Hybrid fault diagnosis for telerobotics system

Mechatronics 20 (2010) 729–738

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Mechatronics journal homepage: www.elsevier.com/locate/mechatronics

Hybrid fault diagnosis for telerobotics system R. Merzouki *, K. Fawaz, B. Ould-Bouamama LAGIS, FRE-CNRS 3303, Polytech’Lille, Avenue Langevin, 59655 Villeneuve d’Ascq, France

a r t i c l e

i n f o

Keywords: Fault detection and isolation (FDI) Networked control systems (NCS) Telerobotics system

a b s t r a c t Fault detection and isolation (FDI) of a class of networked control systems (NCS), applied for telerobotics system is studied in this paper. The considered NCS application is related to telerobotics system, where it is modelled with a hybrid manner, by including the continuous, discrete, uncertain, and stochastic aspects of all the system components. The main considered components of the NCS namely the network system and controlled system are completely decoupled according to their operation characteristics. The network part is taken as a discrete and stochastic system in presence of non-structured uncertainties and external faults, while the controlled part is considered as a continuous system in presence of input and output faults. Two model based fault diagnosis approaches are proposed in this paper. The first concerns a discrete and stochastic observer applied to the network system in order to detect and isolate system faults in presence of induced delay on the network part. The second is based on the analytical redundancy relations (ARR) allows detecting and isolating the input and output system’ faults. Experimental results applied on telerobotics system, show the performance and the limit of the proposed fault diagnosis approach. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Telerobotics system is considered as a class of networked control systems (NCS), which are increasingly used nowadays in wide variety of engineering systems including manufacturing plants, aircraft, automobiles, etc. The standard configuration of the NCS system is summarized in Fig. 1, it is combination of controller, network channel, actuators, system plant and sensors components. In this configuration (see Fig. 1), the transmission delay effects are considered for whole system dynamic. Thus, the main instantaneous delays are those induced from the sensor to the controller CA sSC k and from the controller to the actuator sk . Due to many uncertain factors in such transmission systems, the network-induced delays are generally considered random. Therefore, NCS is generally considered a time-varying system. Modelling, diagnosis and control of NCS are based at first on the time delayed system’ analysis, already studied for several years. Networked manufacturing systems, transport systems, teleoperation systems are typical examples of time delayed systems [5]. Characteristics of the delay depend of several parameters such as the transmission protocol, the length and load of the network and involved equipment. In general, delay occurs during the exchanges of data between different equipment of control system. Data sampling and package losses constitute another source of variable delay which is also taken in modelling step. The simplest * Corresponding author. Tel.: +33 328 76 74 86; fax: +33 328 76 73 01. E-mail address: [email protected] (R. Merzouki). 0957-4158/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2010.01.009

model of the networked control system is to consider the delay as constant parameter for all transfers inside the network but it remains far from the real dynamic. This can be an adequate model even if the network has varying delays, for instance, if the time scale in the control process is much larger than the delay introduced by the network. One way to achieve a constant delay is by introducing the timed buffers after each transfer. By making these buffers longer than the worst case delay time, the transfer time can be viewed as being constant. This method is proposed in [6], but the control delay becomes longer than necessary which can influence on the performance of the system. Fault diagnosis (FD) and fault-tolerant control (FTC) are very important issues for networked control systems, particularly in safety-critical systems. The fast growth of industrial applications around the NCS has encouraged the development and integration of new tools for FD and FTC. In the case of deterministic model based fault detection and isolation applied to NCS, a discrete state observer is used to detect input faults in [7]. Another FD approach of NCS is studied in [7] by using the parity relation approach with the Taylor approximation applied of the input matrix, while in [8,11] a fault diagnosis of NCS using the parity relation method and Stationary Wavelet Transform (SWT). The two approaches are used to ensure a good performance and robustness towards the induced delay, and the SWT technique provides both a frequency filter and a fast time response. In [12], the effect of unknown networked induced delays on conventional observer based residual’ generator is studied. In order to enhance the robustness of FD, an adaptive evaluation

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2. Problem formulation θe

1

θs

1

Act uat or Actuator

Sensor Sensor

Fx1

u(t −τkCA)

Syst em System

In this section, modelling and fault diagnosis approaches of an hybrid networked control system is presented. In this case, the whole mobile robot system is decomposed on transmission channel part and controlled part (see Fig. 2). The first part model is taken discrete, uncertain and stochastic, while the second is continuous with presence non-structured uncertainties. 2.1. Transmission channel modelling and fault diagnosis observer

