Nonlinear Fault Detection Observer Design Based on Spectral Approach to H2 Optimazation
Abstract
The presented paper is devoted to the problem of the fault detection observers design in case of plants with the Lipschitz system nonlinearity. Insensitivity of the observer to external disturbances, which can be presented as a sum of harmonic oscillations with the given central frequency (sea wave disturbance) and a constant signal (ocean currents and wind), is to be guaranteed by the choice of its parameters. The presented technique is based on the special spectral approach in frequency domain, using parametrization of the set of transfer functions of the closed-loop system and guarantying nonuniqueness of the optimal solution, and the modal synthesis. The condition of asymptotic stability of the zero equilibrium position of the estimation error dynamics is also given. A novel approach to analytical synthesis of the adaptive nonlinear fault detection observer is proposed and its effectiveness is demonstrated on the practical example – the marine ship horizontal motion with the constant longitudinal speed under the sea waves action. The MATLAB package is used for numerical simulation of the controlled plat dynamics.
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