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Design of transmultiplexer integer filters

Mariusz Ziółko Michał Nowak
Archives of Control Sciences | 2018 | vol. 28 | No 2 | DOI: 10.24425/123457
Słowa kluczowe fixed point arithmetic MIMO systems integer digital filters
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Abstrakt

The designing of transmultiplexer systems relies on determining filters for the transmitter and receiver sides of multicarrier communication system. The perfect reconstruction conditions lead to the bilinear equations for FIR filter coefficients. Generally there is no way of finding all possible solutions. This paper describes methods of finding a large family of solutions. Particular attention is devoted to obtaining algorithms useful in fixed-point arithmetic needed to design the integer filters. As a result, the systems perform perfect reconstruction of signals. Additionally, a simple method is presented to transform any transmultiplexer into an unlimited number of different transmultiplexers. Finally, two examples of integer filters that meet perfect reconstruction conditions are shown. The first illustrates a FIR filter which does not require multiplications. The frequency properties of filters and signals are discussed for the second example.
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Autorzy i Afiliacje

Mariusz Ziółko
Michał Nowak

The applications of fixed-point theorem in optimisation problems

Krzysztof Chwastek
Archives of Electrical Engineering | 2012 | vol. 61 | No 2 June | 189-198 | DOI: 10.2478/v10171-012-0016-0
Słowa kluczowe optimisation fixed-point theorem hysteresis parameter estimation
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Abstrakt

The fixed-point theorem is widely used in different engineering applications. The present paper focuses on its applications in optimisation. A Matlab toolbox, chich implements the branch-and-bound optimisation method based on the fixed-point theorem, is used for solving different real-life test problems, including estimation of model parameters for the Jiles-Atherton model.

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Autorzy i Afiliacje

Krzysztof Chwastek

On the constrained and unconstrained controllability of semilinear Hilfer fractional systems

Beata Sikora
Archives of Control Sciences | 2023 | vol. 33 | No 1 | 155-178 | DOI: 10.24425/acs.2023.145118
Słowa kluczowe Hilfer fractional derivative fractional systems semilinear control systems nonautonomous systems Rothe’s fixed point theorem generalized Darbo fixed point theorem
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Abstrakt

In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function �� depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe’s fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study.
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Autorzy i Afiliacje

Beata Sikora
1
ORCID: ORCID
  1. Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

Vibration control of a rotating shaft by passive mass-spring-disc dynamic vibration absorber

Nguyen Duy Chinh
Archive of Mechanical Engineering | 2020 | vol. 67 | No 3 | 279-297 | DOI: 10.24425/ame.2020.131693
Słowa kluczowe torsional vibration optimal parameters minimum quadratic torque equivalent viscous resistance fixed-point
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Abstrakt

Shaft is a machine element which is used to transmit rotary motion or torque. During transmission of motion, however, the machine shaft doesn't always rotate with a constant angular velocity. Because of unstable current or due to sudden acceleration and deceleration, the machine shaft will rotate at a variable angular velocity. It is this rotary motion that generates the moment of inertial force, causing the machine shaft to have torsional deformation. However, due to the elasticity of the material, the shaft produces torsional vibration. Therefore, the main objective of this paper is to determine the optimal parameters of dynamic vibration absorber to eliminate torsional vibration of the rotating shaft that varies with time. The new results in this paper are summarized as follows: Firstly, the author determines the optimal parameters by using the minimum quadratic torque method. Secondly, the maximization of equivalent viscous resistance method is used for determining the optimal parameters. Thirdly, the author gives the optimal parameters of dynamic vibration absorber based on the fixed-point method. In this paper, the optimum parameters are found in an explicit analytical solutions, helping the scientists to easily find the optimal parameters for eliminating torsional vibration of the rotating shaft.

