This book addresses two fundamental issues of motor control for both humans and robots: kinematic redundancy and the posture/movement problem. It blends traditional robotic constrained-optimal approaches with neuroscientific and evidence-based principles, proposing a "Task-space Separation Principle," a novel scheme for planning both posture and movement in redundant manipulators. The proposed framework is first tested in simulation and then compared with experimental motor strategies displayed by humans during redundant pointing tasks. The book also shows how this model builds on and expands traditional formulations such as the Passive Motion Paradigm and the Equilibrium Point Theory. Lastly, breaking with the neuroscientific tradition of planar movements and linear(ized) kinematics, the theoretical formulation and experimental scenarios are set in the nonlinear space of 3D rotations which are essential for wrist motions, a somewhat neglected area despite its importance in daily tasks.

Control Systems: Classical, Modern, and AI-Based Approaches provides a broad and comprehensive study of the principles, mathematics, and applications for those studying basic control in mechanical, electrical, aerospace, and other engineering disciplines. The text builds a strong mathematical foundation of control theory of linear, nonlinear, optimal, model predictive, robust, digital, and adaptive control systems, and it addresses applications in several emerging areas, such as aircraft, electro-mechanical, and some nonengineering systems: DC motor control, steel beam thickness control, drum boiler, motional control system, chemical reactor, head-disk assembly, pitch control of an aircraft, yaw-damper control, helicopter control, and tidal power control. Decentralized control, game-theoretic control, and control of hybrid systems are discussed. Also, control systems based on artificial neural networks, fuzzy logic, and genetic algorithms, termed as AI-based systems are studied and analyzed with applications such as auto-landing aircraft, industrial process control, active suspension system, fuzzy gain scheduling, PID control, and adaptive neuro control. Numerical coverage with MATLAB (R) is integrated, and numerous examples and exercises are included for each chapter. Associated MATLAB (R) code will be made available.

This book provides a direct and comprehensive introduction to theoretical and numerical concepts in the emerging field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the book is to offer graduate students and researchers a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs. Coverage includes uncertainty modelling in control problems, variational formulation of PDEs with random inputs, robust and risk-averse formulations of optimal control problems, existence theory and numerical resolution methods. The exposition focusses on the entire path, starting from uncertainty modelling and ending in the practical implementation of numerical schemes for the numerical approximation of the considered problems. To this end, a selected number of illustrative examples are analysed in detail throughout the book. Computer codes, written in MatLab, are provided for all these examples. This book is adressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations.

Rotating Machinery, Hybrid Testing, Vibro-Acoustics & Laser Vibrometry, Volume 8: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the eighth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Rotating Machinery, Hybrid Testing, Vibro-Acoustics & Laser Vibrometry, including papers on: Rotating Machinery Vibro-Acoustics Experimental Techniques Advances in Wind Energy Scanning Laser Doppler Vibrometry Methods Hybrid Test Methods

Special Topics in Structural Dynamics, Volume 6: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the sixth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Experimental Methods Analytical Methods General Dynamics & Modal Analysis General Dynamics & System Identification Damage Detection

This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author's original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations.

This volume contains the proceedings of MeTrApp 2017, the 4th Conference on Mechanisms, Transmissions and Applications, that was held in Trabzon, Turkey, July 3-5, 2017. The topics treated in this volume are Mechanism Design, Parallel Manipulators, Control Applications, Mechanical Transmissions, Cam Mechanisms, and Dynamics of Machinery. The conference was organised by the IFToMM Technical Committees for "Linkages and Mechanical Controls" and "Gearing and Transmissions" under the patronage of the IFToMM and sponsorship of Karadeniz Technical University, Izmir Institute of Technology and IFToMM Turkey (MAKTED). The aim of the conference was to bring together researchers, scientists, industry experts and students to provide, in a friendly and stimulating environment, the opportunity to exchange know-how and promote collaboration in the field of Mechanism and Machine Science.

This book opens with an explanation of the vibrations of a single degree-of-freedom (dof) system for all beginners. Subsequently, vibration analysis of multi-dof systems is explained by modal analysis. Mode synthesis modeling is then introduced for system reduction, which aids understanding in a simplified manner of how complicated rotors behave. Rotor balancing techniques are offered for rigid and flexible rotors through several examples. Consideration of gyroscopic influences on the rotordynamics is then provided and vibration evaluation of a rotor-bearing system is emphasized in terms of forward and backward whirl rotor motions through eigenvalue (natural frequency and damping ratio) analysis. In addition to these rotordynamics concerning rotating shaft vibration measured in a stationary reference frame, blade vibrations are analyzed with Coriolis forces expressed in a rotating reference frame. Other phenomena that may be assessed in stationary and rotating reference frames include stability characteristics due to rotor internal damping and instabilities due to asymmetric shaft stiffness and thermal unbalance behavior.

