![Diagnosis and FTC by Prof. Blanke [pdf] - NTNU](https://img.yumpu.com/12483948/8/500x640/diagnosis-and-ftc-by-prof-blanke-pdf-ntnu.jpg)
Diagnosis and FTC by Prof. Blanke [pdf] - NTNU
Diagnosis and FTC by Prof. Blanke [pdf] - NTNU Diagnosis and FTC by Prof. Blanke [pdf] - NTNU
15 16 Handling of sensor faults by reconfiguration Reconfiguration: Failed sensor measurement is replaced by an estimate, which is used in the feedback loop y = − + ˆ k (1 S( fk)) yk S( fk) y( fk) S is a diagonal matrix S ij=0( i ≠ j) Skk = 1 f ,0 otherwise k Condition for observer k to exist ( A,[ c1,.., ck− 1, ck+ 1,.., cm] ) is observable where c i is a column of C If not fully observable, the unobservable subsystem must at least be stable Model-matching state-feedback O H A B O H A B K + J H A H 2 = J E = ? I A @ F I O I J A 4 A @ A I EC A @ + J H A H E = ? I A @ F I O I J A K . = K J O 2 = J O O u u u u Plant estimator 1 est(y) | y , y , ... 2 3 estimator 2 est(y) | y 1 , y 3 , ... estimator 3 est(y) | y 1 , y 2 , ... y m =[y 1 ,y 2 ,y 3 ] y est y est y est Mogens Blanke – Spring 2006 The nominal (no fault) system in closed state feedback loop: xt () = ( A- BK) xt () yt () = Cxt () after the fault occurs, xt () = Axt f ()- But f () yt () = Cfxt () with new state feeedback controller: xt () = ( Af - BK f f ) xt () yt () = C x( t) f Mogens Blanke – Spring 2006 8
17 18 Model-matching state-feedback (2) Ideal if we could obtain A- BK = A f - B fK f This is only rarely possible (requires redundant actuators). Consider the relaxed condition: ∃K f ⊂{ Kstab} :min( A- BK) − ( A f - B fK f ) ? If the pseudo-inverse of B exists f T −1 T BK f f = A f −( A - BK) ⇒ K f = ( B fBf ) B f ( A f − A + BK) Example on handling of faults Mogens Blanke – Spring 2006 • Simple means needed to handle simple control loop faults • Applied common sense thus far, applied systematic common sense, however. •More challenge to come, though Mogens Blanke – Spring 2006 9
- Page 1 and 2: 1 2 Fault-tolerant Control Lecturer
- Page 3 and 4: 5 6 Structure of Plant + Controller
- Page 5 and 6: 9 10 Fault-tolerant Control Fault-t
- Page 7: 13 14 Handling of fault - reconfigu
- Page 11 and 12: 21 22 Handling of faults - 2 • Ac
- Page 13 and 14: 25 26 Properties of possible archit
- Page 15 and 16: 29 30 Diagnosis and Fault-tolerant
- Page 17 and 18: 33 34 Safety versus fault-tolerance
- Page 19 and 20: 37 38 Models of dynamical systems L
- Page 21 and 22: 41 42 Example on requirements to di
- Page 23 and 24: 45 46 Digraph for linear system Exa
- Page 25 and 26: 49 50 Example 5.3: tank system F =
- Page 27 and 28: 53 54 Example 5.3: controlled tank
- Page 29 and 30: 57 58 Non invertible constraints =
- Page 31 and 32: 61 62 Differential and integral con
- Page 33 and 34: 65 66 SaTool - A tool for Structura
- Page 35 and 36: 69 70 SaTool - A tool for Structura
- Page 37 and 38: 73 74 Constraints - forces from act
- Page 39 and 40: 77 78 The Constraint Editor in SaTo
- Page 41 and 42: 81 82 Parity relations (normal oper
- Page 43 and 44: 85 86 Fault means violation of a co
- Page 45 and 46: 89 90 Maritime uses - Naval and Off
15<br />
16<br />
H<strong>and</strong>ling of sensor faults <strong>by</strong> reconfiguration<br />
Reconfiguration: Failed sensor<br />
measurement is replaced <strong>by</strong> an<br />
estimate, which is used in the<br />
feedback loop<br />
y = − + ˆ<br />
k (1 S( fk)) yk S( fk) y( fk)<br />
S is a diagonal matrix S ij=0(<br />
i ≠ j)<br />
Skk<br />
= 1 f ,0 otherwise<br />
k<br />
Condition for observer k to exist<br />
( A,[ c1,.., ck− 1, ck+ 1,..,<br />
cm]<br />
) is observable<br />
where c i is a column of C<br />
If not fully observable, the unobservable<br />
subsystem must at least be stable<br />
Model-matching state-feedback<br />
O H A B<br />
O H A B<br />
<br />
K<br />
+ J H A H 2 = J<br />
E = ? I A @ F I O I J A <br />
<br />
4 A @ A I EC A @<br />
+ J H A H<br />
E = ? I A @ F I O I J A <br />
<br />
K<br />
. = K J O<br />
2 = J<br />
O<br />
O<br />
u<br />
u<br />
u<br />
u<br />
Plant<br />
estimator 1<br />
est(y) | y , y , ...<br />
2 3<br />
estimator 2<br />
est(y) | y 1 , y 3 , ...<br />
estimator 3<br />
est(y) | y 1 , y 2 , ...<br />
y m =[y 1 ,y 2 ,y 3 ]<br />
y est<br />
y est<br />
y est<br />
Mogens <strong>Blanke</strong> – Spring 2006<br />
The nominal (no fault) system<br />
in closed state feedback loop:<br />
xt ()<br />
= ( A- BK) xt ()<br />
yt () = Cxt ()<br />
after the fault occurs,<br />
xt ()<br />
= Axt f ()- But f ()<br />
yt () = Cfxt ()<br />
with new state feeedback controller:<br />
xt ()<br />
= ( Af - BK f f ) xt ()<br />
yt () = C x(<br />
t)<br />
f<br />
Mogens <strong>Blanke</strong> – Spring 2006<br />
8
Change language