CENTRALIZED AND DECENTRALIZED ADAPTIVE FAULT-TOLERANT CONTROL APPLIED TO INTERCONNECTED AND NETWORKED CONTROL SYSTEM

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1 CENRALIZED AND DECENRALIZED ADAPIVE FAUL-OLERAN CONROL APPLIED O INERCONNECED AND NEWORKED CONROL SYSEM Amina CHALLOUF (a), Adel ELLILI (b), Christohe AUBRUN (c), Mohamed Naceur ABDELKRIM (d) (a,d) Unité de Recherche: Modélisation, Analyse et Commande des Systèmes (MACS), Ecole Nationale d'ingénieurs de Gabès, unisie (b) Institute Suérieure des Etudes echnologiques de Djerba, unisie (c) Centre de Recherche en Automatique de Nancy(CRAN), Nancy-Université, CNRS UMR 7039 Facultés des Sciences et echniques, France (a) amina_chalouf@yahoofr, (b) Adel_ellili@Lycoscom, (c) christoheaubrun@cranuh-nancyfr, (d) naceurabdelkrim@enigrnutn ABSRAC In this work, we focus on monitoring and reconfiguration of an Adative Model Reference (MRA) Fault-olerant Control (FC) for large-scale system his articular class resents an interconnected and networked control system (INCS) Moreover, the system can be decomosed into N-interconnected subsystems communicating with network hen the global outut of INCS and one or more oututs of N- interconnected and networked control subsystems are attacked by sensor faults herefore, an active Fault- olerant (F) aroach, say the model reference adative control of linear systems, is used in order to guarantee not only the stability of an overall INCS globally, but also all local stabilities of N-networked control subsystems with strong interactions, delay and additive faults Moreover, two architectures: centralized and decentralized adative controllers are designed to comensate the sensor faults for different internal structures of systems which are subject of this aer he law adatations which make the different faulty systems stable are given A simulation examle of an overall INCS consisting of three interconnected and networked control subsystems and involving stabilization of unstable steady-states is used to demonstrate the efficiency of the roosed aroach Keywords: adative control, centralized control, decentralized control, fault-tolerant control (FC), interconnected system, networked control system (NCS), reference model (RM), sensor failure 1 INRODUCION he notion of Fault-olerant adative control has been an active area of research (Blanke and al 2003, Bodson and al 1997, Patton 1997, Patton and al 1997) he theory of large-scale systems is devoted to the roblems that arise from some difficulties (Ioannou and al 1985, Huang and al 2010, Lina and al 2006, Mahmoud 1997, Patton and al 2007): -Dimensionality; -Information structure constraints; -Uncertainty; -Delays A system is considered large-scale if it is necessary to artition the given analysis or synthesis into manageable sub-roblems As a result, the overall system is no longer controlled by a centralized controller but by several indeendent controllers which all together reresent a decentralized controller his is the fundamental difference between feedback control of small and large systems On one hand, the develoment in this direction has reached a level of imortant alications where adative controllers are used to enhance stability and imrove oerating conditions of defective systems (Bodson and al 1997, Ioannou and al 1985, Mahmoud 1997, sai and al 2009) On the other hand, her theory is develoed to make a general ractical use of adative controllers in both large-scale and networked control systems [Ioannou and al 1985, Mahmoud 1997, Patton and al 2007) In interconnected and networked control systems, there will be more adative controllers located at different, ossibly distant units, and in control centers Besides, the dynamic of each local subsystem is not known exactly and the local oututs are corruted with noise disturbances and faults via network control In this aer, centralized and decentralized adative FC based on reference model is included in resence of all interactions and over medium of communication between each subsystem wo structures of adative controllers for interconnected and networked system is roosed (Bakule 2008, Challouf and al 2009, Hasheng 2003, Hovakimyan and al 2006, Sundaraandian 2005) Each adative controller is designed to comensate the 101

