Discrete-event Modelling and Diagnosis of Quantised Systems Jan - PDF document

st 1 HYCON PhD School on Hybrid Systems www.ist-hycon.org www.unisi.it Discrete-event Modelling and Diagnosis of Quantised Systems Jan Lunze Ruhr-University Bochum, Germany Lunze@atp.ruhr-uni-bochum.de scimanyd suounitnoc enibmoc smetsys dirbyH lacipyt (snoitauqe ecnereffid ro laitnereffid) scimanyd etercsid dna stnalp lacisyhp fo fo lacipyt (snoitidnoc lacigol dna atamotua) fo senilpicsid gninibmoc yB .cigol lortnoc ,yroeht lortnoc dna smetsys dna ecneics retupmoc dilos a edivorp smetsys dirbyh no hcraeser ,sisylana eht rof sloot lanoitatupmoc dna yroeht fo ngised lortnoc dna ,noitacifirev ,noitalumis egral a ni desu era dna ,''smetsys deddebme`` ria ,smetsys evitomotua) snoitacilppa fo yteirav ssecorp ,smetsys lacigoloib ,tnemeganam ciffart .(srehto ynam dna ,seirtsudni HYSCOM IEEE CSS Technical Committee on Hybrid Systems 11 Siena, July 1 9-22, 2005 - Rectorate of the University of Siena

� � � � Discrete-event modelling and Supervisory control loop diagnosis of quantised systems ������������� Jan Lunze ���� ���� ������������������� Ruhr-University Bochum ��������� Institute of Automation and Computer Control email: Lunze@atp.ruhr-uni-bochum.de �������� ��������� 1. Introduction to discrete-event modelling of hybrid systems �������������� ��������� ��������� ��������� � � 2. Properties of quantised systems � � 3. Some basics of automata theory �������� � �������� � 4. Discrete-event modelling of quantised systems by ab- straction ���������� 5. Diagnosis of automata 6. Diagnosis of quantised systems � 7. Application examples Ways for dealing with hybrid systems • Combine methods elaborated in continuous and discrete– 8. Conclusions event systems theories • Abstract a discrete–event representation of the hybrid system and apply discrete–event systems theory Example: A batch process Model–based diagnosis � ���������������� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��� � � � � � ˙ 1 ˙ Q p − ˙ Q 1 − ˙ � h 1 = Q 12 A 1 Diagnostic problem � ˙ 1 ˙ Q 12 − ˙ � h 2 = Q 2 Given: Model depending on f and z 0 A 2 ˙ � Measured I/O pair ( V, W ) Q 1 = Pos ( V 1 ) S v 2 gh 1 ˙ � Q 12 = Pos ( V 12 l ) S v sgn( h 1 − h 2 ) 2 g | h 1 − h 2 | Consistency-based diagnosis: ˙ � Q 2 = Pos ( V 2 ) S v 2 gh 2 Can the system subject to fault f generate the output Q p = p ( t ) ˙ ˙ Q p 0 W if it obtains the input V ? with • Diagnostic problems include observation problems. 0 ≤ h 1 ( t ) , h 2 ( t ) ≤ h max • Fault detection: 0 ≤ p ( t ) ≤ 1 Inconsistency with the faultless system ⇓ • Fault identification: ˙ x = f ( x ( t ) , u ( t )) Consistency with the system subject to fault f → f is a fault candidate y ( t ) = g ( x ( t ) , u ( t ))

