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1

Diagnosis of ITSC fault in the electrical vehicle powertrain system through signal processing analysis

Ouamara Dehbia, Boukhnifer Moussa, Chaibet Ahmed, Maidi Ahmed

Diagnostyka

|

2023

|

Vol. 24, No. 1

art. no. 2023113

EN

The three-phase induction motor is well suited for a wide range of mobile drives, specifically for electric vehicle powertrain. During the entire life cycle of the electric motor, some types of failures can occur, with stator winding failure being the most common. The impact of this failure must be considered from the incipient as it can affect the performance of the motor, especially for electrically powered vehicle application. In this paper, the intern turn short circuit of the stator winding was studied using Fast Fourier transform (FFT) and Shor-Time Fourier transform (STFT) approaches. The residuals current between the estimated currents provided by the extended Kalman filter (EKF) and the actual ones are used for fault diagnosis and identification. Through FFT, the residual spectrum is sensitive to faults and gives the extraction of inter-turn short circuit (ITSC) related frequencies in the phase winding. In addition, the FFT is used to obtain information about when and where the ITSC appears in the phase winding. Indeed, the results allow to know the faulty phase, to estimate the fault rate and the fault occurrence frequency as well as their appearance time.

2

Analysis of data fusion algorithms for the vessel with the dynamic positioning system

Jaroś Krzysztof, Śmierzchalski Roman, Witkowska Anna

Przegląd Elektrotechniczny

|

2022

|

R. 98, nr 12

35--39

EN

The dynamic positioning (DP) system on the vessel is operated to control the position and heading of the vessel with the use of propellers and thrusters installed on the board. On DP vessels redundant measurement systems of position, heading and the magnitude and direction of environmental forces are required for safety at sea. In this case, a fusion of data is needed from individual measurement devices. The article proposes a new solution data fusion algorithm of particle Kalman filter as a cascade combination of particle filter and extended Kalman filter. The estimation quality of the proposed data fusion algorithm is analysed in comparison with the classic: extended Kalman filter (EKF), nonlinear observer (NO), and particle Kalman filter (PKF). Simulation studies were executed for emergency scenarios to evaluate the robustness of the algorithm analyses to measurement errors.

PL

System dynamicznego pozycjonowania (DP) na statku jest wykorzystywany do sterowania pozycją i kursem statku za pomocą pędników zainstalowanych na pokładzie. Na statkach DP dla zapewnienia bezpieczeństwa na morzu wymagane są redundantne systemy pomiarowe pozycji oraz wielkości i kierunku działania sił środowiskowych. W tym przypadku konieczna jest fuzja danych z poszczególnych urządzeń pomiarowych. W artykule zaproponowano nowy algorytm fuzji danych jako kaskadowe połączenie filtru cząsteczkowego i rozszerzonego filtru Kalmana. Analizowana jest jakość estymacji proponowanego algorytmu fuzji danych w porównaniu z klasycznymi algorytmami: rozszerzonym filtrem Kalmana (EKF), obserwatorem nieliniowym (NO) oraz cząsteczkowym filtrem Kalmana (PKF). Przeprowadzono badania symulacyjne algorytmów fuzji danych dla scenariuszy awaryjnych w celu oceny odporności algorytmów na błędy pomiarowe.

