This research designs a Fault Tolerant Control (FTC) approach that compensates for both actuator and sensor faults by using multiple observers. This method is shown to work for both linear time-variant and linear time-invariant systems. This work takes advantage of sensor redundancy to compensate for sensor faults. A method to calculate the rank of available sensor redundancy is developed to determine how many independent sensors can fail without losing observability. This rank is the upper bound on the number of simultaneous sensor failures that the system can tolerate. Based on this rank, a series of reduced order Kalman observers are created to remove sensors presumed faulty from the internal feedback of the estimators. Actuator redundancy is examined as a potential way to compensate for actuator faults. A method to calculate the available actuator redundancy is designed. This redundancy would allow for the correction of partial and full actuator failures, but few systems exhibit sufficient actuator redundancy. Actuator faults are instead tolerated by replacing the Kalman estimators with Augmented State Observers (ASO). The ASO adds estimates of the actuator faults as additional states of the system in order to isolate and estimate the actuator faults. Then a supervisor is designed to select the observer that correctly identifies the sensor fault set. From that observer, the supervisor collects state estimates and calculates estimates of the sensors and faults. These estimates are then used in feedback with a controller that performs pole placement on the original system.
