Wydział Mechaniczny / Faculty of Mechanical Engineering / W1
Stały URI zbioruhttp://hdl.handle.net/11652/1
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Pozycja Guidance of the resonance energy flow in the mechanism of coupled magnetic pendulums(Elsevier, 2022) Pilipchuk, Valery N.; Polczyński, Krystian; Bednarek, Maksymilian; Awrejcewicz, JanThis paper presents a methodology of controlling the resonance energy exchange in mechanical system consisting of two weakly coupled magnetic pendulums interacting with the magnetic field generated by coils placed underneath. It is shown that properly guided magnetic fields can effectively change mechanical potentials in a way that the energy flow between the oscillators takes the desired direction. Studies were considered by using a specific set of descriptive functions characterizing the total excitation level, its distribution between the pendulums, and the phase shift. The developed control strategies are based on the observation that, in the case of antiphase oscillation, the energy is moving from the pendulum subjected to the repelling magnetic field, to the oscillator under the attracting field. In contrast, during the inphase oscillations, the energy flow is reversed. Therefore, closed-loop controller requires only the information about phase shift, which is easily estimated from dynamic state signals through the coherency index. Advantage of suggested control strategy is that the temporal rate of inputs is dictated by the speed of beating, which is relatively slow compared to the carrying oscillations.Pozycja Magnetic oscillator under excitation with controlled initial phase(Wydawnictwo Politechniki Łódzkiej, 2021) Polczyński, Krystian; Bednarek, Maksymilian; Awrejcewicz, JanThe work contains the results of numerical simulations of the dynamics of a magnetic pendulum system subjected to excitation with a varying initial phase. A magnetic pendulum consists of a magnet fixed to the end of its arm and an electric coil below it. The initial phase of the excitation is presented as a linear function of the dynamic variable of the system, which is the angular position of the pendulum. The obtained basins of attraction indicate the occurrence of multi-periodic solutions in the system depending on the changes in the parameters of this system. The periodicities of the observed solutions are quantified mostly by odd numbers.Pozycja Research of the dynamics of a physical pendulum forced with an electromagnetic field(Wydawnictwo Politechniki Łódzkiej, 2021) Ogińska, Ewelina; Grzelczyk, Dariusz; Awrejcewicz, JanIn this paper, both experimental and numerical results of the dynamics of a pendulum with a neodymium magnet and an aerostatic bearing are presented. The experimental stand includes the pendulum with the neodymium magnet at the end of the rod, whereas four electric coils are placed underneath. The pivot of the pendulum is supported on the aerostatic bearing. As a result, dry friction resistance in the pivot joint can be negligible and it has only a viscous character. The electric current with a given frequency and duty cycle and of a square waveform flows through the coils. Interaction between the neodymium magnet and the electric coils leads to the forced angular motion of the pendulum with the neodymium magnet. Both mathematical and physical models with experimentally confirmed system parameters are derived. The results of the simulation and experiment showed rich dynamics of the system, including various types of regular motion (multi-periodicity) and chaos.Pozycja Implementation of the New Control Methods in Simplification of a Multidimensional Control and Optimization of a Control System Parameters(Wydawnictwo Politechniki Łódzkiej ; Katedra Dynamiki Maszyn - Wydział Mechaniczny Politechniki Łódzkiej, 2015) Pijanowski, Karol; Dąbrowski, Artur; Balcerzak, MarekThe main purpose of this text is to present application of the Largest Lyapunov Exponent (LLE) as a criterion for optimization of the new type of simple controller parameters. Investigated controller is the part of numerically simulated control system. The calculation of LLE was done with a new method [2]. Introduction contains reference to previous publications on inverted pendulum control and Lyapunov stability. Application of the new simple formula for LLE estimation in control systems is discussed. In the next part simulated dynamical system is described and new type of simple controller allowing to control multidimensional system is introduced. In the last part results of the simulation are shown along with conclusions to whole dynamics analysis. Comparison of the proposed regulator with the linearquadratic regulator (LQR) was verified and its better effectiveness with respect to LQR was proved.Pozycja Application of the Lyapunov Exponent Based on Current Vibration Control Parameter ( CVC) in Control of an Industrial Robot(Wydawnictwo Politechniki Łódzkiej ; Katedra Dynamiki Maszyn - Wydział Mechaniczny Politechniki Łódzkiej, 2015) Szaniewski, Mateusz; Dąbrowski, Artur; Balcerzak, Marek; Zawiasa, PiotrControlling dynamics of industrial robots is one of the most important and complicated tasks in robotics. In some works [3, 7], there are algorithms of the manipulators steering with flexible joints or arms. However, introducing them to calculation of trajectory results in complicated equations and a longer time of counting. On the other hand, works [4,5,6]show that improvement of the tool path is possible thanks to the previousidentification of the robot errors and their compensation. This text covers application of Largest Lyapunov Exponent (LLE) as a criterion for control performance assessment (CPA) in a real