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31320 Robust and Fault-tolerant Control
Michał Kramarczyk, s142910
Tomasz Stós, s142914
DTU Electrical Engineering, Technical University of Denmark
Agenda
Fault-tolerant Control:
• Fault detectability
• CUSUM algorithm
• GLR algorithm
• State feedback control
• Virtual Actuator
2 20 May 2015
Robust Control:
• Steady-state to GCC
• Maximal output
uncertainty
• Control reconfiguration
• Final simulation results
DTU Electrical Engineering, Technical University of Denmark
Fault detectability
3 20 May 2015
• ARR’s in symbolic form – backtracking
• ARR’s in analitical form and adding faults
• Transforming to frequency domain and using Final Value Theorem
DTU Electrical Engineering, Technical University of Denmark
CUSUM algorithm
4 20 May 2015
• Known mean value after
fault occurance
• Two-sided CUSUM
• Choosing the treshold h
• Simulink implementation
DTU Electrical Engineering, Technical University of Denmark
GLR algorithm
5 20 May 2015
• Unknown mean value after
fault occurance
• Choosing the window size
• Choosing the treshold h
• Simulink Implementation
DTU Electrical Engineering, Technical University of Denmark
State feedback controller
6 20 May 2015
• Finding the eigenvalues:
• Pole placement
• 3. Creating the controllerand generating time response
2 2
n
sin arccosn i
DTU Electrical Engineering, Technical University of Denmark
Virtual actuator
7 20 May 2015
• Separation principle:
𝜎 = 𝜎{𝐴 − 𝐵𝐾𝐶} ∪ 𝜎{𝐴 − 𝐵𝑓𝑀}
• Static reconfiguration
• Choosing N matrix
𝐵∆ = 𝐵 − 𝐵𝑓𝑁 → 0
• Choosing M matrix
DTU Electrical Engineering, Technical University of Denmark
From steady-space to GCC
8 20 May 2015
• Extracting transfer functions
• Including weigths
• Positive feedback
• Matrix P
DTU Electrical Engineering, Technical University of Denmark
Maximal output uncertainty
9 20 May 2015
• Introducing the uncertainty
• MΔ-structure
• Calculating M
DTU Electrical Engineering, Technical University of Denmark
Maximal output uncertainty
10 20 May 2015
• Condition for robust stability:
• Analysis on Bode plot
1M
DTU Electrical Engineering, Technical University of Denmark
Control reconfiguration
11 20 May 2015
• Fault detection
• Fault isolation
• Switching between controllers
• Operating modes
DTU Electrical Engineering, Technical University of Denmark
Final simulation results
12 20 May 2015
• Fault occurance
• Detection time
• Impact on the output
signal
• Uncontrolled situation
DTU Electrical Engineering, Technical University of Denmark
Thank you!
13 20 May 2015
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