Fault Recoverability Analysis via Cross-Gramian

Engineering systems are vulnerable to different kinds of faults. Faults may compromise safety, cause sub-optimal operation and decline in performance if not preventing the whole system from functioning. Fault tolerant control (FTC) methods ensure that the system performance maintains within an acceptable level at the occurrence of the faults. These techniques cannot be successful if the necessary redundancy does not exist in the system. Fault recoverability which is also known as control reconfigurability is a mathematical measure which quantifies the level of redundancy in connection with feedback control. Fault recoverability provides important and useful information which could be used in analysis and design. However, computing fault recoverability is numerically expensive. In this paper, a new approach for computation of fault recoverability for bilinear systems is proposed. This approach uses cross-gramian and reduces the computations significantly. The contribution of this paper is twofold. Firstly the concept of cross-gramian is extended to support discrete-time bilinear systems and an iterative algorithm for cross-gramian computation is proposed. Secondly a cross-gramian based approach for computation of fault recoverability is proposed which reduces the computational burden significantly. The proposed results are used for an electro-hydraulic drive to reveal the redundant actuating capabilities in the system.