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  1. 21 International Journal of Applied Mathematics and Computer Science
  2. 6 Applied Mathematics and Computer Science
  3. 2 Journal of Applied Computer Science
  4. 2 Przegląd Elektrotechniczny
  5. 1 Archives of Electrical Engineering
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  1. 3 Tatjewski P.
  2. 2 Becerra V. M.
  3. 2 Bernoussi A. S.
  4. 2 Marusak P. M.
  5. 2 Shumsky A.
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  1. 1 2021
  2. 1 2013
  3. 2 2012
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  5. 2 2010
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1
Content available remote Highly nonlinear systems estimation using extended and unscented kalman filters
Laamari Yahia, Allaoui Samia, Chafaa Kheireddine, Bendaikha Abdelmalik
Przegląd Elektrotechniczny
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2021
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R. 97, nr 5
111--115
EN
The main idea of this study is to evaluate the estimation performance of extended and unscented Kalman filters (EKF and UKF). So, these latter are introduced to estimate the dynamic states of a similar model operating with identical covariance matrices in the same situation. The mean square error (MSE) criterion is used to quantify the estimation error between the actual and the estimated values. The simulation results obtained with Matlab/ Simulink software confirm the superiority and efficiency of UKF over EKF, especially when the system is highly non-linear under process and measurement noises, such is the case of the inverted double pendulum mounted on a cart (DIPC).
PL
Główną ideą tego badania jest ocena wydajności estymacji rozszerzonych filtrów Kalmana (EKF i UKF). Te ostatnie zostały wprowadzone w celu oszacowania stanów dynamicznych podobnego modelu działającego z identycznymi macierzami kowariancji. Kryterium błędu średniokwadratowego (MSE) służy do ilościowego określenia błędu oszacowania między wartościami rzeczywistymi i szacunkowymi. Wyniki symulacji uzyskane za pomocą oprogramowania Matlab i Simulink potwierdzają wyższość i wydajność UKF nad EKF, zwłaszcza gdy system jest wysoce nieliniowy
2
Content available Sterowanie procesem destylacji z wykorzystaniem regulatorów rozmytych
Grzelak A., Konkel M., Piotrowski R.
Pomiary Automatyka Robotyka
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2013
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R. 17, nr 10
172--181
PL
Proces destylacji jest popularnym przemysłowym sposobem rozdziału ciekłych mieszanin wieloskładnikowych. W artykule rozważana jest mieszanina etanol-woda, będąca powszechnie destylowanym produktem. Celem artykułu jest omówienie procesu projektowania i symulacyjnej analizy działania trzech układów sterowania kolumną rektyfikacyjną z wykorzystaniem rozmytych regulatorów: P, PD i PI.
EN
Distillation is the most common unit operations in different branches of industry. In the paper a two product distillation process is considered (ethanol-water). The paper presents mathematical model of distillation column. Next, the three fuzzy controllers (P, PD, PI) are designed and implemented in MATLAB/Simulink environment. Finally, the results of simulation and a critical analysis are presented.
3
Content available remote Fault Diagnosis Method Integrated Fuzzy Logic and Particle Filter for Nonlinear Systems
Zhang S., Zhu L.
Przegląd Elektrotechniczny
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2012
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R. 88, nr 11a
283-287
EN
A new fault diagnosis method based on integrated fuzzy logic and particle filter for nonlinear systems is proposed to improve the accuracy of fault diagnosis. The Water Level and Temperature Control System is taken as test-bed process, with different switching states simulating possible system faults. The simulation result show that the proposed method could diagnose fault more accurately than that based on two-valued logic.
PL
W artykule zaprezentowano nową metodę wykrywania awarii w opartą na logice rozmytej i filtrze cząsteczkowym. Metoda dedykowana układom nieliniowym, zwiększa dokładność detekcji stanów niepożądanych. Przeprowadzone badania symulacyjne i eksperymentalne w układzie regulacji temperatury oraz poziomu cieczy, potwierdziły zwiększoną skuteczność algorytmu dla różnych przypadków awarii.
4
Content available Stabilizacja wahadła odwróconego z napędem inercyjnym przy pomocy regulatora LQR
Owczarkowski A., Gośliński J.
