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Thesis (M.S.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on April 15, 2008) Includes bibliographical references.

Robust control is an aspect of control theory which explicitly considers uncertainties and how they affect robust stability in the analysis and design of control decisions. A basic requirement for optimal robust guaranteed control in a real life scenario is the stabilization of systems in the presence of uncertainties or perturbations. In this thesis, the system uncertainties are embedded into a norm bounded uncertainty elements. The perturbation function is modelled as a class of nonlinear uncertainty influencing a neutral system with infinite delay. It is assumed to have delay in state and is input dependent; which implies the effect of control action can directly or indirectly influence the nonlinear perturbation function. In recognition of the fact that stability and controllability are fundamental in obtaining the optimal robust guaranteed cost control design for neutral functional integro-differential systems with infinite delays (NFDSID), total asymptotic stability results were developed using Razumikhin technique, unique properties of eigenvalues, and the uniform stability properties of the functional difference operator for neutral systems. The new results, obtained using Razumikhin’s technique, extend and complement basic stability results in neutral systems to NFDSID. Novel sufficient conditions were developed for the null controllability of nonlinear NFDSID when the controls are constrained. By exploring the knowledge gained through other controllability results; conditions are placed on the perturbation function. This guaranteed that, if the uncontrolled system is uniformly asymptotically stable, and the controlled system satisfies a full rank condition, then the control system is null controllable with constraint if it satisfies some algebraic conditions. The investigation of optimal robust guaranteed cost control method has resulted in a novel delay dependent stability criterion for a nonlinear NFDSID with a given quadratic cost function. The new design is based on a model transformation technique, Lyapunov matrix equation and Lyapunov-Razumikhin stability approach. The Lyapunov-Razumikhin technique is adopted for this investigation because it is considered more scalable for optimal robust guaranteed cost control design for NFDSID. It is demonstrated that a memory less feedback control can be synthesized appropriately to ensure: (i) the closed-loop systems robust stability, and (ii) guarantee that the closed-loop cost function value remains within a specified bound. The problem of designing the optimal guaranteed cost controller is also realized in terms of inequalities. The Lyapunov-Krasovskii method is used to obtain stability conditions in comparison to the Razumikhin method. This method leads to linear matrix inequality (LMI) for the delay-independent case which is known to be conservative. To illustrate the potential practical applicability of the theoretical results; a cascade connection of two fully filled chemical solution mixers, and an integrated lossless transmission line which has a capacitance, inductance, resistance and terminated by a nonlinear function are modelled. A neutral control system model for NFDSID is derived from each of these systems. Simulation studies on the transmission line system confirm the theoretical robust stability results. The new results and methods of analysis expounded in this thesis are explicit, computationally more effective than existing ones and will serve as a working document for the present and future generations in the comity of researchers and industries alike.

This thesis is concerned with the choice of the uncertainty structure in robust control problems. This choice affects the optimization carried out to obtain a robust feedback controller, and determines how robust a feedback loop will be to discrepancies in the parameters or dynamics of the plant model. Firstly, it presents readily applicable distance measures, robust stability margins and associated robust stability and robust performance theorems for several commonly used uncertainty structures for linear time-invariant systems (additive, multiplicative, inverse multiplicative, inverse additive, right coprime factor uncertainty).Secondly, the thesis discusses the robust stabilization problem for linear plants with a coprime factor uncertainty structure where the coprime factors of the plant are not necessarily normalized. The problem considered here is a generalization of the normalized coprime factor robust stabilization problem. It is shown that the minimum of the ratio of (non-normalized) coprime factor distance over (non-normalized) coprime factor robust stability margin, termed the robustness ratio, is an important bound in robust stability and performance results. A synthesis method is proposed which maintains a lower bound on the normalized coprimefactor robust stability margin (as a proxy for nominal performance) while also robustly stabilizing a particular perturbed plant, potentially far outside a normalized coprime factor neighbourhood of the nominal plant. The coprime factor synthesis problem is also considered in a state-space framework. It is shown that it admits a simple and intuitive controller implementation in observer form. Via the solution of one Riccati equation, an optimally robust observer gain L can be obtained for any state-feedback matrix F. One particular method for obtaining a suitable F is also proposed, ensuring that the feedback loop is particularly robust to uncertain lightly damped poles and zeros.