Dynamic objects move in mysterious ways. Their analysis is a difficult subject involving matrices, differential equations and the complex algebra of oscillatory systems. However, in this textbook, the author draws on his long experience of designing autopilots, robots for nuclear inspection and agricultural machine guidance to present the essentials with a light touch. The emphasis is on a deep understanding of the fundamentals rather than rote-learning of techniques. The inertia tensor is presented as a key to understanding motion ranging from boomerangs to gyroscopes. Chains of transformations unravel the motion of a robot arm. To help the reader visualise motion, ranging from unbalanced rotors to vibrating systems with multiple modes and damping, there are abundant simulation examples on a linked website. These will run in any web browser, while their simple code is on open view for modification and experimentation. They show that nonlinear systems present no problems, so that friction damping can be modelled with ease. A particular problem for mechanical engineers is that the vibration topics encroach on the territory of the electrical engineer. State variables open up control theory while the solution of differential equations with sinusoidal inputs is simplified by an understanding of sine-waves as complex exponentials. The linked web site has several areas of mathematics revision to help. A final chapter pokes fun at the misrepresentation of dynamics in cinema productions.

This book explores the outcomes on flow control research activities carried out within the framework of two EU-funded projects focused on training-through-research of Marie Sklodowska-Curie doctoral students. The main goal of the projects described in this monograph is to assess the potential of the passive- and active-flow control methods for reduction of fuel consumption by a helicopter. The research scope encompasses the fields of structural dynamics, fluid flow dynamics, and actuators with control. Research featured in this volume demonstrates an experimental and numerical approach with a strong emphasis on the verification and validation of numerical models. The book is ideal for engineers, students, and researchers interested in the multidisciplinary field of flow control.

This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) "The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields." (Marian Gidea, Mathematical Reviews, Issue 2010 d)

Shock & Vibration, Aircraft/Aerospace and Energy Harvesting, Volume 9: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the ninth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Shock & Vibration, Aircraft/Aerospace and Energy Harvesting including papers on: Shock & Vibration Testing Aircraft/Aerospace Applications Optical Techniques: Digital Image Correlation Vibration Suppression & Control Damage Detection Energy Harvesting

This book develops original results regarding singular dynamic systems following two different paths. The first consists of generalizing results from classical state-space cases to linear descriptor systems, such as dilated linear matrix inequality (LMI) characterizations for descriptor systems and performance control under regulation constraints. The second is a new path, which considers descriptor systems as a powerful tool for conceiving new control laws, understanding and deciphering some controller's architecture and even homogenizing different-existing-ways of obtaining some new and/or known results for state-space systems. The book also highlights the comprehensive control problem for descriptor systems as an example of using the descriptor framework in order to transform a non-standard control problem into a classic stabilization control problem. In another section, an accurate solution is derived for the sensitivity constrained linear optimal control also using the descriptor framework. The book is intended for graduate and postgraduate students, as well as researchers in the field of systems and control theory.

This thesis develops several systematic and unified approaches for analyzing dynamic systems with positive characteristics or a more general cone invariance property. Based on these analysis results, it uses linear programming tools to address static output feedback synthesis problems with a focus on optimal gain performances. Owing to their low computational complexity, the established controller design algorithms are applicable for large-scale systems. The theory and control strategies developed will not only be useful in handling large-scale positive delay systems with improved solvability and at lower cost, but also further our understanding of the system characteristics in other related areas, such as distributed coordination of networked multi-agent systems, formation control of multiple robots.

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

This contributed volume presents the research results of the program "Small machine tools for small work pieces" (SPP 1476), funded by the German Research Society (DFG). The book contains the final report of the priority program, presenting novel approached for size-adapted, reconfigurable micro machine tools. The target audience primarily comprises research experts and practitioners in the field of micro machine tools, but the book may also be beneficial for graduate students.