2 additive faulty sensor he stability of the overall adative control scheme is established he aer is organized as follows: Section 2 recalls the interconnected and networked control system modernization Also, it reresents the controller synthesis for LI and continuous time systems A simulation examle of three interconnected and networked control subsystems subject to sensor faults is used in Section 3 to illustrate the effectiveness and erformance of the two architecture (centralized and decentralized) active fault tolerant control system Finally, a conclusion is included 2 PROBLEM SAEMEN 21 Interconnected System his class of the large-scale system can be comosed of N-interconnected subsystems [Ioannou and al 1985, Mahmoud 1997] Consider an overall interconnected system which is given by the following state saces: () () () () () () X t = AX t + BU t + Dw() t ( S) Y t = CX t + DU t + Vv() t X () 0 = ϕ () t (1) he index designs the rocessus arameters A, B, C, D and V are the arameters system with aroriate dimensions On the other hand, X() t, U() t, Y() t and () W t and V () t n m q are the state vector, the control vector, the outut vector and the external disturbance vectors resectively As black as this class of the large-scale system contains N-interconnected subsystems and based on equation (1), the artitioned matrix X, U and Y are: X () t = X 1, X 2,, X N (2) U (),,, t = U 1 U 2 U N (3) Y (),,, t = Y 1 Y 2 Y N (4) w (),,, t = w 1 w 2 w N (5) In addition, the aroriates matrix A, B, C, D and V be artitioned as follows: A1 A12 L A1N A = M M M A N 1 A N 2 L A N (6) B1 B12 L B1N B = M M M B N 1 B N 2 L B N (7) he matrix B will be full column rank C = C C, L, C 1 2 N (8) and v = v v, L, v 1 2 N (9) Besides, the matrix $A_$ can be viewed as an interconnected matrix, too, consisting N-subsystems defined by them aroriates matrices (A i, B i, C i ), i=1,, N So, we can write: N N N N n = ni, m = mi, = i and q = qi i= 1 i= 1 i= 1 i= 1 (10) Consequently, the arameters of an overall system (S) deend essentially on the arameters of N- interconnected subsystems (S i ) which constituting (Ioannou and al 1985) In oint of i th subsystem is instable, the global system is also instable Like that a global system (S) can regrous N- interconnected subsystems (S i ), the equation (1) can be rewritten into matrix form decomosing in all N- interconnected subsystems as follows: X& i ( s) = Ai Xi ( s) + B U ( s) i i + ( Gij gij ( s) DijWij ( s) ) j + i Si : Yi( s) = CiXi( s) + LiVi( s) ; i, j= 1,, N ( ) Xi( 0) = ϕi( t) n m q Where: Xi i, Ui i andyi i are (11) resectively the local states, the control and the outut of the subsystems (S i ) ni ni ni mi qi ni Ai, Bi and Ci are resectively the arametric matrix of the local states, the control and the outut of the i th rocessus couled with j th subsystems (S j ) 102

3 Figure1: Internal Structure of NCS 22 NCS model he stage of modeling is rather significant at the time of the study of a rocess he systems considered in this work belong to a articular class hey are the systems ordered by a medium of communication, they are known still by the systems ordered in network (NCS) [7,8,9] his class of the system resents the henomenon of delay in their dynamic of which its structure is illustrated by the fig2: Figure 2: Structure of co-oerative Interconnected NCSs and FC Contrary to the ordinary systems whose temoral evolutions can be given starting from the value of state X at the moment resent X& () t = f ( t, X () t ) hose of the systems ordered in network deend rimarily on of the last values of the state X (t) Moreover, the latter resent the henomena of delay and the losses or dulications of the messages during the transmission of the data control/actuator: τ ca and sensor/control: τ sc Generally, three working frameworks are used to reresent a late system: models on ring, infinite models of dimension on oerators and models in the form of differential equations In this resent work, concerning the stability on the one hand and the modeling of communication CP on the other hand, we are interested in the effects of the delay in dynamics of the NCS Plus recisely, we thus consider systems (eq1) rewritten in the form: ( ) ( ) ( τ ) () () ( τ ) X t = AX t + BU t + Dw() t ( S) Y t = CX t + DU t + Vv() t X () 0 = ϕ () t ( 12) At the time of the hase of modeling, as well as the matrices defining a model, it is essential to determine the tye of delay which affects the system (see fig 1) here are three rincial categories of delay: (a) delay in known; (b) raised delay; (c) limited delay he delay can be between control/actuator and/or sensor/control that as (see fig1): τ = τ + τ sc ca Where: 0 τmin τ τmax (13) (14) τ min and τ max reresent resectively the minimum and maximum values of delay All MIMO transfer matrix reresentations have aroriate dimensions and are roer real-rational matrices, stabilisable and detectable A state sace rational roer transfer - function is denoted by: U A B Sys = = Y C D ( ) 1 = C si A B + D 23 Model Reference Adative FC design (15) Consider a LI system defined by eq12 o accommodate the last system, we were imlementing adative FC His rincial is exlained by fig2 offering the structure of co-oerative INCSs and FC he last method is based on reference model It roves the atitude to reach the characteristics secified by the reference model in resence of additive faults on system [11, 12, 13, 14, 15] he last idea is illustrated by fig3 Based on fig3 and in the time domain, the overall reference model is described by the equation: (16) he index m designs the known reference model arameters In this art, we aly the direct method of the fault tolerant adative control he control inut is given by: U P ( t) = ( C 0 ( t) r( t)) + ( G 0 ( t) Y ( t)) (17) With C 0 (t) and G 0 (t) are the arameters of the adjustable controller he derivation of time resonse lant is given by: (18) 103

