Fault hiding and reliable regulation in control systems subject to polynomial exogenous signals

This paper addresses a regulation problem under a fault-tolerance constraint. Specifically, the goal consists in designing a control system which guarantees signal tracking and disturbance rejection when an arbitrary number of sensors and/or actuators faults occur, that is, when some feedback loops open. The considered plants are LTI, asymptotically stable and subject to perturbations, and the exogenous signals are polynomial in time. The regulator is composed by a nominal controller supervised by a reconfiguration block. The former solves the regulation problem above when all the sensors and actuators are operational, and is suitably modified by the latter in case of faults. The structure of the regulator is the one adopted in what is called fault hiding approach to fault-tolerant control. First, it is discussed the extent to which signal tracking and disturbance rejection can be achieved for each pattern of sensors and actuators faults. Further, the actions to be performed by the reconfiguration block are established. Then, the synthesis of the nominal controller is dealt with, and necessary and sufficient conditions for its existence are given. Finally, a nominal controller is proposed, which has the least possible order and renders particularly simple the implementation of the actions of the reconfiguration block.