3

Sterowanie układem lewitacji magnetycznej w warunkach zakłóceń stochastycznych

Mrotek Mikołaj, Szymankiewicz Adrian, Michalski Jacek, Kozierski Piotr

Pomiary Automatyka Robotyka

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2022

|

R. 26, nr 3

5--16

PL

W niniejszej pracy przedstawiono możliwość zredukowania wpływu zakłóceń stochastycznych na jakość regulacji dzięki estymacji stanu z wykorzystaniem algorytmu rozszerzonego filtru Kalmana. Przeprowadzono eksperymenty na laboratoryjnym układzie lewitacji magnetycznej firmy Inteco, którego model matematyczny jest nieliniowy. Przyjęto metodę sterowania z użyciem wektora stanu i algorytmem lokowania biegunów dla modelu zlinearyzowanego w wybranym punkcie pracy. Dla różnych poziomów zaszumienia sygnału pomiarowego zbadano działanie układu ze sprzężeniem zwrotnym od stanu mierzonego oraz estymowanego. W celu oceny regulacji, dla obu realizacji sprzężenia dokonano weryfikacji jakości działania algorytmu. Porównano otrzymane przebiegi czasowe każdej zmiennej stanu oraz obliczone, całkowe wskaźniki jakości bazujące na uchybie regulacji. Jakość estymacji oceniono na podstawie wskaźnika błędu średniokwadratowego oraz bazującego na błędach estymat i pomiarów. Syntezy regulatora dokonano na podstawie modelu ciągłego, a następnie wyznaczono jego postać dyskretną w celu numerycznej implementacji algorytmu rozszerzonego filtru Kalmana. Dokonano synchronizacji bloków wykonawczych z wybranym okresem próbkowania. Wyniki przeprowadzonych badań pozwalają wnioskować o przewadze regulacji w układzie, w którym brana jest informacja o wektorze stanu z estymacji, w porównaniu z bezpośrednim sprzężeniem zwrotnym bez filtracji Kalmana.

EN

This paper presents the possibility of reducing impact of stochastic disturbances on the quality of control by implementation of state estimation using the extended Kalman filter algorithm. Experiments were carried out on the Inteco magnetic levitation laboratory system, which mathematical model is nonlinear. A control method with the use of a state vector and a pole placement algorithm was adopted for the model which was linearized at the selected working point. For different levels of noise in the measurement signal, the operation of the system with a feedback from the measured and estimated state was tested. In order to assess the regulation, the quality of the algorithm was verified for both implementations of the feedback. The obtained time plots of each state variable were compared and the calculated integral quality indices, based on the control error, were compared. The quality of the estimation was assessed on the basis of the following mean square error and based on the errors between estimation and measurements indices. The controller was synthesized on thebasis of the continuous model, and then its discrete form was numerically implement as the extender Kalman filter algorithm. The executive blocks were synchronized with the selected sampling period. The results of the performed research allow to conclude about the advantage of control in the system in which the information about the state vector from the estimation is taken, in comparison with the direct feedback without Kalman filtering.

4

Research on AGV positioning method combined with IMU and UWB

Qiu Jiandong, Zhang Yang, Tang Minan, Ma Panpan, Ran Jiajia

Archives of Transport

|

2022

|

Vol. 64, iss. 4

107--117

EN

Aiming at the problem that automated guided vehicle (AGV) is difficult to locate accurately due to the influence of environment and time drift when it works in the indoor intelligent storage system. In this paper, an extended Kalman filtering (EKF) framework is designed. In order to make full use of the original ranging values of ultra wideband (UWB) and inertial measurement unit (IMU), the framework realizes the fusion positioning between UWB module and IMU module in a tight coupling manner, so as to ensure that the system can still work when the available base station signal is inaccurate. Firstly, for the problem that the traditional UWB positioning method is easily affected by the non-line of sight (NLOS) error in-doors, the calculated positioning coordinate value is unstable. With the help of different NLOS probability distribution curves of different obstacles, the weighted least square method is applied to the UWB positioning method to determine the positioning coordinate value of UWB, which improves the sudden change of AGV positioning coordinate in the static environment. Then the data fusion algorithm is optimized, and the error value of IMU and UWB coordinate is taken as the observation value of EKF, which reduces the influence of cumulative error on IMU positioning results, provides the global optimal estimation of the system optimal state, and improves the fusion positioning accuracy. Finally, the measured data of UWB and IMU systems in indoor complex environment are simulated in MATLAB. The experimental results show that when NLOS signal seriously affects the positioning effect, the UWB and IMU combined positioning system can provide more reliable positioning results than the single IMU positioning system. It improves the positioning accuracy of AGV and provides a new idea for indoor positioning mode.

