Fault-Tolerant Control
6.3 Fault-Tolerant Control Against Valve Faults
xv,ad
xv,m
xv
uv
xv,r
uvr
xv,m xv
uv
uv after DZC
uv into DZC DZC in
equation (9)
Valve after DZC
Fig. 6.6 Design of dead zone compensator for the valve spool
where A1 = xxv,mv,m−−xxv,ad v,r , A2 = uvmx(vx,mv,ad−−xvx,r v,r ) , ur = uvm xv,xm v,r ,
where xv,ad, xv,r show the estimated and preserved dead zones of the spool inde- pendently, which are 13% and 1% percent of the maximum displacement of spool xv,m.
The ELS pump controller contains both feedforward and feedback loops. Firstly, acccording to Eq. (6.4), the feedforward loop evaluates the swash-plate angle approx- imately by the pump flow mapping [11]. Nonlinear leakage flow in terms of pump displacement, pressure and velocity is captured by calibration of the pump flow mapping. Meanwhile, to maintain an appropriate preset pressure margin between the supply pressure and the highest load, a closed-loop control loop containing a PI regulator is introduced to compensate for the flow deviation on the feedforward loop.
up(t)=
[(
Kp pse+Ki
∫tn t0
psedt )
+(∑qi,ref+ps·Cp)
] Vpnm
(6.4)
pse =ps − pa − pm (6.5)
6.3 Fault-Tolerant Control Against Valve Faults 109
Fig. 6.7 Valve fault classification
Assumption 6.2 It is assumed that the rough fault information is confirmed by fault detection and diagnosis (FDD), and only contains locations of faulty valves and the fault types in Fig. 6.7. The assumption is reasonable since the necessary fault information is rough and can be distinguished easily by the developed and applied FDD.
Assumption 6.3 It is assumed that the pressure sensors or the pump have no faults.
For a random fault, the system dynamics become abnormal due to the faulty distur- bance in valve flows or pressures. Although there are only three faults classifications of the valve, different fault locations due to the layout of the IMV, will lead to distinct flow abnormalities in the actuators. Additionally, the performance of the system is significantly influenced by the operating modes in the hydraulic circle, as shown in Chap. 3. Taking both the valve faulty features and operating modes into account, the quasi-static models under typical faults are derived in Table 6.2. It is concluded that multiple factors including fault types, locations, and operating modes should be involved simultaneously in the Valve Fault-tolerant Control (VFTC) [12].
6.3.1 Valve Fault-Tolerant Control (VFTC) Principle
Without the additional hardware redundancy, the analytical redundancy of the system can tolerate certain valve faults by reconfiguring the controller together with the special multi-valve layout. As shown in Table 6.2, the models of IMV faults may result in various abnormal phenomena, such as parameter degenerations, functional destructions, and even flow obstacles.
Table 6.2 Model of different fault situations Fault information Fault-free
condition
Faulty conditions (a represents an unknown small spool displacement, b represents an unknown large spool displacement)
Lost functions Operating
mode
Faulty location
Fault type
NO_1 V1 2/3 qa =
qv(uv1, ∆p1); qb =
−qv(uv2, ∆p2); qs = qa;
q∗a = qv(uv1 ≡ a or b, ∆p1); ➁ Functional destruction
V2 1 q∗b = 0 ➂ Flow
obstacle V3 2/3 q∗a = qv(uv1, ∆p1)
−qv(uv3 ≡ a or b, ∆p3);
➀ Parameter degradation
NO_2 V2 2/3 qa =
−qv(uv3, ∆p3); qb =
qv(uv4, ∆p4); qs = qb
q∗b = qv(uv4, ∆p4)− qv(uv2 ≡ a or b, ∆p2)
➀ Parameter degradation
V4 2/3 q∗b = qv(uv4 ≡ a or b, ∆p4); ➁
Functional destruction
HPR V1 2/3 qa =
qv(uv1, ∆p1); qb =
−qv(uv4, ∆p4); qs = qa−qb
q∗a = qv(uv1 ≡ a or b, ∆p1); ➁ Functional destruction V2 2/3 q∗b = −qv(uv4, ∆p4)
−qv(uv2 ≡ a or b, ∆p2);
➀ Parameter degradation V3 2/3 q∗a = qv(uv1, ∆p1)
−qv(uv3 ≡ a or b, ∆p3);
➀ Parameter degradation
V4 1 q∗b = 0 ➂ Flow
obstacle
LPR V2 3 qa =
−q(uv3, ∆p3); qb = qv(uv2, ∆p2); qs = 0
q∗b = qv(uv2 ≡ a, ∆p2); ➁ Functional destruction
V3 1 q∗b = 0 ➂ Flow
obstacle
3 q∗a =
−qv(uv3 ≡ a, ∆p3)(Requireduv3 <
a)
➀ Parameter degradation V4 3 q∗b = qv(uv2 ≡ a, ∆p2)− qv(uv4 ≡
a, ∆p4)
➅ Parameter degradation REMARK: “NO_1” includes “PE” in Chap. 3; “NO_2” also be marked as “LSR” or “PR” in Chap. 3;
“HPR” also be marked as “HSRE” in Chap. 3; “LPR” includes “LSRR” and “LSRE” in Chap. 3
