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  1. 30 International Journal of Applied Mathematics and Computer Science
  2. 9 Przegląd Elektrotechniczny
  3. 4 Vibrations in Physical Systems
  4. 4 Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
  5. 3 Diagnostyka
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  1. 4 Kaczorek T.
  2. 4 Świszcz P.
  3. 3 Bańka S.
  4. 3 Dworak P.
  5. 3 Jaroszewski K.
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  1. 1 2023
  2. 3 2022
  3. 3 2021
  4. 1 2020
  5. 3 2019
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1
Content available Robust flat filtering control of a two degrees of freedom helicopter subject to tail rotor disturbances
Sánchez-Meza Victor-Gabriel, Lozano-Hernández Yair, Gutiérrez-Frías Octavio, Lozada-Castillo Norma, Luviano-Juárez Alberto
International Journal of Applied Mathematics and Computer Science
|
2023
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Vol. 33, no. 4
521--535
EN
This article deals with modelling and a flatness-based robust trajectory tracking scheme for a two degrees of freedom helicopter, which is subject to four types of tail rotor disturbances to validate the control scheme robustness. A mathematical model of the system, its differential flatness and a differential parametrization are obtained. The flat filtering control is designed for the system control with a partially known model, assuming the non-modelled dynamics and the external disturbances (specially the tail rotor ones) to be rejected by means of an extended state model (ultra-local model). Numerical and experimental assessments are carried out on a characterized prototype whose yaw angle (ψ), given by the z axis, is in free form, while the pitch angle (θ), which results from rotation about the y axis, is mechanically restricted. The proposed controller performance is tested through a set of experiments in trajectory tracking tasks with different disturbances in the tail rotor, showing robust behaviour for the different disturbances. Besides, a comparison study against a widely used controller of LQR type is carried out, in which the proposed controller achieves better results, as illustrated by a performance index.
2
Content available Global stability of discrete-time feedback nonlinear systems with descriptor positive linear parts and interval state matrices
Kaczorek Tadeusz, Ruszewski Andrzej
International Journal of Applied Mathematics and Computer Science
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2022
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Vol. 32, no. 1
5--10
EN
The global stability of discrete-time nonlinear systems with descriptor positive linear parts, positive scalar feedbacks and interval state matrices is addressed. Sufficient conditions for the global stability of this class of nonlinear systems are established. The effectiveness of these conditions is illustrated using numerical examples.
3
Content available Fault-tolerant tracking control for a non-linear twin-rotor system under ellipsoidal bounding
Kukurowski Norbert, Mrugalski Marcin, Pazera Marcin, Witczak Marcin
International Journal of Applied Mathematics and Computer Science
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2022
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Vol. 32, no. 2
171--183
EN
A novel fault-tolerant tracking control scheme based on an adaptive robust observer for non-linear systems is proposed. Additionally, it is presumed that the non-linear system may be faulty, i.e., affected by actuator and sensor faults along with the disturbances, simultaneously. Accordingly, the stability of the robust observer as well as the fault-tolerant tracking controller is achieved by using the ℋ∞ approach. Furthermore, unknown actuator and sensor faults and states are bounded by the uncertainty intervals for estimation quality assessment as well as reliable fault diagnosis. This means that narrow intervals accompany better estimation quality. Thus, to cope with the above difficulty, it is assumed that the disturbances are over-bounded by an ellipsoid. Consequently, the performance and correctness of the proposed fault-tolerant tracking control scheme are verified by using a non-linear twin-rotor aerodynamical laboratory system.
4
Content available A data driven fault isolation method based on reference faulty situations with application to a nonlinear chemical process
Ragot José, Mourot Gilles, Kallas Maya
International Journal of Applied Mathematics and Computer Science
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2022
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Vol. 32, no. 4
635--655
EN
The diagnosis of systems is one of the major steps in their control and its purpose is to determine the possible presence of dysfunctions, which affect the sensors and actuators associated with a system but also the internal components of the system itself. On the one hand, the diagnosis must therefore focus on the detection of a dysfunction and, on the other hand, on the physical localization of the dysfunction by specifying the component in a faulty situation, and then on its temporal localization. In this contribution, the emphasis is on the use of software redundancy applied to the detection of anomalies within the measurements collected in the system. The systems considered here are characterized by non-linear behaviours whose model is not known a priori. The proposed strategy therefore focuses on processing the data acquired on the system for which it is assumed that a healthy operating regime is known. Diagnostic procedures usually use this data corresponding to good operating regimes by comparing them with new situations that may contain faults. Our approach is fundamentally different in that the good functioning data allow us, by means of a non-linear prediction technique, to generate a lot of data that reflect all the faults under different excitation situations of the system. The database thus created characterizes the dysfunctions and then serves as a reference to be compared with real situations. This comparison, which then makes it possible to recognize the faulty situation, is based on a technique for evaluating the main angle between subspaces of system dysfunction situations. An important point of the discussion concerns the robustness and sensitivity of fault indicators. In particular, it is shown how, by non-linear combinations, it is possible to increase the size of these indicators in such a way as to facilitate the location of faults.
