2020 (vol. 30) - Number 4

*A.B. Malinowska, R. Kamocki, R. Almeida, T. Odzijewicz:*

On the existence of optimal consensus control for the fractional Cucker--Smale model

*R. Grymin, W. Bożejko, J. Pempera, M. Wodecki, Z. Chaczko:*

Algorithm for solving the Discrete-Continuous Inspection Problem

*T. Kaczorek, A. Ruszewski:*

Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

*R. Arora, K. Gupta:*

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

*P. Nowak, J. Czeczot, P. Grelewicz:*

Tuning rules for industrial use of the second-order Reduced Active Disturbance Rejection Controller

*M.I. Gomoyunov:*

Optimal control problems with a fixed terminal time in linear fractional-order systems

*Muhafzan, A. Nazra, L. Yulianti, Zulakmal, R. Revina:*

On LQ optimization problem subject to fractional order irregular singular systems

*M. Blizorukova, V. Maksimov:*

On one algorithm for reconstruction of an disturbance in a linear system of ordinary differential equations

ACS Abstract:

**2012 (Volume 22)**

Number 1

On dynamical identification of control in a system with time delay

V. Maksimov(The Ural Federal University and Institute of Mathematics and Mechanics, Ekaterinburg, Russia) |

The problem of identification of a control through results of observations of phase states of dynamical systems described by differential equations with time delay is discussed. The paper presents an algorithm based on the method of feedback control with a model. The algorithm is stable with respect to informational noises and computational errors.

**keywords:** time-delay system, identification, feedback control

On a continuity of characteristic exponents of linear discrete time-varying systems

A. Czornik, P. Mokry, M. Niezabitowski(Silesian University of Technology, Gliwice, Poland) |

In this paper we present a sufficient condition for continuity of Lyapunov exponents of discrete time-varying linear system. Basing on this result we show that Lyapunov exponents of time-invariant systems depend continuously on the time-varying perturbations.

**keywords:** time-varying discrete linear systems, Lyapunov exponents, perturbation theory, characteristic exponents

Wireless communication for control of manipulation systems

K. Belda( Academy of Sciences of the Czech Republic) | V. Rychnovsky, P. Pisa(Czech Technical University in Prague, Czech Rep.) |

The paper deals with a novel application of the wireless data communication for a continual control of the distributed manipulation systems. The solution is intended for industrial robotic plants. A considered way of the wireless communication is based on ZigBee protocol. The protocol is tested for a real time bidirectional data communication within a manipulation system. The system consists of several moving manipulation units, several stationary auxiliary units and one control computer. The computer provides the cooperation of all units in the system in relation to the user requirements. The system is controlled by a simple feedback multi-level control realized in MATLAB - Simulink environment. The paper is focused on the realization of the boards of power electronics, transmitters, optical positional sensors, optical gates and their networking in accordance with ZigBee protocol definition. The behavior of the ZigBee is illustrated by several records from real experiments.

systems.

**keywords:** distributed mechatronic system, model-based control, multi-level control, odometry, optical sensors, standard IEEE 802.15.4, ZigBee protocol

Lagrange and practical stability criteria for dynamical systems with nonlinear perturbations

A.V. Krumov(The Higher School of Transport, Sofia, Bulgaria) |

In the paper two classes of nonlinear dynamical system with perturbations are considered. The sufficient conditions for robust Lagrange and practical stability are proven with theorems, applying the theory of nonlinear operators of the functional analysis. The presented criteria give also the bounds of the analyzed dynamical processes. Three examples comparing the numerical computer solutions and the analytical investigation of the stability of the systems are given. The method can be applied to analytical and computer modeling of nonlinear dynamical systems, synthesis of computer control and optimization.

