Applied sciences

Archives of Control Sciences

Content

Archives of Control Sciences | 2019 | vol. 29 | No 1 |

Abstract

The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix inequalities for the Dstable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-lime linear systems with polytopic uncertainties.

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Abstract

The methane hazard is one of the most dangerous phenomena in hard coal mining. In a certain range of concentrations, methane is flammable and explosive. Therefore, in order to maintain the continuity of the production process and the safety of work for the crew, various measures are taken to prevent these concentration levels from being exceeded. A significant role in this process is played by the forecasting of methane concentrations in mine headings. This very problem has been the focus of the present article. Based on discrete measurements of methane concentration in mine headings and ventilation parameters, the distribution of methane concentration levels in these headings was forecasted. This process was performed on the basis of model-based tests using the Computational Fluid Dynamics (CFD). The methodology adopted was used to develop a structural model of the region under analysis, for which boundary conditions were adopted on the basis of the measurements results in real-world conditions. The analyses conducted helped to specify the distributions of methane concentrations in the region at hand and determine the anticipated future values of these concentrations. The results obtained from model-based tests were compared with the results of the measurements in realworld conditions. The methodology using the CFD and the results of the tests offer extensive possibilities of their application for effective diagnosis and forecasting of the methane hazard in mine headings.

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Abstract

Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear systemthat produces, with a tolerance index ǫ, the same output function when the initial state belongs to a specified set, called ǫ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ǫ-admissible set.

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Abstract

We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L2-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.

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Abstract

We study an elegant snap system with only one nonlinear term, which is a quadratic nonlinearity. The snap systemdisplays chaotic attractors,which are controlled easily by changing a system parameter. By using analysis, simulations and a real circuit, the dynamics of such a snap system has been investigated. We also investigate backstepping based adaptive control schemes for the new snap system with unknown parameters.

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Abstract

This paper presents the design of digital controller for longitudinal aircraft model based on the Dynamic Contraction Method. The control task is formulated as a tracking problem of velocity and flight path angle, where decoupled output transients are accomplished in spite of incomplete information about varying parameters of the system and external disturbances. The design of digital controller based on the pseudo-continuous approach is presented, where the digital controller is the result of continuous-time controller discretization. A resulting output feedback controller has a simple form of a combination of low-order linear dynamical systems and a matrix whose entries depend nonlinearly on certain known process variables. Simulation results for an aircraft model confirm theoretical expectations.

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Abstract

This paper presents a concept of humanoid robot motion generation using the dedicated simplified dynamic model of the robot (Extended Cart-Table model). Humanoid robot gait with equal steps length is considered. Motion pattern is obtained here with use of Preview Control method. Motion trajectories are first obtained in simulations (off-line) and then they are verified on a test-bed. Tests performed using the real robot confirmed the correctness of the method. Robot completed a set of steps without losing its balance.

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Abstract

This work describes a new study to achieve a combination of modified function projective synchronization between three different chaotic systems through adaptive control. Using the Lyapunov function theory, the asymptotic stability of the error dynamics is obtained and discussed. Further, we set some appropriate initial conditions for the state variables and assigning specific values to the parameters and obtain the graphical results, which shows the efficiencies of the new method. Finally, we summarized our work with conclusion and references.

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Abstract

The LQR (linear quadratic regulator) control problem subject to singular system constitutes a optimization problem in which one must be find an optimal control that satisfy the singular system and simultaneously to optimize the quadratic objective functional. In this paper we establish a sufficient condition to obtain the optimal control of discounted LQR optimization problem subject to disturbanced singular system where the disturbance is time varying. The considered problem is solved by transforming the discounted LQR control problem subject to disturbanced singular system into the normal LQR control problem. Some available results in literatures of the normal LQR control problem be used to find the sufficient conditions for the existence of the optimal control for discounted LQR control problem subject to disturbanced singular system. The final result of this paper is in the form a method to find the optimal control of discounted LQR optimization problem subject to disturbanced singular system. The result shows that the disturbance is vanish with the passage of time.

