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Comprehensive online estimation of object signals for a control system with an adaptive approach and incomplete measurements

Kwater Tadeusz, Hawro Przemysław, Krutys Paweł, Gołębiowski Marek, Drałus Grzegorz

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2024

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Vol. 72, nr 4

art. no. e150111

EN

This paper presents the novel estimation algorithm that generates all signals of an object described by nonlinear ordinary differential equations based only on easy-to-implement measurements. Unmeasured signals are estimated by using an adaptive approach. For this purpose, a filtering equation with a continuously modified gain vector is used. Its value is determined by an incremental method, and the amount of correction depends on the current difference between the generated signal and its measured counterpart. In addition, the study takes into account the aging process of measurements and their random absence. The application of the proposed approach can be realized for any objects with a suitable mathematical description. A biochemically polluted river with an appropriate transformation of the notation of partial differential equations was chosen as an object. The results of numerical experiments are promising, and the process of obtaining them involves little computational necessity, so the approach is aimed at the needs of control implemented online.

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The look-up algorithm of monitoring an object described by non-linear ordinary differential equations

Hawro Przemysław, Kwater Tadeusz, Bartman Jacek, Kwiatkowski Bogdan

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2023

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Vol. 71, nr 2

art. no. e144603

EN

The article proposes an adaptive algorithm that generates all object signals, including those for which measurements are not performed due to the difficulties associated with on-line measurements. The algorithm is modeled on the idea of the Kalman filter using its equation, however, the selection of gains is optimized in a different way, i.e. the constant values depend on the adopted ranges of adaptation errors. Moreover, the knowledge of the statistics of all noise signals is not imposed and there is no linearity constraint. This approach allowed to reduce the complexity of calculations. This algorithm can be used in real-time systems to generate signals of objects described by non-linear differential equations and it is universal, which allows it to be used for various objects. In the conducted research, on the example of a biochemically contaminated river, only easily measurable signals were used to generated the object signals, and in addition, in the case of absence some measurements, the functioning of the algorithm did not destabilize.

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The algorithm of adaptive determination of amplification of the PD filter estimating object state on the basis of signal measurable on-line

Kwater Tadeusz, Hawro Przemysław, Bartman Jacek, Mazur Damian

Archives of Control Sciences

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2021

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Vol. 31, No. 1

129--143

EN

The article presents the algorithm that enables adaptive determination of the amplification coefficient in the filter equation provided by Kalman. The method makes use of an estimation error, which was defined for this purpose, and its derivative to determine the direction of correction changes of the gain vector. This eliminates the necessity to solve Riccati equation, which causes reduction of the method computational complexity. The experimental studies carried out using the proposed approach relate to the estimation of state coordinates describing river pollution using the BOD (biochemical oxygen demand) and DO (dissolved oxygen) indicators).The acquired results indicate that the suggested method does better estimations than the Kalman filter. Two indicators were used to measure the quality of estimates: the Root Mean Squared Error (RMSE) and the Mean Percentage Error (MPE).