5

Multilevel neural network DTC with balancing strategy of sensorless DSSM using extended Kalman filter

Elakhdar Benyoussef, Said Barkat, Sadouni Radhwane

Journal of Power Technologies

|

2021

|

Vol. 101, nr 2

96--104

EN

This paper presents direct torque control based on artificial neural networks of a double star synchronous machine without mechanical speed and stator ux linkage sensors. The estimation is performed using the extended Kalman filter, which is known for its ability to process noisy discrete measurements. The proposed approach consists of replacing the switching tables with one artificial neural network controller. The output vector of the artificial neural network controller is directed to a multilevel switching table to decide which reference vector should be applied to control the two five-level diode-clamped inverters. This inverter topology has the inherent problem of DC-link capacitor voltage variations. Multilevel direct torque control based on a neural network with balancing strategy is proposed to suppress the unbalance of DC-link capacitor voltages. The simulation results presented in this paper highlight the improvements offered by the proposed control method based on the extended Kalman filter under various operating conditions.

6

Two cascaded and extended kalman filters combined with sliding mode control for sustainable management of marine fish stocks

Benz Katharina, Rech Claus, Mercorelli Paolo, Sergiyenko Oleg

Journal of Automation Mobile Robotics and Intelligent Systems

|

2020

|

Vol. 14, No. 3

28--35

EN

This paper deals with a possible approach to controlling marine fish stocks using the prey‐predator model described by the Lotka‐Volterra equations. The control strategy is conceived using the sliding mode control (SMC) approach which, based on the Lyapunov theorem, offers the possibility to track desired functions, thus guaranteeing the stability of the controlled system. One of the most important aspects of this model is the identification of some parameters which characterizes the model. In this work two cascaded and Extended Kalman Filters (EKFs) are proposed to estimate them in order to be utilized in SMC. This approach can be used for sustainable management of marine fish stocks: through the developed algorithm, the appropriate number of active fishermen and the suitable period for fishing can be determined. Computer simulations validate the proposed approach.

7

Application of extended Kalman filter for estimation of periodic disturbance and velocity ripple reduction in PMSM drive

Niewiara Ł. J., Tarczewski T., Grzesiak L M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2020

|

Vol. 68, nr 5

983--995

EN

In this paper an application of extended Kalman filter (EKF) for estimation and attenuation of periodic disturbance in permanent magnet synchronous motor (PMSM) drive is investigated. Most types of disturbances present into PMSM drive were discussed and described. The mathematical model of the plant is presented. Detailed information about the design process of the disturbance estimator was introduced. A state feedback controller (SFC) with feedforward realizes the regulation and disturbance compensation. The theoretical analysis was supported by experimental tests on the laboratory stand. Both time- and frequency-domain analysis of the estimation results and angular velocity were performed. A significant reduction of velocity ripple has been achieved.

8

Robust controller for cancer chemotherapy dosage using nonlinear kernel-based error function

Mohite Utkarsha L., Patel Hirenkumar G.

Bio-Algorithms and Med-Systems

|

2020

|

Vol. 16, no. 4

art. no. 20190056

EN

It is well-known that chemotherapy is the most significant method on curing the most death-causing disease like cancer. These days, the use of controller-based approach for finding the optimal rate of drug injection throughout the treatment has increased a lot. Under these circumstances, this paper establishes a novel robust controller that influences the drug dosage along with parameter estimation. A new nonlinear error functionbased extended Kalman filter (EKF) with improved scaling factor (NEF-EKF-ISF) is introduced in this research work. In fact, in the traditional schemes, the error is computed using the conventional difference function and it is deployed for the updating process of EKF. In our previous work, it has been converted to the nonlinear error function. Here, the updating process is based on the prior error function, though scaled to a nonlinear environment. In addition, a scaling factor is introduced here, which considers the historical error improvement, for the updating process. Finally, the performance of the proposed controller is evaluated over other traditional approaches, which implies the appropriate impact of drug dosage injection on normal, immune and tumor cells. Moreover, it is observed that the proposed NEF-EKF-ISF has the ability to evaluate the tumor cells with a better accuracy rate.