τ kCA

Network Channel

u(t)

τ kSC

y(t −τk ) SC

Cont roller Controller

Fig. 1. Architecture of a networked control system.

procedure of the residuals is proposed. The thresholds detection is estimated using an optimization approach which consist to find the control inputs on the specific time interval such as the performance index is maximized. In [16], NCS model with a random delay and based on the Takagi–Sugeno (T–S) technique is proposed, where the main feature of a the T–S fuzzy model is to express the local dynamics of each fuzzy rule by a simple linear-system model. The authors considered an event-driven controller and a clock-driven actuators. In [15], two fault detection and isolation algorithms for NCS are proposed, the first one used the parity space approach and the second is based on a T–S fuzzy-observer. Another iterative diagnosis method of NCS based on the Kalman filtering is developed in [17] and in [4], to compensate the induced delay. From an experimental point of view, a Co-design of a NCS and its diagnosis is presented in [13]. The influence of the transmission delay and the packet losses on two different residual generation schemes have been studied for continuous and discrete systems [18]. Comparison is realized through the simulation of a DC motor, where the control and the diagnosis algorithms are implemented under Matlab/Simulink and True Time software. Other Co-simulation approach is carried out on a system of quadrotor over the network is proposed in [14]. In this paper, a hybrid fault diagnosis schema is presented for telerobotics system. It consists to distinguish the network component from the controlled system of the whole networked control system, according to the component operation. Discrete, uncertain and stochastic model of the transmission channel is concatenated to a continuous model of the process. Then, two fault diagnosis algorithms are used for each component in order to differentiate between network and controlled system faults. The first concerns a stochastic observer based model for state reconstruction and output estimation of the transmission channel. The dynamic of the channel residual is characterized by a discrete-time Markovian jump linear system. The second fault detection and isolation approach for the controlled system is obtained by using the analytical redundancy relations (ARR) technique [2,21]. By this hybrid diagnosis, it can be possible to separate the induced faults on the network component from the input and output faults of the main controlled system. Experimental results are given in this paper to support the proposed hybrid fault diagnosis approach and they are applied for teleoperation of miniature mobile robot. The paper is organized as follows: after the introduction section, the modelling and hybrid fault diagnosis of networked control systems are presented, following by the experimental results. Finally, a conclusion and perspectives are given in the last section.

Assume that the transmission channel to be monitored is a Linear Time Invariant (LTI) system, given by the following discrete form (1)

(

xc ðk þ 1Þ ¼ Ac xc ðkÞ þ Bc uc ðk  sCA k Þ þ Bfc fc ðkÞ þ Bdc dc ðkÞ wðkÞ ¼ ð1  cÞyc ðkÞ þ cyc ðk  sSC k Þ

ð1Þ

with: yc ðkÞ ¼ C c xc ðkÞ þ Dc fc ðkÞ. Rh Rh Where Ac ¼ eAc h ; Bc ¼ 0 eAs Bc ds; Bfc ¼ 0 eAc s Bfc ds; Dc ¼ Dc ; Rh A s Bdc ¼ 0 e c Bdc ds; C c ¼ C c , are respectively matrices of the state, inputs, faults, disturbances and system outputs, while Ac ; Bc ; Bfc Dc ; Bdc and C c are known matrices with of compatible dimensions. h is the sampling period, kh is the time instant, sCA k and sSC k are respectively the instant time delay variable from the controller to the actuator and from the sensor to the controller. The second equation of system (1) describes the stochastic output’ dynamic w(k), which is equal to the real output system when the time delay is absent yc ðkÞ and to the delayed output yc ðk  sSC k Þ in the other case [4]. The switch between the two output configurations is done by a stochastic time-discrete variable c, which is introduced to represent data communication status. c ¼ 0 means that the measurement at time point k arrives correctly without delay, while c ¼ 1 means that this measurement at time point k is delayed by sSC k . In other term, c is a time-discrete Markov chain with two states {0, 1} [4], with stationary transition probability Pk given by (2).



Pk ¼

p00 ðkÞ p01 ðkÞ p10 ðkÞ p11 ðkÞ

 ð2Þ

where pij ¼ PfcðkÞ ¼ jjcðk  1Þ ¼ ig; i; j 2 f0; 1g is the conditional probability of jumping from the ith configuration at ðk  1Þh time instant to jth configuration at kh time instant, therefore, the pij ðkÞ satisfies the following relation [20]:

(

0 6 pij ðkÞ 6 1 p0j ðkÞ þ p1j ðkÞ ¼ 1

ð3Þ

Assumption 1. Sensors and the actuators are clock-driven whereas the controller is event-driven, and the data packets reach the controller and the actuators by their original transmitting sequence if they are not lost [15].

