It was shown how state feedback is used to obtain fault-output decoupling.
Hence, state knowledge is required. This is from a FDI-point-of-view very re-strictive, because full-state knowledge opens the possibility to use other FDI methods. However, in control theory many different control strategies exist that are based on state feedback. In those cases the state knowledge is available anyway, hence, it could be used to improve the FDI possibilities. At present, however, the FDI design is not considered during the controller design for most systems.
A design procedure to obtain successful fault-output decoupling, to ease the fault isolation task, and to meet the controller objectives has been introduced. Its ap-plication has been illustrated on a modified linearized aircraft model for lateral motion. The simulations show that the fault-output decoupling has successfully been achieved.
In this chapter only linear systems were considered to make it more understand-able. However, as the input-output decoupling theory is also well studied for nonlinear systems fault-output decoupling should apply to them as well. The de-sign procedure presented in Section 6.5 is applicable to both linear and nonlinear systems.
There are still a lot of open questions concerning the new idea of fault-output decoupling. They require further research to decide whether it is applicable or not. Hence, some recommendations for further research are given in Chapter 7 at the end of this thesis.
Chapter 7
Conclusions and Recommendations
This thesis considered different aspects of fault detection and isolation (FDI).
The design of nonlinear observers for FDI in nonlinear systems was studied in detail using the so-called geometric approach. This chapter summarizes the work presented in this thesis. The main results and conclusions are reviewed. Direc-tions and recommendaDirec-tions for further investigaDirec-tions are identified.
7.1 Conclusions
Theory and application were combined in this thesis. The thesis first described the geometric approach and discussed how to use this mathematical theory on the fault diagnosis problem. Then application of the theory was illustrated on a nonlinear ship propulsion system. Furthermore, the thesis considered some stability aspects of observer design. Finally, it introduced the novel idea of fault-output decoupling.
A number of conclusions can be drawn based on the accomplishments of this thesis:
The idea of model-based fault detection was explained briefly. This was done by addressing the following aspects: analytical redundancy, residual generation, residual evaluation, robustness concerning model uncertainty, and performance issues.
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A detailed review was given on fault-diagnostic observers using the ge-ometric approach. The review started with a description of the original idea introduced by Massoumnia (1986b) to solve the fundamental prob-lem of residual generation (FPRG) for linear systems. It ended with the latest results for input-affine nonlinear systems by DePersis (1999); De-Persis and Isidori (1999, 2000). Both problem formulations and solutions were presented. Furthermore, the similarities and the common idea of the geometric approaches were pointed out.
A nonlinear ship propulsion system was used as application example. The geometric approach was applied by considering several FPRGs for differ-ent subsystems and fault scenarios. Detailed calculations were given to illustrate the application of the geometric approach and its different geo-metric algorithms. Only two FPRGs could be solved when neglecting the disturbances.
As a result it can be concluded that the FDI problem as stated in Section 4.1.3 cannot be solved for arbitrary fault and disturbance signals.
The results for the two solvable FPRGs were used to design two nonlin-ear observers for FDI. They were designed to detect and isolate the two possible shaft speed loop faults in the propulsion system. Furthermore, a linear observer was designed to detect the pitch loop faults in the system.
For comparison an adaptive nonlinear observer was designed as well. Six residuals were obtained based on these observers.
Different simulations (neglecting the disturbances) were carried out to test the FDI performance of the different observers. From the simulation re-sults it could be seen that all faults could be handled according to the requirements as long as multiple faults could be neglected and additional considerations were made.
It was illustrated how the measurement noise and possible disturbances affect the residuals. A CUSUM-algorithm was used to illustrate that the measurement noise could be handled. However, it was also shown that the disturbances could not be handled. Their occurrence would lead to false alarms. This was also shown by the geometric approach, because the corresponding FPRGs were not solvable.
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The correct tuning of the FDI system is a complex task. It is a optimization problem considering several problems, as finding an appropriate observer structure, tuning of the observer to obtain structured residuals, stability of the observer, robustness issues, and the performance. The geometric approach handles most of these aspects, however, it does not consider the residual dynamics, which might cause problems as shown for the ship propulsion system where some residuals react too slow.
The geometric approach proved to be a powerful tool for FDI design, but additional work is needed to obtain a complete solution for successful FDI.
The subsystems obtained by the geometric approach were also obtained by using the structural analysis (Staroswiecki and Declerck (1989); Cassar et al. (1994)) by Izadi-Zamanabadi (1999)[Section 5.1.3].
Different aspects of the stability of observer-based FDI were addressed.
The stability for the nonlinear observers designed for the ship propulsion system was outlined. Furthermore, the importance of the awareness that linearization along a trajectory leads to a time-variant system was empha-sized.
The novel idea of fault-output decoupling was presented to show how FDI and control design could be combined to improve FDI possibilities. The concepts of complete and efficient fault-output decoupling was defined and illustrated by a simple example.