- Email: [email protected]
Reconfigurable Distributed Control Considering Communication Time Delay Effects
Copyright <0 2001 IFAC IFAC Conference on New Technologies for Computer Control 19-22 November 2001, Hong Kong
RECONFIGURABLE DISTRIBUTED CONTROL CONSIDERING COMMUNICA nON TIME DELAY EFFECTS
Benitez-Perez H.*, and Garcia-Nocetti F.** (*). (**) Departamento de Ingenieria de Sistemas Computacionales y Automatizacion,
IIMAS.UNAM. Apdo. Postal 20-726. Del. A.Obregon. Mexico D.F.. 01000. Mexico. Fa;>:: ++52561601 76. Tel: (*) ++5256223639, (**) ++5256223569 Email: (*)hector(Mlxdea4.iimas.llnam.mx (contact author) (* *) fabian@lL\·dea4.iimas.unam.mx
Abstract: Increasingly, there is a move towards in-built intelligence for sensors and actuators to integrate "smart" peripheral elements as part of a distributed control system. The utilisation of local intelligence to provide local fault detection and fault tolerance opens the incorporation of new variables into the structure of the control law. How to integrate this information into the structure of the control law is presented in here. The main goal is to integrate a decision making procedure between peripheral elements and different control strategies. The re configuration of the control law based upon local health measures is decided by this procedure. Copyright i8 2001 1FAC.
Keywords: Distributed Systems, Process Supervision, Distributed Control, Static Scheduling.
1. Introduction The emergence of smart sensor and actuator technology removes the need for centralised control with feedback loops to dumb peripheral actuators replacing it with a databus connection (Benitez-Perez et aI., 1998).
reconfiguration based upon a fuzzy decision maker working as fuzzy supervisor. The strategy followed in here uses the information generated by smart elements in a decision making procedure. Peripheral elements generate a measure named confidence value, which indicates how the element has been degraded due to the presence of a local fault.
Control systems over distributed systems consider several design parameters such as partitioning allocation and communication policies. These are part of the design and deployment decision. Different aspects over the system are proposed. Firstly, the integration of smart peri)heral elements as autonomous elements capable of self diagnose in order to reconfigure the control strategy. Second, the reconfiguration of the control law based upon a safety degradation measure.
The decision making procedure chooses which control law needs to be used based upon the fault scenario. There are three control strategies, the first one is based upon a predictive control law, the second is based upon a PID controller and the third one is a safety value, which sends the plant to a stable operating point. Due to the use of a distributed system in order to communicate different entities, it is necessary to propose a scheduler taking into account the behaviour of the system under fault free and fault scenarios.
Several strategies for reconfigurable control have been studied for different research groups. For instance Dussud et aI., (1998) present a control law
313
A ball and beam plant, using two arrays of sensors and two actuators, has been selected as case study. This paper has been divided in seven sections. First section is the current introdu-::tion. Second section presents an overview of smart element technology. A description of the proposed scheduler is provided in third section. Fourth section describes briefly the plant model. The control design and the decision making strategy adopted is presented in the fifth section. Sixth section, shows practical results of case study. Finally, seventh section presents some concluding remarks.
The fuzzy system determines how big is the degradation in order to modify the current value of Confidence Value (CV). If the deviation of one of the residuals is considerable with respect to the current parameter this is declared as erroneous condition. Otherwise, the residual is categorised as "good".
3. Scheduler Design Scheduler strategy is integrated by four different types of elements, sensors, decision making module, controller and actuators. This scheduler presents sporadic communications due to the presence of fault scenarios. There are several types of time delays to be considered (Table I). These are related to communication, processing and capture. Time values shown in Table I are from the simulation procedure of the implemented example. There are two possible scenarios, first scenario establishes a fault free situation. Second scenario considers the communication between nodes when a fault scenario appears (Fig. 2).
2. "Smart" Elements Design Smart elements are defined as peripheral elements who have the capabilities of self-diagnose faults, self-compensates disturbances and digital communications (Masten, 1997). These elements arc mainly sensors and actuators. The typical configuration followed in this paper is presented in Fig. I (Benitez-Perez, 1999).
event
r---+-+"JI9---.;:-t--f-t--t--t--+---t-- sensor arr.lY
Fig. 1 Smart Sensor Strategy In Fig. 1 there are two blocks to be considered: the analytical redundancy block and the residual evaluation block. First block is based upon two parameter estimation procedures using two different sampling periods. The first being faster than the second one. First procedure performs the parameters every t, seconds, while, the second one estimates the parameters every t2 seconds. First procedure catches the current performance of the element, meanwhile second one catches the stable perfonnance of the clement. The difference between them gives the residual vector. This vector has a non-zero behaviour when a fault appear. PE I estimates five parameters as well as PE2. Both vectors do not have an exact physical meaning related to the dynamics of the sensor . This is not the aim pursued in this paper. Nevertheless, the relation between residual vector and fault presence is directly proportional. The evaluation block is performed using a fuzzy logic procedure named as res:dual evaluation block (Fig. I). This block fully evaluates the residual vector based upon Mamdani fuzzy rule strategy. This system has been tuned using the experience of the designer. The result of this evaluation procedure is a confidence value which has a range from 0 (catastrophic behaviour) to 1 (fault free scenario). The goal of this evaluation procedure is the identification of faults based upon the behaviour of whole residual vector. This idea uses the directional residuals concept explained in more detail by Gertler (1998).