9

Statistical orbit determination algorithm for satellites in Indian navigation constellation (NavIC): towards extended ephemeris technology for NavIC receiver

Ramanathan T. V., Chipade Radhika A.

Artificial Satellites : Journal of Planetary Geodesy

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2020

|

Vol. 55, No. 2

29--40

EN

Ephemerides are essential for the satellite positioning in Global Navigation Satellite Systems (GNSS) user receivers. Acquisition of navigation data and ephemeris parameters are difficult in remote areas as well as in challenging environments. Statistical orbit determination techniques can help to predict the orbital parameters in the absence of navigation data. The present study is a first step towards the solution for generating orbital parameters and predicting the satellite positions in the absence of navigation data for satellites in NavIC constellation. The orbit determination algorithm predicted the satellite position using single station navigation data. The perturbations affecting the satellite orbits in NavIC constellation were also studied and an algorithm using perturbation force models is proposed for the satellites in NavIC constellation. Extended Kalman Filter (EKF) was used to address the non-linear dynamics model of the perturbation forces and distance of the ground station from the centre of Earth was used as measurement to solve the measurement equation. The satellite orbits were predicted up to 1 hour using the single station navigation data. The root mean square error (RMSE) of 12.59 m and 13.03 m were observed for NavIC satellites in Geosynchronous and Geostationary orbits, respectively, after 1 hour. The Kolmogorov-Smirnov test used to assess the goodness of fit of the proposed EKF algorithm for orbit prediction was found to be significant at 1% level of significance.

10

Łączna synchronizacja podstawy czasu i fali nośnej z użyciem rozszerzonego filtru Kalmana

Haza Grzegorz

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

|

2019

|

nr 6

211--216, CD

PL

W tym artykule zaproponowano algorytm łącznej synchronizacji parametrów zegara taktującego i resztkowej fali nośnej z wykorzystaniem rozszerzonego filtru Kalmana (EKF). Opracowany algorytm został porównany z metodą rozdzielnej synchronizacji bazującą na pętlach fazowych drugiego rzędu (PLL) z dedykowanymi detektorami błędu.

EN

In this paper the algorithm of joint synchronization for symbol timing and carrier frequency using Extended Kalman Filter (EKF) is proposed. Performance of the algorithm is compared with synchronization method based on the second order phase locked loops (PLL) with a given timing and frequency error detectors.

11

Personal navigation system using ultrawideband technology

Kaniewski Piotr, Pasek Przemysław

Przegląd Elektrotechniczny

|

2019

|

R. 95, nr 11

136--139

EN

This paper describes a high-accuracy personal navigation system based on measurements of distances between ultrawideband (UWB) radio modules. The paper contains a description of the physical model of the presented system. Furthermore, positioning algorithms implemented in the proposed system are discussed with emphasis on the Extended Kalman Filter. Subsequently, the process of experiments is described, and chosen results are given.

PL

W artykule przedstawiono system nawigacji personalnej o wysokiej dokładności pozycjonowania, oparty na pomiarach odległości pomiędzy modułami ultraszerokopasmowymi (UWB). Artykuł zawiera opis fizycznego modelu systemu. Ponadto, omówione zostały algorytmy pozycjonujące zaimplementowane w systemie, przy czym najwięcej uwagi poświęcono rozszerzonemu filtrowi Kalmana. Następnie, omówiono przebieg badań oraz podano ich wybrane wyniki.

