Dissertations / Theses on the topic 'Varying control'

The tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying frequency conditions. These contributions can be organized as follows: One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an integrated controller design which assures closed-loop stability under such conditions. In this thesis two design methodologies are presented, which assure stability of the repetitive control system working under varying sampling period for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy. On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the system more appropriate for applications where signals have only odd-harmonic components, as in power electronics systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery once the system goes out of saturation. The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads. These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current harmonics and reactive power compensation.

High fidelity, compliant robot control requires a sufficiently accurate dynamics model. Often though, it is not possible to obtain a dynamics model sufficiently accurately or at all using analytical methods. In such cases, an alternative is to learn the dynamics model from movement data. This thesis discusses the problems specific to dynamics learning for control under nonstationarity of the dynamics. We refer to the cause of the nonstationarity as the context of the dynamics. Contexts are, typically, not directly observable. For instance, the dynamics of a robot manipulator changes as the robot manipulates different objects and the physical properties of the load – the context of the dynamics – are not directly known by the controller. Other examples of contexts that affect the dynamics are changing force fields or liquids with different viscosity in which a manipulator has to operate. The learned dynamics model needs to be adapted whenever the context and therefore the dynamics changes. Inevitably, performance drops during the period of adaptation. The goal of this work, is to reuse and generalize the experience obtained by learning the dynamics of different contexts in order to adapt to changing contexts fast. We first examine the case that the dynamics may switch between a discrete, finite set of contexts and use multiple models and switching between them to adapt the controller fast. A probabilistic formulation of multiple models is used, where a discrete latent variable is used to represent the unobserved context and index the models. In comparison to previous multiple model approaches, the developed method is able to learn multiple models of nonlinear dynamics, using an appropriately modified EM algorithm. We also deal with the case when there exists a continuum of possible contexts that affect the dynamics and hence, it becomes essential to generalize from a set of experienced contexts to novel contexts. There is very little previous work on this direction and the developed methods are completely novel. We introduce a set of continuous latent variables to represent context and introduce a dynamics model that depends on this set of variables. We first examine learning and inference in such a model when there is strong prior knowledge on the relationship of these continuous latent variables to the modulation of the dynamics, e.g., when the load at the end effector changes. We also develop methods for the case that there is no such knowledge available. Finally, we formulate a dynamics model whose input is augmented with observed variables that convey contextual information indirectly, e.g., the information from tactile sensors at the interface between the load and the arm. This approach also allows generalization to not previously seen contexts and is applicable when the nature of the context is not known. In addition, we show that use of such a model is possible even when special sensory input is not available by using an instance of an autoregressive model. The developed methods are tested on realistic, full physics simulations of robot arm systems including a simplistic 3 degree of freedom (DOF) arm and a simulation of the 7 DOF DLR light weight robot arm. In the experiments, varying contexts are different manipulated objects. Nevertheless, the developed methods (with the exception of the methods that require prior knowledge on the relationship of the context to the modulation of the dynamics) are more generally applicable and could be used to deal with different context variation scenarios.

This dissertation addresses fundamental theoretical problems relevant to flight control for aerial vehicles and weapons in highly uncertain dynamical environment. The approach taken in this dissertation is the L1 adaptive control, which is elaborated from its design perspective for output feedback solution and is extended to time-varying reference systems to support augmentation of gain-scheduled baseline controllers. Compared to conventional adaptive controllers, L1 control has the following advantages: i) it has guaranteed uniformly bounded transient response for system's both signals, input and output; ii) it enables fast adaptation while maintains a bounded away from zero time-delay margin. The proposed adaptive control approach can recover the nominal performance of the flight control systems in the presence of rapid variation of uncertainties. Furthermore, the benefit of L1 adaptive control is its promise for development of theoretically justified tools for Verification and Validation (V&V) of adaptive systems. Adaptive control for uncertain systems usually needs to handle two types of uncertainties: matched and unmatched uncertainties. Both of these two uncertainties will appear in practical flight control problems. In this dissertation, adaptive approaches which can compensate for these two types of uncertainties will be discussed respectively. Two architectures of L1 adaptive control, namely L1 state feedback adaptive control and L1 output feedback adaptive control, are studied. The state feedback adaptive control is applied for compensation of matched uncertainties. Although the state feedback scheme is capable of handling certain type of unmatched uncertainties, such approach is not explored in this dissertation. On the other hand, the output feedback approach is mainly aimed to solve problems in the presence of unmatched uncertainties. The dissertation first discusses the state feedback L1 adaptive control for time-invariant reference systems. The adaptive controller is designed to augment an existing baseline controller. The closed loop system of the plant and the baseline controller is time-invariant. This closed loop system, which is a Linear Time Invariant (LTI) system, determines the dynamics of the reference system. The adaptive feedback can compensate for nonlinear state- and time-dependent uncertainty with uniformly bounded transient response. In this dissertation we discuss the Multi-Input Multi-Output (MIMO) extension of the method. Two flight control examples,Unmanned Combat Aerial Vehicle (UCAV) and Aerial Refueling Autopilot, are considered in the presence of nonlinear uncertainties and control surface failures. The L1 adaptive controller without any redesign leads to scaled response for system's both signals, input and output, dependent upon changes in the initial conditions, system parameters and uncertainties. The time-delay margin analysis for these two examples verifies the theoretical claims. Next, the output feedback approach is studied. The adaptive output feedback controller can be applied to reference systems that do not verify the Strict Positive Real (SPR) condition for their input-output transfer function. In this dissertation, specific design guidelines are presented that render the approach suitable for practical applications. A missile autopilot design example is given to demonstrate the benefits of the design approach. Finally, the L1 state feedback adaptive controller is extended to time-varying reference systems. The adaptive controller intends to augment a gain-scheduled baseline controller. The reference system, which is determined by the closed loop system of the plant and the baseline gain-scheduled controller, is time-varying. The adaptive controller with time-varying reference system is proved to have guaranteed performance bounds similar to those obtained for the case of linear time-invariant reference systems. With this result, the aerial refueling application can be extended to a complete scenario, which includes a racetrack maneuver for an aircraft. The concluding chapter discusses the challenging issues for future research.
Ph. D.