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oontroller
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Fig. 2 Scheduler for Fault Free Scenario e-"CftI
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Fig. 3 Scheduler for Fault Scenario For fault free scenario the time related to the sensing node is tl+o ps+od.+t.:=6.67 milliseconds. Time related to control node is Opc+Odc+ t2=2.8 milliseconds. When a fault scenario appears a new element is considered. Its name is decision making node. In order to incorporate this node to the system scheduler works as follows. The selected sensor transmits its value to control node. Due to its CV is less than a threshold, it transmits this value to the Decision Making node. This node processes the information and transmits its result to control node. Finally, control node decides which law is used in order to send a result to the actuators. Time delays are considered as follows,
314
sensor uses tsc=3 milliseconds (Fig. 3). The communication between sensor and control nodes is t,a= 2 milliseconds and the communication between decision making and contlol node is ('1= 2 milliseconds. Decision Making node spends t<1m= I millisecond in processing its information. Having recruit all necessary information control node process it during 1,,1=2.0 milliseconds. Afterwards, this result is sent to actuators nodes. The systems spends in this action t.,2+4=1.57 milliseconds. Finally the actuator node spends tAI=2.0 milliseconds in order to modify the plant. The total time spent for each scenario is 11.5 and 17.73 milliseconds, respectively. This calculation is based upon summation of every time concerned. For fault free scenario the sum is as follows tl+Ops+Ods+t., + 0pc+Od<+ t1+ tAl having as a result 11.5 milliseconds. For fault scenario the sum is next td01+ t,.2+(,.1+ t2+t3+tc2+t4+ tcl+t A1 · This sum gives as a result 17.73 milliseconds. As the reader may realize this difference performs an overhead due to reconfiguration strategy. This is overtaken by the use ofPID controller as mentioned further on.
A(:-')y(tl = :-J 8(z-' lu(/-I) +c(z-' le(t)
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=1+2.0ISz-' + 1.032:- 2
Where y is the output, u is the input, z is the space variable, A, Band C are the representative polynomials of the system. d is a time delay variable that for this particular case is considered to be zero. This representation must be modified to that one expressed next. In this case, C term is no considered as part of the error. ~ .(t)=~u(t-J)+e(t) C C (4.2) or
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A modification under equation 4.2 must be made to this stage in order to determine a suitable representation for predictive control.
A = M = (I -z-I)A = 1-I .032z- 1 + i.032z-2 -1.032z-3 (4.3)
For the case of this simulation, CANbus standard is used to establish time delays as shown in Table I.a and Table I.b.
Sensors and actuators models are considered lineal by the inherent self calibration within these elements. Due to this assumption, the plant model depends exclusively the dynamical behaviour of the ball and beam. Time delays produced by communication scheduler are considered as part of the dynamic behaviour. Control laws integrate this behaviour in both ca<;es (fault and f:lUIt free scenario).
Clock synchronisation is time stamping over each communication process. Time delays related to sensing, controlling and processing information are ba<;ed upon the response of the dynamics tested in a PIlI computer. The implementation of this scheduler is achieved using State-Flow toolbox from Matlab 5.3 (MATLAB, 1998).
The only considered fault scenario is the degradation of any of these peripheral elements per time. Just one sensor is considered to be faulty. The condition of the fault scenario is noise over one peripheral element. There are three main possible scenarios, fault free, non-catastrophic and catastrophic. The first scenario presents the obvious behaviour of the plant. In this case, the used control law is a predictive control strategy.
4. Plant Design The strategy followed in this paper is based upon Fig. 4. There is a reconfiguration approach based upon a confidence measure array generated by a group of "smart" sensors. Each "smart" sensor produces its own confidence value. This array is evaluated by a decision making module in order to choose one of the available control laws.
The second scenario degrades system up to a established threshold in order to reconfigure the control law. In this case, the control law is based upon a PID controller in order to stabilise the plant. Last scenario presents a catastrophic situation. The control law used is a constant value. This is due to safety conditions of the beam without considers the ball. In fact, the ball is expected to be lost but the beam is stable.
Plant
5. Reconfigurable Control Integration Having defined the "smart" element strategy, the scheduler behaviour and the dynamics of the plant, next step is the integration of both into the dynamics of the control law. As mentioned in section I, different strategies may be followed. For instance, Nilsson (1998) uses stochastic control in order to integrate random time delays due to disturbances within the system.