5
Content available remote New multipoint algorithm for eliminating chaotic vibrations in complex non-linear systems
Basiński Radosław, Siwek Krzysztof
Przegląd Elektrotechniczny
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2021
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R. 97, nr 6
91--96
EN
The paper presents a very effective algorithm for stabilizing unstable periodic orbits, consisting of slight changes in selected parameters of a chaotic system at any time of sampling. Modification of the parameters leads to minimization of the distance of the phase trajectory from the fixed point on the cross-section of the generalized Poincaré map. By modifying several parameters, it is possible to effectively eliminate chaotic vibrations in complex non-linear dynamical systems in the presence of strong disturbances and noise.
PL
W pracy przedstawiono efektywny algorytm stabilizacji niestabilnych orbit okresowych, polegający na niewielkich zmianach wybranych parametrów układu chaotycznego w każdej chwili próbkowania. Modyfikacja parametrów prowadzi do minimalizacji odległość trajektorii fazowej od punktu stałego na przekroju uogólnionego odwzorowania Poincarégo. Realizacja zagadnienia sterowania poprzez zmianę kilku parametrów umożliwia efektywną eliminację drgań chaotycznych w złożonych nieliniowych układach dynamicznych w obecności silnych zakłóceń i szumów.
6
Content available Conditions and a computation method of the constrained regulation problem for a class of fractional-order nonlinear continuous-time systems
Si Xindong, Yang Hongli, Ivanov Ivan G.
International Journal of Applied Mathematics and Computer Science
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2021
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Vol. 31, no. 1
17--28
EN
The constrained regulation problem (CRP) for fractional-order nonlinear continuous-time systems is investigated. New existence conditions of a linear feedback control law for a class of fractional-order nonlinear continuous-time systems under constraints are proposed. A computation method for solving the CRP for fractional-order nonlinear systems is also presented. Using the comparison principle and positively invariant set theory, conditions guaranteeing positive invariance of a polyhedron for fractional-order nonlinear systems are established. A linear feedback controller model and the corresponding algorithm of the CRP for fractional nonlinear systems are also proposed by using the obtained conditions. The presented model of the CRP is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Numerical examples illustrate the proposed method.
7
Content available A computationally inexpensive algorithm for determining outer and inner enclosures of nonlinear mappings of ellipsoidal domains
Rauh Andreas, Jaulin Luc
International Journal of Applied Mathematics and Computer Science
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2021
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Vol. 31, no. 3
399--415
EN
A wide variety of approaches for set-valued simulation, parameter identification, state estimation as well as reachability, observability and stability analysis for nonlinear discrete-time systems involve the propagation of ellipsoids via nonlinear functions. It is well known that the corresponding image sets usually possess a complex shape and may even be nonconvex despite the convexity of the input data. For that reason, domain splitting procedures are often employed which help to reduce the phenomenon of overestimation that can be traced back to the well-known dependency and wrapping effects of interval analysis. In this paper, we propose a simple, yet efficient scheme for simultaneously determining outer and inner ellipsoidal range enclosures of the solution for the evaluation of multi-dimensional functions if the input domains are themselves described by ellipsoids. The Hausdorff distance between the computed enclosure and the exact solution set reduces at least linearly when decreasing the size of the input domains. In addition to algebraic function evaluations, the proposed technique is-for the first time, to our knowledge-employed for quantifying worst-case errors when extended Kalman filter-like, linearization-based techniques are used for forecasting confidence ellipsoids in a stochastic setting.
8
Content available Global stability of nonlinear feedback systems with fractional positive linear parts
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
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2020
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Vol. 30, no. 3
493--499
EN
The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k1e ≤ f(e) ≤ k2e for some positive k1 and k2. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1/k1,−1/k2).
9
Content available Two-stage instrumental variables identification of polynomial Wiener systems with invertible nonlinearities
Janczak Andrzej, Korbicz Józef
International Journal of Applied Mathematics and Computer Science
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2019
|
Vol. 29, no. 3
571--580
EN
A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.
10
Content available LMI-based robust control of uncertain nonlinear systems via polytopes of polynomials
Sánchez Marcelino, Bernal Miguel
International Journal of Applied Mathematics and Computer Science
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2019
|
Vol. 29, no. 2
275--283
EN
This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.
11
Content available Absolute stability of a class of fractional positive nonlinear systems
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 1
93--98
EN
The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.
