Fault tolerant margins of an UAV at uncertain environment

In fault tolerant control, the damaged and healthy states of a sensor output or a control input are captured by using an uncertain parameter. For instance, the control input u(t) resulting from an actuator is modeled au(t) and the healthy and damaged conditions are inferred from a which takes the values σ=1 and σ in [0, 1), respectively [1-3]. Given a stabilizing controller, a range of σ-values in the interval [0,1) for which the closed loop system would remain stable is referred as the fault-tolerant margin. In this paper, several of these margins are presented when aerodynamic parameter variations due to an uncertain atmospheric condition in an unmanned aerial vehicle (UAV) are present. It is shown that the fault tolerant margins are extremely sensitive to these parameter perturbations. Some perturbation locations can significantly reduce the stable range for parameter values as well as for the fault tolerant margins. An UAV model is considered to illustrate the fault tolerant margins and admissible parameter variations. Secondly, the algorithm applied to compute the fault tolerant margins is used to solve the examples of Professor Ross B Barmish et al [29] and hence the exact stability margins for a two parameter system are illustrated. However, when the number of parameters increases, the algorithm becomes computationally intensive.