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Bibliografia

[1] G.B. Warburton. Optimum absorber parameters for various combinations of response and excitation parameters. Earthquake Engineering and Structural Dynamics, 10(3):381–401, 1982. doi: 10.1002/eqe.4290100304.
[2] R.W. Luft. Optimal tuned mass dampers for buildings. Journal of the Structural Division, 105(12): 2766–2772, 1979.
[3] J.P. Den Hartog. Mechanical Vibrations. 4th edition, McGraw-Hill, New York, 1956.
[4] E.S. Taylor. Eliminating crankshaft torsional vibration in radial aircraft engines. SAE Technical Paper 360105, 1936. doi: 10.4271/360105.
[5] R.R.R. Sarazin. Means adapted to reduce the torsional oscillations of crankshafts. Patent 2079226, USA, 1937.
[6] J.F. Madden. Constant frequency bifilar vibration absorber. Patent 4218187, USA, 1980.
[7] H.H. Denman. Tautochronic bifilar pendulum torsion absorbers for reciprocating engines. Journal of Sound and Vibration, 159(2):251–277, 1992. doi: 10.1016/0022-460X(92)90035-V.
[8] C.P. Chao, S.H. Shaw, and C.T. Lee. Stability of the unison response for a rotating system with multiple tautochronic pendulum vibration absorbers. Journal of Applied Mechanics, 64(1):149–156, 1997. doi: 10.1115/1.2787266.
[9] C.T. Lee, S.W. Shaw, and V.T. Coppola. A subharmonic vibration absorber for rotating machinery. Journal of Vibration and Acoustics, 119(4):590–595, 1997. doi: 10.1115/1.2889766.
[10] A.S. Alsuwaiyan and S.W. Shaw. Performance and dynamic stability of general-path centrifugal pendulum vibration absorbers. Journal of Sound and Vibration, 252(5):791–815, 2002. doi: 10.1006/jsvi.2000.3534.
[11] S.W. Shaw, P.M. Schmitz, and A.G. Haddow. Tautochronic vibration absorbers for rotating systems. Journal of Computational and Nonlinear Dynamics, 1(4):283–293, 2006. doi: 10.1115/1.2338652.
[12] J. Mayet and H. Ulbrich. Tautochronic centrifugal pendulum vibration absorbers: General design and analysis. Journal of Sound and Vibration, 333(3):711–729, 2014. doi: 10.1016/j.jsv.2013.09.042.
[13] E. Vitaliani, D. Di Rocco, and M. Sopouch. Modelling and simulation of general path centrifugal pendulum vibration absorbers. SAE Technical Paper 2015-24-2387, 2015. doi: 10.4271/2015-24-2387.
[14] C. Shi, S.W. Shaw, and R.G. Parker. Vibration reduction in a tilting rotor using centrifugal pendulum vibration absorbers. Journal of Sound and Vibration, 385:55–68, 2016. doi: 10.1016/j.jsv.2016.08.035.
[15] K. Liu and J. Liu. The damped dynamic vibration absorbers: revisited and new result. Journal of Sound and Vibration, 284(3-5):1181–1189, 2005. doi: 10.1016/j.jsv.2004.08.002.
[16] N. Hoang, Y. Fujino, and P. Warnitchai. Optimal tuned mass damper for seismic applications and practical design formulas. Engineering Structures, 30(3):707–715, 2008. doi: 10.1016/j.engstruct.2007.05.007.
[17] G. Bekdaş and S.M. Nigdeli. Estimating optimum parameters of tuned mass dampers using harmony search. Engineering Structures, 33(9):2716–2723, 2011. doi: 10.1016/j.engstruct.2011.05.024.
[18] K. Ikago, K. Saito, and N. Inoue. Seismic control of single-degree-of-freedom structure using tuned viscous mass damper. Earthquake Engineering and Structural Dynamics, 41(3):453–474, 2012. doi: 10.1002/eqe.1138.
[19] H. Garrido, O. Curadelli, and D. Ambrosini. Improvement of tuned mass damper by using rotational inertia through tuned viscous mass damper. Engineering Structures, 56:2149–2153, 2013. doi: 10.1016/j.engstruct.2013.08.044.
[20] M.G. Soto and H. Adeli. Tuned mass dampers. Archives of Computational Methods in Engineering, 20(4):419–431, 2013. doi: 10.1007/s11831-013-9091-7.
[21] X.T. Vu, N.D. Chinh, D.D. Khong, and V.C Tong. Closed-form solutions to the optimization of dynamic vibration absorber attached to multi-degree-of-freedom damped linear systems under torsional excitation using the fixed-point theory. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multibody Dynamics, 232(2):237–252, 2018. doi: 10.1177/1464419317725216.
[22] N.D. Chinh. Determination of optimal parameters of the tuned mass damper to reduce the torsional vibration of the shaft by using the principle of minimum kinetic energy. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multibody Dynamics, 233(2):327–335, 2019. doi: 10.1177/1464419318804064.
[23] N.D. Chinh. Optimal parameters of tuned mass dampers for machine shaft using the maximum equivalent viscous resistance method. Journal of Science and Technology in Civil Engineering, 14(1): 127–135, 2020. doi: 10.31814/stce.nuce2020-14(1)-11.
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Autorzy i Afiliacje

Nguyen Duy Chinh
1
  1. Faculty of Mechanical Engineering, Hung Yen University of Technology and Education, HungYen, Vietnam.

Controllability of time varying semilinear non-instantaneous impulsive systems with delay, and nonlocal conditions

Dalia Cabada Katherine Garcia Cristi Guevara Hugo Leiva
Archives of Control Sciences | 2022 | vol. 32 | No 2 | 335-357 | DOI: 10.24425/acs.2022.141715
Słowa kluczowe exact controllability semilinear time varying control systems non-instantaneous impulses delay nonlocal conditions Rothe’s fixed point theorem
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Abstrakt

In this paper we prove the exact controllability of a time varying semilinear system considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously. It is done by using the Rothe’s fixed point theorem together with some sub-linear conditions on the nonlinear term, the impulsive functions, and the function describing the nonlocal conditions. Furthermore, a control steering the semilinear system from an initial state to a final state is exhibited.
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Autorzy i Afiliacje

Dalia Cabada
1
Katherine Garcia
2
Cristi Guevara
3
Hugo Leiva
2
ORCID: ORCID
  1. School of Mathematical and Statistical Sciences, Arizona State University, United States of America
  2. School of Mathematical Sciences and Information Technology, Yachay Tech University, Ecuador
  3. Arizona Department of Education, United States of America

Nonlocal controllability of mild solutions for neutral evolution equations with state-dependent delay in Fréchet spaces

Chahrazed Boudefla Selma Baghli-Bendimerad
Archives of Control Sciences | 2024 | vol. 34 | No 1 | 117-148 | DOI: 10.24425/acs.2024.149655
Słowa kluczowe neutral evolution equations mild solution controllability infinite delay statedependent delay nonlocal conditions fixed point nonlinear alternative semigroup theory Fréchet spaces
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Abstrakt

In this paper, we prove the controllability of mild solutions of neutral functional evolution equations with state-dependent delay and nonlocal conditions. We establish the non local controllability of mild solutions under certain conditions by combining Avramescu’s nonlinear alternative for the sum of compact and contraction operators in Fréchet spaces with semigroup theory.
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Autorzy i Afiliacje

Chahrazed Boudefla
1
ORCID: ORCID
Selma Baghli-Bendimerad
1
ORCID: ORCID
  1. Po. Box 89, Laboratory of Mathematics, Djillali LiabesUniversity of Sidi Bel-Abbès 22000, Algeria

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