**keywords:** Lagrange, stability criteria, dynamical systems, nonlinear perturbation

Generalized semi-opened axial dispersion model

D. Bartova(ICT in Prague, Czech Rep.) | B. Jakes, J. Kukal(CTU in Prague, Czech Rep.) |

The axial dispersion model (ADM) is studied and then generalized by a new form of the left boundary condition of semi-open flow system. The resulting parameter driven model covers the traditional axial models: axial closed-opened dispersion model with enforced input concentration (AEO), axial closed-opened dispersion model with input Danckwerts’ condition (ACO), and axial opened-opened model (AOO). It also enables development of the degraded axial model (ADO). The research is concerned with both modeling and mathematical solution. Also, many numerical aspects of computer realization are discussed.

**keywords:** axial dispersion, flow models, analytical solution, generalization, limit cases, numerical aspects

Checking of the positivity of descriptor linear systems with singular pencils

T. Kaczorek(Bialystok University of Technology, Poland) |

A method for checking of the positivity of descriptor continuous-time and discrete-time linear systems with singular pencil is proposed. The method is based on elementary row and column operations on the matrices of descriptor systems. Necessary and sufficient conditions for the positivity of the descriptor systems are established.

**keywords:** checking, positivity, descriptor, linear, system, singular pencil

A hybrid PSO approach for solving non-convex optimization problems

T. Ganesan, P. Vasant, I. Elamvazuthy(University Technology Petronas, Malaysia) |

The aim of this paper is to propose an improved particle swarm optimization (PSO) procedure for non-convex optimization problems. This approach embeds classical methods which are the Kuhn-Tucker (KT) conditions and the Hessian matrix into the fitness function. This generates a semi-classical PSO algorithm (SPSO). The classical component improves the PSO method in terms of its capacity to search for optimal solutions in non-convex scenarios. In this work, the development and the testing of the refined the SPSO algorithm was carried out. The SPSO algorithm was tested against two engineering design problems which were; ’optimization of the design of a pressure vessel’ (P1) and the ’optimization of the design of a tension/compression spring’ (P2). The computational performance of the SPSO algorithm was then compared against the modified particle swarm optimization (PSO) algorithm of previous work on the same engineering problems. Comparative studies and analysis were then carried out based on the optimized results. It was observed that the SPSO provides a better minimum with a higher quality constraint satisfaction as compared to the PSO approach in the previous work.

**keywords:** Kuhn-Tucker conditions (KT), non-convex optimization, particle swarm optimization (PSO), semi-classical particle swarm optimization (SPSO)

Stabilization of multi DC bus link voltages of multilevel NPC VSI. Application to double stator induction motors

D. Beriber, A. Talha(University of Sciences and Technology Houari Boumediene, Algeria) | M.S. Boucherit(The National Polytechnic School of Algiers, Algeria) |

Voltage source multilevel inverters have become very attractive for power industries in power electronics applications during last years. The main purposes of studying multilevel inverters are the generation of output voltage signals with low harmonic distortion and reduction of switching frequency. An important issue of the multilevel inverter is the capacitor voltagebalancing problem. The unbalance of different DC voltage sources of multilevel neutral point clamped (NPC) voltage source inverter (VSI) constitutes the major limitation for the use of this new power converter. In this paper, we present study on the stability problem of the input DC voltages of the three-level Neutral Point Clamping (NPC) voltage source inverter (VSI). This inverter is useful for application in high voltage and high power area. In the first part, we remind the model of double stator induction motors (DSIM). Then, we develop control models of this inverter using the connection functions of the semi-conductors. We propose a Pulse Width Modulation (PWM) strategy to control this converter. The inverter is fed by constant input DC voltages. In the last part, we study the stability problem of the input DC voltages of the inverter. A cascade constituted by two three-level PWM rectifiers - two three-level NPC VSI - DSIM is discussed. The results obtained show that the input DC voltages of the inverters are not stable. To solve this problem, we propose to use a half clamping bridge. This solution is very promising in order to stabilize the input DC voltages of this converters.

**keywords:** multilevel, VSI, NPC, PWM, rectifier, clamping bridge

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