SC Assumption 2. sCA k and sk are respectively the induced delay variables, supposed bounded and identified according to the considered network channel. In the NCS, the random variation of induced delay does not make the communication always perfect due to the problems of packet losses and data congestions. Fig. 3 gives the scheduling of the delay from the controller to actuator, where some sampling controls are lost ðuc ðk þ 1Þ; uc ðk þ 4Þ; . . .Þ and delay grows up according to the data arrival. According to the system (1) and by considering the identified delays of the network channel on the control part, the fault diagnosis observer is then designed as follows:

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Fig. 2. Hybrid diagnosis schema of networked control system applied to mobile robot.

uc (k − 1)

uc ( k + 2) uc ( k )

( k − 1) h

uc (k +1)? kh

uc (k + 3)

uc (k + 6) uc (k + 5)?

uc (k + 7)

uc (k + 4)?

(k + 1)h (k + 2)h (k + 3)h (k + 4)h (k + 5)h (k + 6)h (k + 7)h Fig. 3. Scheduling sequence of the delay.

(

^xc ðk þ 1Þ ¼ Ac ^xc ðkÞ þ Bc uc ðk  sCA k Þ þ LðwðkÞ  v ðkÞÞ SC ^ ^ v ðkÞ ¼ ð1  cÞyc ðkÞ þ cyc ðk  sk Þ

ð4Þ

where v(k) is the injection output of the observer (see Fig. 2). L is the observer gain vector, calculated using the LMI algorithm under free SC fault [4]. The presence of variables sCA k and sk in the observer formulation, implicates that these delay variables are considered known. By putting the estimation error: ec ðkÞ ¼ xc ðkÞ  ^ xc ðkÞ, then from (1) and (4), the state error at instant ðk þ 1Þh is given as follows:

8 ^ > < ec ðk þ 1Þ ¼ xc ðk þ 1Þ  xc ðk þ 1Þ ¼ ½Ac  ð1  cÞLC c ec ðkÞ  cLC c ec ðk  sSC k Þ > : þBdc dc ðkÞ þ ½Bfc  ð1  cÞLDc fc ðkÞ  cLDc fc ðk  sSC k Þ ð5Þ

A stochastic Lyapunov function (6) is considered to demonstrate the observer convergence:

V k ðhðkÞ; cðkÞÞ ¼ eTc ðkÞPðcðkÞÞec ðkÞ þ

k1 X l¼ks

eTc ðlÞQec ðlÞ

ð6Þ

SC k

The theorem proofed in [4] shows that the free-jump system (5) is stochastically stable if there exist Q > 0 and P i > 0; i 2 f0; 1g satisfying the following sufficient condition of the coupled LMI modes:

0 Ms ¼ @

e i Ac  P ei þ Q ATci P i

e i Bc ATci P i

e i Ac Bc i P i

e i Bc Q þ BTci P i

1 A s > > > > > xs ðk þ 2Þ ¼ As xs ðk þ 1Þ þ Bs us ðk þ 1Þ þ Bds ds ðk þ 1Þ þ Bfs fs ðk þ 1Þ > > > > > > ¼ A2s xs ðkÞ þ As Bs us ðkÞ þ Bs us ðk þ 1Þ þ As Bds ds ðkÞ > > > > < þB d ðk þ 1Þ þ A B f ðkÞþ B f ðk þ 1Þ

It corresponds to the formulation of static redundancy. After multiplying the both sides of the equation by the parity matrix W s ðqÞ, orthogonal to C s ðqÞ, the generalized parity vector or residual vector r s ðk; qÞ is obtained:

ds

s

s fs s

ð12Þ Rh

fs ðk;qÞ

Y s ðk; qÞ ¼ C s ðqÞxs ðkÞ þ Bs ðqÞU s ðk; qÞ þ Bds ðqÞds ðk; qÞ þ ðBfs ðqÞ þ Dfs ðqÞÞfs ðk; qÞ

ð14Þ

s fs s

> .. > > > . > > > q > P > q qi > > xs ðk þ qÞ ¼ As xs ðkÞ þ As ½Bs us ðk þ i  1Þ þ Bds ds ðk þ i  1Þ > > > i¼1 > > : þBfs fs ðk þ i  1Þ Rh