6.3 Fault-Tolerant Control Against Valve Faults 111
Cotnrol signal
reconfiguration Control loop
reconfiguration Mode reconfiguration FTC
Decision Mechanism
pa pb
ps
pr Pressure
feedback vref
up Normal controller
uv1, uv2 uv3, uv4 Mode
switch Valve control
Pump control
Fig. 6.8 Proposed VFTC system for IMCS
With the flexible control allocation in IMV, the key idea of VFTC is to reconfigure the normal controller when one of the valves faults. To build analytical redundancy associated with different faults, three reconfigurable control strategies are described, as shown in Fig. 6.8. To address the issue of parameter degradation, the core idea is to enlarge the control signals to compensate for flow degradation of the system dynamics. When functional destructions, it is recommended to exchanged control loops with fault-free valves to achieve optimal control performance. In case of a flow obstacle, the VFTC aims to alter the path of the flow to bypass the obstructed valve. Additionally, a VFTC decision mechanism is designed to allocate the required reconfigurable controller according to the fault information.
6.3.2 Control Signal Reconfiguration (Parameter Degradation)
The adverse effects of each valve fault can be analyzed according to Table 6.2. Under NO mode, the faults of bypass valves, including an abnormal opening or a leakage, would result in unexpected bypass flows. Under LPR mode, an abnormally large opening of the outlet orifice would also result in an excess flow than the required one.
To tolerate the above faults, a flow degradation is required for disturbances that exceed the required flow of the hydraulic actuator. Then, to alleviate the adverse effects, a flow compensation method is introduced to increase the current control signal of both the valve and the pump. However, an under-matched compensated flow has little effect on the fault tolerance capability, whereas an over-matched compensated
flow can cause other derived issues. Therefore, the challenge is how to match the actual flow disturbance with the supply flow accurately, especially without spool displacement and actuator velocity sensors.
As shown in Fig. 6.9, reconfigurations of the control signals are designed as follows. Under NO mode, the meter-in valve V1 loses its ability to control the velocity due to the unexpected flow disturbance caused by V3. As a result, the original control variable v by the V1 valve is changed to the backpressure pb. Alternatively, the fault- free meter-out valve V2, which is originally employed to control backpressure, is now changed to control the velocity v. This reconfiguration endeavors V2 to reject the flow disturbance such that the system can still track the desired motion. At the same time, by Eqs. (6.6) and (6.7), V1 is automatically enlarged such that the required pb is maintained under the reference velocity. Under LPR mode, the same control reconfiguration strategy by the VFTC is designed to compensate for flow disturbance caused by the abnormally large opening of V3.
u∗v2 = qv −1 (vref Ab, pb − pr) (6.6)
Fig. 6.9 VFTC design to reconfigure control signal
6.3 Fault-Tolerant Control Against Valve Faults 113
u∗v1 = K p(pref − pb)+ Ki∫
(pref − pb)dt (6.7) Then, the flow disturbance can be estimated by the difference between the reference flow qref and estimated qv1 as:
q
∆
v1 = qv(
u∗v1, ps − pa)
(6.8)
qc = q∆v1 − vref Aa (6.9)
The estimated flow disturbance is then utilized for the pump control through a feedforward unit:
u∗p =
[(
Kp pse+Ki
∫tn t0
psedt )
+(∑qref+ps·Cp+qc)
] Vpnm
(6.10)
6.3.3 Control Loop Reconfiguration (Functional Destruction)
As depicted in Table 6.2, if the valve spool is jammed in an intermediate displacement, then the regulation of the valve opening is disabled, which conducts a constant spool displacement. In this case, flows still cross this valve with an uncontrollable pressure drop, which degrades the precision of the actuator velocity and supply pressure. As shown in Fig. 6.10, the VFTC considers the faulty valve as a fixed orifice with an unknown throttling area, and then the control loop is flexibly configured utilizing the independent control of the inlet and outlet.