With the current climate crisis with the global temperature increasing due to fossil fuels being used there are big investments in green energy. Wind power is a good alternative to fossil fueled power and already has a widespread use. One of the problems with wind poweris control and keeping the grid frequency stable during peaks and lows of power generation. In this master thesis there is a goal to implement a system which can regulate wind mills while always trying to use as much wind power as possible. A model was built in Matlab to represent the final product which was translated into a SCADA system. A fully integrated communication from SCADA computer to PLC to IED to wind mill and back was built. The simulation in the SCADA system gave satisfactory result where the wind power wasutilized to the maximum, and other conditions met. The laboratory experiment with an Arduino represented as the wind mill lacked in communication and the model did not achieveperfect results in every case. There is future work to be done, improved communication, additional or alternative automatic control and creating a bigger system with several powerproducers integrated.

Varying missile configurations may create uncertainty for a missile control algorithm developed with linear control theory, for instance the control system performance requirements may not be satisfied anymore. Missile configuration may change during the missile design period due to variations in subsystem locations, subsystem weights and missile geometry. Likewise, burning propellant, deployment of aerodynamic surfaces and wings with varying sweep angle can be considered as in-flight missile configuration changes. This thesis study addresses development and analysis of an adaptive missile control algorithm to account for the uncertain effects caused by varying missile configuration. Control algorithms, designed using pole placement, are augmented with adaptive neural networks. The resulting controller is a type of model reference adaptive controller. Adaptation characteristics of the augmented control algorithms are investigated to changing center of pressure location and missile geometry. Analyses are performed for three different missile configurations using simulation.

