Sensor failure tolerant observer design
File(s)
Author(s)
Luo, Wenjia
Type
Thesis
Abstract
Control systems play a pivotal role in the operation of processes such as manufacturing, telecommunications and electronics. As these systems increase in complexity, they become vulnerable to failures and the implementation of Failure Tolerant Control methodologies becomes essential.
This thesis focuses on designing a failure-tolerant observer that satisfies pole location constraints to improve the system response under a range of sensor failure scenarios, determined by the number of sensors $m$ and a minimum number of assumed working sensors $p$, while optimising the failure-free performance. Thus $p$ defines a failure-tolerance level for the design.
A failure-tolerant observer design methodology based on regional pole placement is presented. A semi-definite relaxation (SDR) technique is used to alleviate the computational burden. This results in only a few linear matrix inequality (LMI) sufficient conditions, but at the expense of reduced performance. To compensate, block Hadamard product approaches are suggested to provide more degrees of freedom to improve the solution.
For optimum stability, a novel algorithm, based on the Separation Theorem is derived which decouples the system and Lyapunov matrices. After deriving an initial solution via the quadratic method, the technique provides a methodology for addressing the non-linearity of the problem. The algorithm can be run iteratively until an acceptable performance is obtained.
The application of failure tolerance threshold $p$ reduces the failure-tolerant abilities, but it also reduces the number of failure scenarios, making the problem tractable. The SDR technique further decreases the number of LMIs to one when only stability is concerned. There is therefore a trade-off between performance, failure-tolerance level and computational complexity. To address this, a novel technique (the Equal-to-$q$ SDR technique) is derived. By compressing the number of LMIs into $(m-p)$ (rather than one), this reduces the computational load, while ensuring that the performance and failure-tolerant abilities meet the desired specifications.
This thesis focuses on designing a failure-tolerant observer that satisfies pole location constraints to improve the system response under a range of sensor failure scenarios, determined by the number of sensors $m$ and a minimum number of assumed working sensors $p$, while optimising the failure-free performance. Thus $p$ defines a failure-tolerance level for the design.
A failure-tolerant observer design methodology based on regional pole placement is presented. A semi-definite relaxation (SDR) technique is used to alleviate the computational burden. This results in only a few linear matrix inequality (LMI) sufficient conditions, but at the expense of reduced performance. To compensate, block Hadamard product approaches are suggested to provide more degrees of freedom to improve the solution.
For optimum stability, a novel algorithm, based on the Separation Theorem is derived which decouples the system and Lyapunov matrices. After deriving an initial solution via the quadratic method, the technique provides a methodology for addressing the non-linearity of the problem. The algorithm can be run iteratively until an acceptable performance is obtained.
The application of failure tolerance threshold $p$ reduces the failure-tolerant abilities, but it also reduces the number of failure scenarios, making the problem tractable. The SDR technique further decreases the number of LMIs to one when only stability is concerned. There is therefore a trade-off between performance, failure-tolerance level and computational complexity. To address this, a novel technique (the Equal-to-$q$ SDR technique) is derived. By compressing the number of LMIs into $(m-p)$ (rather than one), this reduces the computational load, while ensuring that the performance and failure-tolerant abilities meet the desired specifications.
Version
Open Access
Date Issued
2023-11
Date Awarded
2024-05
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Jaimoukha, Imad
Publisher Department
Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)