control law is aimed at solving the regulation problem for the variables with

respect to constant reference variables . Define

which can be fulfilled imposing separately three inequalities. the first inequality

gives

The consequence of the above control law is

6



CHAPTER 3

FAULT TOLERANT CONTROL SCHEME

In this section, the proposed fault tolerant control scheme will be described. In the

scenario considered in this paper, each thruster is an actuator potentially affected by

faults. The basic idea is that, whenever a failure is detected and identified, a supervisor

performs a control reconfiguration exploiting thrusters redundancy (three propellers are

enough to control the ROV trajectory). Accordingly, the FDI scheme considered here

consists of: 1) a supervisor, in charge of performing the control reconfiguration among

the available set of redundant inputs, according to the output of the FDI device; 2)

a fault detection (FD) unit, based on residual analysis; 3) a fault isolation (FI) unit,

monitoring the three decoupled sliding surfaces, each of which is affected by a unique

thruster; 4) a robust sliding mode-based control law, designed on a decoupled model

of the ROV, able to guarantee the desired control performances accounting also for the

faulty thruster. The addressed potential faults belong to a wide class. First, the so-

called abrupt fault are considered. They are described by a step function, modeling

the case when the faulty variable is instantaneously stuck to an unknown but bounded

value. Such fault may occur when a failure of a component produce a sudden deviation

of the actuator dynamics as for example a valve completely failing to open or close,

a short circuit in the motor circuitry. This type of thruster faults has the following

model where the failure times are unknown. In other words where the failure times are

unknown. In other words, when a fault does occur on a thruster, this causes the complete

and permanent unavailability of the considered actuator at unknown time instant. This

means that, from the unknown time instant , it is not possible to recover the thruster

functionality and thus only the remaining working thrusters can be used to control the

vehicle. The case when a thruster undergoes a failure occurs.

Also, the behavior of a faulty device can be consequence of deterioration, obsoles-

cence or cumulation phenomena (cumulation of sediment, wear of impeller casing, silt

within pipelines, leaks in the machinery, erosion). These phenomena produce a small

instantaneous deviation of the actuator behavior, but it cumulates in time; as a result,

these faults can result in a loss of efficiency within the system.



A usual way to mathematically describe such temporal behavior is assuming

that the development of the fault is given by

where , i.e., the loss of effectiveness slowly changes from zero (i.e., no fault is

present) to a steady-state value . The following Assumption is needed. Assumption 4:

Only one of the four thrusters can undergo a fault, i.e., multiple thruster faults cannot

be admitted. Moreover, it is assumed that any fault does not compromise controllability

of the plant driven by the remaining healthy thrusters.

8



CHAPTER 4

FAULT DETECTION: THE RESIDUAL GENERATOR MODULE

The residual generator module is able to generate the residuals exploiting the main ideas

of the structural analysis . Structural analysis is a tool which investigates the structural

properties of dynamical system by analyzing its structural model . The basic tool for

the structural analysis is the concept of matching on matrix incidence or on a bipartite

graph.Amatching is a causal assignment which associates some system variables with

the system constraints from which they can be calculated. Variables contained in con-

straints that cannot be matched, cannot be calculated. Variables contained in constraints

that can be matched in several ways, can be calculated by different (redundant) means,

thus providing means for fault detection and a possibility for reconfiguration . Match-

ing on a structure graph of a dynamic system can disclose which subset of equations

provide a redundant description of the system. The matching process is essentially a

way to indicate which equations (or constraints) in a nonlinear system are needed to

find a solution for its variables. When there are more equations than needed, excess

equations can be used to check for validity of observations. If such an excess equation,

called unmatched constraint and known as residual, is not valid, this will indicate the

presence of a fault in the system.

The matching algorithm identifies the overdetermined parts of the system . The

result is a list of matched and unmatched constraints. The matched constraints result

while the unmatched constraints .

Each of the unmatched constraints gives a parity equation

Figure 4.1: Incidence Matrix.