L'anàlisi i el disseny dels sistemes de control de temps real és una tasca complexa, que requereix la integració de dues disciplines, la dels sistemes de control i la dels sistemes de temps real. Tradicionalment però, els sistemes de control de temps real s'han dissenyat diferenciant, de forma independent, dues fases, primerament el disseny del controlador, i després, la seva implementació en un computador. Això ha desembocat en solucions no òptimes tant en termes de planificabilitat del sistema i com en el rendiment dels sistemes controlats.
Normalment, els mètodes i models de la teoria de control de temps discret no consideren durant la fase de disseny dels controladors les limitacions que es puguin derivar de la implementació. En la fase de disseny s'assumeix que els algorismes de control s'executaran en processadors dedicats i que els processadors seran prou ràpids i determinístics per no haver-se de preocupar del comportament temporal que aquests algorismes de control tindran en temps d'execució. Tot i així, quan els recursos - per exemple, processadors - són limitats, apareixen variacions temporals en l'execució dels algorismes de control. En concret, en els sistemes de planificació de tasques de temps real, un algorisme de control s'implementa en una tasca periòdica caracterizada per restriccions temporals estàndards com períodes i terminis. És sabut que, en la planificació de tasques de temps real, les variacions temporals en l'execució d'instàncies de tasques és permesa sempre i quan les restriccions de planificabilitat estiguin garantides. Aquesta variabilitat per tasques de control viola l'estricte comporament temporal que la teoria de control de temps discret pressuposa en l'execució dels algorismes de control.
Això té dos efectes negatius: la variabilitat temporal en l'execució de les tasques de control degrada el rendiment del sistema controlat, fins i tot causant inestabilitat. A més, si es minimitza la probabilitat d'aparició d'aquesta variabilitat en l'execució de les tasques de control a través d'especificacións més limitants, la planificabilitat del conjunt de tasques del sistema disminueix.
Cal tenir en compte que la teoria de control no dóna directrius de com incloure, en la fase de disseny dels controladors, aquesta variabilitat en l'execució de tasques que es deriva de les limitacions d'implementació. A més, la teoria de sistemes de temps real no proporciona ni models de tasques ni restriccions temporals que puguin ser usats per garantir l'execució periòdica, i sense variabilitats temporals, de tasques sense sobrelimitar la planificabilitat dels sistema.
En aquesta tesi es presenta un entorn integrat i flexible de planificació i de control per a l'anàlisi i el disseny de sistemes de control de temps real que dóna solucions als problemes esmentats anteriorment (baixa planificabilitat en el sistema i degradació del rendiment dels sistemes controlats). Mostrem que, fusionant les activitats de la comunitat de temps real amb les de la comunitat de control, això és, integrant la fase de disseny de controladors amb la fase d'implementació en un computador, es millora tant la planificabilitat del sistema com el rendiment dels sistemes controlats.
També es presenta una nova aproximació al disseny de controladors de temps discret que té en compte les limitacions derivables de la implementació i relaxa les tradicionals assumpcions dels controladors de temps discret (mostreig i actuació equidistants). En lloc d'especificar, en la fase de disseny, únics valors pel període de mostreig i pel retard temporal, especifiquem un conjunt de valors tant per l'un com per l'altre. Aquesta nova aproximació al disseny de controladors es basa en la idea d'ajustar, en temps d'execució, els paràmetres del controlador d'acord amb el comportament temporal específic de la implementació (per exemple, d'acord amb la variabilitat en l'execució de les tasques deguda a la planificació). Els llaços de control resultants esdevenent sistemes variants en el temps, amb mostreig irregular i retards temporals variables. Per a aquests sistemes, i utilitzant formulació en l'espai d'estat, presentem una anàlisi completa d'estabilitat, així com l'anàlisi de la resposta.
També mostrem com, a partir de les propietats temporals d'aquesta nova aproximació al disseny de controladors, podem obtenir restriccions temporals més flexibles per a les tasques de control. Les restriccions temporals estàndards, per a les tasques periòdiques en els sistemes de temps real, són constants per a totes les instàncies d'una tasca. Això és, només un sol valor per a una restricció és aplicable a totes les instàncies. Les noves restriccions temporals que presentem per a tasques de control no forcen a aplicar un valor específic, sinó que permeten aplicar valors diferents a cada instància d'una tasca, tenint en compte, per exemple, la planificabilitat d'altres tasques.
Aquestes restriccions temporals flexibles per a tasques de control ens permeten obtenir planificacions viables i sistemes de control estables a partir de conjunts de tasques (incloent tasques de control i d'altres) que no eren planificables en usar mètodes estàndards tant de planificació de temps real com de disseny de controladors. A més, associant informació de rendiment de control a aquestes noves restriccions temporals per a tasques de control, mostrem com podem prendre decisions de planificació que, anant més enllà de complir amb les restriccions temporals, milloren el rendiment dels sistemes controlats quan aquests sofreixen perturbacions.
The analysis and design of real-time control systems is a complex task, requiring the integration and good understanding of both control and real-time systems theory. Traditionally, such systems are designed by differentiating two separate stages: first, control design and then its computer implementation, leading to sub-optimal solutions in terms of both system schedulability and controlled systems performance.
Traditional discrete-time control models and methods consider implementation constraints only to a very small extent. This is due to the fact that in the control design stage, controllers are assumed to execute in dedicated processors and processors are assumed to be fast and deterministic enough not to worry about the timing that the controlling activities may have on the implementation. However, when resources (e.g., processors) are limited, timing variations in the execution of control algorithms occur. Specifically, a control algorithm in traditional real-time scheduling is implemented as a periodic task characterized by standard timing constraints such as period and deadline. In real-time scheduling, timing variations in task instance executions (i.e., jitters) are allowed as far as the schedulability constraints are preserved. Consequently, the resulting jitters for control task instances do not comply with the strict timing demanded by discrete-time control theory.
This has two pervasive effects: the presence of jitters for control tasks degrades the controlled system performance, even causing instability. On the other hand, minimizing the likelihood of jitters for control tasks by over-constraining the control task specification reduces the schedulability of the entire task set.
It is worth mentioning that control theory offers no advice on how to include, into the design of controllers, the effects that implementation constraints have in the timing of the control activities (e.g., scheduling inherent jitters). Also, real-time theory lacks task models and timing constraints that can be used to guarantee a periodic task execution free of jitters without over-constraining system schedulability.
In this thesis we present a flexible integrated scheduling and control analysis and design framework for real-time control systems that solves the problems outlined above: poor system schedulability and controlled systems performance degradation. We show that by merging the activities of the control and real-time communities, that is, by integrating control design with computer implementation, both system schedulability and controlled systems performance are improved.
We present a new approach to discrete-time controller design that takes implementation constraints into account and relaxes the equidistant sampling and actuation assumptions of traditionally designed discrete-time controllers. Instead of specifying a single value for the sampling period and a single value for the time delay at the design stage, we specify a set of values for both the sampling period and for the time delay. This new approach for the controller design relies on the idea of adjusting controller parameters at run time according to the specific implementation timing behaviour, i.e., scheduling inherent jitters. The resulting closed-loop systems are based on irregularly sampled discrete-time system models with varying time delays. We have used state space formulation to present a complete stability and response analysis for such models.
We also show how to derive more flexible timing constraints for control tasks by exploiting the timing properties imposed by this new approach to discrete-time controller design. Real-time scheduling standard timing constraints for periodic tasks are constant for all task instances. That is, a single value of a constraint (e.g., period or deadline) holds for all task instances. Our flexible timing constraints for control tasks do not set specific values. Rather, they provide ranges and combinations to choose from (at each control task instance execution), taking into account, for example, schedulability of other tasks.
That is, these more flexible timing constraints for control tasks allow us to obtain feasible schedules and stable control systems from task sets (including control and non-control tasks) that are not feasible using traditional real-time scheduling and discrete-time control design methods. In addition, by associating control performance information with these new timing constraints for control tasks, we show how scheduling decisions, going beyond meeting timing constraints, can be taken to improve the performance of the controlled systems when they are affected by perturbations.