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Abstract

The positivity and absolute stability of a class of nonlinear continuous-time and discretetime 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 nonlinear systems are also given.

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Abstract

This paper presents a robust control technique for small-scale unmanned helicopters to track predefined trajectories (velocities and heading) in the presence of bounded external disturbances. The controller design is based on the linearized state-space model of the helicopter. The multivariable dynamics of the helicopter is divided into two subsystems, longitudinallateral and heading-heave dynamics respectively. There is no strong coupling between these two subsystems and independent controllers are designed for each subsystem. The external disturbances and model mismatch in the longitudinal-lateral subsystem are present in all (matched and mismatched) channels. This model mismatch and external disturbances are estimated as lumped disturbances using extended disturbance observer and an extended disturbance observer based sliding mode controller is designed for it to counter the effect of these disturbances. In the case of heading-heave subsystem, external disturbances and model mismatch only occur in matched channels so a second order sliding mode controller is designed for it as it is insensitive to matched uncertainties. The control performance is successfully tested in Simulink.

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Editorial office

Editor-in-Chief prof. dr hab. inż. Andrzej Świerniak

Deputy/ Managing Editor
Zbigniew Ogonowski, Silesian University of Technology, Gliwice, Poland

Editorial Advisory Board

Andrzej Bargiela, University of Nottingham, UK
Roman Barták, Charles University, Prague, Czech Rep.
Jacek Błażewicz, Poznań University of Technology, Poland
Reggie Davidrajuh, University of Stavanger, Norway
Andreas Deutsch, Technische Universität Dresden, Germany
Moritz Diehl, University of Freiburg, Germany
Władysław Findeisen, Warsaw University of Technology, Poland
Marcelo D.Fragoso, LNCC/MCT, Rio de Janeiro, Brasil
Avner Friedman, MBI Ohio State University, Columbus, USA
Alberto Gandolfi, IASI, Rome, Italy
Ryszard Gessing, Silesian University of Technology, Gliwice, Poland
Henryk Górecki, AGH University of Science and Technology, Poland
David Greenhalgh, University of Strathclyde, Glasgow, UK
Mats Gyllenberg, University of Helsinki, Finland
Wassim M. Haddad, Georigia University, Atlanta, USA
Raimo P. Hämäläinen, Aalto University School of Science, Finland
Alberto Isidori, Università di Roma "La Sapienza" Italia
Laszlo Kevicky, Hungarian Academy of Sciences, Hungary
Marek Kimmel, Rice University Houston, USA
Jerzy Klamka, Silesian University of Technology, Gliwice, Poland
Józef Korbicz, University of Zielona Góra, Poland
Irena Lasiecka, University of Virginia, USA
Urszula Ledzewicz, Southern Illinois University at Edwardsville, USA
Magdi S Mahmoud, KFUM, Dahram, Saudi Arabia
Krzysztof Malinowski, Warsaw University of Technology, Poland
Wojciech Mitkowski, AGH University of Science and Technology, Poland
Bozenna Pasik-Duncan, University of Kansas, Lawrence, USA
Ian Postlethwaite, Newcastle University, Newcastle, UK
Eric Rogers, University of Southampton, UK
Heinz Schaettler, Washington University, St Louis, USA
Ryszard Tadeusiewicz, AGH University of Science and Technology, Poland
Jan Węglarz, Poznań University of Technology, Poland
Liu Yungang, Shandong University, PRC
Valery D. Yurkevich, Novosibirsk State Technical University, Russia

Contact

Institute of Automatic Control
Silesian University of Technology
Akademicka 16
44-101 Gliwice, Poland

acs@polsl.pl
http://acs.polsl.pl/

 

 

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  1. R. E. Kalman: Mathematical description of linear dynamical system. SIAM J. Control. 1(2), (1963), 152-192.
  2. F. C. Shweppe: Uncertain dynamic systems. Prentice-Hall, Englewood Cliffs, N.J. 1970.


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Zbigniew Ogonowski
Institute of Automatic Control
Silesian University of Technology
Akademicka 16
44-101 Gliwice, Poland

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