Dfs ðqÞ

Rh

with, As ¼ eAs h ; Bs ¼ 0 eAs s Bs ds; Bds ¼ 0 eAs s Bds ds; Bfs ¼ 0 eAs s Bfs ds; Rh C c ¼ C c ; Dfs ¼ 0 eAs s Dfs ds are respectively the state, input, nonstructured uncertainties, output and faults matrixes. When, an interval of measurements is considered such as ½k; k þ q, the outputs ys ðkÞ are deduced as follows:

rs ðk; qÞ ¼ W s ðqÞ½Y s ðk; qÞ  Bs ðqÞU s ðk; qÞ

ð15Þ

It depends only on the system outputs Y s ðk; qÞ and the system inputs U s ðk; qÞ. The parity vector is close to zero when all the faults and disturbances are neglected, otherwise it diverges from its normal operating variation. Then, the robustness of the FDI depends principally on the design of the fault threshold, in order to avoid the non-detection, delay in detection and false alarm cases. When the measurement window is relatively important, the obtained relations (15) will not be necessarily independents. Thus, it is interesting to use other techniques such as inter and auto redundancy, allowing to avoid this inconvenient [19].

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3. Experimental results Experimental results are done on a telerobotics system composed by a miniature robot of Fig. 6 connected to the control/command part via a serial cable channel. The main of this experiment is to show the feasibility of the proposed hybrid fault diagnosis approach presented in the previous section on a real system. Certainly, the system is adequate to simulate different faults on the cable and on the robot in presence or absence of the generated transmission delays. Concerning the closed loop effect, the considered network controlled system has only the controlled part which can be configured in closed loop, while the communication part is configured in open loop. So, in this case the closed loop for controlled system’ states regulation does not affect the performance of the FDI algorithm, because the faults induced from the delay on the communication part are not compensated by the closed loop regulation of the controlled part. The experimental results while introducing an induced delay’ fault shows that the robot continuous in its motion but diverges from the planned trajectory, because the referred velocities have been affected by the fault.

3.1. Modelling and fault diagnosis of serial cable The transmission channel (serial cable) is modelled as a succession of symmetrical RLC cells [1,3], in order to preserve the equality of all electrical equations for the couple (voltage, current) of each point of the channel, during the transmission. In this application, two concatenated cells are used to model 2 m length of the cable. The discrete uncertain state space model (1) described in the previous section is obtained from the dynamic circuit of Fig. 4 and are given as follows:

0 Rl Ll

B 1 BC B l B Ac ¼ B B 0 B B 0 @ 0 0 0 B B1 B Cc ¼ B B0 B @0

2 Ll

0

0

1 Cl

0

1 Ll

Rl Ll

1 Ll

0

1 Cl

0

0 0 1T

2 Ll

0

C 0C C 0C C ; C 1A 0 0

0

1

0

C 0 C C C 0 C C; C 1 C Cl A

Rl Ll

0 1 1 B C B0C B C C Bfc ¼ B B 0 C; B C @0A 0

021 Ll

B C B0C B C C Bc ¼ B B 0 C; B C @0A 0 0 1 0 B C B0C B C C Bdc ¼ B B 0 C; B C @0A 0

0

1

I0 B C B U1 C B C C xc ðkÞ ¼ B B I1 C; B C @ U2 A Is

Consider that the transition probability matrix is given by   0:6 0:3 Pk ¼ , and the measurement signal is: 0:2 0:7

wðkÞ ¼ ð1  cðkÞÞyðkÞ þ cðkÞyðk  2Þ By using the FD observer of (4), we can get the state error and residual equation as following. The observer gain L will be designed with algorithm under fault free (16)

(

ec ðk þ 1Þ ¼ ½Ac  ð1  cÞLC c ec ðkÞ  cLC c ec ðk  2Þ þ Bdc dc ðkÞ rc ðkÞ ¼ ð1  cÞC c ec ðkÞ þ cC c ec ðk  2Þ ð16Þ

The stochastic variable c modelled with a Markov chain is taken with the following profile (see Fig. 5). 3.2. Robot modelling and ARR generation The physical system used for the fault diagnosis of telerobotics system is a miniature mobile robot Khepera II [22], it contains a double active wheels controlled in speed or position (see Fig. 6a) Detailed kinematic, geometric and dynamic models of the robot are given in [3]. Then, continuous state space model of the robot is given in (17).

