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Extensive disturbance rejection methods have been established for time-invariant systems. However, the development of these techniques has not focused on application to time-periodic systems in particular until recently. The filtered-X LMS algorithm is regarded as the best disturbance rejection technique for aperiodic systems by many, as has been proven in the acoustics industry for rejecting unwanted noise. Since this is essentially a feedforward approach, we might expect its performance to be good with respect to time-periodic systems in which the disturbance frequency is already known. The work presented in this thesis is an investigation of the performance of the filtered-X LMS algorithm for disturbance rejection in time-periodic systems. Two cases are examined: a generalized linear, time-periodic system and the helicopter rotor blade in forward flight. Results for the generalized system show that the filtered-X LMS algorithm does converge for time-periodic disturbance inputs and can produce very small errors. For the helicopter rotor blade system the algorithm is shown to produce very small errors, with a 96%, or 14 dB, reduction in error from the open-loop system. The filtered-X LMS disturbance rejection technique is shown to provide a successful means of rejecting timeperiodic disturbances for time-periodic systems. / Master of Science

The focus of this dissertation is to improve autonomous navigation in unstructured terrain conditions, with specific application to unmanned casualty extraction in disaster scenarios. Robotic systems are being widely employed for search and rescue applications, especially in disaster scenarios. But a majority of these are focused solely on the search aspect of the problem. This dissertation proposes a conceptual design of a Semi-Autonomous Victim Extraction Robot (SAVER) capable of safe and effective unmanned casualty extraction, thereby reducing the risk to the lives of first responders. In addition, the proposed design addresses the limitations of existing state-of-the-art rescue robots specifically in the aspect of head and neck stabilization as well as fast and safe evacuation. One of the primary capabilities needed for effective casualty extraction is reliable navigation in unstructured terrain conditions. Autonomous navigation in unstructured terrain, particularly for systems with tracked locomotion mode involves unique challenges in path planning and trajectory tracking. The dynamics of robot-terrain interaction, along with additional factors such as slip experienced by the vehicle, slope of the terrain, and actuator limitations of the robotic system, need to be taken into consideration. To realize these capabilities, this dissertation proposes a hybrid navigation architecture that employs a physics engine to perform fast and accurate state expansion inside a graph-based planner. Tracked skid-steer systems experience significant slip, especially while turning. This greatly affects the trajectory tracking accuracy of the robot. In order to enable efficient trajectory tracking in varying terrain conditions, this dissertation proposes the use of an active disturbance rejection controller. The proposed controller is capable of estimating and counter acting the effects of slip in real-time to improve trajectory tracking. As an extension of the above application, this dissertation also proposes the use of support vector machine architecture to perform terrain identification, solely based on the estimated slip parameters. Combining all of the above techniques, an overall architecture is proposed to assist and inform tele-operation of tracked robotic systems in unstructured terrain conditions. All of the above proposed techniques have been validated through simulations and experiments in indoor and simple outdoor terrain conditions. / Doctor of Philosophy / This dissertation explores ways to improve autonomous navigation in unstructured terrain conditions, with specific applications to unmanned casualty extraction in disaster scenarios. Search and rescue applications often put the lives of first responders at risk. Using robotic systems for human rescue in disaster scenarios can keep first responders out of danger. To enable safe robotic casualty extraction, this dissertation proposes a novel rescue robot design concept named SAVER. The proposed design concept consists of several subsystems including a declining stretcher bed, head and neck support system, and robotic arms that conceptually enable safe casualty manipulation and extraction based on high-level commands issued by a remote operator. In order to enable autonomous navigation of the proposed conceptual system in challenging outdoor terrain conditions, this dissertation proposes improvements in planning, trajectory tracking control and terrain estimation. The proposed techniques are able to take into account the dynamic effects of robot-terrain interaction including slip experienced by the vehicle, slope of the terrain and actuator limitations. The proposed techniques have been validated through simulations and experiments in indoor and simple outdoor terrain conditions. The applicability of the above techniques in improving tele-operation of rescue robotic systems in unstructured terrain is also discussed at the end of this dissertation.

Positive systems, which carry the well known property of confining the state, output, and/or input variables to the nonnegative orphant, are of great practical importance, as the nonnegative property occurs quite frequently in numerous applications and in nature. These type of systems frequently occur in hydrology where they are used to model natural and artificial networks of reservoirs; in biology where they are used to describe the transportation, accumulation, and drainage processes of elements and compounds like hormones, glucose, insulin, and metals; and in stocking, industrial, and engineering systems where chemical reactions, heat exchanges, and distillation processes take place. The interest of this dissertation is in two key problems: positive stabilization and the positive servomechanism problem. In particular, this thesis outlines the necessary and sufficient conditions for the stabilization of positive linear time-invariant (LTI) systems using state feedback control, along with providing an algorithm for constructing such a stabilizing regulator. Moreover, the results on stabilization also encompass the two problems of the positive separation principle and stabilization via observer design. The second, and most emphasized, problem of this dissertation considers the positive servomechanism problem for both single-input single-output (SISO) and multi-input multi-output (MIMO) stable positive LTI systems. The study of the positive servomechanism problem focuses on the tracking problem of nonnegative constant reference signals for unknown/known stable SISO/MIMO positive LTI systems with nonnegative unmeasurable/measurable constant disturbances via switching tuning clamping regulators (TcR), linear quadratic clamping regulators (LTQcR), and ending with MPC control. Finally, all theoretical results on the positive servomechanism problem are justified via numerous experimental results on a waterworks system.

