
Dynamics and Control of Hybrid Mechanical Systems.
Title:
Dynamics and Control of Hybrid Mechanical Systems.
Author:
Leonov, Gennady.
ISBN:
9789814282321
Personal Author:
Physical Description:
1 online resource (264 pages)
Series:
World Scientific Series on Nonlinear Science: Series B
Contents:
Contents -- Preface -- Biography: Ilya Izrailevich Blekhman -- 1. Huijgens' Synchronization: A Challenge H. Nijmeijer, A.Y. Pogromsky -- References -- 2. Lyapunov Quantities and Limit Cycles of Two-dimensional Dynamical Systems N.V. Kuznetsov, G.A. Leonov -- Abstract -- 2.1 Introduction -- 2.2 Computation of Lyapunov quantities and small limit cycles -- 2.2.1 Computation of Lyapunov quantities in Euclidean coordinates and in the time domain -- 2.2.1.1 Approximation of solution in Euclidean coordinates -- 2.2.1.2 Computation of Lyapunov quantities in the time domain -- 2.2.2 Application of Lyapunov function to the computation of Lyapunov quantities -- 2.2.3 Lyapunov quantities of Lienard equation -- 2.3 Transformation between quadratic systems and Lienard equation -- 2.4 Method of asymptotic integration for Lienard equation with discontinuous right-hand side and large limit cycles -- 2.5 Four limit cycles for Lienard equation and the corresponding quadratic system -- Acknowledgments -- References -- 3. Absolute Observation Stability for Evolutionary Variational Inequalities G.A. Leonov, V. Reitman -- Abstract -- 3.1 Introduction -- 3.2 Evolutionary variational inequalities -- 3.3 Basic assumptions -- 3.4 Absolute observation - stability of evolutionary inequalities -- 3.5 Application of observation stability to the beam equation -- References -- 4. A Discrete-time Hybrid Lurie Type System V.N. Belykh, B. Ukrainsky -- Abstract -- 4.1 Introduction -- 4.2 Reduction to a normal form -- 4.3 Existence of invariant domain -- 4.4 Conditions of hyperbolicity -- Acknowledgments -- References -- 5. Frequency Domain Performance Analysis of Marginally Stable LTI Systems with Saturation R.A. van den Berg, A.Y. Pogromsky, J.E. Rooda -- Abstract -- 5.1 Introduction -- 5.2 LTI system with saturation -- 5.2.1 System description.
5.2.2 Case: electromechanical system -- 5.2.3 Motivating example: nonlinear behavior -- 5.3 Convergent systems and simulation-based frequency domain analysis -- 5.3.1 Convergent systems -- 5.3.2 Convergent system design -- 5.3.3 Performance analysis in frequency domain -- 5.4 Frequency domain analysis based on describing function approach -- 5.4.1 Describing function method -- 5.4.2 Performance analysis example -- 5.5 Conclusion -- Acknowledgments -- References -- 6. Reduction of Steady-State Vibrations in a Piecewise Linear Beam System using Proportional and Derivative Control R.H.B. Fey, R.M.T. Wouters, H. Nijmeijer -- Abstract -- 6.1 Introduction -- 6.2 Experimental set-up -- 6.3 Steady-state behavior of the uncontrolled system -- 6.4 Control objectives and PD controller design approach -- 6.5 Dynamic model -- 6.6 Effects of separate P-action and separate D-action -- 6.7 PD control -- 6.7.1 Control objective 1 -- 6.7.2 Control objective 2 -- 6.8 Comparison with passive control via a linear DVA -- 6.9 Conclusions -- Acknowledgments -- References -- 7. Hybrid Quantised Observer for Multi-input-multi- output Nonlinear Systems A.L. Fradkov, B.R. Andrievskiy, R.J. Evans -- Abstract -- 7.1 Introduction -- 7.2 Description of state estimation over the limited-band communication channel -- 7.3 Coding procedure -- 7.4 Evaluation of state estimation error -- 7.5 Example. State estimation of nonlinear oscillator -- 7.6 Conclusions -- Acknowledgments -- References -- 8. Tracking Control of Multiconstraint Nonsmooth Lagrangian Systems C. Morarescu, B. Brogliato, T. Nguyen -- Abstract -- 8.1 Introduction -- 8.2 Basic concepts . -- 8.2.1 Typical task -- 8.2.2 Exogenous signals entering the dynamics -- 8.2.3 Stability analysis criteria -- 8.3 Controller design -- 8.4 Tracking control framework -- 8.4.1 Design of the desired trajectories.
