Robust and Fault Tolerant Control

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


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


CUSUM algorithm

4 20 May 2015

• Known mean value after

fault occurance

• Two-sided CUSUM

• Choosing the treshold h

• Simulink implementation


GLR algorithm

5 20 May 2015

• Unknown mean value after

fault occurance

• Choosing the window size

• Choosing the treshold h

• Simulink Implementation


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


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


From steady-space to GCC

8 20 May 2015

• Extracting transfer functions

• Including weigths

• Positive feedback

• Matrix P


Maximal output uncertainty

9 20 May 2015

• Introducing the uncertainty

• MΔ-structure

• Calculating M


Maximal output uncertainty

10 20 May 2015

• Condition for robust stability:

• Analysis on Bode plot

1M


Control reconfiguration

11 20 May 2015

• Fault detection

• Fault isolation

• Switching between controllers

• Operating modes


Final simulation results

12 20 May 2015

• Fault occurance

• Detection time

• Impact on the output

signal

• Uncontrolled situation


Thank you!

13 20 May 2015

Robust and Fault Tolerant Control

Documents

Transcript of Robust and Fault Tolerant Control