Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts


Book Description

This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original contribution to the field of discontinuous mechanical systems based on mathematical and numerical modeling as well as the control of such systems. Each chapter provides the reader with both the theoretical background and results of verified and useful computations, including solutions of the problems of modeling and application of friction laws in numerical computations, results from finding and analyzing impact solutions, the analysis and control of dynamical systems with discontinuities, etc. The contents offer a smooth correspondence between science and engineering and will allow the reader to discover new ideas. Also emphasized is the unity of diverse branches of physics and mathematics towards understanding complex piecewise-smooth dynamical systems. Mathematical models presented will be important in numerical experiments, experimental measurements, and optimization problems found in applied mechanics.




Lagrangian and Hamiltonian Methods for Nonlinear Control 2003


Book Description

This is the second of a series of IFAC Workshops initiated in 2000. The first one chaired and organized by Profs. N. Leonard and R. Ortega, was held in Princeton in March 2000. This proceedings volume looks at the role-played by Lagrangian and Hamiltonian methods in disciplines such as classical mechanics, quantum mechanics, fluid dynamics, electrodynamics, celestial mechanics and how such methods can be practically applied in the control community. *Presents and illustrates new approaches to nonlinear control that exploit the Lagrangian and Hamiltonian structure of the system to be controlled *Highlights the important role of Lagrangian and Hamiltonian Structures as design methods




Nonsmooth Mechanics


Book Description

Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.




Feedback Systems


Book Description

The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory




Dynamical Systems in Applications


Book Description

The book is intended for all those who are interested in application problems related to dynamical systems. It provides an overview of recent findings on dynamical systems in the broadest sense. Divided into 46 contributed chapters, it addresses a diverse range of problems. The issues discussed include: Finite Element Analysis of optomechatronic choppers with rotational shafts; computational based constrained dynamics generation for a model of a crane with compliant support; model of a kinetic energy recuperation system for city buses; energy accumulation in mechanical resonance; hysteretic properties of shell dampers; modeling a water hammer with quasi-steady and unsteady friction in viscoelastic conduits; application of time-frequency methods for the assessment of gas metal arc welding conditions; non-linear modeling of the human body’s dynamic load; experimental evaluation of mathematical and artificial neural network modeling for energy storage systems; interaction of bridge cables and wake in vortex-induced vibrations; and the Sommerfeld effect in a single DOF spring-mass-damper system with non-ideal excitation.







Control of Machines with Friction


Book Description

It is my ambition in writing this book to bring tribology to the study of control of machines with friction. Tribology, from the greek for study of rubbing, is the discipline that concerns itself with friction, wear and lubrication. Tribology spans a great range of disciplines, from surface physics to lubrication chemistry and engineering, and comprises investigators in diverse specialities. The English language tribology literature now grows at a rate of some 700 articles per year. But for all of this activity, in the three years that I have been concerned with the control of machines with friction, I have but once met a fellow controls engineer who was aware that the field existed, this including many who were concerned with friction. In this vein I must confess that, before undertaking these investigations, I too was unaware that an active discipline of friction existed. The experience stands out as a mark of the specialization of our time. Within tribology, experimental and theoretical understanding of friction in lubricated machines is well developed. The controls engineer's interest is in dynamics, which is not the central interest of the tribologist. The tribologist is more often concerned with wear, with respect to which there has been enormous progress - witness the many mechanisms which we buy today that are lubricated once only, and that at the factory. Though a secondary interest, frictional dynamics are note forgotten by tribology.




Computation for Humanity


Book Description

The exponential progress and accessibility of computing has vastly increased data flows and revolutionized the practice of science, engineering, and communication. Computing plays a critical role in advancing research across almost every scientific discipline. Computation for Humanity: Information Technology to Advance Society is a guide for the creation of services, products, and tools that facilitate, support, and enhance progress of humanity toward more sustainable life. This book: Provides a deep understanding of the practical applications of computation to solve human-machine problems Delivers insight into theoretical approaches in an accessible manner Provides a comprehensive overview of computational science and engineering applications in selected disciplines Crosses the boundaries between different domains and shows how they interrelate and complement one another Focuses on grand challenges and issues that matter for the future of humanity Shows different perspectives of computational thinking, understanding, and reasoning Provides a basis for scientific discoveries and enables adopting scientific theories and engineering practices from other disciplines Takes a step back to provide a human-related abstraction level that is not ultimately seen in pure technological elaborations/collections The editors provide a collection of numerous computation-related projects that form a foundation from which to cross-pollinate between different disciplines and further extensive collaboration. They present a clear and profound understanding of computing in today's world, and provide fundamental solutions to some of the most pertinent humanity-related problems.




Dynamics With Friction, Modeling, Analysis And Experiments, Part Ii


Book Description

The dynamics of dissipative mechanical and structural systems is being investigated at various institutions and laboratories worldwide with ever-increasing sophistication of modeling, analysis and experiments.This book offers a collection of contributions from these research centers that represent the state-of-the-art in the study of friction oscillators. It provides the reader with the fruits of a team effort by leaders in this fascinating field.The present part II of this volume on Dynamics with Friction is a continuation of the previous part I, and is designed to help synthesize our current knowledge regarding the role of friction in mechanical and structural systems as well as everyday life. The topics covered include interaction of vibration and friction at dry sliding contacts, friction-induced instability in disks, dynamics of lubricated flexible links in kinematic chains, modal interactions in periodic structures, dynamics of an experimentally excited beam, transient waves in viscoelastic materials, dynamic stability of plates with damping, friction modeling and dynamic computation, damping through use of passive and semi-active dry friction forces.This book gives a comprehensive picture of dynamics of dissipative mechanical and structural systems. It also gives an up-to-date account of the present state of the field. It will be of interest to engineers, rheologists, material scientists, applied mathematicians, physicists and historians of science and technology.




Modeling and Analysis of Dynamic Systems


Book Description

This text is intended for a first course in dynamic systems and is designed for use by sophomore and junior majors in all fields of engineering, but principally mechanical and electrical engineers. All engineers must understand how dynamic systems work and what responses can be expected from various physical systems.