8 1 0 0€1 > 0 0 fmm 0 0 u_ 1 > u > > B > > 0 fIzz C CB a_ C Ba €C B0 0 > > CB C B C B > ¼ > C@ h_ 1 A @ €h1 A B f1 0 > 0 0 > A @ > J1 > > € > f h h_ 2 2 2 > 0 0 0 > J2 > > 1 0 > 0 1 1 1 > > 0 0 > m m <  d C B 0 0 C U  B C F x1 B 2Idz 2I s1 B C z C þB þB 1 0 C > R > C B > @ J1 A U s2 > @ J 1 0 A F x2 > > 1 > 0 > 0 R J2 > J2 > > 0 _ 1 > > u > >     > > _ C > 0 0 1 0 B h_ 1 > BaC > ¼ > @ h_ 1 A > h_ 2 0 0 0 1 > > : h_ 2

where, Fx1 and Fx2 are respectively the longitudinal traction efforts acted on each motorized wheel, estimated in off-line [10]. U s1 and

CA uc ðkÞ ¼ U 0 ðkÞ; yc ðkÞ ¼ Rf Is ðkÞ and sSC k ¼ sk ’ 2. DAc elements are calculated as the tenth of their nominal values. l corresponds to the channel length, Rl ; Ll and C l , are respectively the resistance, inductance and the capacity of the cable of length l and they are identified experimentally according to the cable material nature. Rf is the internal robot impedance and U 1 ; U 2 are respectively the input and output cable voltages which are measured.

I0

U0

R L/2

LL/2

LL/2

Cl

U1

R L/2

I1

ð17Þ

Fig. 5. Considered Markov process.

R L/2

CL

LL/2

LL/2

Cl

U2

Cell 2

Cell 1 Fig. 4. Two symetric RLC cells.

R L/2

Is

Rf

Us

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The serial cable RS232 contains two principal commonly-used signals:  Transmitted Data (TxD), where Data are sent from Data Terminal Equipment (DTE) to Data Circuit-terminating Equipment (DCE).  Received Data (RxD), where Data sent from DCE to DTE.

Fig. 6. (a) Khepera II robot. (b) Robot description schema.

U s2 are the control inputs, m is the robot mass, f1 ; J1 ; f 2 ; J 2 are respectively the viscous friction parameters and the inertias of the two actuated wheels, fm , fz are the viscous mechanical resistive €; € €; a _ a_ ; h_ 1 ; h_ 2 , are parameters of the robot structure. u h1 ; € h2 ; u; the longitudinal, the yaw and the angular accelerations and velocities of the robot wheels. From the considered dynamic model of (17), we want to detect actuator fault of the robot wheels. Thus, two analytical redundancy relations can be exploited (18) from four possible ARR, in order to detect and isolate the actuator and sensor faults present on the electromechanical system of each wheel. The generated residuals are defined from the algebraic difference between the system dynamics in normal and faulty situations. They are obtained after elimination of the unknown variables from each constitutive relation on the dynamic system model.

   2  8 2 2 2 > r 1 ¼ J 1 þ mR þ IzdR2  €h1 þ mR  IzdR2  €h2 > 4 4 > > >    2  > 2 2 2 > > < þ f1 þ fm4R þ fzdR2  h_ 1 þ fm4R  fzdR2  h_ 2  U s1  2    > I R2 I R2 mR mR2 > > r 2 ¼ 4  zd2  €h1 þ J 2 þ 4 þ zd2  €h2 > > >  2    > 2 2 2 > : þ fm4R  fzdR2  h_ 1 þ f2 þ fm4R þ fzdR2  h_ 2  U s2

ð18Þ

The FDI algorithm is implemented on the supervisor system, distant from the communication and the controlled systems as it is shown in Fig. 7.

To generate the cable faulty situation, only the transmitted data (TxD) are affected. In this case the robot continue working using the old velocities’ reference In the studied case, the measured states are the two angular velocities of the traction actuators and the voltage at the end side of the transmission cable. The identified robot and cable parameters are given in Fig. 8. Four cases of experiments are done, they concern the fault free situation, the robot actuators faults, the transmission channel fault and the generated delay fault respectively. Residuals, control inputs, estimation error and trajectory of the robot are displayed for each case. In order to avoid the false alarm case, residual threshold are considered for the evaluation step. These threshold represents the sum of the absolute element values of the uncertainty state matrix DAc .