Fig. 4 Reconfigurable Control Scheme There are two arrays of sensors and two actuators. Each of them on each side of the beam. The model of the plant uses one sensor who is reporting the actual position of the ball and one actuator who is moving the beam. The plant dynamics are shown next:
315
The decision making procedure is based upon two thresholds in order to define the boundaries of these three control laws. Table 2 shows this classification. The selection of control law a degradable condition based upon one faulty element. If every CV element are between 0.79 and 1.0 then first control law is selected. If one of the CV measurements is between 0.49 to 0.78 the control law is selected. Finally, if one of the CV measurements drops its value to below 0.48 last control law is chosen.
Alternative techniques, such as, predictive control (Camacho et aI., 1998) are feasible due to incorporation of time delays to the control structure. The use of "smart" elements information into the control law is based upon the use of arrays of confidence values from peripheral elements. The approach followed is the reconfiguration of the control law through the selection of different control strategies. These are integrated to a decision making algorithm in order to switch from one control law to another (Fig. 2). In case of catastrophic conditions this switch tends to move the system to a safc mode. Just one sensor is considered to be faulty.
Good O.79
Remember that in this case, the measure of one sensor is given to the controller. This is to deternline the actual position of the ball.
O.O
Bad
Safe
Values
I
V V V
Thresholds
Table 2 Threshold Decision Making Procedure First controller considers CV at 100% of its value where the input is 100% trustable. Second control strategy establishes the input at its 50% trust. This is due to the presence of a fault. Last control law is based upon a safe value in order to maintain the system within a safe condition. For last two cases second scheduler is used (Fig. 3). The structure of the predictive control law is based upon eqn. 5.1 . y=Gu+ f (5.1) Where y is the current output,fis the variance matrix u is the current input and G is a recursive polynomial based upon eqn. 5.2.
6. Evaluated Example The results presented in this paper have been perfornled in a simulation implemented in MATLAB ver 5.3. Having defined the four major elements (peripheral elements, scheduling algorithm, plant and controller) the evaluation is performed next. Three scenarios are considered. First scenario is a fault free scenario where the response of the plant is ideal. Second scenario is a fault scenario based upon the loss of 50 percent of confidence in the "smart" sensor output. Finally a catastrophic condition is presented where CV is zero, then the control no longer uses the current sensor output. In order to be stable, the controller is switched to a safe value, which is constant. The current input of the plant is a pulse train whose indicates the current position of the ball. The output of the plant represents the current force applied to the beam. A fault is applied to one of the sensors, the fault is noise modifying the output of the sensor who is meac;uring the current position of the ball. Due to this condition, the presence of the fault has an effect into the system by eliminating one sensor within the configuration.
= Ej.,B = (E j + Fiz·J)s (5.2) where Ej;, and Fj are elements of a diophantine eqn. ei i.,
5.3. l=Ej(z·I)A(z·I)+z-IFj(z-l)
(5.3)
Where A represents the dynamics of the system. Having resolved eqn. 5.3, the control law is expressed as:
u =0.00 11(t-I)+0.02y\t-l)-0.OO lv(! -2)-0.05y(t-3) (5.4) Second structure differs from first option in the control strategy. This second approach is based upon a PID controller tuned from the conditions of a local fault .
Fig. 5 presents four windows, firstly the current input related to the movement of the beam, second is the current control output, third is confidence value response from current sensor element and last window shows the response of decision making procedure.
The appearance of a fault scenario decreases the certainty of the current position. Then, the controller is defined with this uncertainty. Constant values are tuned considering the lost of current position during a time interval. These values are kl=O.1, k2=-O.12 and k3=O.O. Where u =k e+k fedt+k de is the control o
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.'
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Fig. 5 shows the response of the sensor, the plant and the controller during a fault free scenario. Fig. 6 shows the response of the system when CV presents a fault condition at 2000 seconds. This CV degrades the system 50% of the current value. In here, the control law is switched to a classical PID controller where the output of the faulty sensor is still considered. This fault is active during 500 seconds.
law, u is the control output and e is the system error. Final implementation is based upon the use of a safe constant who considers the ball is on the middle of the beam. The constant value is k=O which makes the current position to the beam turn to be horizontal. This structure set the system to a constant value.
316
The response of the plant during a catastrophic scenario is presented in Fig. 7. In here, the faulty sensor is switched off. This fault appears at 2500 seconds as a degradation of the system after the appearance of first fault. This last fault is active during 500 seconds.
The presence of communication delays has an effect on the response of the controllers. For instance Fig. 8 shows the fault free scenario as part of the system. Solid line represents the response of the controller using the communication delays. Dashed line shows the response of the controller without considering time delays . .-~~----~----~~-------
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Fig. 8 Control Result from Fault Free Scenario Alternatively, Fig. 9 Shows the fault scenario that degrades the system upto 50% of correct response. In this case communication delays are considered. Solid line shows the controller response taking into account the communication delays shown in Fig. 3. Dashed line shows the response of the controller without considering these time delays. The reader may appreciate the degradation suffered due to the non consideration of time delays even by the use of control reconfiguration strategy.