The focus of this study is to be able to control the air-to-surface missile throughout the entire flight, with emphasis on the propulsion phase to increase the impact range of the missile. A major difficulty in controlling the missile during the propulsion phase is the important change in mass of the missile. This results in sliding the center of gravity (cg) point and changing inertias. Moreover, aerodynamic coefficients and stability derivatives are not assumed to be constant at predetermined ranges
conversely, they depend on Mach number, angle of attack, and side slip angle. Consequently, as the change of missile mass, cg point, inertia terms, and stability and aerodynamic coefficients come together apart from flight operation stages, a great number of points need to be taken into account when designing the controller. This makes controlling the missile all the more complicated. In this thesis, first the equations of motion are derived, in which, mass of the missile is not assumed constant. Thus, not only the variation of mass but also the variation of inertias is incorporated in the equations of motion. From the derived v equations of motion, a nonlinear inverse dynamics controller that can achieve desired guidance for a conceptually developed air-to-surface missile has been designed, tested and verified for a modeled missile with six degrees of freedom. For brevity of the study, conceptual design and aerodynamic calculations are not given in detail. Nevertheless, improvements for conceptual design are suggested. As a result, it is shown that the controller works efficiently: the missile is able to hit the target with less than 12 m circular error of probability (CEP). Finally, studies and improvements are proposed.

This dissertation studies the model reduction and distributed control problems for interconnected systems, i.e., systems that consist of multiple interacting agents/subsystems. The study of the analysis and synthesis problems for interconnected systems is motivated by the multiple applications that can benefit from the design and implementation of distributed controllers. These applications include automated highway systems and formation flight of unmanned aircraft systems. The systems of interest are modeled using arbitrary directed graphs, where the subsystems correspond to the nodes, and the interconnections between the subsystems are described using the directed edges. In addition to the states of the subsystems, the adopted frameworks also model the interconnections between the subsystems as spatial states. Each agent/subsystem is assumed to have its own actuating and sensing capabilities. These capabilities are leveraged in order to design a controller subsystem for each plant subsystem. In the distributed control paradigm, the controller subsystems interact over the same interconnection structure as the plant subsystems. The models assumed for the subsystems are linear time-varying or linear parameter-varying. Linear time-varying models are useful for describing nonlinear equations that are linearized about prespecified trajectories, and linear parameter-varying models allow for capturing the nonlinearities of the agents, while still being amenable to control using linear techniques. It is clear from the above description that the size of the model for an interconnected system increases with the number of subsystems and the complexity of the interconnection structure. This motivates the development of model reduction techniques to rigorously reduce the size of the given model. In particular, this dissertation presents structure-preserving techniques for model reduction, i.e., techniques that guarantee that the interpretation of each state is retained in the reduced order system. Namely, the sought reduced order system is an interconnected system formed by reduced order subsystems that are interconnected over the same interconnection structure as that of the full order system. Model reduction is important for reducing the computational complexity of the system analysis and control synthesis problems. In this dissertation, interior point methods are extensively used for solving the semidefinite programming problems that arise in analysis and synthesis.
Ph. D.
The work in this dissertation is motivated by the numerous applications in which multiple agents interact and cooperate to perform a coordinated task. Examples of such applications include automated highway systems and formation flight of unmanned aircraft systems. For instance, one can think of the hazardous conditions created by a fire in a building and the benefits of using multiple interacting multirotors to deal with this emergency situation and reduce the risks on humans. This dissertation develops mathematical tools for studying and dealing with these complex systems. Namely, it is shown how controllers can be designed to ensure that such systems perform in the desired way, and how the models that describe the systems of interest can be systematically simplified to facilitate performing the tasks of mathematical analysis and control design.