Positive systems, which carry the well known property of confining the state, output, and/or input variables to the nonnegative orphant, are of great practical importance, as the nonnegative property occurs quite frequently in numerous applications and in nature. These type of systems frequently occur in hydrology where they are used to model natural and artificial networks of reservoirs; in biology where they are used to describe the transportation, accumulation, and drainage processes of elements and compounds like hormones, glucose, insulin, and metals; and in stocking, industrial, and engineering systems where chemical reactions, heat exchanges, and distillation processes take place. The interest of this dissertation is in two key problems: positive stabilization and the positive servomechanism problem. In particular, this thesis outlines the necessary and sufficient conditions for the stabilization of positive linear time-invariant (LTI) systems using state feedback control, along with providing an algorithm for constructing such a stabilizing regulator. Moreover, the results on stabilization also encompass the two problems of the positive separation principle and stabilization via observer design. The second, and most emphasized, problem of this dissertation considers the positive servomechanism problem for both single-input single-output (SISO) and multi-input multi-output (MIMO) stable positive LTI systems. The study of the positive servomechanism problem focuses on the tracking problem of nonnegative constant reference signals for unknown/known stable SISO/MIMO positive LTI systems with nonnegative unmeasurable/measurable constant disturbances via switching tuning clamping regulators (TcR), linear quadratic clamping regulators (LTQcR), and ending with MPC control. Finally, all theoretical results on the positive servomechanism problem are justified via numerous experimental results on a waterworks system.

In this thesis work construction of the angular acceleration signal of a 2-DOF gimbal platform and use of this signal for improving the stabilization performance is aimed. This topic can be divided into two subtopics, first being the construction of angular acceleration and the second being the use of this information in a way to improve system performance. Both problems should be tackled in order to get satisfactory results. The most important output of this work is defined as the demonstration of the improvements obtained both theoretically and on experimental setup. Although the system to be studied is a two axis gimbal platform, the results obtained can be applied to other servo control problems. It is possible to define different performance criteria for a servo control problem and different techniques will be addressed with different control objectives. For this thesis work, the performance criterion is defined as the stabilization performance of the platform. As a result, disturbance rejection characteristics of the controller emerges as the main topic and methods for rejecting these disturbances such as the friction torques and externally applied moments are focused on throughout the studies. As expected, remarkable improvement is achieved as a result of the use of acceleration feedback.

This thesis presents decentralized model reference adaptive control techniques for systems with full-state feedback and systems with output feedback. The controllers are strictly decentralized, that is, each local controller uses feedback from only local subsystems and no information is shared between local controllers. The full-state feedback decentralized controller is effective for multi-input systems, where the dynamics matrix and control-input matrix are unknown. The decentralized controller achieves asymptotic stabilization and command following in the presence of sinusoidal disturbances with known spectrum. We present a construction technique of the reference-model dynamics such that the decentralized controller is effective for systems with arbitrarily large subsystem interconnections. The output-feedback decentralized controller is effective for single-input single-output subsystems that are minimum phase and relative degree one. The decentralized controller achieves asymptotic stabilization and disturbance rejection in the presence of an unknown disturbance, which is generated by an unknown Lyapunov-stable linear system.

Este trabalho apresenta um estudo de controladores repetitivos e ressonantes-repetitivos aplicados a fontes ininterruptas de energia (UPSs, do termo em inglês, Uninterruptible Power Supplies). Primeiramente, o desempenho dos controladores repetitivos é analisado a partir das exigências e dos procedimentos de testes definidos pela norma IEC 62040-3. A partir destes resultados, são discutidas as principais causas para o erro de seguimento de um sinal de referência e é avaliado o impacto de metodologias de correção aplicadas na função de transferência do controlador repetitivo. No contexto dos controladores ressonantes-repetitivos duas topologias são analisadas: a primeira é composta por um controlador ressonante sintonizado na frequência fundamental do sinal a ser seguido em paralelo com um controlador repetitivo sintonizado na mesma frequência; a segunda topologia é composta pelo mesmo paralelo entre os controladores ressonante e repetitivo, mas um filtro complementar é adicionado em série com o controlador repetitivo visando alocar a operação de cada controlador em faixas de frequências distintas. Então uma variação do controlador ressonante-repetitivo com filtro é proposta, na qual o filtro é utilizado para corrigir a fase do laço do controlador repetitivo e consequentemente aumentar a magnitude nas frequências de interesse. A partir desta estrutura proposta, uma representação no espaço de estados do sistema em malha fechada é obtida e o projeto do controlador é realizado através da solução de um problema de otimização com restrições na forma de Desigualdades Matriciais Lineares (do inglês, Linear Matrix Inequalities - LMIs). Resultados de simulação utilizando Matlab/PSIM são apresentados para demostrar a melhoria de desempenho do sistema com o controlador proposto. / This work presents a study of repetitive and resonant-repetitive controllers applied to Uninterruptible Power Supplies (UPSs). First, the performance of repetitive controllers is analyzed in terms of requirements and test procedures defined in the IEC 62040-3 standard. From these results the main causes of the reference tracking error are discussed and the impact of correction methodologies applied to repetitive controller transfer function is evaluated. In the context of the resonant-repetitive controllers two topologies are analyzed: the first is composed of a resonant controller tuned to the fundamental frequency of the signal to be followed in parallel with a repetitive controller tuned to the same frequency; the second topology is composed of the same parallel connection between the resonant and the repetitive controllers but a complementary filter is added in series with the repetitive controller aiming to restrict each controller action to different frequency bands. Then a variation of the resonant-repetitive controller with a filter is proposed, in which the filter is used to correct the phase of the repetitive controller loop and consequently increase the magnitude at the frequencies of interest. From this proposed structure, a state space model representing the closed loop system is obtained and the controller design is carried out by the solution of an optimization problem based on LMI (Linear Matrix Inequality) constraints. Simulation results in Matlab/PSIM are presented to demonstrate the improvement on system performance with the proposed controller.