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
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2012
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nr 4a
7-10
PL
Niniejszy artykuł opisuje metodę stabilizacji obiektu zwanego wahadłem odwróconym z napędem inercyjnym IWP (ang. Interia Wheel Pendulum). Jest to nieliniowy układ mechaniczny w postaci wahadła odwróconego składającego się z masztu i kola zamachowego umieszczonego na szczycie napędzanego silnikiem prądu stałego. Autorzy zaproponowali stabilizację przy pomocy regulacji LQR, która do funkcjonowania wymaga linearyzacji i dyskretyzacji równań matematycznych obiektu. Wykonano działania symulacyjno-eksperymentalne potwierdzające poprawność działania proponowanej metody.
EN
Work is about stabilizing the inverted pendulum object called IWP (Inertia Wheel Pendulum). It is a non-linear mechanical system in the form of an inverted pendulum containing a flywheel mounted on top accelerated by DC motor. The authors suggested stabilization by LQR control, which requires the linearization and discretization of the mathematical equations of the object. Simulation and experiment have confirmed proper operation of the proposed method.
5
Content available remote Integrated design of observer based fault detection for a class of uncertain nonlinear systems
Chen W., Khan A, Q., Abid M., Ding S. X.
International Journal of Applied Mathematics and Computer Science
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2011
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Vol. 21, no 3
423-430
EN
Integrated design of observer based Fault Detection (FD) for a class of uncertain nonlinear systems with Lipschitz nonlinearities is studied. In the context of norm based residual evaluation, the residual generator and evaluator are designed together in an integrated form, and, based on it, a trade-off FD system is finally achieved in the sense that, for a given Fault Detection Rate (FDR), the False Alarm Rate (FAR) is minimized. A numerical example is given to illustrate the effectiveness of the proposed design method.
6
Content available remote Constrained controllability of nonlinear stochastic impulsive systems
Karthikeyan S., Balachandran K.
International Journal of Applied Mathematics and Computer Science
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2011
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Vol. 21, no 2
307-316
EN
This paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.
7
Content available remote Adaptive control scheme based on the least squares support vector machine network
Mahmoud T. K.
International Journal of Applied Mathematics and Computer Science
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2011
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Vol. 21, no 4
685-696
EN
Recently, a new type of neural networks called Least Squares Support Vector Machines (LS-SVMs) has been receiving increasing attention in nonlinear system identification and control due to its generalization performance. This paper develops a stable adaptive control scheme using the LS-SVM network. The developed control scheme includes two parts: the identification part that uses a modified structure of LS-SVM neural networks called the multi-resolution wavelet least squares support vector machine network (MRWLS-SVM) as a predictor model, and the controller part that is developed to track a reference trajectory. By means of the Lyapunov stability criterion, stability analysis for the tracking errors is performed. Finally, simulation studies are performed to demonstrate the capability of the developed approach in controlling a pH process.
8
Content available remote Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systems
Tong S., Liu C., Li Y.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 4
637-653
EN
In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.
9
Content available remote Protector control: Extension to a class of nonlinear distributed systems
Qaraai Y., Bernoussi A. S.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 3
427-443
EN
We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a simulation example.
10
Contribution to problem of chaos control in the dynamics systems
Kratochvil C, Heriban Ρ, Sveda Ρ.
Modelling and Optimization of Physical Systems
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2009
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z. 8
77--80
EN
Chaos is present in many aspect of life. Physics is usually the field where chaos control became a paradigma and discipline itself. It is very difficult to detect and control chaotic behavior in nonlinear engineering dynamical Systems. This contribution introduces some basic concepts for controlling chaos and describes some mathematical methods for controlling chaos in dynamic systems
11
Forced dynamics speed control of the drive with linear PMSM
Vavrúš V., Pospíšil M., Szychta E., Luft M.
Logistyka
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2009
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nr 6
CD-CD
EN
Forced dynamics control of the drive with linear permanent magnet synchronous motor is presented and verified. This, a relatively new control method offers an accurate realisation of a dynamic speed response with prescribed acceleration, which can be selected for given transport application by the user. In addition to this, vector control condition, which requires right angle between the stator current vector and moving part flux vector, is maintained as it is in conventional drives. To achieve prescribed speed response of moving part, the derived control law requires estimation of an external force, which is obtained from the set of two observers. The observer of moving part speed, which works in pseudo-sliding mode, is completed with the second one, having filtering effect to eliminate chattering of the previous one. The proposed control algorithms with precisely defined acceleration, one of which is suitable for traction application, are verified by simulations and experimentally. Preliminary experiments confirmed that the moving part speed response is capable to follow prescribed smooth acceleration fairly closely.
