5.5 Summary
6.1.2 DES Model of the EFI System
The DES model of the EFI system is defined as G = hX, S,=, X0i. Each state x ∈ X in the EFI system model is distinguished by an enumeration of the set of state variables S. There exist two pressure sensors and one exhaust oxygen sensor in the EFI system.
The control commands issued by the ECU and outputs of the sensors are considered as the state variables. Table 6.1 summarizes the state variables and their meaning. The EFI system represented by modelGis shown in Figure 6.2. In order to model the faulty behaviors in G, we assume a ‘Stuck Closed’ failure of the throttle valve in the Air Flow Subsystem (fault type F1) and a ‘Pump On’ failure of the fuel pump in the Fuel Flow Subsystem (fault type F2). The control subsystem is assumed to be fault-free in our case.
The model G has a set of states X = {x1, x2, ..., x12}, and a set of transitions
= = {τ1, τ2, ..., τ12, τF1, τF2}. The occurrence of the fault types F1 and F2 in the sys- tem model G are represented through unmeasurable transitions τF1 and τF2, respec- tively. All states reachable through the transitionτFi are faulty (of typeFi) and labeled with Fi, i.e., xd(C) = {Fi},1 where i ∈ {1,2}. Corresponding to the nominal states, xd(C) = {N}. An enumeration of the variables corresponding to each state in G is
1ddenotes the state number.
6.1 DES Modeling and Fault Diagnosis of an Electronic Fuel Injection System
Table 6.1: State variables and their meaning.
State variable Meaning
SV Status of the throttle valve (Open (1)/Closed (0)) SP Status of the fuel pump (ON (1)/OFF (0))
SOS
Readings of the oxygen sensor
(Presence (O)/Absence of Oxygen (N O))
SV S Readings of the air-pressure sensor (PS1) located in the intake manifold (Pressure (P1)/No Pressure (N P1))
SP S Readings of the fuel-pressure sensor (PS2) located in the fuel rail (Pressure (P2) /No Pressure (N P2))
C Unmeasurable status variable associated with a state
x1 N
x3 N
x5 N
x7 N
x11 F2
x12 F2
x9 F2
x10 F2
x2 F1
x4 F1
x6 F1
x8 F1
1
2
3 4
5
6
7
8
12 9
10
11
2 1
Figure 6.2: The model of the EFI system: G.
presented in Table 6.2. It may be noted that, all state variables except C are mea- surable, that is, Sm = {SV, SP, SOS, SV S, SP S} and Su = {C}. We have modeled the
‘Stuck Closed’ fault only from initial state x1 and ‘Pump On’ fault only from state x5 because the corresponding fault causing transitions become unmeasurable from these states. The fault causing transitions from other states are measurable resulting in triv- ial fault diagnosability and hence, we have not considered them. The behavior of G
Table 6.2: State variables of the model G.
State State variables State State variables
x1 SV = 0, SP = 0, N O, N P1, N P2 x6 SV = 1, SP = 1, N O, N P1, P2 x3 SV = 1, SP = 0, N O, P1, N P2 x8 SV = 1, SP = 0, N O, N P1, N P2
x5 SV = 1, SP = 1, O, P1, P2 x9 SV = 1, SP = 1, O, P1, P2
x7 SV = 1, SP = 0, N O, P1, N P2 x10 SV = 1, SP = 0, O, P1, P2 x2 SV = 0, SP = 0, N O, N P1, N P2 x11 SV = 0, SP = 0, N O, N P1, P2 x4 SV = 1, SP = 0, N O, N P1, N P2 x12 SV = 1, SP = 0, O, P1, P2
(shown in Figure 6.2) is explained as follows:
• The nominal behavior of Gis represented through the set of states {x1, x3, x5, x7} and transitions τ1, τ2, τ3, τ4. The initial state X0 ={x1} defined by SV = 0, SP = 0, SOS =N O, SV S =N P1, SP S =N P2, denotes the ‘Closed’ status of the throttle valve and ‘OFF’ status of the fuel pump. The pressure sensors P S1 and P S2 do not detect air or fuel flows in the system at this state and hence, SV S = N P1 and SP S = N P2. When the ECU issues the command to open the throttle valve (SV = 1), G moves from state x1 to state x3 through the transition τ1. Here, the sensor reading SV S =P1 shows the flow of air in the system due to the opening of the valve. G moves to state x5 from state x3 through the transition τ2 when the ECU issues the command to start the fuel pump (SP = 1). Statex5 with its state variablesSV = 1, SP = 1, SOS =O, SV S =P1, SP S =P2 represents the functioning of the engine due to the flow of air and fuel in the system. When the ECU issues the command to stop the fuel pump (SP = 0), G moves from state x5 to state x7 through the transition τ3. Here, the sensor P S2 gives the reading SP S =N P2
6.1 DES Modeling and Fault Diagnosis of an Electronic Fuel Injection System
which shows no fuel flow in the system. Gmoves back to its initial statex1through the transition τ4 when the ‘Closed’ command is issued to the throttle valve from the ECU (SV = 0).
• Due to the occurrence of the faultF1,Gmoves from nominal to its faulty behavior represented through the set of states {x2, x4, x6, x8} and the set of transitions {τ5, τ6, τ7, τ8}. G moves from the nominal state x1 to the faulty state x2 through the unmeasurable transitionτF1. All the states afterτF1 have the label F1, that is, xd(C) = {F1}, where d ∈ {2,4,6,8}. All state variables in x2 barring C assume the same set of values as that of x1 and hence, these two states are considered as measurement equivalent (represented as x1Ex2; see Definition 2.4.1). From x2, G moves to faulty state x4 on transition τ5 representing the situation when the ECU has issued the command to open the valve (SV = 1) but sensor P S1 does not detect any air pressure (SV S = N P1). G moves from x4 to x6 on τ6 representing the situation when there is fuel flow (SP = 1, SP S = P2) but no air flow (SV S = N P1) even though SV = 1. Subsequently, when the ECU issues the command to stop the fuel pump,G moves fromx6 to faulty state x8 on transition τ7. At x8, SV = 1, SP = 0, SOS =N O, SV S =N P1, SP S =N P2. G moves back to state x2 through the transition τ8 when the ECU issues the command to close the valve.
• Similarly, as a result of the faultF2, Gmoves from nominal to its faulty behavior represented by the states x9, x10, x11, x12 and the transitions τ9, τ10, τ11, τ12. G moves from the nominal state x5 to its measurement equivalent faulty state x9 (x5Ex9) through the unmeasurable transitionτF2. All the states afterτF2 have the label F2, that is, xd(C) = {F2}, where d ∈ {9,10,11,12}. From x9, G moves to faulty state x10 on transition τ9 representing the situation when there is both air and fuel flow in the system (SV S =P1, SP S =P2) even though the desired status of the pump is ‘OFF’ (SP = 0). G moves from x10 to x11 on τ10 to model the situation when fuel pressure is detected (SP S =P2) even though both air and fuel flow are desired to be stopped (SV = 0, SP = 0). Subsequently, when the ECU
issues the command to open the valve, G moves from x11 to faulty state x12 on transition τ11. Gmoves back to statex9 through the transitionτ12 when the ECU issues the command to start the pump.