New Approaches in Automation and Robotics

The book New Approaches in Automation and Robotics offers in 22 chapters a collection of recent developments in automation, robotics as well as control theory. It is dedicated to researchers in science and industry, students, and practicing engineers, who wish to update and enhance their knowledge on modern methods and innovative applications. The authors and editor of this book wish to motivate people, especially under-graduate students, to get involved with the interesting field of robotics and mechatronics. We hope that the ideas and concepts presented in this book are useful for your own work and could contribute to problem solving in similar applications as well. It is clear, however, that the wide area of automation and robotics can only be highlighted at several spots but not completely covered by a single book

Linear structure of nonlinear dynamic systems via Koopman decomposition

Doctor of PhilosophyDepartment of Mechanical and Nuclear EngineeringMingjun WeiLinear structure and invariant subspaces of nonlinear dynamics are revealed, extending the superposition principle and invariant subspaces from linear dynamics. They are achieved by considering dynamics in its dual space and the local spectral Koopman theory. The Koopman eigenfunctions constitute invariant subspaces under the given dynamic system, providing convenient bases for the linear structure. On the other hand, the locality and infinite dimensionality are identified as two unique properties of nonlinear dynamics, where the former refers to the spectral problem is locally defined, and the latter refers to Koopman spectrums are recursively proliferated by nonlinear interaction. Koopman spectral theory is studied. For a linear time-invariant (LTI) system, its linear spectrum is a subset of Koopman spectrums. High order Koopman spectrum can be obtained for nonlinear observables using the proliferation rule. For a linear time-variant system (LTV), Koopman decomposition is obtained by the eigenvalue problem of its fundamental matrix. Besides the general LTV, the periodic LTV system is studied using the Floquet theory. The Floquet spectrums are found to be Koopman spectrums. For a nonlinear system, a local Koopman spectrum problem is defined for a parameterized semigroup Koopman operator, and the simple local spectra are found to be conditionally continuous from the operator perturbation theory. The proliferation is found to recursively applicable to nonlinear dynamics. Moreover, the hierarchy structure of the Koopman decomposition of nonlinear systems is discovered, by decomposing dynamics into base and perturbation on top of it. The numerical algorithm, dynamic mode decomposition (DMD), is examined for its applicability to capture the spectra and modes for a variety of dynamic systems. A more robust and efficient framework based on generalized eigenvalue problem (GEV) is proposed, which is then solved by a least-square solution (LS) or a total least square solution (TLS). Therefore, two algorithms, DMD-LS and DMD-TLS algorithm, are developed. DMD-LS algorithm is mathematically equivalent to the standard DMD algorithm first proposed by Schmid (2010) but more robust. DMD-TLS is more accurate for noise data. A residue-based criterion is developed to choose dynamically important or true DMD modes from trivial or spurious modes that often appear in DMD computations. Linear structure via Koopman decomposition is first applied to a linear dynamic system and an asymptotic nonlinear system, for example. Then flow past fixed cylinder of a Hopf bifurcation process is numerically studied via DMD technique. The equivalence of Koopman decomposition to the GSA is verified at the primary instability stage. The Fourier modes, the least stable Floquet modes, and their high-order derived Koopman modes are found to be the superposition of countable infinite Koopman modes when the flow reaches periodic by considering continuity of Koopman spectrum and the invariance of Koopman modes to the nonlinear transition process. The nonlinear modulation effects, namely, the modulation of the mean flow and the resonance phenomena is explained similarly. The coherent structures are also found to be related to the decomposition. A DMD based model order reduction method is implemented based on Galerkin projection. The model reduction approach is applied to both the transitional and the periodic stages of flow passing a fixed cylinder. Accurate dynamics and frequencies are rebuilt

Friction compensation in the swing-up control of viscously damped underactuated robotics

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering in the Control Research Group School of Electrical and Information Engineering, Johannesburg, 2017In this research, we observed a torque-related limitation in the swing-up control of underactuated mechanical systems which had been integrated with viscous damping in the unactuated joint. The objective of this research project was thus to develop a practical work-around solution to this limitation. The nth order underactuated robotic system is represented in this research as a collection of compounded pendulums with n-1 actuators placed at each joint with the exception of the first joint. This system is referred to as the PAn-1 robot (Passive first joint, followed by n-1 Active joints), with the Acrobot (PA1 robot) and the PAA robot (or PA2 robot) being among the most well-known examples. A number of friction models exist in literature, which include, and are not exclusive to, the Coulomb and the Stribeck effect models, but the viscous damping model was selected for this research since it is more extensively covered in existing literature. The effectiveness of swing-up control using Lyapunov’s direct method when applied on the undamped PAn-1 robot has been vigorously demonstrated in existing literature, but there is no literature that discusses the swing-up control of viscously damped systems. We show, however, that the application of satisfactory swing-up control using Lyapunov’s direct method is constrained to underactuated systems that are either undamped or actively damped (viscous damping integrated into the actuated joints only). The violation of this constraint results in the derivation of a torque expression that cannot be solved for (invertibility problem, for systems described by n > 2) or a torque expression which contains a conditional singularity (singularity problem, for systems with n = 2). This constraint is formally summarised as the matched damping condition, and highlights a clear limitation in the Lyapunov-related swing-up control of underactuated mechanical systems. This condition has significant implications on the practical realisation of the swing-up control of underactuated mechanical systems, which justifies the investigation into the possibility of a work-around. We thus show that the limitation highlighted by the matched damping condition can be overcome through the implementation of the partial feedback linearisation (PFL) technique. Two key contributions are generated from this research as a result, which iii include the gain selection criterion (for Traditional Collocated PFL), and the convergence algorithm (for noncollocated PFL). The gain selection criterion is an analytical solution that is composed of a set of inequalities that map out a geometric region of appropriate gains in the swing-up gain space. Selecting a gain combination within this region will ensure that the fully-pendent equilibrium point (FPEP) is unstable, which is a necessary condition for swing-up control when the system is initialised near the FPEP. The convergence algorithm is an experimental solution that, once executed, will provide information about the distal pendulum’s angular initial condition that is required to swing-up a robot with a particular angular initial condition for the proximal pendulum, along with the minimum gain that is required to execute the swing-up control in this particular configuration. Significant future contributions on this topic may result from the inclusion of more complex friction models. Additionally, the degree of actuation of the system may be reduced through the implementation of energy storing components, such as torsional springs, at the joint. In summary, we present two contributions in the form of the gain selection criterion and the convergence algorithm which accommodate the circumnavigation of the limitation formalised as the matched damping condition. This condition pertains to the Lyapunov-related swing-up control of underactuated mechanical systems that have been integrated with viscous damping in the unactuated joint.CK201