� � ������������� ����������������������� � ��� � ��� � � �� � ��� � � �� � ˙ 1 ˙ Q p − ˙ Q 1 − ˙ Q 12 − ˙ � h 1 = Q 12 h A 1 � ˙ 1 � ˙ ˙ Q 12 + ˙ Q 12 h − ˙ � h 2 = Q 2 1 ˙ Q p − ˙ Q 1 − ˙ Q 12 − ˙ � A 2 h 1 = Q 12 h √ 2 gh 1 � Pos ( V 1 ) S v if h 1 > 0 A 1 ˙ Q 1 = � ˙ 0 else 1 ˙ Q 12 + ˙ Q 12 h − ˙ � h 2 = Q 2 � ˙ Q 12 = Pos ( V 12 l ) S v sgn( h 1 − h 2 ) 2 g | h 1 − h 2 | A 2 √ 2 gh 1 ⎧ � Pos ( V 12 h ) S v sgn( h 1 − h 2 ) 2 g | h 1 − h 2 | if h 1 , h 2 > h v ⎧ Pos ( V 1 ) S v if h 1 > 0 ⎪ ⎪ ˙ ⎪ ⎪ Q 1 = ⎨ ⎪ � ⎪ Pos ( V 12 h ) S v 2 g | h 1 − h v | if h 1 > h v , h 2 ≤ h v ˙ ⎨ Q 12 h = 0 else ⎪ � ⎩ − Pos ( V 12 h ) S v 2 g | h 2 − h v | if h 2 > h v , h 1 ≤ h v ⎪ ⎪ ⎪ ⎪ ˙ � ⎪ 0 if h 1 , h 2 ≤ h v Q 12 = Pos ( V 12 l ) S v sgn( h 1 − h 2 ) 2 g | h 1 − h 2 | ⎩ √ 2 gh 2 � Pos ( V 2 ) S v if h 2 > 0 ˙ ⎧ = � Q 2 Pos ( V 12 h ) S v sgn( h 1 − h 2 ) 2 g | h 1 − h 2 | if h 1 , h 2 > h v 0 else ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ˙ ⎪ � = 0 if h 1 ≥ h 1 max Q p ⎪ Pos ( V 12 h ) S v 2 g | h 1 − h v | if h 1 > h v , h 2 ≤ h v ⎪ ˙ ⎪ Q p ∈ [0 . 8 ˙ ˙ Q p 0 , ˙ ⎨ Q 12 h = Q p 0 ] if h 1 < h 1 max � − Pos ( V 12 h ) S v 2 g | h 2 − h v | if h 2 > h v , h 1 ≤ h v ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ Pos ( V 1 ( t )) , Pos ( V 12 l ( t )) ∈ { 0 , 1 } 0 if h 1 , h 2 ≤ h v ⎪ ⎪ ⎪ ⎩ √ 2 gh 2 ⎧ Pos ( V 2 ) S v if h 2 > 0 ⎧ ⎧ 1 if h 1 ( t ) > l 11 1 if h 1 ( t ) > l 12 ˙ ⎪ ⎪ ⎪ Q 2 = ⎨ L 11 ( t )= ⎨ L 12 ( t )= ⎨ 0 else 0 else 0 else ⎪ ⎩ ⎪ ⎪ ⎩ ⎩ p ( t ) ˙ ⎧ Q p 0 if h 1 < h 1 max ⎧ ⎧ 1 if h 1 ( t ) > l 21 1 if h 1 ( t ) > l 22 ˙ ⎪ Q p = ⎨ ⎪ ⎪ L 21 ( t )= ⎨ L 22 ( t )= ⎨ 0 if h 1 ≥ h 1 max 0 else 0 else ⎪ ⎩ ⎪ ⎪ ⎩ ⎩ ⎧ 1 if h 1 ( t ) > l 23 ⎪ L 23 ( t )= ⎨ 0 else ⎪ ⎩ � ������������������������������ Diagnosis of the tank system � ������������������������������ � ��� � � �� � ˙ 1 ˙ Q p − ˙ Q 1 − ˙ Q 12 − ˙ � h 1 = Q 12 h A 1 �� � ��� � � � ˙ 1 ˙ Q 12 + ˙ Q 12 h − ˙ � h 2 = Q 2 A 2 √ 2 gh 1 ⎧ Pos ( V 1 ) S v if h 1 > 0 ˙ ⎨ Q 1 = 0 else ⎩ ˙ � Q 12 = (1 − f 3 ) Pos ( V 12 l ) S v sgn( h 1 − h 2 ) 2 g | h 1 − h 2 | 0.6 ⎧ � (1 − f 2 ) Pos ( V 12 h ) S v sgn( h 1 − h 2 ) 2 g | h 1 − h 2 | if h 1 , h 2 > h v 0.5 ⎪ Pegel links / m ⎪ ⎪ 0.4 ⎪ � ⎪ (1 − f 2 ) Pos ( V 12 h ) S v 2 g | h 1 − h v | if h 1 > h v , h 2 ≤ h v ˙ ⎪ ⎨ Q 12 h = 0.3 � − (1 − f 2 ) Pos ( V 12 h ) S v 2 g | h 2 − h v | if h 2 > h v , h 1 ≤ h v ⎪ ⎪ 0.2 ⎪ ⎪ ⎪ 0 if h 1 , h 2 ≤ h v ⎪ ⎩ 0.1 √ 2 gh 2 ⎧ 0 Pos ( V 2 ) S v if h 2 > 0 ˙ ⎨ 0 20 40 60 80 100 120 Q 2 = Zeit / s 0 else ⎩ ⎧ (1 − f 1 ) p ( t ) ˙ 0.6 Q p 0 if h 1 < h 1 max ˙ ⎨ Q p = 0.5 0 if h 1 ≥ h 1 max Pegel rechts / m ⎩ 0.4 Pos ( V 1 ( t )) , Pos ( V 12 l ( t )) ∈ { 0 , 1 } 0.3 f 1 , f 2 , f 3 , f 4 ∈ { 0 , 1 } 0.2 ⎧ ⎧ 1 if h 1 ( t ) > l 11 1 if h 1 ( t ) > l 12 0.1 ⎨ ⎨ L 11 ( t ) = L 12 ( t ) = 0 0 else 0 else ⎩ ⎩ 0 20 40 60 80 100 120 Zeit / s ⎧ ⎧ 1 if h 1 ( t ) > l 21 (1 − f 4 ) if h 1 ( t ) > l 22 ⎨ ⎨ L 21 ( t ) = L 22 ( t ) = 0 else 0 else Is the tank system faulty? ⎩ ⎩ ⎧ 1 if h 1 ( t ) > l 23 ⎨ L 23 ( t ) = 0 else ⎩