Zwięzły kurs analizy numerycznej

"...Materiał przedstawiony w tej książce to wybrane przez autorów metody numeryczne prezentowane studentom różnych kierunków studiów inżynierskich w trakcie wykładów, ćwiczeń i laboratoriów. Mamy nadzieję, że przygotowane w zwartej postaci podstawowe informacje z analizy numerycznej ułatwią studentom usystematyzowanie i przyswojenie wiedzy. Uczestnictwo w wykładzie,ćwiczeniach i laboratoriach umiejscowi tę wiedzę w kontekście zastosowań oraz pozwoli na rozwinięcie praktycznych umiejętności...

Adaptive, Observer-Based Synchronization of Different Chaotic Systems

In this study, the problem of master–slave synchronization of two different chaotic systems is considered and solved under a novel set of assumptions. The mathematical model of each of them contains unknown, constant parameters. Only a single output of the master system is available, and only a single input of the slave system is a control input. The proposed, novel approach is based on the active cooperation of the adaptive observer of the master system and adaptive controller of the slave. The tuning function technique is included in the observer–controller design to avoid overparameterization. Complexity explosion and unacceptable increases in adaptive parameters are prevented by proper adaptive techniques application. Due to the selected observer type, the derivation is restricted to the defined class of master systems—output-nonlinear parametric (ONP) systems. Linear transformation of several popular chaotic systems (e.g., Arneodo, Arneodo–Coullet, Genesio–Tesi, Lur’e) into the ONP form is discussed. The stability of the whole, closed-loop system is derived using Lyapunov techniques and examples of implementation (synchronization of Arneodo and 3D jerk systems) are provided

Observer-Based, Robust Position Tracking in Two-Mass Drive System

Precise motion control remains one of the most important problems in modern technology. It is especially difficult in the case of two-mass systems with flexible coupling if only the motor position and velocity are measured. We propose a new methodology of control system design in this situation. The concept is founded on a robust observer design, based on a linear matrix inequality (LMI) solution. The observer cooperates with the original nonlinear controller. The presented approach allows us to solve the position tracking problem for a two-mass drive, with unknown parameters, in the presence of disturbances (for instance, nonlinear friction-like torques) acting on both ends of the flexible shaft. Under this set of assumptions, the problem was never solved previously. The closed-loop system stability is investigated, and the uniform ultimate boundedness of state estimation errors and tracking errors is proven using Lyapunov techniques. Numerical properties of the design procedure and characteristic features of the observer, controller, and closed-loop system are demonstrated by several examples

Stabilność nieliniowych układów dynamicznych

Teoria stabilności nieliniowych układów dynamicznych wchodzi w zakres podstawowego kursu teorii sterowania dla studentów automatyki i robotyki oraz mechatroniki. Zazwyczaj omawia się podstawowe definicje stabilności i twierdzenia najważniejsze dla bezpośredniej metody Lapunowa, służące do badania stabilności punktów równowagi układów stacjonarnych i autonomicznych. Tymczasem w ostatnich dziesięcioleciach teoria stabilności układów nieliniowych była ciągle rozwijana i sukcesywnie pojawiały się twierdzenia rozszerzające jej zastosowania. Rozdziały w tej części książki mają charakter encyklopedycznego przeglądu aktualnego stanu wiedzy w tym zakresie. Podano najpierw definicje precyzujące różne pojęcia stabilności (rozdział pierwszy), a następnie twierdzenia, które można zastosować przy badaniu stabilności układów stacjonarnych (rozdział drugi) i niestacjonarnych (rozdział trzeci). Przedstawione pojęcia zilustrowano kilkoma przykładami. Dowody twierdzeń podano jedynie wtedy, gdy ułatwiają one zrozumienie istoty zjawisk. Sporo miejsca poświęcono ograniczoności i ostatecznej ograniczoności trajektorii, które są bardzo „praktycznym” rodzajem stabilności układów nieliniowych

Adaptive, Observer-Based Synchronization of Different Chaotic Systems

In this study, the problem of master–slave synchronization of two different chaotic systems is considered and solved under a novel set of assumptions. The mathematical model of each of them contains unknown, constant parameters. Only a single output of the master system is available, and only a single input of the slave system is a control input. The proposed, novel approach is based on the active cooperation of the adaptive observer of the master system and adaptive controller of the slave. The tuning function technique is included in the observer–controller design to avoid overparameterization. Complexity explosion and unacceptable increases in adaptive parameters are prevented by proper adaptive techniques application. Due to the selected observer type, the derivation is restricted to the defined class of master systems—output-nonlinear parametric (ONP) systems. Linear transformation of several popular chaotic systems (e.g., Arneodo, Arneodo–Coullet, Genesio–Tesi, Lur’e) into the ONP form is discussed. The stability of the whole, closed-loop system is derived using Lyapunov techniques and examples of implementation (synchronization of Arneodo and 3D jerk systems) are provided

Finite-Time, Robust, and Adaptive Motion Control with State Constraints: Controller Derivation and Real Plant Experiments

The paper refers to one of the most important problems in industrial automation and robotics—effective motion control in the presence of state variable constraints. A new, nonlinear, adaptive, robust, and practically applicable motion controller for a motor-driven servo is proposed. The developed controller guarantees that the transient of the motion is practically finished in a predefined time, and after this moment, the desired motion trajectory is tracked with specified accuracy, inviolable, time-variable constraints imposed on the position and the velocity are preserved, and all these features are robust against disturbances and violations of the system’s parameters. This approach, distinguished by the fact that the settling time and the quasi-steady-state tracking accuracy are explicitly available design parameters, has never been described before. The controller is based on a special type of time-varying barrier Lyapunov function (BLF), responsible for the finite-time tracking and for meeting the constraints. The derivation of the controller is based on Lyapunov stability theory. A mixture of robust adaptive, nonlinear control techniques is applied to prove the system’s stability. Numerous simulations and experiments with a real permanent-magnet motor- driven servo prove the practical applicability and usefulness of the presented approach