12

Fault Tolerant Control Based on Extended Kalman Filter of Squirrel-Cage Induction Machines

Khadar Saad, Mekhalfia Fadhila, Kouzou Abdellah

Acta Energetica

|

2019

|

nr 4

6--23

EN

Fault-tolerant control systems possess the ability of rejecting the effect of faults. They are capable of maintaining overall system stability and acceptable performance in degraded modes. Through many researches, the analysis, modeling, and simulation of various inverter and machine faults have been carried out for the purpose of providing a fault tolerance. However, most of them are based on systems redundancy principle. Among the real-time based approaches for the fault detection and diagnosis, there are several strategies such as the pseudo inverse method, the linear quadratic approach and Extended Kalman Filter based Fault Tolerant Control (EKF-FTC). In recent years the application of Kalman filter approaches has gained an increasing attention in fundamental research and application. In this paper, a FTC method dedicated to Induction Motor (IM) drive is presented. The proposed method based on an additive term to the backstepping control which based on the error of current during the appearance of fault and the adaptive gain of the Kalman filter. This method improves the performance of the backstepping control to maintain the operation despite the appearance of faults. The main objective is to ensure a minimum level of performance of the drive system that is malfunctioning.

PL

Odporne na błędy układy sterowania mają zdolność eliminacji wpływu zakłóceń. Potrafią one utrzymywać ogólną stabilność i akceptowalne działanie systemu w trybach awaryjnych. Dzięki wielu badaniom przeprowadzono analizę, modelowanie i symu- lację różnych błędów falownika i maszyny w celu zapewnienia odporności na błędy. Większość z nich wynika jednak z zasady redundancji systemów. Wśród strategii wykrywania i diagnozowania błędów w czasie rzeczywistym można wyróżnić przykładowo metodę pseudoodwrotną, metodę liniowo-kwadratową i sterowanie odporne na błędy przy użyciu rozszerzonego filtra Kalmana (EKF-FTC). W ostatnich latach metodom z użyciem filtra Kalmana poświęca się coraz więcej uwagi w podstawowych bada- niach i zastosowaniach. W niniejszym artykule przedstawiono metodę FTC zastosowaną do napędu silnika indukcyjnego (IM). Proponowana metoda polega na dodaniu do sterowania metodą całkowania wstecznego (ang. backstepping) członu addytywnego, która polega na wystąpieniu uchybu prądu w razie błędu i wzmocnienia adaptacyjnego filtra Kalmana. Metoda ta poprawia wydaj- ność sterowania za pomocą wstecznego całkowania w celu podtrzymania pracy pomimo wystąpienia błędów. Głównym celem jest zapewnienie minimalnego poziomu wydajności niesprawnego układu napędowego.

13

Simulation analysis of extended Kalman filter applied for estimating position and speed of a brushless DC motor

Chojowski M.

Power Electronics and Drives

|

2018

|

Vol. 3 (38), No. 1

145--155

EN

The purpose of this paper was to present a method for the estimation of the rotor speed and position of brushless DC (BLDC) motor. The BLDC motor state equations were developed, and the model was discretised. Extended Kalman filter has been designed to observe specific states from the state vector, needed for the sensorless control (rotor position) and to determine the speed, which may be useful to use as a feedback for the controller. A test was carried out to determine the noise covariance matrices in a simulation manner.

14

Introduction to the Special Section on State and Parameter Estimation Methods for Sensorless Drives

Barut M., Hinkkanen M., Orlowska-Kowalska T.

Power Electronics and Drives

|

2018

|

Vol. 3 (38), No. 1

111-113

EN

This short article constitutes an introductory part of the Special Section (SS) on State and Parameter Estimation Methods in Sensorless Drives. In the current issue of the journal, the first part of this section is published. Accepted articles are focussed mainly on estimation of the state variables and parameters for vector-controlled induction motor (IM) drives, using different concepts, such as different types of Kalman filters (KFs) and model reference adaptive systems (MRASs). The KF was also proposed for brushless DC motor (BLDC). Also, neural networks (NNs) have been proposed for mechanical state variables’ estimation of the drive system with elastic couplings.

15

Extended Kalman filter based speed-sensorless load torque and inertia estimations with observability analysis for induction motors

Zerdali E., Barut M.

