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Diagnosis and FTC by Prof. Blanke [pdf] - NTNU
Diagnosis and FTC by Prof. Blanke [pdf] - NTNU Diagnosis and FTC by Prof. Blanke [pdf] - NTNU
59 60 Purpose and scope of part 2 • Matching – a graph method to find the nonlinear parity relations that can later be used in diagnosis. • Define maximal and complete matching • Investigate matching on an oriented graph • Discuss causality • Dealing with algebraic constraints • Dealing with loops in graphs Complete matching Mogens Blanke – Spring 2006 A matching M is a subset of edges such that no edge have common node (neither in C nor in X). Let M be number of edges in M, then M ≤ min C X A matching is complete in X if M = X. It is complete in C if M = C . Figure: One incomplete and two complete matchings in X for the tank example. ( , ) Mogens Blanke – Spring 2006 30
61 62 Differential and integral constraints (repeat) Differential constraint dh c6: h= dt Integral constraint c : h( t) = h( τ) dτ + h(0) 6 t ∫ 0 Obvious assumptions (5.2) All constraints in C are compatible The constraints provide a solution to the behaviour of a physical system. (5.3) All constraints in C are independent Mogens Blanke – Spring 2006 Mogens Blanke – Spring 2006 31
- 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 and 8: 13 14 Handling of fault - reconfigu
- Page 9 and 10: 17 18 Model-matching state-feedback
- 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: 57 58 Non invertible constraints =
- 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
61<br />
62<br />
Differential <strong>and</strong> integral constraints<br />
(repeat)<br />
Differential constraint<br />
dh<br />
c6: h=<br />
dt<br />
Integral constraint<br />
c : h( t) = h( τ) dτ + h(0)<br />
6<br />
t<br />
∫<br />
0<br />
Obvious assumptions<br />
(5.2) All constraints in C are compatible<br />
The constraints provide a solution to the<br />
behaviour of a physical system.<br />
(5.3) All constraints in C are independent<br />
Mogens <strong>Blanke</strong> – Spring 2006<br />
Mogens <strong>Blanke</strong> – Spring 2006<br />
31
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