Solution of Fault Accommodation Problem in Nonlinear Systems by Methods of Linear Algebra

Abstract

Solution of the problem of fault accommodation in nonlinear dynamic systems is related to constructing the control law which provides full decoupling with respect to fault effects. The possibility of this solution is strictly limited by the demand on the system state vector availability (this vector is immediately included into control law description). As a rule, not all components of the state vector are immediately measurable at practice. Also, it is impossible to estimate full state vector for the system with unknown (affected by the faults) dynamics. The purpose of this article is to solve the problem of full decoupling by constructing a compensator that is independent of the fault effects a nd is based on a new control law. A solution is based on so-called logic-dynamic approach using only linear methods to solve the problem for nonlinear systems. The implementation of this method does not require a preliminary estimation of the parameters. It is assumed that fault detection and isolation procedure is performed by known methods. Assume the fault occurred and detected, then a solution of the control problem is performed on the basis of additional system that corresponding in a definite sense to the initial model. To solve the problem of accommodation, an efficient algorithm based on a logical-dynamic approach is presented, as a result of which a compensator is constructed. Additional system does not contain unknown vector that describes defects. As a result, fault accommodation effect is achieved. Theoretical results are demonstrated by illustrative and illustrative example.