Diagnosis and FTC by Prof. Blanke [pdf] - NTNU

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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

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