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A New Robust Fault Detection Approach to Nonlinear Dynamical Systems

Jabbari, Biyouk | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43155 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Sadati, Nasser
  7. Abstract:
  8. In this thesis the problem of optimal robust fault detection has been studied. Optimal Fault Detection Filter (FDF) design, by using a Linear Matrix Inequality (LMI) structure for both linear systems with polytopic uncertainties and nonlinear Lipschitz systems has been considered. In this regard, a novel LMI is introduced which is capable of calculating the maximum lower bound of H− index with great accuracy.Then, based on the parameter-dependent Lyapunov function and the property of having convexity in combination of certain state space equations, the result is extended to polytopic uncertain systems. Afterward the design of an optimal observer-based residual generator, in the sense of H−/H∞ criteria, has been explored. In order to analyze the optimality of the FDF, we have used the fact that in analytical solution the transfer function from disturbance to residual is an all-pass filter. The parameters of the optimal filter for minimum phase systems were found by solving a convex optimization problem with LMI constraints. Moreover an iterative algorithm for non-minimum phase case and polytopic uncertain systems was presented. It is worth to mention that our proposed algorithm, in comparison with other common iterative methods, is more accurate and has higher convergence rate. Finally these latter algorithms were generalized to Lipschitz nonlinear systems and derived two algorithms; One based on model matching, and the other based on the direct use of H−/H∞ critera in time domain. These methods are tested on two nonlinear benchmark examples,Three-Tank system (DTS200) and inverted pendulum (LIP100), both from Amira company. Simulation results demonstrate the effectiveness of the developed algorithms in early detection of possible faults. At the end, some hints for further research work are presented
  9. Keywords:
  10. Riccati Equation ; Linear Matrix Inequality (LMI) ; Optimal Fault Detection ; Polytopic Uncertainty ; Lipschitz Systems

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