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

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79 80 Matching of a structure graph Matching of a structure graph means to relate unknown variables to known ones through constraints (solve for the unknown variables) A matching is complete if all unknown variables are matched Constraints that are not used by a complete matching (unmatched constraints) areusedto test the correctness of the solution These are parity relations of the problem and are used for diagnosis Mogens Blanke – Spring 2006 Unmatched constraints are parity relations • Unmatched constraints constitute parity relations • Select one (shown by white color) • Trace the matching backwards (yellow) to get an analytic expression for the parity relation Mogens Blanke – Spring 2006 40
81 82 Parity relations (normal operation) Autogenerated parity relations r1 = a1( u1, b1( y1)) r2 = a2( u2, b2( y2)) r3 = a3( u3, b3( y3)) r4 = c4( c2( b3( y3), m7( wm )), c3( b1( y1), b2( y2),... m7( wm)), d1( m1( vm)), m3( h2), m6( cm)) r5 = c5( m3( h2), m6( cm), d2( m5( p2)), m1( vm)) r6 = c6( c1( b1( y1), b2( y2), b3( y3), m7( wm )) ,... d3( m3( h2))) r7 = m2( h1, m3( h2)) r = m ( p , m ( p )) 8 4 1 5 2 Auto-generated parity relations Autogenerated parity relations in ”clear” equation language 8 2 1 Mogens Blanke – Spring 2006 r1 = gp( u1) − y1 r2 = gp( u2) −y2 r3 = gp( u3) − y3 r4 = X −1⎡c ( 1) ( 2) ( ) ⎤ T y + cT y + gw wm −1 M ⎢ ⎥−A ( h2) c Y ⎣ cb( y3) + gw( wm) ⎦ d − v dt r5 = d A( h2) vm + cm − p2 dt r6= ⎛− lc( 2 1 1) + ( 2)... ⎞ − y Ty lc y Ty dh2 I ⎜ ⎟− ⎜ N 2 + ( 3) + ( ) ⎟ ⎝ lc x by gwwm ⎠ dt r7 = h2 −h1 r = p −p m m Mogens Blanke – Spring 2006 41
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 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: 77 78 The Constraint Editor in SaTo
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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