Utilization of LMI methods for fault tolerant control of a flexible cable with faulty actuators

The objective here is to introduce a fault tolerant controller in a system describing cable dynamics with actuator outages (float type failures). The system under study employs a finite number of actuators and it is assumed that the nature of failures renders the actuators completely inoperative at some unknown time instances. The issue of placing a finite number of actuators along the span of the cable with respect to a fault-tolerant measure is first discussed. By using the control distribution matrix for all possible combinations of healthy/faulty actuators and expressing the resulting dynamics as a differential inclusion and then using already established results from convex optimization, a common stabilizing feedback for all possible healthy/faulty actuator combinations is found by solving an appropriate LMI problem that renders the system quadratically stabilizable. The proposed fault-tolerant scheme for actuator outages is simulated for a flexible cable and whose results demonstrate its performance enhancement over the case of a nonfault-tolerant controller