control system. The main task is to find a simple and effective method to search for the best configuration of a controller in a control system. In this context, CPA criterion based on calculation of LLE by means of a new method [9-11] is presented in the article.Pozycja Nonlinear Dynamics of Continuous Elastic Systems(Springer, 2004) Awrejcewicz, Jan; Krys'ko, Vadim A.; Vakakis, Alexander F.This monograph is devoted to recent advances in nonlinear dynamics of continuous elastic systems. A major part of the book is dedicated to the analysis of non-homogeneous continua, e.g. plates and shells characterized by sudden changes in their thickness, possessing holes in their bodies or/and edges, made from different materials with diverse dynamical characteristics and complicated boundary conditions. New theoretical and numerical approaches for analyzing the dynamics of such continua are presented, such as the method of added masses and the method of proper orthogonal decomposition. The presented hybrid approach leads to results that cannot be obtained by other standard theories in the field. The demonstrated methods are illustrated by numerous examples of application.Pozycja Implementation of the New Control Methods in Simplification of a Multidimensional Control and Optimization of a Control System Parameters.(Lodz University of Technology. Faculty of Mechanical Engineering. Department Division of Dynamics., 2015) Pijanowski, Karol; Dąbrowski, Artur; Balcerzak, MarekThe main purpose of this text is to present application of the Largest Lyapunov Exponent (LLE) as a criterion for optimization of the new type of simple controller parameters. Investigated controller is the part of numerically simulated control system. The calculation of LLE was done with a new method [2]. Introduction contains reference to previous publications on inverted pendulum control and Lyapunov stability. Application of the new simple formula for LLE estimation in control systems is discussed. In the next part simulated dynamical system is described and new type of simple controller allowing to control multidimensional system is introduced. In the last part results of the simulation are shown along with conclusions to whole dynamics analysis. Comparison of the proposed regulator with the linearquadratic regulator (LQR) was verified and its better effectiveness with respect to LQR was proved.Pozycja Application of the Lyapunov Exponent Based on Current Vibration Control Parameter (CVC) in Control of an Industrial Robot.(Lodz University of Technology. Faculty of Mechanical Engineering. Department Division of Dynamics., 2015) Szaniewski, Mateusz; Dąbrowski, Artur; Balcerzak, Marek; Zawiasa, PiotrControlling dynamics of industrial robots is one of the most important and complicated tasks in robotics. In some works[3,7], there are algorithms of the manipulators steering with flexible joints or arms. However, introducing them to calculation of trajectory results in complicated equations and a longer time of counting. On the other hand, works [4,5,6]show that improvement of the tool path is possible thanks to the previousidentification of the robot errors and their compensation. This text covers application of Largest Lyapunov Exponent (LLE) as a criterion for control performance assessment (CPA) in a real control system. The main task is to find a simple and effective method to search for the best configuration of a controller in a control system. In this context, CPA criterion based on calculation of LLE by means of a new method [9–11] is presented in the article.Pozycja Matematyczne i numeryczne metody analizy bifurkacji i dynamiki chaotycznej układów mechanicznych z tarciem i uderzeniami(Wydawnictwo Politechniki Łódzkiej, 2006) Awrejcewicz, Jan; Pyryev, Jurij; Kudra, Grzegorz; Olejnik, Paweł; Wydział Mechaniczny. Politechnika Łódzka.; Faculty of Mechanical Engineering. Lodz University of Technology.; Kapitaniak, Tomasz; Wodziński, Piotr; Kaźmierczak, Marek; Olejnik, Paweł; Jakubowski, Krzysztof; Świder, Jerzy; Grądzki, RyszardKsiążka obejmuje wprowadzenie do podstaw teoretycznych, modelowania i metod numerycznych, związanych z analizą dynamiki bifurkacyjnej i chaotycznej układów mechanicznych z tarciem i uderzeniami. Autorzy przedstawiają oryginalne metody modelowania i analizy wybranych układów mechanicznych niegładkich oraz prezentują nowe wyniki uzyskane w tym obszarze dynamiki nieliniowej układów dyskretnych.Pozycja Application of artificial neural networks in parametrical investigations of the energy flow and synchronization.(Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej, 2010) Dąbrowski, Artur; Jach, Anna; Kapitaniak, TomaszDynamics of nonlinear systems is a very complicated problem with many aspects to be recognized. Numerous methods are used to investigate such systems. Their careful analysis is connected with long-time simulations. Thus, there is great need for methods that would simplify these processes. In the paper, an application of Artificial Neural Networks (ANNs) supporting the recognition of the energy flow and the synchronization with use of Impact Maps is introduced. This connection applies an idea of the Energy Vector Space in the system with impacts. An energy flow direction change with the synchronization as a transitional state is shown. A new type of the index allowing one to control the system dynamic state is introduced. Results of the numerical simulations are used in the neural network teaching process. Results of a comparison of the straight impact map simulation and the neural network prediction are shown. Prediction of system parameters for the energy flow synchronization state with use of the neural network is presented.