The full abstract for this thesis is available in the body of the thesis, and will be available when the embargo expires.
Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate

The dynamic response characteristics of modern unmanned aerial vehicles (UAVs) are highly nonlinear and vary substantially with flight conditions due to their reduced dimensions compared to normal aircraft. In this thesis, design frameworks that are based on parameter dependent Lyapunov functions (PDLFs) are developed for UAV flight control systems. These design frameworks or procedures can systematically deal with aircraft systems with nonlinear and parameter dependent dynamics, and uncertainty in the mathematical models. To this end, we analyse robust stability and performance of LPV systems and present two LPV controller design methods using the PDLF approach: Two-Degree-of-Freedom (2DoF) and loop shaping with coprime factorisation. We formulate and solve the control problem for an LPV plant with measurable parameters and an output feedback structure. The solvability conditions are reduced to LMIs and can be solved approximately using finite-dimensional convex programming. A parameter dependent performance approach is used in a 2DoF/PDLF design and constitutes a flexible generalisation for calibrations of local performance. In loop shaping/PDLF design, a left coprime factorisation is derived by H2 filtering, and then a loop shaping design is implemented in the PDLF framework. We also incorporate pole placement constraints into the LMI synthesis to improve controller performance. To be able to use the robust gain-scheduling synthesis results, an LPV model of the UAV is developed and validated. The gain scheduling controller design of longitudinal/lateral-directional dynamics of the UAV is illustrated in the design example. It is shown that a flight control system can be built with satisfactory robust stability and performance.

In response to environmental concerns, demands for improved energy efficiency and a desire to create a more pleasant working environment; building designers are looking for ways to make better use of natural light. However, whilst natural light is both free and non-polluting, it can also produce high levels of visual contrast and glare, and unwanted heat. Most current design techniques estimate the natural internal illumination that results from an overcast sky; they do not include the contribution by direct sunlight entering the space, which is often the source of unwanted characteristics. Whilst a sophisticated computer ray-tracing program (RADIANCE) exists that can predict the full range of natural illumination, each prediction can take several minutes (or longer) to calculate. The time required to examine how a natural lighting design behaves over a typical year can therefore be prohibitive. Techniques for estimating the illumination provided by artificial lights also predict illumination under static conditions. Current techniques are therefore unsuitable for examining the dynamic behaviour of a lighting design, which links the automatic control of artificial lights to the changing levels of natural light. The aim of this research was to develop a computer based lighting design tool that overcomes these limitations. Based on the calculation of lighting coefficients, the numeric relationship between the luminance of light sources and the illuminance they produce, the Dynamic Lighting System (DLS) is able to calculate time-varying illuminance from a combination of natural light and artificial lights controlled by a lighting control system. The DLS has been written using the platform independent programming language Java. It is therefore able to run unaltered on most computer platforms, although in practice is limited to platforms on which the ray-tracing program RADIANCE will run, as RADIANCE is used to calculate coefficients. The DLS has been tested by comparing predicted levels of illuminance with levels measured in a test room under real sky conditions. These comparisons showed a high degree of correlation, but with a few large discrepancies. Possible causes of these discrepancies are offered and suggestions made about how they might be eliminated.

For variable-speed wind energy conversion systems, control objectives may be different in partial and full load regions (or in low and high wind speed regions). Typical control objectives are to maximize the energy capture in low wind speeds, and to maintain the generated power and the rotational turbine speed within safety limits during high wind speeds. In such a case, it is difficult to design a single robust controller covering both partial load and full load conditions. This paper presents a systematic switching control method for a variable-speed variable-pitch wind turbine over a wide wind speed region. The whole framework is based on the linear parameter-varying (LPV) control theory, which is an extension of robust control for linear systems to nonlinear ones.

Two LPV controllers are designed, each suitable in a different wind speed region. A hysteresis switching logic is applied to guarantee the stability when the switching event occurs between the two controllers. Nonlinear simulations are conducted to demonstrate the proposed control scheme.

