Novel frameworks for the design of fault‐tolerant control using optimal sliding‐mode control

This paper describes 2 schemes for a fault‐tolerant control using a novel optimal sliding‐mode control, which can also be employed as actuator redundancy management for overactuated uncertain linear systems. By using the effectiveness level of the actuators in the performance indexes, 2 schemes for redistributing the control effort among the remaining (redundant or nonfaulty) set of actuators are constructed based on an ℋ2 ‐based optimal sliding‐mode control. In contrast to the current sliding‐mode fault‐tolerant control design methods, in these new schemes, the level of control effort required to maintain sliding is penalised. The proposed optimal sliding‐mode fault‐tolerant control design schemes are implemented in 2 stages. In the first stage, a state feedback gain is derived using an LMI‐based scheme that can assign a number of the closed‐loop eigenvalues to a known value whilst satisfying performance specifications. The sliding function matrix related to the particular state feedback derived in the first stage is obtained in the second stage. The difference between the 2 schemes proposed for the sliding‐mode fault‐tolerant control is that the second one includes a separate control allocation module, which makes it easier to apply actuator constraints to the problem. Moreover, it will be shown that, with the second scheme, we can deal with actuator faults or even failures without controller reconfiguration. We further discuss the advantages and disadvantages of the 2 schemes in more details. The effectiveness of the proposed schemes are illustrated with numerical examples.