IDENTIFICATION OF FAULTS IN DRIVES BASED ON OPTIMAL CONTROL METHODS
Abstract
The paper exams the problem of identifying faults in the drives of robotic systems, the dynamics
model of which is described by linear differential equations. It is proposed to search for a
solution to the fault identification problem based on the solution of an auxiliary optimal control
problem for a dynamical system in which the role of an unknown vector function describing
emerging faults is performed by some auxiliary control, which should provide a minimum for the
residual functional. Based on the solution of the auxiliary optimal control problem, a fault diagnostic
observer is proposed. In this case, the fault itself is found through the solution of the corresponding
algebraic Riccati equation and the differential equation for the auxiliary variable. Unlike
popular approaches to solving the problem of fault identification based on observers operating
in a sliding mode, the proposed method allows us to expand the class of systems for which the
identification problem can be solved. It is known that the methods of sliding mode observers design
impose certain restrictions on the systems under consideration. The proposed approach based
on optimal control can also give results for systems with nonlinear dynamics. In this case, methods
of approximate solution of optimal control problems based on the representation of the system in
linear 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 be
the subject of further research. The stated theory is shown on the example of fault identification in
a DC drive. Different cases are considered for a system with complete observations (the entire
state vector is known) and with incomplete observations. It was shown during the simulation that
the quality of faults identification can be improved by selecting the appropriate values of the penalty
matrices in the residual functional, while it is possible to achieve good diagnostics separately
through various channels of faults occurrence. The paper presents recommendations on the choice
of penalty matrices. The simulation results confirmed the operability of the diagnostic observers
synthesized using the proposed method.
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