This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

This book covers the topics of theoretical principles, dynamics model and algorithm, mission analysis, system design and experimental studies of space nets system, aiming to provide an initial framework in this field and serve as a ready reference for those interested. Space nets system represents a forefront field in future development of aerospace technologies. However, it involves new challenges and problems such as nonlinear and distorted nets structure, complex rigid flexible coupling dynamics, orbital transfer of space flexible composite and dynamics control. Currently, no comprehensive books on space nets dynamics and design are available, so potential readers can get to know the working mechanism, dynamics elements, and mission design of the space nets system from a Chinese perspective.

This book offers valuable insights and provides effective tools useful for imagining, creating, and promoting novel and challenging developments in structural mechanics. It addresses a wide range of topics, such as mechanics and geotechnics, vibration and damping, damage and friction, experimental methods, and advanced structural materials. It also discusses analytical, experimental and numerical findings, focusing on theoretical and practical issues and innovations in the field. Collecting some of the latest results from the Lagrange Laboratory, a European scientific research group, mainly consisting of Italian and French engineers, mechanicians and mathematicians, the book presents the most recent example of the long-term scientific cooperation between well-established French and Italian Mechanics, Mathematics and Engineering Schools. It is a valuable resource for postgraduate students, researchers and practitioners dealing with theoretical and practical issues in structural engineering.

This book on the dynamics of rail vehicles is developed from the manuscripts for a class with the same name at TU Berlin. It is directed mainly to master students with pre-knowledge in mathematics and mechanics and engineers that want to learn more. The important phenomena of the running behaviour of rail vehicles are derived and explained. Also recent research results and experience from the operation of rail vehicles are included. One focus is the description of the complex wheel-rail contact phenomena that are essential to understand the concept of running stability and curving. A reader should in the end be able to understand the background of simulation tools that are used by the railway industry and universities today.

By establishing an alternative foundation of control theory, this thesis represents a significant advance in the theory of control systems, of interest to a broad range of scientists and engineers. While common control strategies for dynamical systems center on the system state as the object to be controlled, the approach developed here focuses on the state trajectory. The concept of precisely realizable trajectories identifies those trajectories that can be accurately achieved by applying appropriate control signals. The resulting simple expressions for the control signal lend themselves to immediate application in science and technology. The approach permits the generalization of many well-known results from the control theory of linear systems, e.g. the Kalman rank condition to nonlinear systems. The relationship between controllability, optimal control and trajectory tracking are clarified. Furthermore, the existence of linear structures underlying nonlinear optimal control is revealed, enabling the derivation of exact analytical solutions to an entire class of nonlinear optimal trajectory tracking problems. The clear and self-contained presentation focuses on a general and mathematically rigorous analysis of controlled dynamical systems. The concepts developed are visualized with the help of particular dynamical systems motivated by physics and chemistry.

This book presents essential methods of deformation compatibility control, and explicitly addresses the implied conditions on the methods' deformation compatibility. Consequently, these conditions can be considered in engineering structure design, while the conditions on stable equilibrium can be taken into account in the design method. Thus, the designed deformation and the actual deformation of the respective structure are approximately identical, guaranteeing both the flexibility of the construction material in force transmission and the equilibrium of force in the structure. Though equilibrium theory in engineering structures has been extensively studied, there has been comparatively little research on compatibility. In the limited researches available, the topics are primarily the theories and assumptions on the deformation compatibility, while few systematic works focus on the mechanical theoretical principles and methods of deformation compatibility control. As such, the flexibility of the construction material in force transmission and the stable equilibrium of the structure as a whole cannot be guaranteed based on these research results. Successfully addressing this important gap in the literature, the book is intended for researchers and postgraduates in engineering mechanics, civil engineering and related areas.

This book presents essential studies and applications in the context of sliding mode control, highlighting the latest findings from interdisciplinary theoretical studies, ranging from computational algorithm development to representative applications. Readers will learn how to easily tailor the techniques to accommodate their ad hoc applications. To make the content as accessible as possible, the book employs a clear route in each paper, moving from background to motivation, to quantitative development (equations), and lastly to case studies/illustrations/tutorials (simulations, experiences, curves, tables, etc.). Though primarily intended for graduate students, professors and researchers from related fields, the book will also benefit engineers and scientists from industry.

This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.

The papers in this volume present and discuss the frontiers in the mechanics of controlled machines and structures. They are based on papers presented at the International Workshop on Advanced Dynamics and Model Based Control of Structures and Machines held in Vienna in September 2015. The workshop continues a series of international workshops held in Linz (2008) and St. Petersburg (2010).