12
Content available Reduced-order perfect nonlinear observers of fractional descriptor discrete-time nonlinear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2017
|
Vol. 27, no. 2
245--251
EN
The purpose of this work is to propose and characterize fractional descriptor reduced-order perfect nonlinear observers for a class of fractional descriptor discrete-time nonlinear systems. Sufficient conditions for the existence of these observers are established. The design procedure of the observers is given and demonstrated on a numerical example.
13
Content available Fault detection in nonlinear systems via linear methods
Zhirabok A., Shumsky A., Solyanik S., Suvorov A.
International Journal of Applied Mathematics and Computer Science
|
2017
|
Vol. 27, no. 2
261--272
EN
The problem of robust linear and nonlinear diagnostic observer design is considered. A method is suggested to construct the observers that are disturbance decoupled or have minimal sensitivity to the disturbances. The method is based on a logic-dynamic approach which allows us to consider systems with non-differentiable nonlinearities in the state equations by methods of linear algebra.
14
Content available Nonlinear control of underwater robotic vehicle in plane motion
Garus J.
Zeszyty Naukowe Akademii Marynarki Wojennej
|
2016
|
R. 57 nr 3 (206)
15--23
EN
A control system supporting motion of an underwater robotic vehicle along a reference trajectory in the horizontal plane is presented in the paper. A waypoint line-of-sight scheme and nonlinear PD control law are applied to calculate command signals. Parameters of the proposed control law are tuned using genetic algorithms. The validity and advantages of the approach are illustrated through numerical simulation results.
PL
W artykule przedstawiono koncepcję system automatycznego sterowania ruchem płaskim robota podwodnego wzdłuż trajektorii odniesienia. Układem odpowiedzialnym za wyznaczanie sygnałów sterujących jest autopilot, w którym zaimplementowano nieliniowy regulator PD. Parametry regulatora dostrojono z wykorzystaniem algorytmów genetycznych. Zamieszczono wyniki badań symulacyjnych ruchu robota w płaszczyźnie poziomej z wykorzystaniem zaproponowanego algorytmu sterowania.
15
Content available Free vibrations of the partially tensioned geometrically non-linear system subjected to Euler’s load
Uzny S., Sokół K., Osadnik M.
Vibrations in Physical Systems
|
2016
|
Vol. 27
399--406
EN
In this study the fixed-fixed column subjected to axial Euler’s load has been investigated. The load is placed between the fixed ends of the structure and its location can be changed along column’s length. The boundary problem of free vibrations of the mentioned system has been formulated on the basis of Bernoulli – Euler theory and taking into account non-linear axial deformation relationship. Due to non-linear expressions the solution of the problem was done with small parameter method. In the paper the change of the first vibration frequency in relation to location and magnitude of the loading force was obtained. The relationship between natural vibration frequency and the amplitude is also discussed.
16
Content available remote Analiza wpływu zmiany parametrów R,L,C strony pierwotnej układu zapłonowego na wartość energii wyładowania iskrowego
Różowicz S.
Przegląd Elektrotechniczny
|
2016
|
R. 92, nr 5
216--220
PL
W pracy przedstawiono analizę wpływu zmiany parametrów strony pierwotnej układu zapłonowego na wartość energii wyładowania iskrowego. Przeprowadzono również analizę zakresu zmian wartości energii wyładowania iskrowego dla zmiennych wartości wszystkich elementów strony pierwotnej układu. Badania symulacyjne przeprowadzono w autorskim programie opracowanym w środowisku Matlab-Simulink, a zweryfikowano je eksperymentalnie na stanowisku badawczym bateryjnych układów zapłonowych.
EN
The paper discusses how the parameter change of the primary side of the ignition system affects the value of spark discharge energy. The extent of changes in spark discharge energy values for changing values of all elements of the primary system is analyzed. Simulation studies are carried out in the program, developed by the authors in Matlab - Simulink and verified experimentally on a test stand for battery ignition systems.
17
Content available State estimation for miso non-linear systems in controller canonical form
Schwaller B., Ensminger D., Dresp-Langley B., Ragot J.
International Journal of Applied Mathematics and Computer Science
|
2016
|
Vol. 26, no. 3
569--583
EN
We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.
18
Content available Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2016
|
Vol. 26, no. 2
277--283
EN
Fractional descriptor reduced-order nonlinear observers for a class of fractional descriptor continuous-time nonlinear systems are proposed. Sufficient conditions for the existence of the observers are established. The design procedure for the observers is given and demonstrated on a numerical example.
19
Content available Descriptor fractional discrete-time linear system with two different fractional orders and its solution
Sajewski Ł.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2016
|
Vol. 64, nr 1
15--20
EN
Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.
20
Content available A Hamiltonian approach to fault isolation in a planar vertical take-off and landing aircraft model
Rodriguez-Alfaro L. H., Alcorta-Garcia E., Lara D., Romero G.
International Journal of Applied Mathematics and Computer Science
|
2015
|
Vol. 25, no. 1
65--76
EN
The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler–Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible) specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.
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