Chapter 7
Observer-Based Robust Fault Detection
for Fuzzy Multi-model Jumping System
To enhance the reliability and security of dynamics, the subject of model-based
FD has been actively studied in the past twenty years, such as [257, 258]. The
main method used in this chapter is to select an appropriate threshold and a suitable
evaluation function. When the value of the evaluation function exceeds the selected
threshold, a fault alarm is generated. Using this method, the main problem to be
solved is how to distinguish faults and disturbances when the system has model
uncertainties. Usually we will adopt the observer-based robust FD method, which
is considered to be the robustness scheme of the detected system. In the robust
FD system, the residual generator not only includes the influence of disturbance
and modeling errors, but also maintains the sensitivity to faults and robustness to
unknown inputs. In [259], a scheme to measure the performance between robustness
and sensitivity is proposed. Inspired by this, more attention has been paid to the
robust FD observer (FDO) design problem for nonlinear dynamics, such as H ∞ /H −
approach [118] and H 2 /H ∞ scheme [260].
In this chapter, the robust FDO design problem for nonlinear multi-model jumping
system is investigated. For the purpose of linearizing the nonlinear multi-model
jumping system, we use the Takagi–Sugeno (T–S) fuzzy method [261] to solve this
problem. Then, the H ∞ FDO scheme is transformed into improving the sensitivity
to faults and reducing the influences of the unknown inputs. Moreover, by utilizing
the LMIs method, sufficient conditions for the existence of the fuzzy robust FDO are
given and proved. Finally, the robust FDO design approach is transformed into an
optimization problem. Simulation results display the effectiveness of the advanced
method.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5_7
117
Observer-Based Robust Fault Detection
for Fuzzy Multi-model Jumping System
To enhance the reliability and security of dynamics, the subject of model-based
FD has been actively studied in the past twenty years, such as [257, 258]. The
main method used in this chapter is to select an appropriate threshold and a suitable
evaluation function. When the value of the evaluation function exceeds the selected
threshold, a fault alarm is generated. Using this method, the main problem to be
solved is how to distinguish faults and disturbances when the system has model
uncertainties. Usually we will adopt the observer-based robust FD method, which
is considered to be the robustness scheme of the detected system. In the robust
FD system, the residual generator not only includes the influence of disturbance
and modeling errors, but also maintains the sensitivity to faults and robustness to
unknown inputs. In [259], a scheme to measure the performance between robustness
and sensitivity is proposed. Inspired by this, more attention has been paid to the
robust FD observer (FDO) design problem for nonlinear dynamics, such as H ∞ /H −
approach [118] and H 2 /H ∞ scheme [260].
In this chapter, the robust FDO design problem for nonlinear multi-model jumping
system is investigated. For the purpose of linearizing the nonlinear multi-model
jumping system, we use the Takagi–Sugeno (T–S) fuzzy method [261] to solve this
problem. Then, the H ∞ FDO scheme is transformed into improving the sensitivity
to faults and reducing the influences of the unknown inputs. Moreover, by utilizing
the LMIs method, sufficient conditions for the existence of the fuzzy robust FDO are
given and proved. Finally, the robust FDO design approach is transformed into an
optimization problem. Simulation results display the effectiveness of the advanced
method.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5_7
117