State estimators and observers for continuous and discrete linear systems. Part 1. Differential asymptotic state estimators

• Autorzy: Byrski J. , Byrski W.

Identyfikatory

DOI

10.5604/01.3001.0012.8169

• Języki publikacji: EN

Abstrakty

EN

In the paper an overview of state estimators and state observers used in linear systems, will be presented. The state estimators and observers can be used in many applications like the state reconstruction for the control purposes or for the diagnosis and fault detection in technical processes or for the virtual measurements of inaccessible variables of the system as well as for the best filtration of the differential equation solution. As the standard most commonly the Kalman filter and Luenberger type observers are used. Although the Kalman filter guarantees optimal filtering quality of the state, reconstructed from the noisy measurements, both Kalman filter and the Luenberger observer guarantee only asymptotic quality of the real state changes and tracking, basing on the current measurements of the system output and input signals. Unfortunately, the value of the estimation error at any moment of time cannot be calculated. The discussion on differences between continuous and two types of discrete Kalman Filter will be presented. This paper is planned to be the introduction to presentation of another type of the state observers which have the structure given by the integral operators. Based on measurements of the system output and input signals on some predefined finite time interval, they can reconstruct, after this interval, the observed state exactly.

Słowa kluczowe

EN

linear estimator; Kalman filter; Luenberger observer; exact state observer; linear system

PL

estymator liniowy; filtr Kalmana; obserwator Luenbergera; dokładny obserwator stanu; system liniowy

• Wydawca: Państwowa Wyższa Szkoła Zawodowa w Tarnowie
• Czasopismo: Science, Technology and Innovation
• Rocznik: 2018
• Tom: Vol. 3, no. 2
• Strony: 62--68
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Byrski J.

• AGH University of Science and Technology, Department of Applied Computer Science, Al. Mickiewicza 30, Krakow 30-305, Poland

autor

Byrski W.

• AGH University of Science and Technology, Department of Automatic Control and Robotics, Al. Mickiewicza 30, Krakow 30-305, Poland

Bibliografia

• 1. Kalman R., Contribution to the theory of optimal control. Conf. on Ordinary Differential Equation. Mexico City, Bol. Soc. Mat. Mex. 1960; 5:102–119.
• 2. Kalman R., A new approach to linear filtering and prediction problems, Journal of Basic Engineering, 1960; 82(1):35–45.
• 3. Kalman R., Bucy R., New results in linear filtering and prediction theory, Journal of Basic Eng. Transaction of ASME, 1961; 83D:95–108.
• 4. Luenberger D., Observers for multivariable systems. IEEE Transactions on Automatic Control, 1966; 11:190– 197.
• 5. Kwakernaak H., Sivan R., Linear Optimal Control Systems, Wiley, 1972.
• 6. Nazarzadeh J., Razzaghi M., Nikravesh K.Y., Solution of the Matrix Riccati Equation for the Linear Quadratic Control Problems, Math. Comput. Modeling, 1998; 27(7):51–55.
• 7. Ledyaev Y.S., On analytical solution of matrix Riccati equations, Proceedings of the Steklov Institute of Mathematics, 2011; 273(1):214–228.
• 8. Franklin G., Powell D., Workman M., Digital Control of Dynamic System. Addison Wesley,1990.
• 9. Chui C.K., Chen G., Kalman Filtering with Real-time Applications, Second Edition, Springer-Verlag, Berlin, 1991.