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<p>Generating and stabilizing periodic motions in nonlinear systems is a challenging task. In the control system community this topic is also known as limit cycle control. In recent years a framework known as Virtual Holonomic Constraints (VHC) has been developed as one of the solutions to this problem. The aim of this thesis is to give an insight into this approach and its practical application.</p><p>The contribution of this work is primarily the experimental validation of the theory. A step by step procedure of this methodology is given for motion planning, as well as for controller design. Three particular setups were chosen for experiments: the inertia wheel pendulum, the Furuta pendulum and the two-link planar pendulum. These under-actuated mechanical systems are well known benchmarking setups for testing advanced control design methods.</p><p>Further application is intended for cases such as biped robot walking/running, human and animal locomotion analysis, etc.</p>

Whether it is a car, a mobile phone, or a computer, we are noticing how automation and production with robots plays an important role in the industry of our modern world. We find it in factories, manufacturing products, automotive cruise control, construction equipment, autopilot on airplanes, and countless other industrial applications.         Automation technology can vary greatly depending on the field of application. On one end, we have systems that are operated by the user and rely fully on human ability. Examples of these are heavy-mobile equipment, remote controlled systems, helicopters, and many more. On the other end, we have autonomous systems that are able to make algorithmic decisions independently of the user.         Society has always envisioned robots with the full capabilities of humans. However, we should envision applications that will help us increase productivity and improve our quality of life through human-robot collaboration. The questions we should be asking are: “What tasks should be automated?'', and “How can we combine the best of both humans and automation?”. This thinking leads to the idea of developing systems with some level of autonomy, where the intelligence is shared between the user and the system. Reasonably, the computerized intelligence and decision making would be designed according to mathematical algorithms and control rules.         This thesis considers these topics and shows the importance of fundamental mathematics and control design to develop automated systems that can execute desired tasks. All of this work is based on some of the most modern concepts in the subjects of robotics and control, which are synthesized by a method known as the Virtual Holonomic Constraints Approach. This method has been useful to tackle some of the most complex problems of nonlinear control, and has enabled the possibility to approach challenging academic and industrial problems. This thesis shows concepts of system modeling, control design, motion analysis, motion planning, and many other interesting subjects, which can be treated effectively through analytical methods. The use of mathematical approaches allows performing computer simulations that also lead to direct practical implementations.

Generating and stabilizing periodic motions in nonlinear systems is a challenging task. In the control system community this topic is also known as limit cycle control. In recent years a framework known as Virtual Holonomic Constraints (VHC) has been developed as one of the solutions to this problem. The aim of this thesis is to give an insight into this approach and its practical application. The contribution of this work is primarily the experimental validation of the theory. A step by step procedure of this methodology is given for motion planning, as well as for controller design. Three particular setups were chosen for experiments: the inertia wheel pendulum, the Furuta pendulum and the two-link planar pendulum. These under-actuated mechanical systems are well known benchmarking setups for testing advanced control design methods. Further application is intended for cases such as biped robot walking/running, human and animal locomotion analysis, etc.

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Made available in DSpace on 2015-04-22T22:00:51Z (GMT). No. of bitstreams: 1 Dissertacao Final Gisele Lira.pdf: 2945367 bytes, checksum: 57a06468ad5309a2985be8b8ca0281d4 (MD5) Previous issue date: 2010-08-27 / FAPEAM - Fundação de Amparo à Pesquisa do Estado do Amazonas / The sub-actuated mechanical system of the double inverted pendulum on a cart is a complex subject in the field of control theory. The main reason researchers have focus their attention on this system is its characteristic difficulty on balancing two rods in vertical only using the movement of the cart. Although the evolution of the control theory throughout the years, the development of a robust controller is still an open question. In order to provide a study on more efficient control techniques, considering aspects of efficiency and robustness, we performed a comparative study from which we chose the most appropriate to make part of the model presented in this work. Since there is no a common standard in the different control laws applied to the system, it is modeled, linearized and its dynamic movements are studied. Three control techniques are designed to this modeled system: linear quadratic regulator (LQR), fuzzy logic control and sliding mode control. To the last technique we applied an improvement in the switching function in order to decrease the effects of the chattering problem, using the saturation function. The asymptotic stability of the sliding mode surfaces in each one of these subsystems is proved theoretically using the Barbalat s lemma and the Lyapunov stability. The results of the simulations to the LQR and fuzzy control applied to the linearized system proved its efficiency in stabilizing the system, and the fuzzy controller as a better approximation of the state variables of the equilibrium point, however, their response is slow. The results with the sliding mode controller also present better results when compared to the LQR, with a faster response. The results with the hierarchical sliding mode controller proved its efficiency in face of the uncertainty of the system and the function used to decrease the effects of the chattering problem showed itself useful. / O sistema mecânico sub-atuado duplo pêndulo invertido sobre um carro é um sistema complexo em termos da teoria de controle. O principal motivo de interesse de pesquisadores por este sistema é a dificuldade característica deste sistema em equilibrar duas hastes na vertical apenas com o movimento do carro. Apesar da evolução da teoria de controle ao longo dos anos, o desenvolvimento de um controlador robusto ainda é uma questão aberta. A fim de promover uma análise sobre as técnicas de controle existentes, considerando aspectos de eficiência e robustez, um estudo comparativo foi realizado e, a partir dele, foram escolhidas as mais eficientes para fazer parte do modelo proposto neste trabalho. Devido a dificuldade de padronização entre as diferentes leis de controle aplicadas ao sistema, o mesmo é modelado, linearizado e seus movimentos dinâmicos são estudados. Três técnicas de controle são projetadas para este sistema modelado, sendo elas regulador linear quadrático LQR, controle por lógica fuzzy e controle por modo deslizante. Para este último aplicamos uma melhoria na função de chaveamento visando a atenuação do problema de chattering, utilizando a função de saturação. A estabilidade assintótica das superfícies de modo deslizante de cada um destes subsistemas é provada teoricamente usando o lema de Barbalat e a teoria de estabilidade de Lyapunov. Os resultados de simulações para o controle LQR e fuzzy aplicados ao sistema linearizado comprovam sua eficiência na estabilização do sistema, sendo que o controlador fuzzy possui uma melhor aproximação das variáveis de estado do ponto de equilíbrio, contudo, sua resposta é lenta. Os resultados com o controlador por modo deslizante apresentam também melhores resultados frente ao LQR, com uma resposta mais rápida. Os resultados com o controlador por modo deslizante hierárquico comprovam sua eficiência frente às incertezas do sistema e a função utilizada para atenuação do fenômeno de chattering mostrou-se eficaz.

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