Fig. 5 Fault Free Scenario 2 ·
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Fig. 9 Control Result from Fault Scenario 7. Conclusions This research work has shown the implementation of an on-line control reconfiguration approach. This is based upon a local fault diagnosis procedure integrated to peripheral elements which reports the condition of each element during a fault scenario. The result of each "smart" element is uscd by a decision making scheme in order to choose a suitable control law. Three different control strategies are proposed. First control law uses the whole number of sensors and actuators, this is using a predictive control law. Second control considers the degradation of one sensor due to the presence of a local fault. For this case a PlO controller is proposed. Finally a safe control status is performed in order to maintain the plant in a constant operating point, This drives the plant to a safe status during catastrophic conditions. The integration of local Fault Diagnosis with a supervisor presents the possibility of on-line control reconfiguration. The strategy of having different control strategies shows how the system can degraded its performance in a safety mode. There is a
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Fig. 7 Catastrophic Scenario at 2500 Seconds For the case of second and third scenario there is an error which presents non-zero conditions due to the fault. This residual existence is propagated to the control scheme. At this point, the decision making procedure decides which control is going to be used. This condition can present undesirable glitches during transitions. The problem is eliminated through the use of similar controllers. This means that the control laws are designed with equivalent performance responses.
317
potential risk of glitches when the decision making module switches from one condition to another. This is avoided by using the three control laws at the same time but just one of them closing to the feedback loop. This research has presented a strategy of control reconfiguration based upon local fault diagnosis using smart peripheral elements. Further work is necessary from the decision making module in order to produce a smooth transition from one controller to other. Further research is proposed in order to integrate local confidence values into the control law as additional parameters.
Control, Lund Institute Sweden.
Algorithms alld Arclzitectures for Real-Time Control AARTC'98, pp. 89-94, Cancun, Mexico. Benitez-Perez, H. (1999). Sma.t Distributed Systems, PhD. Thesis AC&SE Dept. University of Sheffield, UK. Camacho E. B. and Bordons A. (1998) Model Predictive Control. Springer-Verlag, USA . Dussud M., Galichot S. and Foulloy L. (1998). Application of Fuzzy Logic Control for Continuous Casting Mold Level
Control,lEEE TrallSactions on Control Systems Technology, vol.6, no.2, pp.246-56. Gertler 1. (1998). Fault Detection and Diagnosis in Engineering s.vstems, Marce! Dekker Inc . Marcos M ., Portillo J. and Bass J. M. (2000) MATLAB-Based Real-Time Framework for Distributed Control Systems, 6TH IFAC
Workshop on Algorithms and Architectures For Real-Time Control, AAR TC '2000, pp. 197 -202, Palma de Mallorca, Spain. Masten, M . K. (1997). Electronics: The intelligence in Intelligent Control, IFAC S.vmposium on
Intelligent Components and Instrument for Control Applications, Annecy, France, pp.
Time Consume (micro seconds) 450 50 0 100 pre- 3000
Var
Name
c b i t.: Or.
Communication Blocking Interference Capture sensor information Overhead time from processing sensor information Overhead from time postprocessing sensor information Communication time from sensor node to control node Overhead of Pre-processing Information from control node Overhead of Process Information from control node Control Process Time Communication time from control node to actuator node Processing time from actuator ) and2
Ods tl
Acknowledgements The authors would like to thank to DlSCA-IIMASUNAM and CONACYT (Num. I35561-A and CONACYT -UNAM Sub-RedlI/002/2000) for their finacial support. 8. References Almeida L., Pasadas R. and Fonseca 1. A. (1999). Using a Planning ScheduIer to Improve the Flexibility of Real-Time Fieldbus Networks, Control Engineering Practice, vol 7, pp. 101-108, Pergamon. Benitez-Pcrez, H., Thompson, H. A. and FIeming, P. J. (1998). Simulation of Distributed Fault Tolerant Heterogeneous Architectures for Real-Time Control, 51h IFAC Works/zop on
of Technology,
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Table La Time variable from Fault Free Scenario Time Consume (micro seconds) Overhead time [Tom pre-processing 1000 °rs sensor information Overhead time from post-processing 1000 Ods sensor information Capture sensor information 1000 !c c Communication 450 Blocking b 50 Interference i 0 Communication time from sensor 575 tJ node to decision making module Communication time from sensor 575 t2 node to control node Processing time before sending 2000 t.. l information Processing time before sending 2000 t..2 information Overhead of Pre-processing 3000 O~m Information Overhead of Process Information 3000 Onm Processing time before sending 1000 tdln information from Decision Making to Controller It 1= t.., Processinl! time from control node 1000 Communication time from Decision 575 t3 making node to control node Communication time from control 575 ~ node to actuator node Processing time from actuator ) and 2000 tAl 2 Var
Name
Table 1.b Time variables from Fault Scenario
1-11. Mathworks (1998). System Identification Too/box User's Guide, MATLAB . Nilsson, 1. (1998). Rea!-Time Control with Delays"; PhD. Thesis, Department of Automatic
318
RECONFIGURABLE DISTRIBUTED CONTROL CONSIDERING COMMUNICA nON TIME DELAY EFFECTS
Benitez-Perez H.*, and Garcia-Nocetti F.** (*). (**) Departamento de Ingenieria de Sistemas Computacionales y Automatizacion,
IIMAS.UNAM. Apdo. Postal 20-726. Del. A.Obregon. Mexico D.F.. 01000. Mexico. Fa;>:: ++52561601 76. Tel: (*) ++5256223639, (**) ++5256223569 Email: (*)hector(Mlxdea4.iimas.llnam.mx (contact author) (* *) fabian@lL\·dea4.iimas.unam.mx
Abstract: Increasingly, there is a move towards in-built intelligence for sensors and actuators to integrate "smart" peripheral elements as part of a distributed control system. The utilisation of local intelligence to provide local fault detection and fault tolerance opens the incorporation of new variables into the structure of the control law. How to integrate this information into the structure of the control law is presented in here. The main goal is to integrate a decision making procedure between peripheral elements and different control strategies. The re configuration of the control law based upon local health measures is decided by this procedure. Copyright i8 2001 1FAC.
