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Reaching phase elimination in variable structure control of the third order system with state constraints

Andrzej Bartoszewicz, A. Nowacka (2006)

Kybernetika

In this paper the design of a time varying switching plane for the sliding mode control of the third order system subject to the velocity and acceleration constraints is considered. Initially the plane passes through the system representative point in the error state space and then it moves with a constant velocity to the origin of the space. Having reached the origin the plane stops and remains motionless. The plane parameters (determining angles of inclination and the velocity of its motion) are...

Reduced resistive MHD in Tokamaks with general density

Bruno Després, Rémy Sart (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this paper is to derive a general model for reduced viscous and resistive Magnetohydrodynamics (MHD) and to study its mathematical structure. The model is established for arbitrary density profiles in the poloidal section of the toroidal geometry of Tokamaks. The existence of global weak solutions, on the one hand, and the stability of the fundamental mode around initial data, on the other hand, are investigated.

Reduced resistive MHD in Tokamaks with general density

Bruno Després, Rémy Sart (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to derive a general model for reduced viscous and resistive Magnetohydrodynamics (MHD) and to study its mathematical structure. The model is established for arbitrary density profiles in the poloidal section of the toroidal geometry of Tokamaks. The existence of global weak solutions, on the one hand, and the stability of the fundamental mode around initial data, on the other hand, are investigated.

Redundancy relations for fault diagnosis in nonlinear uncertain systems

Alexey Shumsky (2007)

International Journal of Applied Mathematics and Computer Science

The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into...

Regulation of p53 by siRNA in radiation treated cells: Simulation studies

Krzysztof Puszyński, Roman Jaksik, Andrzej Świerniak (2012)

International Journal of Applied Mathematics and Computer Science

Ionizing radiation activates a large variety of intracellular mechanisms responsible for maintaining appropriate cell functionality or activation of apoptosis which eliminates damaged cells from the population. The mechanism of such induced cellular death is widely used in radiotherapy in order to eliminate cancer cells, although in some cases it is highly limited by increased cellular radio-resistance due to aberrations in molecular regulation mechanisms of malignant cells. Despite the positive...

Robust hierarchical sliding mode control with state-dependent switching gain for stabilization of rotary inverted pendulum

Muhammad Idrees, Shah Muhammad, Saif Ullah (2019)

Kybernetika

The rotary inverted pendulum (RIP) system is one of the fundamental, nonlinear, unstable and interesting benchmark systems in the field of control theory. In this paper, two nonlinear control strategies, namely hierarchical sliding mode control (HSMC) and decoupled sliding mode control (DSMC), are discussed to address the stabilization problem of the RIP system. We introduced HSMC with state-dependent switching gain for stabilization of the RIP system. Numerical simulations are performed to analyze...

Rough modeling - a bottom-up approach to model construction

Terje Loken, Jan Komorowski (2001)

International Journal of Applied Mathematics and Computer Science

Traditional data mining methods based on rough set theory focus on extracting models which are good at classifying unseen obj-ects. If one wants to uncover new knowledge from the data, the model must have a high descriptive quality-it must describe the data set in a clear and concise manner, without sacrificing classification performance. Rough modeling, introduced by Kowalczyk (1998), is an approach which aims at providing models with good predictive emphand descriptive qualities, in addition to...

RTC-method for the control of nuclear reactor power

Wajdi A. Ratemi (1998)

Kybernetika

In this paper, a new concept of the Reactivity Trace Curve (RTC) for reactor power control is presented. The concept is demonstrated for a reactor model with one group of delayed neutrons, where the reactivity trace curve is simply a closed form exponential solution of the RTC-differential equation identifier. An extended reactor model of multigroup (six groups) of delayed neutrons is discussed for power control using the RTC-method which is based on numerical solution of the governing equation...

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