PL
W artykule jest prezentowany i weryfikowany układ sterowania dynamicznego napędu z liniowym synchronicznym silnikiem z magnesami trwałymi. Ta stosunkowo nowa metoda sterowania powoduje dokładną realizację dynamicznie zadanej prędkości z zadanym może być wybrana przez użytkownika dla danego zastosowania w transporcie. Warunek sterowania wektorowego, który wymaga prawidłowego kąta pomiędzy wektorem prądu stojana a wektorem strumienia części ruchomej jest utrzymany, jak w tradycyjnych napędach. Aby osiągnąć zadaną odpowiedź prędkości części ruchomej, przedstawione prawo sterowania wymaga estymacji zewnętrznego wymuszenia otrzymywanego poprzez układ dwóch obserwatorów. Obserwator prędkości części ruchomej, który pracuje w trybie 'pseudosliding' jest uzupełniony przez drugi, mający właściwość filtracji eliminującej zakłócenia wprowadzane przez pierwszy obserwator. Proponowane algorytmy sterowania z dokładnie zdefiniowanym przyśpieszeniem, mogą być użyteczne w zastosowaniach trakcyjnych. Są one zweryfikowane poprzez badania symulacyjne i eksperymentalne. Wstępne wyniki badań eksperymentalnych potwierdziły, że odpowiedź części ruchomej jest zdolna dość dokładnie nadążyć za przyśpieszeniem.
12
Content available remote Recursive identification algorithm for dynamic systems with output backlash and its convergence
Dong R., Tan Q., Tan Y.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 4
631-638
EN
This paper proposes a recursive identification method for systems with output backlash that can be described by a pseudo-Wiener model. In this method, a novel description of the nonlinear part of the system, i.e., backlash, is developed. In this case, the nonlinear system is decomposed into a piecewise linearized model. Then, a modified recursive general identification algorithm (MRGIA) is employed to estimate the parameters of the proposed model. Furthermore, the convergence of the MRGIA for the pseudo-Wiener system with backlash is analysed. Finally, a numerical example is presented.
13
Content available remote Input constraints handling in an MPC/feedback linearization scheme
Deng J., Becerra V. M., Stobart R.
International Journal of Applied Mathematics and Computer Science
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2009
|
Vol. 19, no 2
219-232
EN
The combination of model predictive control based on linear models (MPC) with feedback linearization (FL) has attracted interest for a number of years, giving rise to MPC+FL control schemes. An important advantage of such schemes is that feedback linearizable plants can be controlled with a linear predictive controller with a fixed model. Handling input constraints within such schemes is difficult since simple bound contraints on the input become state dependent because of the nonlinear transformation introduced by feedback linearization. This paper introduces a technique for handling input constraints within a real timeMPC/FL scheme, where the plant model employed is a class of dynamic neural networks. The technique is based on a simple affine transformation of the feasible area. A simulated case study is presented to illustrate the use and benefits of the technique.
14
Content available remote Effective dual-mode fuzzy DMC algorithms with on-line quadratic optimization and guaranteed stability
Marusak P. M., Tatjewski P.
International Journal of Applied Mathematics and Computer Science
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2009
|
Vol. 19, no 1
127-141
EN
Dual-mode fuzzy dynamic matrix control (fuzzy DMC-FDMC) algorithms with guaranteed nominal stability for constrained nonlinear plants are presented. The algorithms join the advantages of fuzzy Takagi-Sugeno modeling and the predictive dual-mode approach in a computationally efficient version. Thus, they can bring an improvement in control quality compared with predictive controllers based on linear models and, at the same time, control performance similar to that obtained using more demanding algorithms with nonlinear optimization. Numerical effectiveness is obtained by using a successive linearization approach resulting in a quadratic programming problem solved on-line at each sampling instant. It is a computationally robust and fast optimization problem, which is important for on-line applications. Stability is achieved by appropriate introduction of dual-mode type stabilization mechanisms, which are simple and easy to implement. The effectiveness of the proposed approach is tested on a control system of a nonlinear plant-a distillation column with basic feedback controllers.
