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This book demonstrates how delay differential equations (DDEs) can be used to compliment the laboratory investigation of human balancing tasks. This approach is made accessible to non-specialists by comparing mathematical predictions and experimental observations. For example, the observation that a longer pole is easier to balance on a fingertip than a shorter one demonstrates the essential role played by a time delay in the balance control mechanism. Another balancing task considered is postural sway during quiet standing. With the inverted pendulum as the driver and the feedback control depending on state variables or on an internal model, the feedback can be identified by determining a critical pendulum length and/or a critical delay. This approach is used to identify the nature of the feedback for the pole balancing and postural sway examples. Motivated by the question of how the nervous system deals with these feedback control challenges, there is a discussion of ''microchaotic'' fluctuations in balance control and how robust control can be achieved in the face of uncertainties in the estimation of control parameters. The final chapter suggests some topics for future research. Each chapter includes an abstract and a point-by-point summary of the main concepts that have been established. A particularly useful numerical integration method for the DDEs that arise in balance control is semi-discretization. This method is described and a MATLAB template is provided. This book will be a useful source for anyone studying balance in humans, other bipedal organisms and humanoid robots. Much of the material has been used by the authors to teach senior undergraduates in computational neuroscience and students in bio-systems, biomedical, mechanical and neural engineering. .

Differential equations --- Human biochemistry --- Biotechnology --- differentiaalvergelijkingen --- medische biochemie --- bio-engineering --- biotechnologie

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The book presents the recently introduced and already widely cited semi-discretization method for the stability analysis of delayed dynamical systems with parametric excitation. Delay-differential equations often come up in different fields of engineering, such as feedback control systems, machine tool vibrations, and balancing/stabilization with reflex delay. The behavior of such systems is often counter-intuitive and closed form analytical formulas can rarely be given even for the linear stability conditions. The same holds for parametrically excited systems. If parametric excitation is coupled with the delay effect, then the governing equation is a delay-differential equation with time-periodic coefficients, and the stability properties are even more intriguing. The semi-discretization method is a simple but efficient method that is based on the discretization with respect to the delayed term and the periodic coefficients only. This discretization results in a system of ordinary differential equations that can be solved using standard techniques, which are part of basic engineering curriculums. The method can effectively be used to construct stability charts in the space of system parameters. These charts provide a useful tool for engineers, since they present an overview on the effects of system parameters on the local dynamics of the system. The book presents the application of the method to different engineering problems, such as dynamics of turning and milling processes with constant and with varying spindle speeds, stick balancing with reflex delay, force control processes in the presence of feedback delay, and stabilization using time-periodic control gains. The book is designed for graduate and PhD students as well as researchers working in the field of delayed dynamical systems with application to mechanical, electrical and chemical engineering, control theory, biomechanics, population dynamics, neuro-physiology, and climate research.

Ergodic theory. Information theory --- Mathematics --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- toegepaste wiskunde --- controleleer --- ingenieurswetenschappen --- informatietheorie

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This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike. .

Differential geometry. Global analysis --- Ergodic theory. Information theory --- Classical mechanics. Field theory --- Mechanical properties of solids --- Electrical engineering --- Engineering sciences. Technology --- patroonherkenning --- differentiaal geometrie --- automatisering --- dynamica --- informatietheorie --- optica