Reference for citation: Bui V. H., Margun A. A., Bobtsov A. A. Synthesis of an observer of state variables and sinusoidal disturbance for a linear nonstationary system with unknown parameters. Journal of Instrument Engineering. 2024. Vol. 67, N 3. P. 209—219 (in Russian). DOI: 10.17586/0021-3454-2024-67-3-209-219.

Abstract. The problem of synthesizing an observer of a vector of state variables for a class of linear nonstationary systems with an arbitrary relative degree r under conditions of external multi-harmonic disturbances is considered. The input signal is assumed to be unknown. At the first stage of solving the problem, an observer of the vector of state variables is synthesized from the measurements of the output variable. To implement it, it is necessary to measure the r-th derivative of the output signal. To overcome this limitation, an auxiliary observer is introduced, which provides an estimate of the initial observation error using the method of dynamic expansion of the regressor with a finite convergence time. Based on the obtained estimate, the reconstruction of the signals required to construct an output observer in the form of an autoregressive model is carried out. The proposed algorithm provides an estimate of the state vector of an object based on output in a finite time. A rigorous mathematical proof of the obtained solution is given. The results of computer simulation in the MatLab Simulink software environment are presented, demonstrating the effectiveness and efficiency of the proposed approach. The developed algorithm can be used in various technical systems to create virtual sensors and solve diagnostic problems.

Keywords: output observer, external disturbance, non-stationary systems, finite convergence time

Acknowledgement: the research was supported by the Ministry of Science and Higher Education of the Russian Federation, state assignment No. 2019-0898.

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