On considère la synthèse de la commande basée sur un asservissement affecté par des retards. L’approche utilisée repose sur des méthodes ensemblistes. Une partie de cette thèse est consacrée à une conception de commande active pour la compensation des retards qui apparaissent dans des canaux de communication entre le capteur et correcteur. Ce problème est considéré dans une perspective générale du cadre de commande tolérante aux défauts où des retards variés sont vus comme un mode particulier de dégradation du capteur. Le cas avec transmission de mesure retardée pour des systèmes avec des capteurs redondants est également examiné. Par conséquent, un cadre unifié est proposé afin de régler le problème de commande basé sur la transmission des mesures avec retard qui peuvent également être fournies par des capteurs qui sont affectés par des défauts soudains.Dans la deuxième partie le concept d’invariance positive pour des systèmes linéaires à retard à temps discret est exposé. En ce qui concerne l’invariance pour cette classe des systèmes dynamiques, il existe deux idées principales. La première approche repose sur la réécriture d’un tel système dans l’espace d’état augmenté et de le considérer comme un système linéaire. D’autre part, la seconde approche considère l’invariance dans l’espace d’état initial. Cependant, la caractérisation d’un tel ensemble invariant est encore une question ouverte, même pour le cas linéaire. Par conséquent, l’objectif de cette thèse est d’introduire une notion générale d’invariance positive pour des systèmes linéaires à retard à temps discret. Également, certains nouveaux éclairages sur l’existence et la construction pour les ensembles invariants positifs robustes sont détaillés. En outre, les nouveaux concepts d’invariance alternatives sont décrits
We considered the process regulation which is based on feedback affected by varying delays. Proposed approach relies on set-based control methods. One part of the thesis examines active control design for compensation of delays in sensor-to controller communication channel. This problem is regarded in a general perspective of the fault tolerant control where delays are considered as a particular degradation mode of the sensor. Obtained results are also adapted to the systems with redundant sensing elements that are prone to abrupt faults. In this sense, an unified framework is proposed in order to address the control design with outdated measurements provided by unreliable sensors.Positive invariance for linear discrete-time systems with delays is outlined in the second part of the thesis. Concerning this class of dynamics, there are two main approaches which define positive invariance. The first one relies on rewriting a delay-difference equation in the augmented state-space and applying standard analysis and control design tools for the linear systems. The second approach considers invariance in the initial state-space. However, the initial state-space characterization is still an open problem even for the linear case and it represents our main subject of interest. As a contribution, we provide new insights on the existence of the positively invariant sets in the initial state-space. Moreover, a construction algorithm for the minimal robust D-invariant set is outlined. Additionally, alternative invariance concepts are discussed

Most of the methodologies dealing with viscoelastic damping focused exclusively on the frequency dependence behavior of the material. Only a few looked into the temperature dependence of the model, although none of them has taken a more serious investigation on the control design subjected to temperature disturbances. The general purpose of this work is to develop and investigate structures with damping modeled by means of internal variables. Thermodynamic principles are used to develop models, which are based on a generalized Maxwell element. Initially, studies are conducted to verify how the method of reduced variables can be applied to account for temperature dependence, as well as to evaluate the number of internal variables necessary for good accuracy of material properties representation. Lumped and finite element models are characterized and validated against other methods. A constrained layer damping model is experimentally validated for many temperatures. A control analysis is carried out on the models with the purpose to identify the role played by the internal variables on the control design. The results show that moving the internal poles is very expensive in terms of control energy. It is also shown that it is not always possible to eliminate the internal coordinates in the reduced order model if the system is highly damped. The problem of having the internal pole moved is solved by applying partial pole placement. This technique shows similar performance as compared to the linear quadratic Gaussian regulator. The control designs are implemented and it is shown that good regulation can be achieved for a fixed temperature. It is further shown that the controller will lose its performance when the model is subjected to temperature changes. To investigate the behavior of the model under different temperatures, a linear temperature-dependent model is developed, which clearly shows how the temperature affects the time response of the model. This model is used as a baseline to develop an adaptive and a time-varying controllers. With the aid of the shift factor, the eigenvalue variation with temperature is used as a time-varying function in the design. The results show that good track performance and regulation can be achieved with a control law that is capable of compensating for temperature variations.
Ph. D.