Keywords: Distributed Systems, Process Supervision, Distributed Control, Static Scheduling.
1. Introduction The emergence of smart sensor and actuator technology removes the need for centralised control with feedback loops to dumb peripheral actuators replacing it with a databus connection (Benitez-Perez et aI., 1998).
reconfiguration based upon a fuzzy decision maker working as fuzzy supervisor. The strategy followed in here uses the information generated by smart elements in a decision making procedure. Peripheral elements generate a measure named confidence value, which indicates how the element has been degraded due to the presence of a local fault.
Control systems over distributed systems consider several design parameters such as partitioning allocation and communication policies. These are part of the design and deployment decision. Different aspects over the system are proposed. Firstly, the integration of smart peri)heral elements as autonomous elements capable of self diagnose in order to reconfigure the control strategy. Second, the reconfiguration of the control law based upon a safety degradation measure.
The decision making procedure chooses which control law needs to be used based upon the fault scenario. There are three control strategies, the first one is based upon a predictive control law, the second is based upon a PID controller and the third one is a safety value, which sends the plant to a stable operating point. Due to the use of a distributed system in order to communicate different entities, it is necessary to propose a scheduler taking into account the behaviour of the system under fault free and fault scenarios.
Several strategies for reconfigurable control have been studied for different research groups. For instance Dussud et aI., (1998) present a control law
313
A ball and beam plant, using two arrays of sensors and two actuators, has been selected as case study. This paper has been divided in seven sections. First section is the current introdu-::tion. Second section presents an overview of smart element technology. A description of the proposed scheduler is provided in third section. Fourth section describes briefly the plant model. The control design and the decision making strategy adopted is presented in the fifth section. Sixth section, shows practical results of case study. Finally, seventh section presents some concluding remarks.
The fuzzy system determines how big is the degradation in order to modify the current value of Confidence Value (CV). If the deviation of one of the residuals is considerable with respect to the current parameter this is declared as erroneous condition. Otherwise, the residual is categorised as "good".
3. Scheduler Design Scheduler strategy is integrated by four different types of elements, sensors, decision making module, controller and actuators. This scheduler presents sporadic communications due to the presence of fault scenarios. There are several types of time delays to be considered (Table I). These are related to communication, processing and capture. Time values shown in Table I are from the simulation procedure of the implemented example. There are two possible scenarios, first scenario establishes a fault free situation. Second scenario considers the communication between nodes when a fault scenario appears (Fig. 2).
2. "Smart" Elements Design Smart elements are defined as peripheral elements who have the capabilities of self-diagnose faults, self-compensates disturbances and digital communications (Masten, 1997). These elements arc mainly sensors and actuators. The typical configuration followed in this paper is presented in Fig. I (Benitez-Perez, 1999).
event
r---+-+"JI9---.;:-t--f-t--t--t--+---t-- sensor arr.lY
Fig. 1 Smart Sensor Strategy In Fig. 1 there are two blocks to be considered: the analytical redundancy block and the residual evaluation block. First block is based upon two parameter estimation procedures using two different sampling periods. The first being faster than the second one. First procedure performs the parameters every t, seconds, while, the second one estimates the parameters every t2 seconds. First procedure catches the current performance of the element, meanwhile second one catches the stable perfonnance of the clement. The difference between them gives the residual vector. This vector has a non-zero behaviour when a fault appear. PE I estimates five parameters as well as PE2. Both vectors do not have an exact physical meaning related to the dynamics of the sensor . This is not the aim pursued in this paper. Nevertheless, the relation between residual vector and fault presence is directly proportional. The evaluation block is performed using a fuzzy logic procedure named as res:dual evaluation block (Fig. I). This block fully evaluates the residual vector based upon Mamdani fuzzy rule strategy. This system has been tuned using the experience of the designer. The result of this evaluation procedure is a confidence value which has a range from 0 (catastrophic behaviour) to 1 (fault free scenario). The goal of this evaluation procedure is the identification of faults based upon the behaviour of whole residual vector. This idea uses the directional residuals concept explained in more detail by Gertler (1998).