First, the velocity loop of the meter-in valve V1 must be switched off, which is exhibited by Switch S1 in Fig. 6.10. Second, if the faulty cylinder is a low-load actuator, then the velocity controller is switched from V1 to V2 (by Switch S2), such that the desired velocity can be tracked again. Now, the control signal of V2 is given by Eq. (6.6). Third, if the faulty cylinder is the highest load actuator, then the pressure loop is still controlled by V2, but the pump controller is switched from a closed loop to an open loop (by Switch S3). With these multiple switching, the supply pressure depends on the fixed hydraulic resistance in faulty V2, and the velocity of the faulty actuator is controlled by the pump controller in Eq. (6.11). Nevertheless, the loss of supply flow accuracy is unavoidable without the control of the pump closed-loop.
Furthermore, the supply pressure may increase abnormally when the failure spool displacement is small.
u∗p = (∑qref+ps·Cp)
Vpnm (6.11)
Fig. 6.10 VFTC design to reconfigure valve and pump control loop
6.3.4 Operating Mode Reconfiguration (Flow Obstacle)
As indicated in Table 6.2, if a single valve fails in the closed state, the valve will block the flow required for the inlet and outlet of the cylinder. Furthermore, this faulty valve cannot be utilized anymore unless a new valve is replaced offline. In this case, by reconfiguring the operation mode of the VFTC, the system can continue to work, but the energy saving performance is reduced. As depicted in Fig. 6.11, in load quadrants I, II, and IV, the mode-switching logic contains two or three optional modes, not just one. When a fault occurs, the original mode in the optimal efficiency is converted to the suboptimal mode by activating the standby fault-free valve. Then, the influence of the blocked faulty valve can be avoided by the substituted flow path.
However, the reconfigurable modes from LPR/HPR to NO give up the saved energy using flow or pressure regenerations. Additionally, for the high load in quadrant I, the reconfigurable mode from NO to HPR also accompanies a higher pressure, and thereby the feasibility of such reconfiguration is subject to the maximal pump pressure.
6.3 Fault-Tolerant Control Against Valve Faults 115
Initial state Vref=0
Qua. I Qua.II
Qua.III
FL vref
+
-
+
pr
Qua.IV vref
Fl
v Fl
v
Fl
v Fl
v FL<FL,lim
qv>qv,lim
FL<FL,lim
qv>qv,lim Light load
NO_2 NO_1
LPR NO_1 LPR HPR
High load
V2 Fault
V4 Fault
V2 Fault
V3 Fault
V2&V3 Fault
HPR V4 Fault NO_2
Fig. 6.11 VFTC design to reconfigure operating mode
6.3.5 Design of the VFTC Decision Mechanism
How to assign the reconfigurable controllers is a key element in resolving a random valve fault. There exist three degrees of fault tolerance from low to high: fail-safe, fail-tolerant, and fail-operational. Based on this definition and the distinguished capabilities of reconfigurable controllers, the decision criterion is as follows:
a. Fault case 1: in order to avoid the blockage of the flow path caused by abnormal closing of the valve, the pattern must be reconfigured.
b. Fault case 2/3 in the valves with speed control loops: a control loop reconfigura- tion is chosen to restore motion tracking capability through coordinated control of the fault-free valves and pump.
c. Fault case 2/3 in the bypass: control signals are reconfigured to compensate for the accidental leakage caused by the abnormal opening of the bypass valve.
d. Fault case 2 in meter-out valves under LPR modes: in order to compensate for the abnormally large flow due to the excessively large outlet opening, the control signal must be reconfigured.
Based on the above rules, the decision-making mechanism is shown in Fig. 6.12.
Mode Control
loop Control
signal Reconfigurable
controller NO_1
HPR LPR NO_2
Fault location
V1
V3 V4
V2 Case 1
Case 3 Case 2 Fault type
Mode Control
loop Control
signal NO_1
HPR LPR NO_2
V1
V3 V4 V2
Case 1
Case 3 Case 2 Mode
Control loop Control
signal NO_1
HPR LPR NO_2
V1
V3 V4 V2
Case 1
Case 3 Case 2
Mode Control
loop Control
signal NO_1
HPR LPR NO_2
V1
V3 V4 V2
Case 1
Case 3 Case 2 Operating
mode Operating
mode Reconfigurable
controller Fault
location Fault type
Fig. 6.12 Flow chart of VFTC decision mechanism