15 Janvier – Thesis defense - Rim Rammal

09 h30 Amphi Jean-Paul Dom - Laboratory IMS / Building A31 (Talence campus)

Characterization of flat outputs for the diagnostic of integer or non-integer systems: application for the diagnostic of a hydraulic system and a thermal system.

The differential flatness is a property of dynamic systems that allows the transformation of a very complex system into a simpler one called flat system. Roughly speaking, a dynamic system is said to be flat if, and only if, there exists a vector, called flat output vector and formed by the state and input variables, such that all the system states, inputs and outputs can be expressed in function of this new vector and its successive time derivatives. The differential flatness property has many applications in automatic control theory, such as trajectory planning, trajectory tracking and the designing of robust controllers. Moreover, the flatness property has recently entered the field of fault detection and isolation. In short, fault detection and isolation is a sub-domain of automatic control engineering that deals with monitoring a system, identifying when a fault has occurred, and determining the type of fault and its location. Fault detection is performed by analyzing the difference between sensor and actuator measurements and their expected values, derived from any model and called redundant values. It is common to say that an error is detected if the deviation or residue exceeds a certain predefined threshold. Fault isolation, in turn, must make it possible to locate the fault in the machine. The most recent method of fault detection and isolation, based on the flatness property, calculates redundant variables from the measurement of the flat output of the system and its successive time derivatives. Then, the residues are deduced from the difference between the measured variables and the redundant variables. Fault detection by this method is guaranteed. However, the use of a single flat output does not allow, in some cases, to isolate some faults. The idea proposed by the developers of the method was to use several flat outputs to increase the number of the residual signals, which would increase the chances of isolating more faults. However, it was also noticed that the choice of these flat outputs is not arbitrary. That is, there are flat outputs that, when used together, increase the isolability of faults and others that do not. One of the objectives of this manuscript is to characterize the flat outputs in order to obtain a better fault isolability. This characterization is then verified by simulations and experiments on a hydraulic system, the three-tank system.
Over the last decade, numerous studies have shown that there are systems such as thermal systems, viscoelastic systems and chemical systems that can be modeled by fractional differential equations. Therefore, classical methods of fault detection and isolation, originally developed to deal with integer order systems, were not suitable for fractional order systems, and fault detection and isolation methods specific to fractional order systems had to be developed. A second objective of this manuscript is to extend the characterization of flat outputs, proposed for the class of integer order flat systems to the class of fractional order linear flat systems, and then to apply this characterization to the detection and isolation of faults that may appear on the sensors and actuators of these systems. The effectiveness of this characterization is also verified by simulations on a bi-dimensional thermal system.

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