H--+--+--ht.t-t-"'2...f...,...;:-t---+---t--t--+
oontroller
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+0
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Fig. 2 Scheduler for Fault Free Scenario e-"CftI
...
........
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...... I "'
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'.
Fig. 3 Scheduler for Fault Scenario For fault free scenario the time related to the sensing node is tl+o ps+od.+t.:=6.67 milliseconds. Time related to control node is Opc+Odc+ t2=2.8 milliseconds. When a fault scenario appears a new element is considered. Its name is decision making node. In order to incorporate this node to the system scheduler works as follows. The selected sensor transmits its value to control node. Due to its CV is less than a threshold, it transmits this value to the Decision Making node. This node processes the information and transmits its result to control node. Finally, control node decides which law is used in order to send a result to the actuators. Time delays are considered as follows,
314
sensor uses tsc=3 milliseconds (Fig. 3). The communication between sensor and control nodes is t,a= 2 milliseconds and the communication between decision making and contlol node is ('1= 2 milliseconds. Decision Making node spends t<1m= I millisecond in processing its information. Having recruit all necessary information control node process it during 1,,1=2.0 milliseconds. Afterwards, this result is sent to actuators nodes. The systems spends in this action t.,2+4=1.57 milliseconds. Finally the actuator node spends tAI=2.0 milliseconds in order to modify the plant. The total time spent for each scenario is 11.5 and 17.73 milliseconds, respectively. This calculation is based upon summation of every time concerned. For fault free scenario the sum is as follows tl+Ops+Ods+t., + 0pc+Od<+ t1+ tAl having as a result 11.5 milliseconds. For fault scenario the sum is next td01+ t,.2+(,.1+ t2+t3+tc2+t4+ tcl+t A1 · This sum gives as a result 17.73 milliseconds. As the reader may realize this difference performs an overhead due to reconfiguration strategy. This is overtaken by the use ofPID controller as mentioned further on.
A(:-')y(tl = :-J 8(z-' lu(/-I) +c(z-' le(t)
(4.1)
B =O+O.OOl3z-' + 0.0016:-'
C = 1+ 1.5977;-' +0.825Sz-' A
=1+2.0ISz-' + 1.032:- 2
Where y is the output, u is the input, z is the space variable, A, Band C are the representative polynomials of the system. d is a time delay variable that for this particular case is considered to be zero. This representation must be modified to that one expressed next. In this case, C term is no considered as part of the error. ~ .(t)=~u(t-J)+e(t) C C (4.2) or
v' = . ;" 11
...(t) 1+1.5977=-' +().82558= ' I/(t)
1-1.5977;-' + O.82558z'
A modification under equation 4.2 must be made to this stage in order to determine a suitable representation for predictive control.
A = M = (I -z-I)A = 1-I .032z- 1 + i.032z-2 -1.032z-3 (4.3)
For the case of this simulation, CANbus standard is used to establish time delays as shown in Table I.a and Table I.b.
Sensors and actuators models are considered lineal by the inherent self calibration within these elements. Due to this assumption, the plant model depends exclusively the dynamical behaviour of the ball and beam. Time delays produced by communication scheduler are considered as part of the dynamic behaviour. Control laws integrate this behaviour in both ca<;es (fault and f:lUIt free scenario).
Clock synchronisation is time stamping over each communication process. Time delays related to sensing, controlling and processing information are ba<;ed upon the response of the dynamics tested in a PIlI computer. The implementation of this scheduler is achieved using State-Flow toolbox from Matlab 5.3 (MATLAB, 1998).
The only considered fault scenario is the degradation of any of these peripheral elements per time. Just one sensor is considered to be faulty. The condition of the fault scenario is noise over one peripheral element. There are three main possible scenarios, fault free, non-catastrophic and catastrophic. The first scenario presents the obvious behaviour of the plant. In this case, the used control law is a predictive control strategy.
4. Plant Design The strategy followed in this paper is based upon Fig. 4. There is a reconfiguration approach based upon a confidence measure array generated by a group of "smart" sensors. Each "smart" sensor produces its own confidence value. This array is evaluated by a decision making module in order to choose one of the available control laws.
The second scenario degrades system up to a established threshold in order to reconfigure the control law. In this case, the control law is based upon a PID controller in order to stabilise the plant. Last scenario presents a catastrophic situation. The control law used is a constant value. This is due to safety conditions of the beam without considers the ball. In fact, the ball is expected to be lost but the beam is stable.
Plant
5. Reconfigurable Control Integration Having defined the "smart" element strategy, the scheduler behaviour and the dynamics of the plant, next step is the integration of both into the dynamics of the control law. As mentioned in section I, different strategies may be followed. For instance, Nilsson (1998) uses stochastic control in order to integrate random time delays due to disturbances within the system.
