An algebraic approach to stable online parameter identification and fault detection

In this paper, a new solution is proposed for the online parameter identification problem with the frequency-shifting-based algebraic approach. Using the difference operator with the complex frequency shift in the operational domain, the annihilation of unknown initial conditions is obtained. This approach enables the stable time-varying state-space realization of the estimator, while the application of complex frequency shift results with periodic functions in the input matrix, providing a simplified periodic reinitialization procedure, which is necessary for fault detection applications. Simulation results on a second-order mechanical system illustrate the performances of the proposed approach. The comparison between the identification methods with real frequency shift and complex frequency shift is presented in the case of an abrupt change of the value of the unknown parameter. The robustness to the measurement noise of the approach with complex frequency shift is also demonstrated.