The paper studies the possibility of constructing observer-based residuals to detect faults in a nonlinear discrete-time system. The residuals are generated in such a manner that they detect one specific fault and are not affected by other faults and disturbances. Thus, a bank of residuals has been found to detect and isolate different faults in the system. An algebraic method called functions’ algebra is used to construct an algorithm which computes the residuals. The key fact in residual generation is that any discrete-time observable system can be taken into the extended observer form. This form is used to construct the observer to estimate the system states under the assumption that there are no faults in the system. The state estimates are then compared to the measured values of the states. An example is added to illustrate the theoretical results. In the example it is also demonstrated how to combine the fault detection with the plant reconfiguration step of fault tolerant control.
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