Fig. 4 Reconfigurable Control Scheme There are two arrays of sensors and two actuators. Each of them on each side of the beam. The model of the plant uses one sensor who is reporting the actual position of the ball and one actuator who is moving the beam. The plant dynamics are shown next:
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The decision making procedure is based upon two thresholds in order to define the boundaries of these three control laws. Table 2 shows this classification. The selection of control law a degradable condition based upon one faulty element. If every CV element are between 0.79 and 1.0 then first control law is selected. If one of the CV measurements is between 0.49 to 0.78 the control law is selected. Finally, if one of the CV measurements drops its value to below 0.48 last control law is chosen.
Alternative techniques, such as, predictive control (Camacho et aI., 1998) are feasible due to incorporation of time delays to the control structure. The use of "smart" elements information into the control law is based upon the use of arrays of confidence values from peripheral elements. The approach followed is the reconfiguration of the control law through the selection of different control strategies. These are integrated to a decision making algorithm in order to switch from one control law to another (Fig. 2). In case of catastrophic conditions this switch tends to move the system to a safc mode. Just one sensor is considered to be faulty.
Good O.79
Remember that in this case, the measure of one sensor is given to the controller. This is to deternline the actual position of the ball.
O.O
Bad
Safe
Values
I
V V V
Thresholds
Table 2 Threshold Decision Making Procedure First controller considers CV at 100% of its value where the input is 100% trustable. Second control strategy establishes the input at its 50% trust. This is due to the presence of a fault. Last control law is based upon a safe value in order to maintain the system within a safe condition. For last two cases second scheduler is used (Fig. 3). The structure of the predictive control law is based upon eqn. 5.1 . y=Gu+ f (5.1) Where y is the current output,fis the variance matrix u is the current input and G is a recursive polynomial based upon eqn. 5.2.
6. Evaluated Example The results presented in this paper have been perfornled in a simulation implemented in MATLAB ver 5.3. Having defined the four major elements (peripheral elements, scheduling algorithm, plant and controller) the evaluation is performed next. Three scenarios are considered. First scenario is a fault free scenario where the response of the plant is ideal. Second scenario is a fault scenario based upon the loss of 50 percent of confidence in the "smart" sensor output. Finally a catastrophic condition is presented where CV is zero, then the control no longer uses the current sensor output. In order to be stable, the controller is switched to a safe value, which is constant. The current input of the plant is a pulse train whose indicates the current position of the ball. The output of the plant represents the current force applied to the beam. A fault is applied to one of the sensors, the fault is noise modifying the output of the sensor who is meac;uring the current position of the ball. Due to this condition, the presence of the fault has an effect into the system by eliminating one sensor within the configuration.
= Ej.,B = (E j + Fiz·J)s (5.2) where Ej;, and Fj are elements of a diophantine eqn. ei i.,
5.3. l=Ej(z·I)A(z·I)+z-IFj(z-l)
(5.3)
Where A represents the dynamics of the system. Having resolved eqn. 5.3, the control law is expressed as:
u =0.00 11(t-I)+0.02y\t-l)-0.OO lv(! -2)-0.05y(t-3) (5.4) Second structure differs from first option in the control strategy. This second approach is based upon a PID controller tuned from the conditions of a local fault .
Fig. 5 presents four windows, firstly the current input related to the movement of the beam, second is the current control output, third is confidence value response from current sensor element and last window shows the response of decision making procedure.
The appearance of a fault scenario decreases the certainty of the current position. Then, the controller is defined with this uncertainty. Constant values are tuned considering the lost of current position during a time interval. These values are kl=O.1, k2=-O.12 and k3=O.O. Where u =k e+k fedt+k de is the control o
I
2
.'
dt
Fig. 5 shows the response of the sensor, the plant and the controller during a fault free scenario. Fig. 6 shows the response of the system when CV presents a fault condition at 2000 seconds. This CV degrades the system 50% of the current value. In here, the control law is switched to a classical PID controller where the output of the faulty sensor is still considered. This fault is active during 500 seconds.
law, u is the control output and e is the system error. Final implementation is based upon the use of a safe constant who considers the ball is on the middle of the beam. The constant value is k=O which makes the current position to the beam turn to be horizontal. This structure set the system to a constant value.
316
The response of the plant during a catastrophic scenario is presented in Fig. 7. In here, the faulty sensor is switched off. This fault appears at 2500 seconds as a degradation of the system after the appearance of first fault. This last fault is active during 500 seconds.
The presence of communication delays has an effect on the response of the controllers. For instance Fig. 8 shows the fault free scenario as part of the system. Solid line represents the response of the controller using the communication delays. Dashed line shows the response of the controller without considering time delays . .-~~----~----~~-------
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Tome
Fig. 8 Control Result from Fault Free Scenario Alternatively, Fig. 9 Shows the fault scenario that degrades the system upto 50% of correct response. In this case communication delays are considered. Solid line shows the controller response taking into account the communication delays shown in Fig. 3. Dashed line shows the response of the controller without considering these time delays. The reader may appreciate the degradation suffered due to the non consideration of time delays even by the use of control reconfiguration strategy.