8.4.2 Design of q¤d(¢) and qd(¢) on the phases Ik -- 8.5 Design of the desired contact force during constraint phases -- 8.6 Strategy for take-off at the end of constraint phases -- 8.7 Closed-loop stability analysis -- 8.8 Illustrative example -- 8.9 Conclusions -- References -- 9. Stability and Control of Lur'e-type Measure Di®erential Inclusions N. van de Wouw, R. I. Leine -- Abstract -- 9.1 Introduction -- 9.2 Preliminaries -- 9.3 Measure differential inclusions -- 9.4 Convergent systems -- 9.5 Convergence properties of Lur'e-type measure di®erential inclusions -- 9.6 Tracking control of Lur'e-type measure differential inclusions -- 9.7 Example of a mechanical system with a unilateral constraint -- 9.8 Conclusions -- References -- 10. Synchronization between Coupled Oscillators: An Experimental Approach D.J. Rijlaarsdam, A.Y. Pogromsky, H. Nijmeijer -- Abstract -- 10.1 Introduction -- 10.2 Experimental set-up -- 10.2.1 Adjustment of the systems' properties -- 10.3 Example 1: Coupled Duffing oscillators -- 10.3.1 Problem statement and analysis -- 10.3.2 Experimental and numerical results -- 10.4 Example 2: Two coupled rotary disks -- 10.4.1 Problem statement -- 10.4.2 Experimental results -- 10.5 Conclusion and future research -- Acknowledgments -- References -- 11. Swinging Control of Two-pendulum System under Energy Constraints M. S. Ananyevskiy, A.L. Fradkov, H. Nijmeijer -- Abstract -- 11.1 Introduction -- 11.2 Control algorithm: formulation of the problem and approach -- 11.2.1 Special case: Energy control for Hamiltonian systems -- 11.3 Two pendulums under a single force -- 11.3.1 Control problem formulation -- 11.3.2 Control algorithm design -- 11.3.3 Control algorithm analysis -- 11.4 Conclusion -- Acknowledgment -- References -- 12. Two Van der Pol-Duffing Oscillators with Huygens Coupling V.N. Belykh, E.V. Pankratova, A.Y. Pogromsky.
Abstract -- 12.1 Introduction -- 12.2 Problem statement -- 12.3 Synchronization of oscillators driven by Van der Pol control input -- 12.4 Synchronization of oscillators driven by Van der Pol-Du±ng control input -- 12.5 Conclusions -- Acknowledgments -- References -- 13. Synchronization of Diffusively Coupled Electronic Hindmarsh-Rose Oscillators E. Steur, L. Kodde, H. Nijmeijer -- Abstract -- 13.1 Introduction -- 13.2 Preliminaries -- 13.3 Synchronization of diffusively coupled Hindmarsh-Rose oscillators -- 13.4 Experimental setup -- 13.5 Synchronization experiments -- 13.6 Conclusions -- Acknowledgments -- References -- 14. Multipendulum Mechatronic Setup for Studying Control and Synchronization A.L. Fradkov, B.R. Andrievskiy, K.B. Boykov, B.P. Lavrov -- Abstract -- 14.1 Introduction -- 14.2 Design of mechanical part -- 14.3 Electronics of the multipendulum setup -- 14.3.1 System for data exchange with control computer -- 14.3.2 Architecture of the data exchange system -- 14.3.3 Computer-process interface -- 14.3.4 Electronic modules of the set-up -- 14.3.5 Communications protocol -- 14.4 Conclusions -- Acknowledgments -- References -- 15. High-frequency Effects in 1D Spring-mass Systems with Strongly Non-linear Inclusions B.S. Lazarov, S.O. Snaeland, J.J. Thomsen -- Abstract -- 15.1 Introduction -- 15.2 Mechanical model -- 15.3 Band gap effects in periodic structures -- 15.4 Approximate equations governing the slow and the fast motion -- 15.4.1 Example 1: linear plus cubic non-linearity -- 15.4.2 Example 2: essentially non-linear damping and restoring forces -- 15.5 Numerical examples . -- 15.5.1 Inclusions with linear plus cubic non-linear behaviour -- 15.5.2 Non-linear inclusions with non-local interaction -- 15.5.3 Linear chains with non-linear damping forces -- 15.6 Conclusions -- Acknowledgments -- References.
Abstract:
The papers in this edited volume aim to provide a better understanding of the dynamics and control of a large class of hybrid dynamical systems that are described by different models in different state space domains. They not only cover important aspects and tools for hybrid systems analysis and control, but also a number of experimental realizations. Special attention is given to synchronization - a universal phenomenon in nonlinear science that gained tremendous significance since its discovery by Huygens in the 17th century. Possible applications of the results introduced in the book include control of mobile robots, control of CD/DVD players, flexible manufacturing lines, and complex networks of interacting agents. The book is based on the material presented at a similarly entitled minisymposium at the 6th European Nonlinear Dynamics Conference held in St Petersburg in 2008. It is unique in that it contains results of several international and interdisciplinary collaborations in the field, and reflects state-of-the-art technological development in the area of hybrid mechanical systems at the forefront of the 21st century.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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