Parameters

Values

Parameters

Values

J1 , J 2

0.1 ∗10 −3 ( kg .m 2 )

fm

f1 , f 2

0.0003

N .m.s rd N .m.s 0.0005 rd

N .m.s rd

fz

0.0001

R

0.005 (m)

r1

0.01 (m)

d

0.04 (m)

Iz

0.0058 (kg.m2 )

Rl

3.2 (Ω)

m

0.250 (kg )

Cl

110 ∗10−12 ( F )

Ll

250 ∗10−9 ( H )

R0

100 (Ω)

Rf

1000 (Ω)

Fig. 7. FDI algorithm implementation.

Fig. 8. Simulation model parameters.

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 Free fault case After generating the different residuals, a planned trajectory (see Fig. 12) is considered. In this case, the time evolution of the input and the output of the system in normal situation. In Fig. 9a superposed signals of desired and output velocities for each wheels are presented. The regulation is made by the robot PID speed controllers (with: K P ¼ 3790; K I ¼ 803; K D ¼ 104; 1 unit = 8 mm/s), where the controls and residuals signals are given respectively in Figs. 10 and 11. The convergence of the residuals to zero indicates that the global system is in normal situation. In Fig. 12, the trajectories of the robot is presented.  Actuator fault case After simulating an actuator fault by adding a faulty profile signal to the existing control signal of actuator 1 of Fig. 13, then the residuals of Fig. 14 and the robot trajectories of Fig. 15 show the influence of the introduced fault on the system performance. In this case this disturbing fault does not effect the transmission cable operation as it is shown by the results.

Fig. 11. Residuals signal of actuators 1, 2 and transmission channel.

Fig. 9. Desired and output velocities of wheel 1 and 2.

Fig. 12. Trajectory of the robot.

Fig. 10. Controls signal of actuators 1 and 2.

Fig. 13. Controls signal with actuator 1 fault.

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Fig. 14. Residuals signal with actuator 1 fault.

Fig. 16. Control signal with channel fault.

Fig. 15. Trajectory with actuator 1 fault.

 Transmission channel fault case In this case, the resistance Rl is varied manually by putting a resistive potentiometer in serial. This manoeuvring allows to simulate a cut in the transmission channel, we can notice that controls signal of Fig. 16 are almost insensitive to this fault because the robot residuals are in function of the input control signals coming from the transmission channel. Residual r 3 (see Fig. 17) is sensible to this cable fault including the estimation error (see Fig. 18), which it is derived from zero when the fault is occurred. The deviation on the robot trajectory (see Fig. 19) shows that the robot continues its trajectory by considering the last data references before the cable fault. Thus, it does not follow the desired trajectory.

Fig. 17. Residuals signal with channel fault.

 Delay fault case The generated delay for one input cable (actuator 1) is taken into account by using the Markov process with the stochastic variable c (see Fig. 5) in order to show its influence on the whole system dynamic. Desired robot trajectory is considered as an hexagon path. Then, the time evolution of the control signal is given by Fig. 20, where the residual r 3 (see Fig. 21) is the most sensitive to this generated delay. The estimation error of Fig. 22 shows the FD observer convergence and we can notice that the robot drifted completely its trajectory (see Fig. 23) after applying the delay sequence of Fig. 5.

Fig. 18. Estimation error with channel fault.

In the case of dual robotic system as a real application of telerobotics, with Master and Slave parts, the given FDI algorithm should be implemented for each side in order to detect and isolate faults in the controlled system (Master and Slave robots) with their associated input and output transmission channels. Then, we can con-

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Fig. 22. Estimation error with delay.

Fig. 19. Robot trajectory with channel fault.

Fig. 23. Robot trajectory with delay.

4. Conclusion

Fig. 20. Controls signal with delay.

Hybrid fault diagnosis approach applied on telerobotics system is studied. This system is considered as a class of NCS, where the networked system is decoupled from the controlled system according their operation characteristics. Then, two fault detection and isolation approaches are implemented for the both systems, in order to detect and differentiating the global system faults from the induced time delay. Experimental results are done on a miniature robot with serial transmission cable, in order to test the feasibility of the proposed hybrid monitoring in term of performance and robustness. For a perspective work, it is desirable that the experiments will be done on a telerobotics system with more complex and variable transmission channel such as the wireless. References

Fig. 21. Residuals with delay.

sider that the Master side will be the global supervisor by collecting the monitoring state given by the Slave part with those given by the Master part, in order to decide for the future scenario of the dual configuration.

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