ИДЕНТИФИКАЦИЯ ДЕФЕКТОВ В ПРИВОДАХ НА ОСНОВЕ МЕТОДОВ ОПТИМАЛЬНОГО УПРАВЛЕНИЯ

Abstract

The paper exams the problem of identifying faults in the drives of robotic systems, the dynamicsmodel of which is described by linear differential equations. It is proposed to search for asolution to the fault identification problem based on the solution of an auxiliary optimal controlproblem for a dynamical system in which the role of an unknown vector function describingemerging faults is performed by some auxiliary control, which should provide a minimum for theresidual functional. Based on the solution of the auxiliary optimal control problem, a fault diagnosticobserver is proposed. In this case, the fault itself is found through the solution of the correspondingalgebraic Riccati equation and the differential equation for the auxiliary variable. Unlikepopular approaches to solving the problem of fault identification based on observers operatingin a sliding mode, the proposed method allows us to expand the class of systems for which theidentification problem can be solved. It is known that the methods of sliding mode observers designimpose certain restrictions on the systems under consideration. The proposed approach basedon optimal control can also give results for systems with nonlinear dynamics. In this case, methodsof approximate solution of optimal control problems based on the representation of the system inlinear form with state-dependent coefficients (the so-called State-dependent Riccati Equation,SDRE) are likely to be effective. The improvement of the proposed method in this direction will bethe subject of further research. The stated theory is shown on the example of fault identification ina DC drive. Different cases are considered for a system with complete observations (the entirestate vector is known) and with incomplete observations. It was shown during the simulation thatthe quality of faults identification can be improved by selecting the appropriate values of the penaltymatrices in the residual functional, while it is possible to achieve good diagnostics separatelythrough various channels of faults occurrence. The paper presents recommendations on the choiceof penalty matrices. The simulation results confirmed the operability of the diagnostic observerssynthesized using the proposed method.