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Many mechanical systems exhibit nonlinear movement and are subject to perturbations from a desired equilibrium state. These perturbations can greatly reduce the efficiency of the systems. It is therefore desirous to analyze the asymptotic stabilizability of an equilibrium solution of nonlinear systems; an excellent method of performing these analyses is through study of Jacobian linearization's and their properties. Two enlightening examples of nonlinear mechanical systems are the Simple Inverted Pendulum and the Inverted Pendulum on a Cart (PoC). These examples provide insight into both the feasibility and usability of Jacobian linearizations of nonlinear systems, as well as demonstrate the concepts of local stability, observability, controllability and detectability of linearized systems under varying parameters. Some examples of constant disturbances and effects are considered. The ultimate goal is to examine stabilizability, through both static and dynamic feedback controllers, of mechanical systems

Segway has been a popular production as an alternative transporter since its invention at the end of 20th century. Millions of people like for its ergonomic design and high-tech elements. It is predicted to be an innovational product to change a person's life style. This thesis focuses on building a simple low cost, home-made Segway style scooter. This project uses two electric scooter motors, two 12V car batteries, one accelerometer and several microprocessors to build up the whole system. Significantly, this project also explains how to build a Brushed Direct Current (BDC) motor driver with a rated output power of more than 350W and the capability of coping with up to 120A transient peak current and up to 40A continuous current. Four-quadrant operation and eight modes of DC motor operation are discussed. A mathematical model of the Segway style scooter is also introduced in details. This including the modelling of a BDC motor, a two-wheeled inverted pendulum and their combination. The linearization of these models is used. At the end the linearized model is simulated in computer software.

The restoration of arm-free standing in paraplegic individuals can be accomplished with the help of functional electrical stimulation (FES). The key component of such a system is a controller that can modulate FES induced muscle contractions in real-time, such that artificially produced forces in the legs and abdominal muscles are able to generate stable standing posture. A 57 year-old individual with chronic ASIA-A (American Spinal Injury Association), T3/4 level spinal cord injury (SCI) participated in this study. The objective was to determine if a proportional-derivative (PD) or proportional-integral-derivative (PID) controller could be used to regulate FES induced muscle contractions in the ankle joint to allow it to maintain balance of the entire body during quiet standing, while exhibiting physiological dynamics seen in able-bodied individuals while doing so.

The restoration of arm-free standing in paraplegic individuals can be accomplished with the help of functional electrical stimulation (FES). The key component of such a system is a controller that can modulate FES induced muscle contractions in real-time, such that artificially produced forces in the legs and abdominal muscles are able to generate stable standing posture. A 57 year-old individual with chronic ASIA-A (American Spinal Injury Association), T3/4 level spinal cord injury (SCI) participated in this study. The objective was to determine if a proportional-derivative (PD) or proportional-integral-derivative (PID) controller could be used to regulate FES induced muscle contractions in the ankle joint to allow it to maintain balance of the entire body during quiet standing, while exhibiting physiological dynamics seen in able-bodied individuals while doing so.

abstract: This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering. / Dissertation/Thesis / M.S. Electrical Engineering 2011

Falls are one of the most serious problems among the elderly, resulting in fatal physical injuries. Early identification of people at a high risk of falling is needed to facilitate rehabilitation to reduce future fall risk. The overall goal of this dissertation was to develop biomechanical models that identify dynamic limits of balance control in daily functional activities associated with falling, including sit-to-stand (STS) movement, standing (stance perturbation), and walking. Poor performance of STS movement has been identified as one of the risk factors of falls among elderly individuals. We proposed a novel method to identify dynamic limits of balance control during STS movement using whole body center of mass (COM) acceleration and assessed its feasibility to differentiate individuals with difficulty in STS movement from healthy individuals. The results demonstrated that our model with COM acceleration could better differentiate individuals with difficulty in STS movement from healthy individuals than the traditional model with COM velocity. Poor postural control ability is also a risk factor of falls. Postural recovery responses to backward support surface translations during quiet standing were examined for healthy young and elderly adults. The results demonstrated that functional base of support (FBOS) and ankle dorsiflexor strength could be sensitive measures to detect elderly individuals with declined balance control. Our biomechanical model, which determines a set of balance stability boundaries, showed a better predictive capability than the statistical model for identifying unstable balance recovery trials, while the statistical model better predicted stable recovery trials. Lastly, walking requires a fine momentum control where COM acceleration could play an important role. Differences in control of dynamic stability during walking were examined with our proposed boundaries of dynamic stability. Elderly fallers adapted a more conservative gait strategy than healthy individuals, demonstrating significantly slower forward COM velocity and acceleration with their COM significantly closer to the base of support at toe-off, which could be indicative of a poor momentum control ability. Overall, this study demonstrated that COM acceleration would provide further information on momentum control, which could better reveal underlying mechanisms causing imbalance and provide an insightful evaluation of balance dysfunction. This dissertation includes unpublished co-authored material.

The diploma thesis deals with putting the pendulum into upright position and its stabilization on a real system. The opening chapter describes the limiting various implementation inverse pendulums, the use of major laboratory tasks in industry, and the selection of appropriate methods for stabilization. The real system was properly identified and parameterized. The mathematical model of the inverse pendulum was derived using the Lagrange method of the second type, the nonlinear system was converted into a status description and linearized for the needs of the state controller design. The system was simulated in the Matlab Simulink environment. The LQR controller was chosen as the regulator stabilizing in upright cases. A Kalman controller in discrete form was prepared for the filter signal and estimation of residual states. The energy method was chosen for the upright pendulums. The proposed methods were tested and implemented in simulation and on a real system.

The goal of this work is modelling and design of an inverted pendulum prototype. The work presents a mathematical model of a rotary pendulum, modelling of a BLDC motors and also a 3D model of the pendulum prototype is present. The work mentions design of the state space controller and swing up control of the inverted pendulum. Dynamics obtained from the mathematical model is used to create a 3D dynamic model of a pendulum, with the use of the Simscape toolbox. The work deals with control of a BLDC motors with use of vector control. The algorithm is implemented on the CompactRIO platform. Later, hardware is developed, containing STMicroelectronis microcontroller, capable of replacing the CompactRIO platform.

京都大学 / 0048 / 新制・課程博士 / 博士(人間・環境学) / 甲第18353号 / 人博第666号 / 新制||人||160(附属図書館) / 25||人博||666(吉田南総合図書館) / 31211 / 京都大学大学院人間・環境学研究科共生人間学専攻 / (主査)准教授 神﨑 素樹, 教授 森谷 敏夫, 准教授 久代 恵介, 教授 小田 伸午 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DFAM