Le but de cette thèse est le développement et l'application de différentes méthodes de contrôle pour le contrôle actif du bruit en présence de perturbations incertaines et variables dans le temps. Une conception de contrôleur basée sur un modèle est appliquée et une méthodologie complète pour l'identification du modèle est introduite. Dans ce contexte, un banc d'essai reconfigurable basé sur un silencieux de bruit pour gaines a été conçu et construit. Il est entièrement équipé de capteurs et d'actionneurs afin de tester les algorithmes développés dans diverses configurations.Un schéma contre-réaction feedback est établi pour les cas où des perturbations en bande étroite sont présentes. Sur la base du Principe du Modèle Interne, des contrôleurs linéaires fixes et robustes sont conçus et comparés avec le contrôleur par contre-réaction adaptatif proposé en utilisant un paramétrage Youla-Kučera. Dans le cas où les perturbations présentent des caractéristiques à large bande, un système de rétroaction feedforward est proposé. Cette approche nécessite l'introduction d'un capteur supplémentaire qui crée un couplage positif interne, nécessitant une conception spécifique afin d'éviter d'éventuelles instabilités. Dans ce cadre, les compensateurs adaptatifs IIR et FIR, ainsi que les compensateurs adaptatifs avec paramétrage Youla-Kučera sont comparés.La qualité des modèles estimés pour la conception des contrôles ainsi que les capacités de contrôle elles-mêmes sont illustrées par les performances expérimentales des contrôleurs mis en œuvre sur le banc d'essai pour diverses conditions de configuration des tests
The aim of this thesis is the development and application of different control methods for Active Noise Control in the presence of uncertain and time-varying disturbances. A model-based controller design is applied and a full methodology for model identification is introduced. In this context, a reconfigurable test bench based on a noise silencer for ducts has been designed and built. It is fully equipped with sensors and actuators in order to test the developed algorithms in diverse configurations.A feedback scheme is established for the case where narrowband disturbances are present. Based on the Internal Model Principle, fixed linear and robust controllers are designed and compared with the proposed adaptive feedback controller using a Youla-Kučera parametrization. For the case where disturbances have broadband characteristics, a feedforward scheme is proposed. This approach requires the introduction of an additional sensor which creates an internal positive coupling, requiring a specific design in order to avoid possible instabilities. In this framework, Infinite (IIR) and Finite (FIR) Impulse Responses adaptive feedforward compensators, as well as Youla-Kučera parametrized adaptive feedforward compensators are compared.The estimated models' quality for control design as well as the control capabilities themselves are illustrated by the experimental performance of the controllers implemented on the test bench for various tests setup conditions

A mathematical model of a small fixed-wing aircraft was developed through application of parameter estimation techniques to simulated flight test data. Multiple controllers were devised based on this model for path following, including a self-scheduled linear parameter-varying (LPV) controller with path curvature as a scheduling parameter. The robustness and performance of these controllers were tested in a rigorous MATLAB simulation environment that included steady winds and gusts, measurement noise, delays, and model uncertainties. The linear controllers designed within were found to be robust to the disturbances and uncertainties in the simulation environment, and had similar or better performance in comparison to a nonlinear control law operating in an inner-outer loop structure. Steps are being taken to implement the resulting controllers on the unmanned aerial vehicle (UAV) testbed in the Nonlinear Systems Laboratory at Virginia Tech.
Master of Science

We consider the solution of nonlinear optimal control problems subject to stochastic perturbations with incomplete observations. In particular, we generalize results obtained by Ito and Kunisch in [8] where they consider a receding horizon control (RHC) technique based on linearizing the problem on small intervals. The linear-quadratic optimal control problem for the resulting time-invariant (LTI) problem is then solved using the linear quadratic Gaussian (LQG) design. Here, we allow linearization about an instationary reference trajectory and thus obtain a linear time-varying (LTV) problem on each time horizon. Additionally, we apply a model predictive control (MPC) scheme which can be seen as a generalization of RHC and we allow covariance matrices of the noise processes not equal to the identity. We illustrate the MPC/LQG approach for a three dimensional reaction-diffusion system. In particular, we discuss the benefits of time-varying linearizations over time-invariant ones.

L'amélioration permanente de la qualité et des performances des systèmes automatiques constitue un défi majeur dans la théorie du contrôle. La théorieHinf a permis d'améliorer considérablement les performances des correcteurs. Ces derniers reposent sur des modèles mathématiques qui sont potentiellement d'ordre élevé (c.-à-d. comprenant un nombre élevé d'équations différentielles). De plus, l'ajout de poids de pondérations spécifiant les performances à respecter accroit encore plus leur ordre. La complexité algorithmique résultante peut alors rendre leur implantation difficile voire même impossible pour un fonctionnement en temps réel.Les travaux présentés visent à réduire l'ordre de correcteurs Hinf dans le but de faciliter leur intégration tout en respectant les performances imposées d'une part et proposent une majoration de l'erreur introduite par l'étape de réduction d'autre part.Dans la littérature, de nombreuses méthodes pour la réduction d'ordre de modèles et de correcteurs des systèmes LTI ont été développées. Ces techniques ont été étudiées, comparées et testées sur un ensemble de benchmarks. S'appuyant sur ces travaux, nous proposons une extension aux systèmes linéaires à paramètres variants (LPV). Pour valider leurs performances, une application sur une commande d'une suspension semi-active a montré l'efficacité des algorithmes de réduction développés
The work presented in this dissertation is related to the Hinf-LPV-controller orderReduction. This latter consists of the design of a robust reduced-order LPV-controller for LPV-systems. The order reduction issue has been very fairly investigated. However, the case of LPV-control design is slightly discussed. This thesis focuses primarily on two topics: How to obtain an LPV-reduced-order controller even the high order generated by the classical synthesis and how this reduced order controller can deal with a practical engineering problem (semi-active suspension control). In view of this, the order-reduction topic and the Hinf-synthesis theory have been widely studied in this thesis. This study, has allowed the development of a new method forH1-LPV-controller order reduction