Passivity enforcement via chordal methods

Orientador: Prof. Dr. Gustavo Henrique da Costa OliveiraTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia Elétrica. Defesa : Curitiba, 27/08/2019Inclui referências: p. 164-175Resumo: Neste documento são propostos três algoritmos inéditos associados aos problemas subsequentes de aferição e imposição da passividade, a qual é uma propriedade qualitativa, geral e fundamental na modelagem matemática de transitórios eletromagnéticos de sistemas elétricos passivos, como transformadores. Esses algoritmos baseiam-se numa combinação de teoria dos grafos e otimização convexa. O primeiro deles consiste na aferição de subsistemas passivos contidos num sistema não passivo, intuitivamente busca-se partes passivas contidas num todo não passivo. Já na etapa de imposição de passividade, o segundo algoritmo é consequência natural do primeiro: retendo apenas os parâmetros associados às partes passivas e descartando os demais, parte-se de um sistema passivo parcialmente especificado para se determinar novos parâmetros em substituição àqueles descartados de modo que o sistema como um todo seja passivo. A possibilidade de determinação dos novos parâmetros depende de uma propriedade topológica de um grafo associado às matrizes de parâmetros do modelo, tal propriedade é denominada cordalidade. O terceiro algoritmo aborda novamente a questão de imposição da passividade e também faz uso da cordalidade, não mais como condição de existência de solução, mas sim como uma forma de explorar a esparsidade das matrizes de parâmetros. O problema de imposição da passividade encerra dois desafios no seu processo de solução, a saber: (i) compensação de parâmetros resultando na degradação do modelo bem como (ii) longos tempos de solução. Os algoritmos ora propostos são uma resposta a essas questões e os resultados obtidos demonstraram-se comparáveis àqueles já existentes na literatura especializada, em alguns casos apresentando melhorias, seja em termos de aproximação ou tempo computacionais. Os algoritmos foram testados a partir de dados de medição de um Transformador de Potencial Indutivo bem como de um Transformador de Potência. Palavras-chave: Macro-modelagem Passiva. Teoria de Sistemas. Álgebra Linear Aplicada. Análise de Transitórios. Transformadores.Abstract: Three novel algorithms are herein proposed to solve passivity assessment and enforcement problems. Passivity is a general, qualitative and fundamental property pertaining to the modeling associated with electromagnetic transients in passive power systems, such as transformers. These algorithms make combined use of Graph Theory and Convex Optimization. The first algorithm is concerned with passivity assesment. In particular, it searches for passive subsystems embedded into a larger nonpassive system and eventually specifies a partially specified passive system. Focusing on the subsequent step, algorithm two is a natural consequence of the preceeding one: retaining only the parameter set associated with passive subsystems as determined before, this partially specified passive system is used to further determine the remaining parameters so that the entire system be fully specified and passive. The existence condition for finding a fully specified system hinges on the fulfillment of a topological property of the graph associated the parameter matrices, namely chordality. The third algorithm also solves the passivity enforcement problem by making use of chordality, not as an existence condition, but rather by exploiting chordal sparsity patterns obtained with the parameter matrices. Solving passivity enforcement problems entails two persisting challenges, namely: (i) passivity compensations to parameters prompting increased model degradation as well as (ii) large computation times. The algorithms herein proposed tackle these issues and yield results comparable to those already in use, sometimes resulting in improved performance in terms of either approximation accuracy or runtime. These results herein reported entail data from actual measurements of an Inductive Voltage Transformer and a Power Transformer. Keywords: Passive Macromodeling. System Theory. Applied Linear Algebra. Transient Analysis. Transformers

Joint University Program for Air Transportation Research, 1989-1990

Research conducted during the academic year 1989-90 under the NASA/FAA sponsored Joint University Program for Air Transportation research is discussed. Completed works, status reports and annotated bibliographies are presented for research topics, which include navigation, guidance and control theory and practice, aircraft performance, human factors, and expert systems concepts applied to airport operations. An overview of the year's activities for each university is also presented