Linear Quadratic State Feedback Optimal Control against Actuator Failures

This paper is concerned with the synthesis of a robust and optimal controller for open-loop unstable systems possessing actuator redundancy. The designed linear quadratic state feedback regulator can maintain the close-loop stability in the presence of some certain actuator failures. At the first design stage, a discriminance of actuator functional redundancy is given, which is the precondition to design the robust controller. Then a synthesis method based on a sufficient condition which guarantees the existence of the state-feedback fault-tolerant law is presented. The robust Linear Quadratic (LQ) regulator synthesis is shown to be equivalent to a standard LQ regulator design with a given dynamic performance index of the system. The effectiveness of this method has been verified on the fault control system design for the double electromagnets suspension model of maglev train.