Fig. 5 Fault Free Scenario 2 ·
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Fig. 9 Control Result from Fault Scenario 7. Conclusions This research work has shown the implementation of an on-line control reconfiguration approach. This is based upon a local fault diagnosis procedure integrated to peripheral elements which reports the condition of each element during a fault scenario. The result of each "smart" element is uscd by a decision making scheme in order to choose a suitable control law. Three different control strategies are proposed. First control law uses the whole number of sensors and actuators, this is using a predictive control law. Second control considers the degradation of one sensor due to the presence of a local fault. For this case a PlO controller is proposed. Finally a safe control status is performed in order to maintain the plant in a constant operating point, This drives the plant to a safe status during catastrophic conditions. The integration of local Fault Diagnosis with a supervisor presents the possibility of on-line control reconfiguration. The strategy of having different control strategies shows how the system can degraded its performance in a safety mode. There is a
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Fig. 7 Catastrophic Scenario at 2500 Seconds For the case of second and third scenario there is an error which presents non-zero conditions due to the fault. This residual existence is propagated to the control scheme. At this point, the decision making procedure decides which control is going to be used. This condition can present undesirable glitches during transitions. The problem is eliminated through the use of similar controllers. This means that the control laws are designed with equivalent performance responses.
317
potential risk of glitches when the decision making module switches from one condition to another. This is avoided by using the three control laws at the same time but just one of them closing to the feedback loop. This research has presented a strategy of control reconfiguration based upon local fault diagnosis using smart peripheral elements. Further work is necessary from the decision making module in order to produce a smooth transition from one controller to other. Further research is proposed in order to integrate local confidence values into the control law as additional parameters.
Control, Lund Institute Sweden.
Algorithms alld Arclzitectures for Real-Time Control AARTC'98, pp. 89-94, Cancun, Mexico. Benitez-Perez, H. (1999). Sma.t Distributed Systems, PhD. Thesis AC&SE Dept. University of Sheffield, UK. Camacho E. B. and Bordons A. (1998) Model Predictive Control. Springer-Verlag, USA . Dussud M., Galichot S. and Foulloy L. (1998). Application of Fuzzy Logic Control for Continuous Casting Mold Level
Control,lEEE TrallSactions on Control Systems Technology, vol.6, no.2, pp.246-56. Gertler 1. (1998). Fault Detection and Diagnosis in Engineering s.vstems, Marce! Dekker Inc . Marcos M ., Portillo J. and Bass J. M. (2000) MATLAB-Based Real-Time Framework for Distributed Control Systems, 6TH IFAC
Workshop on Algorithms and Architectures For Real-Time Control, AAR TC '2000, pp. 197 -202, Palma de Mallorca, Spain. Masten, M . K. (1997). Electronics: The intelligence in Intelligent Control, IFAC S.vmposium on
Intelligent Components and Instrument for Control Applications, Annecy, France, pp.
Time Consume (micro seconds) 450 50 0 100 pre- 3000
Var
Name
c b i t.: Or.
Communication Blocking Interference Capture sensor information Overhead time from processing sensor information Overhead from time postprocessing sensor information Communication time from sensor node to control node Overhead of Pre-processing Information from control node Overhead of Process Information from control node Control Process Time Communication time from control node to actuator node Processing time from actuator ) and2
Ods tl
Acknowledgements The authors would like to thank to DlSCA-IIMASUNAM and CONACYT (Num. I35561-A and CONACYT -UNAM Sub-RedlI/002/2000) for their finacial support. 8. References Almeida L., Pasadas R. and Fonseca 1. A. (1999). Using a Planning ScheduIer to Improve the Flexibility of Real-Time Fieldbus Networks, Control Engineering Practice, vol 7, pp. 101-108, Pergamon. Benitez-Pcrez, H., Thompson, H. A. and FIeming, P. J. (1998). Simulation of Distributed Fault Tolerant Heterogeneous Architectures for Real-Time Control, 51h IFAC Works/zop on
of Technology,
Ope Ode
!cl t2 tAl
3000 575 1000 1000 250 575 2000
Table La Time variable from Fault Free Scenario Time Consume (micro seconds) Overhead time [Tom pre-processing 1000 °rs sensor information Overhead time from post-processing 1000 Ods sensor information Capture sensor information 1000 !c c Communication 450 Blocking b 50 Interference i 0 Communication time from sensor 575 tJ node to decision making module Communication time from sensor 575 t2 node to control node Processing time before sending 2000 t.. l information Processing time before sending 2000 t..2 information Overhead of Pre-processing 3000 O~m Information Overhead of Process Information 3000 Onm Processing time before sending 1000 tdln information from Decision Making to Controller It 1= t.., Processinl! time from control node 1000 Communication time from Decision 575 t3 making node to control node Communication time from control 575 ~ node to actuator node Processing time from actuator ) and 2000 tAl 2 Var
Name
Table 1.b Time variables from Fault Scenario
1-11. Mathworks (1998). System Identification Too/box User's Guide, MATLAB . Nilsson, 1. (1998). Rea!-Time Control with Delays"; PhD. Thesis, Department of Automatic
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