The detection equations are derived by back tracing the matching of the unknown

variables involved in the unmatched constraints until only known variables are part of

the expression. Back tracing unknown variables to known variables gives three residu-

als:



The role of the decision module is to determine whether the residuals differ signif-

icantly from zero and, from pattern of zero and nonzero residuals, to decide which are

the most likely fault/ failure effects, and in turn, which components could be the origin

of a fault or a failure. Residual evaluation consists to detect a change in the mean of

a normally distributed random sequence, which can be achieved by sequential change

detection algorithms like the cumulative sum (CUSUM) algorithm . This algorithm

is chosen to design the decision module of the failure detection system of the ROV.

Assumption 5: No faults occur during an initial transient phase immediately after the

startup of the ROV. This is not a limiting assumption, in view of the ROV types of

utilization and the missions the vehicle is expected to carry out.

10



CHAPTER 5

FAULT ISOLATION

Once a failure is detected by FD module, the sliding-mode controller can be also ex-

ploited to perform fault isolation. Indeed, it can be simply performed using the follow-

ing check on the components of the sliding surface , since each component is affected

only by a single thruster

It follows that, whenever a fault has been detected by the FD module, the thruster

associated to the nonzero component of the sliding surface (if any) is to be considered

the failed actuator. In case no violation is detected by the FI module, then the occur-

rence a false alarm will be signaled to the supervisor.

Remark 6: The practical implementation of the previous rule requires of course the

use of a nonzero threshold , which could also coincide with the width of the boundary

layer needed, as well known, to avoid chattering .

Remark 7: About the eventual effect of sliding modes on fault signatures, it should

be noticed that if a fault detected by the residual generator does not affect any compo-

nent of the sliding surface, it simply means that the controller and the whole control

system is behaving correctly. It follows that signatures are not destroyed, but the fault

is isolated as soon as it becomes serious enough to disturb the effectiveness of the con-

troller.



CHAPTER 6

CONTROL RECONFIGURATION

After a failure has been detected and isolated by the FD and FI module respectively, the

supervisor has to perform a control reconfiguration to preserve the desired performances

in face of the failure occurrence. In particular, the inherent redundancy of the considered

ROV can be exploited for fault accommodation. Consider the transformed decoupled

plant , derived setting to an arbitrary value, for an arbitrary integer . Assume that a fault

is detected, and that the failed thruster isolated by the FI module (i.e., associated to the

increasing component of the sliding surface) is the th. It is then convenient to rewrite

the model as follows:

and to transform the system by a nonlinear change of coordinates of the form , thus

getting the model.In other words the plant model is rearranged including the previously

unused thruster among the working actuators, and including the th failed thruster in the

bounding functions . Then, the sliding mode controller is derived using this model,

following the lines described in Section III-C. In particular, the bounding functions are

derived using the upper bound for the failed actuator , which appears in the function .



CHAPTER 7

CONCLUSION

In view of the robustness properties of sliding-mode control, this procedure guarantees

the robust asymptotical vanishing of the tracking errors also in the presence of a faulty

actuator (with known upper bound), i.e., that robust regulation is achieved asymptoti-

cally. Eventhough one of the actuator fails due to some reason it will be detected by

the fault detection module and then the corresponding thruster will be isolated by the

fault isolation module.After that control reconfiguration is done and the ROV will now

operate using the three healthy actuators.



REFERENCES

[1] Maria Letizia Corradini, Andrea Monteriu, and Giuseppe Orlando, “An Actua-

tor Failure Tolerant Control Scheme for an Underwater Remotely Operated Ve-

hicle,” IEEE Trans. Control Syst.Tech, vol. 19, no. 5, pp. 1036-1046, Sep. 2011.

[2] M.Blanke, H.Niemann, nd T.Lorentzen, “Structural Analysis- A case study of

romer satellite.”Proc,IFAC Safeprocess,Washington,DC,2003.

[3] V.Coocquempot, R.Izadi-Zamanabadi, M.Staroswiecki, and M.Blanke, “Resid-ual generation for the ship benchmark using structural approach,”Proc.UKACC

Int.Conf.(Conf.Publ.455), pp. 1480-1485, 1998.

[4] V.Utkin, “Sliding Modes in Control Optimization,” Berlin,Germany, Springer Ver-

lag, 1992.

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