4 When C 0 (t) = C 0 * and G 0 (t) = C 0 * he motivation being that there exist nominal arameter values of the adative controller: he udate laws are given by: (19) (20) hus, the exression of the adative law control becomes: (21) Since, the error dynamic equation between the lant time resonses Y f (t) and reference model Y m (t) with the adjustable arameters of the regulator is given by: (22) Now let us consider for the arameters error the following notations: (23) In the following reresentation, the right-hand sides only contain states (e 0,ф r,ф Y ) Consider then the Lyaunov function candidate corresonding: aking the derivative of Lyaunov function: (24) (25) Figure 3: Functional diagram of Interconnected NCS in resence of sensor faulty Consider the overall system (eq1) consisting of three interconnected and networked control sub-systems (Sys 1 ), (Sys2) and (Sys 3 ) with unit reference inut (r(t)=1) On one hand based on fig2, the transfer function of overall interconnected networked control reference model (eq17) is giving as follows: 3 2 Ym 0348s 3s s s Sysm = = e U m s + 55s s s But, the transfer function of overall interconnected networked control system without external disturbances is giving as follows: s 3s s s Sys = e s + 55s s s 3125 So reference to the last transfer function, the overall interconnected and networked control system Sys is unstable On the other hand, the interconnection vector functions are resectively: G 12 =-05, G 21 =05, g 12 = and the total delay is: τ= 0348 where the delays into sensor/control and control/actuator are giving resectively: τ sc = τ ca = 0174 he global Interconnected NCS (Sys ) is unstable hen as the fault f s (t) is additive( fig4) it can attack the total outut Y (t)or one or more oututs Y (t) of the total system Sys It is clearly, at the moment t = 20sec, we generate the offset fault with amlitude 1 where A m >0 is arbitrarily chosen by the designer So that the system is stable, it is necessary that V 0 and V & 0 what is checked his involves that the adative system is stable in the sense of Lyaunov (Bakule2008) 3 HREE INERCONNECED AND NEWORKED CONROL SUBSYSEMS EXAMPLE In this simulation arty, we interest at a numerical examle where N=3 illustrated by figure 3 in order to demonstrate the efficiency of the roosed control Figure 4: Offset fault he time resonse Y f (t) of the lant becomes: 104

5 () = () + (), = 1,, Yf t Y t fs t i N (26) We use the control law (18) for various tyes of faults he figures (4) and (5) illustrate the trajectories of the overall INCS time resonses Y f (t), the reference model Y m (t) and the error e 0 (t) in the resence of faulty sensor (see resectively figure5 and 6) he global and distributed oututs resectively Y fg (t) and Y f (t)are reconfigured where a change then it recovers the desired outut Y m (t) of reference model In figure7, the errors between the oututs defective rocessus and his reference model towards zeros for centralized and decentralized adative controllers Figure 5: Dynamic global outut resonses via MR Adative FC he figure 6 illustrates the dynamic global controls trajectories: U (t) were imlemented on two different interconnected and networked control subsystems: Sys i i=1,2,3, into to accommodate the defective overall Interconnected NCS: Sys f Figure 6: Dynamic distributed outut resonses via adative model reference FC 4 MAIN RESULS AND INERPREAIONS Here, to study the influence and the differences between centralized and decentralized architecturally adative controllers based on reference model, the figure5 and figure 6 illustrate the various resonse trajectories It is clearly that the accommodation of Interconnected NCS f is realized by the roosed control laws such that are find simulation results In addition, it is clearly that the adative FC is imlemented to three subsystems hey are LI, continuous times, interconnected and networked control subsystems Sys i,i=1,2,3 All constitute an overall interconnected NCS system Sys which his arameters deend essentially on all subsystems Besides, the resonses of defective lant Y f (t) are controlled by centralized control: U(t) and decentralized controls: u 1 (t) and u 2 (t) Figure 7: State errors In the resence of additive defects, the accommodation of the N-interconnected and networked control subsystems is assured by the fault tolerant adative control based on reference model We can note that the decentralized architecture