Power Electronics and Drives

|

2018

|

Vol. 3 (38), No. 1

115--127

EN

This paper aims to introduce a novel extended Kalman filter (EKF) based estimator including observability analysis to the literature associated with the high performance speed-sensorless control of induction motors (IMs). The proposed estimator simultaneously performs the estimations of stator stationary axis components of stator currents and rotor fluxes, rotor mechanical speed, load torque including the viscous friction term, and reciprocal of total inertia by using measured stator phase currents and voltages. The inertia estimation is done since it varies with the load coupled to the shaft and affects the performance of speed estimation especially when the rotor speed changes. In this context, the estimations of all mechanical state and parameters besides flux estimation required for high performance control methods are performed together. The performance of the proposed estimator is tested by simulation and real-time experiments under challenging variations in load torque and velocity references; and in both transient and steady states, the quite satisfactory estimation performance is achieved.

16

Dynamic performance of estimator-based speed sensorless control of induction machines using extended and unscented Kalman filters

Horváth K., Kuslits M.

Power Electronics and Drives

|

2018

|

Vol. 3 (38), No. 1

129--144

EN

This paper presents an estimator-based speed sensorless field-oriented control (FOC) method for induction machines, where the state estimator is based on a self-contained, non-linear model. This model characterises both the electrical and the mechanical behaviours of the machine and describes them with seven state variables. The state variables are estimated from the measured stator currents and from the known stator voltages by using an estimator algorithm. An important aspect is that one of the state variables is the load torque and, hence, it is also estimated by the estimator. Using this feature, the applied estimator-based speed sensorless control algorithm may be operated adequately besides varying load torque. In this work, two different variants of the control algorithm are developed based on the extended and the unscented Kalman filters (EKF, UKF) as state estimators. The dynamic performance of these variants is tested and compared using experiments and simulations. Results show that the variants have comparable performance in general, but the UKF-based control provides better performance if a stochastically varying load disturbance is present.

17

Estymacja respiracji wykorzystująca pomiar stężenia tlenu w SBR

Piotrowski R.

Gaz, Woda i Technika Sanitarna

|

2018

|

Nr 4

138--144

PL

Biologiczna oczyszczalnia ścieków jest złożonym nieliniowym systemem przemysłowym. Jednym z istotnych i kosztownych procesów tam zachodzących jest napowietrzanie ścieków. Z procesem tym związana jest respiracja, czyli szybkość zużywania tlenu przez bakterie oczyszczające ścieki. Jest to jeden z najważniejszych parametrów, decydujący o efektywności oczyszczania ścieków. Niestety koszt zakupu urządzeń do pomiaru respiracji - respirometrów jest bardzo wysoki i w oczyszczalniach ścieków nie są one instalowane. W artykule dokonano estymacji respiracji, w oparciu o pomiar stężenia tlenu w biologicznej oczyszczalni typu wsadowego. W tym celu wykorzystano rozszerzony filtr Kalmana. W badaniach symulacyjnych przedstawiono wyniki estymacji respiracji dla biologicznej oczyszczalni ścieków typu SBR.

EN

Biological wastewater treatment plant is a complex, nonlinear, industrial system. One of the significant and costly process taking place there is aeration of wastewater. This process involves the respiration - the rate of oxygen consumption by the bacteria. It is one of the most important parameter deciding on the efficiency of wastewater treatment. Unfortunately, the cost of buying respiratory equipment - respirometers is very high and in wastewater treatment plants they are not installed. The paper presents estimation of respiration based on the measurement of dissolved oxygen. For this purpose, the extended Kalman filter is used. Simulation results for the biological wastewater treatment plant type SBR are presented.

18

Comparison of Particle Filter and Extended Kalman Particle Filter

Michalski J., Kozierski P., Zietkiewicz J.