15
Content available remote How to compensate a spreading disturbance for a class of nonlinear systems
Quaraai Y., Bernoussi A. S., El Jai A.
International Journal of Applied Mathematics and Computer Science
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2008
|
Vol. 18, no 2
171-187
EN
We consider a system which is assumed to be affected by an expanding disturbance which occurs at the initial time. The compensation of the disturbance is accomplished by extending the concept of remediability to a class of nonlinear systems. The results are implemented and illustrated with a nonlinear distributed model.
16
Content available remote Determining the weights of a Fourier series neural network on the basis of the multidimensional discrete Fourier transform
Halawa K.
International Journal of Applied Mathematics and Computer Science
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2008
|
Vol. 18, no 3
369-375
EN
This paper presents a method for training a Fourier series neural network on the basis of the multidimensional discrete Fourier transform. The proposed method is characterized by low computational complexity. The article shows how the method can be used for modelling dynamic systems.
17
Content available remote Actuator fault tolerance in control systems with predictive constrained set-point optimizers
Marusak P. M., Tatjewski P.
International Journal of Applied Mathematics and Computer Science
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2008
|
Vol. 18, no 4
539-551
EN
Mechanisms of fault tolerance to actuator faults in a control structure with a predictive constrained set-point optimizer are proposed. The structure considered consists of a basic feedback control layer and a local supervisory set-point optimizer which executes as frequently as the feedback controllers do with the aim to recalculate the set-points both for constraint feasibility and economic performance. The main goal of the presented reconfiguration mechanisms activated in response to an actuator blockade is to continue the operation of the control system with the fault, until it is fixed. This may be even long-term, if additional manipulated variables are available. The mechanisms are relatively simple and consist in the reconfiguration of the model structure and the introduction of appropriate constraints into the optimization problem of the optimizer, thus not affecting the numerical effectiveness. Simulation results of the presented control system for a multivariable plant are provided, illustrating the efficiency of the proposed approach.
18
Content available remote Redundancy relations for fault diagnosis in nonlinear uncertain systems
Shumsky A.
International Journal of Applied Mathematics and Computer Science
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2007
|
Vol. 17, no 4
477-489
EN
The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into a strict feedback form. Algebraic and geometric tools are used for this transformation. The features of the method are made particular for uncertain systems with a linear structure.
19
Content available remote Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form
Orłowski P.
International Journal of Applied Mathematics and Computer Science
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2007
|
Vol. 17, no 4
505-513
EN
Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems given in the state space dependent form. The method for numerical estimation of the maximal norm of the output trajectory deviation with applications to robust control synthesis is proposed based on the introduced three-term additive uncertainty model. Theoretical deliberations are complemented with a numerical, water-tank system example.
20
Content available remote Generalizations of the Cayley-Hamilton theorem with applications
Kaczorek T.
Archives of Electrical Engineering
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2007
|
Vol. 56, nr 1
3-41
EN
New generalizations of the classical Cayley-Hamilton theorem for rectangular matrices, block matrices, matrices depending on parameters, discrete-time and continuous-time systems with delays, polynomial matrices with commuting matrices, n-D polynomial matrices, singular systems, right and left inverse of polynomial matrices, rational matrices, impulse response matrices and nonlinear time-varying systems are presented. Some applications of the generalizations and illustrating examples are also given.
PL
W pracy podano nowe uogólnienia klasycznego twierdzenia Cayley-Hamiltona na: macierze prostokątne, macierze blokowe, macierze zależne od parametrów, macierze układów ciągłych i dyskretnych z opóźnieniami, macierze wielomianowe z macierzami przemiennymi, macierze wielomianowe o elementach będącymi funkcjami n zmiennych, macierze układów singularnych, prawe i lewe odwrotności macierzy wielomianowych, macierze wymierne, macierze odpowiedzi impulsowych oraz na macierze układów nieliniowych o parametrach zmiennych w czasie. Podano również pewne zastosowania tych uogólnień twierdzenia Cayley-Hamiltona. Rozważania zostały zilustrowane przykładami.
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