Fault-Tolerant Control for Systems with Unmatched Actuator Faults and Disturbances

A fault-tolerant control (FTC) scheme for a class of nonlinear systems with unmatched actuator redundancy and unmatched disturbances is proposed in this note. A methodology to construct unified smooth sliding mode control laws and update laws is proposed such that the equivalent injections of the first-order time derivatives of the unmatched actuator faults and unmatched disturbances can appear in the unmatched channels. The unmatched actuator faults and unmatched disturbances are completely canceled by these equivalent injections. Based on this methodology and using the backstepping design procedure, a set of smooth FTC sliding surfaces, FTC laws and update laws are then designed. With the help of the FTC law selecting mechanism, the output tracking errors of the closed-loop FTC system converge to zero asymptotically, and time-varying faults and disturbances are reconstructed. A simulation example is presented to illustrate the effectiveness of the proposed FTC method.