Studia z Automatyki i Informatyki

|

2017

|

T. 42

43--51

EN

In this paper, three state estimation algorithms, namely: Extended Kalman Filter, Particle Filter (Bootstrap Filter) and Extended Kalman Particle Filter, have been presented. Particle Filter and Extended Kalman Particle Filter algorithms have been compared with a different number of particles and the results have been presented together with Extended Kalman Filter. Estimation quality has been checked for three nonlinear objects (one- and multidimensional systems) and evaluated through the aRMSE quality index value. Based on the obtained results it was concluded that Extended Kalman Particle Filter provide better estimation quality for low number of particles in comparison to simple particle filter. However it is not met for highly nonlinear system.

PL

W pracy zostały zaprezentowane trzy algorytmy estymacji - rozszerzony filtr Kalmana, filtr cząsteczkowy (algorytm Bootstrap) i rozszerzony cząsteczkowy filtr Kalmana. Algorytmy filtru cząsteczkowego i rozszerzonego cząsteczkowego filtru Kalmana zostały porównane dla różnej liczby cząsteczek, a wyniki zestawione z wynikami działania rozszerzonego filtru Kalmana. Jakość estymacji została sprawdzona dla trzech nieliniowych obiektów (systemy jedno- i wielowymiarowe) i oceniona za pomocą wskaźnika jakości aRMSE. Na podstawie otrzymanych wyników stwierdzono, że rozszerzony cząsteczkowy filtr Kalmana zapewnia lepszą jakość estymacji dla niewielkiej liczby cząsteczek w porównaniu do zwykłego filtru cząsteczkowego. Jednakże nie jest to spełnione dla silnie nieliniowego obiektu.

19

Porównanie metod estymacji stanu systemów dynamicznych

Michalski J., Kozierski P., Ziętkiewicz J.

Pomiary Automatyka Robotyka

|

2017

|

R. 21, nr 4

41--47

PL

W pracy poruszono problem estymacji stanu dla układów dynamicznych oraz przedstawiono wybrane jego rozwiązania. Zaproponowano cztery metody estymacji: rozszerzony filtr Kalmana, bezśladowy filtr Kalmana, filtr cząsteczkowy oraz filtr Kalmana, stosowany dla obiektów liniowych. Metody te zastosowano dla trzech obiektów nieliniowych oraz dla dwóch obiektów liniowych (systemy jedno- i wielowymiarowe). Wszystkie obiekty zostały opisane za pomocą równań stanu. Przedstawiono także trzy różne wskaźniki jakości, reprezentujące błędy względne oraz bezwzględne, a także porównano ich działanie dla różnego typu obiektów. W wyniku przeprowadzonych symulacji stwierdzono, że najlepszą jakość estymacji zapewnia filtr cząsteczkowy, ale jednocześnie ta metoda jest najwolniejsza.

EN

In this paper the problem of state estimation of dynamical systems has been discussed and selected solutions have been presented. Four methods of state estimation have been proposed: Extended Kalman Filter, Unscented Kalman Filter, Particle Filter and Kalman Filter for a linear system. These methods have been applied to three nonlinear objects and to two linear objects (one- and multivariable systems). All plants have been described using state equations. Three quality indices has been used, which present relative and absolute errors. They were compared for different objects. As a result of the simulation, it was found that the best estimation quality is provided by the particle filter, but this method is also the slowest.

20

Sky-hook control and Kalman filtering in nonlinear model of tracked vehicle suspension system

Jurkiewicz A., Kowal J., Zając K.

Acta Mechanica et Automatica

|

2017

|

Vol. 11, no. 3

222--228

EN

The essence of the undertaken topic is application of the continuous sky-hook control strategy and the Extended Kalman Filter as the state observer in the 2S1 tracked vehicle suspension system. The half-car model of this suspension system consists of seven logarithmic spiral springs and two magnetorheological dampers which has been described by the Bingham model. The applied continuous skyhook control strategy considers nonlinear stiffness characteristic of the logarithmic spiral springs. The control is determined on estimates generated by the Extended Kalman Filter. Improve of ride comfort is verified by comparing simulation results, under the same driving conditions, of controlled and passive vehicle suspension systems.