of adative FC imlanted of an overall interconnected networked control system ermits to build high erformances and marvelous accommodation he actual class of system may be robust to change all delay arameters If the sum of delay τ oversteing the limited values, the rocessus cannot be stable he adative fault tolerant controllers are based on udated controller arameterizations C * 0 and G * 0 hey are udated by some adative laws and they are designed to minimize the deviation of outut caused by the fault f s (t) Moreover, the figure8 illustrates simulation results of various trajectories (centralized and decentralized) controls Figure 8: rajectories of global and distributed controls So, many strong oints of the resent fault tolerant adative control schemes in comarison with the existing techniques for two reresentations (centralized/decentralized) of INCSs are the following: 105

6 (i) they are two structures of large-scale system which differ from one another in the model used to reresent the couling between N-subsystems on which the controls are based; (ii) sensor faulty dynamics are included in the adatation loo and hence any on-line estimation arameters of overall system and N-interconnected subsystems will not cause significant of resence of sensor faults; (iii) the resent aroach can be regarded as a generic one leading to different secific schemes that result from the choice of controller models of different degrees of comlexity here exists a tradeoff between models comlexities and system erformances for some tracking tasks his can be used for the choice of aroriate fault tolerant adative control structures for desirable tasks; (iv) the aroriate selection of decentralized techniques to be emloyed on N-interconnected subsystems distributed; (v) a major oint in the resent develoment from the two architectures (centralized/decentralized) of controls that are high erformances and marvelously reconfigurations of the distributed fault tolerant adative controls 5 CONCLUSION Model reference adative FC imlemented on interconnected and networked control system subject to comensate faulty sensor was studied in this aer he main contributions include essentially: 1) Modeling NCSs subject to both access interactions and delay in resence of faulty sensors; 2) Determining different architectures (centralized and decentralize) of adative model reference controllers for N-interconnected and networked control subsystems A simulation examle of three interconnected and networked control subsystems was studied to illustrate effectiveness of the roosed method REFERENCES Blanke,M,Kinneaert,M,LUNZE,J,Staroswiecki,M, 2003 Diagnosis and fault tolerant control Sringer, Berlin, Heidelberg, New York Bodson, M, Greszkiewicz, EJ, 1997 Multivariable Adative Algorithms for Reconfigurable Flight Control IEEE ransaction on Control systems echnology, 5( 2) Patton, RJ, 1997 Fault-tolerant control: he1997 situation In IFAC Fault Detection, Suervision and Safety for echnical Processes, Kingston Uon Hull, UK Patton R J, Kilinkhieo, 2009 An Adative Aroach to Active Fault-olerant Control ) he Oen Automation and Control Systems Journal, 2(3) Ioannou, P, Koktovic, P, 1985 Decentralized Adative Control of Interconnected Systems with Reducedorder Models Ataomatica, 21( 4) Mahmoud, MS, 1997 Adative Stabilization ofa class of Interconnected Systems Comuters Elect Engng, 23( 4) Huang, D, Nguang, SK, 2010 Robust fault estimator design for uncertain networked control systems with random time delays: An ILMI aroach Information Sciences180(3) Lina, L, Chen, HC, 2006 Robust control of interconnected network schemes subject to random time varying communication delays , Int J Electron Commun (AEÜ) 60(2) Patton, RJ, Kambhamati, C, Casavola, A, Zhang, P, Ding, S Sauter, D, 2007 A Generic Strategy for Fault-olerance in Control Systems Distributed Over a Network 1-17 Euroean Journal of Control12(4) sai, NCSue, CYang, 2009 Integrated model reference adative control and time-varying angular rate estimation for micro-machined gyroscoe International Journal of Control Bakule, L, 2008 Decentralized control: An overview Annual Reviews in Control 32(3) Challouf, A, elli, A, Abdelkrim M N, 2009 Fault- olerant Adative control of linear Systems alied to A Robot H4 Le 3éme Colloque de Recherché Aliqué et detransfert de echnologie " 2éme conférence internationale Nouvember ( unisie) Hansheng, W, 2003 Decentralized adative robust control for a class of large scale systems with uncertainties in the interconnections International Journal of Control, 76(3) Hovakimyan and Ramachandra A, 2006 Decentralized adative outut feedback control via inut/outut inversion International Journal of Control, 79( 12) Sundaraandian, V, 2005 Distributed Control Schemes for Large-Scale Interconnected Discrete- ime Linear Systems Mathematical and Comuter Modelling, 41(2) 106