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<p>Power generation using wind turbines is a highly researched control field.</p><p>Many control designs have been proposed based on continuous-time models</p><p>like PI-control, or state observers with state feedback but without special</p><p>regard to robustness to model uncertainties. The aim of this thesis was to</p><p>design a robust digital controller for a wind turbine.</p><p>The design was based on a discrete-time model in the polynomial framework</p><p>that was derived from a continuous-time state-space model based on</p><p>data from a real plant. A digital controller was then designed by interactive</p><p>pole placement to satisfy bounds on sensitivity functions.</p><p>As a result the controller eliminates steady state errors after a step</p><p>response, gives sufficient damping by using dynamical feedback, tolerates</p><p>changes in the dynamics to account for non linear effects, and avoids feedback</p><p>of high frequency un modeled dynamics.</p>

This thesis presents a detailed design, calibration, and control of a modular and reconfigurable robot (MRR) system. A MRR system not only includes modular mechanical hardware, but also modular electrical hardware, control algorithms and software. Also, those modular components can be easily constructed into various manipulator configurations to accomplish a wider range of tasks. MRRs represent the next generation of industrial manipulators that cope with the transition from mass to customer-oriented production. The main contributions of this thesis are: 1) mechanical design and calibration of multi-input multi-output (MIMO) joint modules of MRR, and 2) control design to handle multiple configuration and overcome disturbance due to dynamics uncertainty. From the mechanical design point of view, this thesis presents two main topics: 1) each joint is not only modularly designed, but also has multiple-input multiple-output (MIMO) physical connection ports, which contributes to the concept of reconfigurability. Strictly speaking, single-input single-output (SISO) modular joint falls into the category of modular manipulator, and the robot reconfiguration is achieved by integrating different types of modules. For example, with single revolute MIMO joint module, both rotary and pivotal joint can be generated. On the other hand, if you would like to switch from rotary movement to pivotal movement with a SISO joint module, using another pivotal joint module is the only way to achieve this goal, and 2) for precise automation application, joints and links should be accurately connected and oriented when reconfigured. Our proposed modular joint has four connection ports which can be configured as either a rotary joint or a pivotal joint. In addition, key and keyway connection mechanism provides high accuracy in positioning the link onto the joint. Therefore, this structure reduces or eliminates MRRs system calibration time when reconfigured. Furthermore, zero link offset when used as a pivotal joint increases the robot dexterity, maximizes the reachability, and results in kinematics simplicity. The main challenge in the control of an MRR system with harmonic drives (HD) is the significant uncertainties due to friction, unmodelled dynamics, varying payload, gravitation, dynamic coupling between motions of joints, and the configuration changes. In order to compensate all unpredictable effects, we proposed a decentralized saturation-type robust control scheme based on direct-Lyapunov method and backstepping techniques. To better understand the system dynamics behavior, the HD flexspline compliance and friction calibration and results are also provided. The results are used for controller design. The proposed controller is verified through both computer simulation and experimental analysis.

This thesis presents a detailed design, calibration, and control of a modular and reconfigurable robot (MRR) system. A MRR system not only includes modular mechanical hardware, but also modular electrical hardware, control algorithms and software. Also, those modular components can be easily constructed into various manipulator configurations to accomplish a wider range of tasks. MRRs represent the next generation of industrial manipulators that cope with the transition from mass to customer-oriented production. The main contributions of this thesis are: 1) mechanical design and calibration of multi-input multi-output (MIMO) joint modules of MRR, and 2) control design to handle multiple configuration and overcome disturbance due to dynamics uncertainty. From the mechanical design point of view, this thesis presents two main topics: 1) each joint is not only modularly designed, but also has multiple-input multiple-output (MIMO) physical connection ports, which contributes to the concept of reconfigurability. Strictly speaking, single-input single-output (SISO) modular joint falls into the category of modular manipulator, and the robot reconfiguration is achieved by integrating different types of modules. For example, with single revolute MIMO joint module, both rotary and pivotal joint can be generated. On the other hand, if you would like to switch from rotary movement to pivotal movement with a SISO joint module, using another pivotal joint module is the only way to achieve this goal, and 2) for precise automation application, joints and links should be accurately connected and oriented when reconfigured. Our proposed modular joint has four connection ports which can be configured as either a rotary joint or a pivotal joint. In addition, key and keyway connection mechanism provides high accuracy in positioning the link onto the joint. Therefore, this structure reduces or eliminates MRRs system calibration time when reconfigured. Furthermore, zero link offset when used as a pivotal joint increases the robot dexterity, maximizes the reachability, and results in kinematics simplicity. The main challenge in the control of an MRR system with harmonic drives (HD) is the significant uncertainties due to friction, unmodelled dynamics, varying payload, gravitation, dynamic coupling between motions of joints, and the configuration changes. In order to compensate all unpredictable effects, we proposed a decentralized saturation-type robust control scheme based on direct-Lyapunov method and backstepping techniques. To better understand the system dynamics behavior, the HD flexspline compliance and friction calibration and results are also provided. The results are used for controller design. The proposed controller is verified through both computer simulation and experimental analysis.