This thesis introduces, develops and applies methods for analysing nonlinear systems with the multiple challenges of time-varying, non-polynomial, uncertain or large-scale proper- ties. Both computational and analytic methods using Lyapunov functions are developed and the methods are applied to a range of examples. Generalised Absolute stability is introduced, which is a method of treating polynomial systems with non polynomial, uncertain or time-varying feedback. Analysis is completed with Sum of Squares programming, and this method extends both the applicability of sum of squares as well as existing absolute stability theory. Perturbation methods for invariant Sum of Squares and Semidefinite programs are introduced, which significantly improves scalability of computations and al- lows sum of squares programming to be used for large scale systems. Finally, invariance principles are introduced for nonlinear, time-varying systems. The concept of trajectories leaving sets uniformly in time is introduced, which allows a non-autonomous version of Barbashin-Krasovskii theorem.

This thesis presents new approaches to feed-drive control of computer numerical control (CNC) machine tools machine tools with a significant range of dynamic variations during machining operations. Several sources which can cause dynamic variations of feed-drive systems are considered, such as the change of table position, the reduction of workpiece mass, and the variations of tool-path orientation. Feed-drive systems having the dynamic variations are modeled as linear parameter varying (LPV) models. For the LPV models, three control methods are proposed to achieve satisfactory control performance of feed-drive systems. In the first method, we propose a parallel structure of an LPV gain-scheduled controller which aims at both tracking control and the vibration suppression by taking into account the resonant modes' variations which are peculiar to ball-screw drives. In the second method, instead of designing one LPV controller, a set of gain-scheduled controllers are designed to compensate for a wide range of dynamic variations. In this method, switching between two adjacent controllers may result in a transient jump of control signal at switching instants. In the third method, to ensure a smooth control signal, we present a novel method to design a smooth switching gain-scheduled LPV controller. The moving region of the gain-scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching. Then, one gain-scheduled LPV controller is assigned to each of the local subregions, while for each switching subregion, a function interpolating local LPV controllers associated with its neighbourhood subregions is designed. This interpolating function imposes the constraint of smooth transition on controller system matrices. The smooth switching controller design problem amounts to solving a feasibility problem which involves non-linear matrix inequalities that are solvable by a proposed iterative descent algorithm. The developed smooth switching controller is applied to control problems in both parallel and serial CNC machine tool mechanisms. Finally, for the multi-axis CNC machine tools, a multi-input-multi-output (MIMO) LPV feedback controller is designed to directly minimize contouring error in the task coordinate frame system.
Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate

This thesis considers two areas of robust control. Part I considers continuous H control. The theory is applied to a scalar flexible transmission system that has non-minimum phase zeros and lightly damped modes that vary with applied load. A robust solution is obtained that gives good performance results. The capabilities of H techniques are more fully demonstrated on a research civil aircraft model (RCAM) flight control problem. A novel architecture for an autopilot to fly the RCAM along the final approach to landing is designed. Good results are obtained for the autopilot that incorporates controllers designed using both two degree-of-freedom H mixed sensitivity and H loop shaping techniques. In terms of a pre-defined mission scenario the overall results for performance, robustness, ride quality, safety and control effort are some of the best published, they demonstrate to the aerospace community the applicability and benefits of the methods. Part II considers discrete time-varying finite horizon control. A number of new results in this area are presented, some being specialisations or extensions of existing finite horizon and time-invariant results, for example, means of computing the finite horizon norm and relationships between symplectic matrix equations and Riccati equations. Furthermore, normalised (coprime) factorisations and controller parameterisation results have enabled the optimum norm for the normalised left factored plant problem to be explicitly formulated. Formulae for a particular class of the problem are presented. A simplifying formula for the solution to the control Riccati equation of the problem is derived and a class of sub-optimal solutions, using non-zero terminal weights, is considered. The controller formulae are applied to a one-degree-of-freedom intercept problem with encouraging results. Robustness to relative lateral position errors and target acceleration perturbations are compared for the zero and non-zero terminal state weight cases.

碩士
南台科技大學
機械工程系
92
In this research﹐the Cerebellar Model Articulation Controller(CMAC) has been applied to motion control systems with varying friction characteristics to achieve the control accuracy at the micro/nano level. Also﹐the factors of CMAC controller﹐such as learning rates﹐memory size and generalization number﹐are investigated in detail. In the motion control system﹐the friction﹐backlash and hysteresis characteristics are usually varying along the traveling distance. Therefore﹐it is difficult to control such system with good accuracy by using traditional PID control algorithm. However﹐the Cerebellar Model Articulation Controller(CMAC) has the advantages of learning and generalization. It is found that the CMAC control algorithm together with PD control has the ability to overcome above problems. In addition﹐the selections of learning rates﹐memory size and generalization number are closey related to the accuracy of motion control. Hence﹐the relationships between the accuracy and above factors of CMAC controller ( learning rates﹐memory size and generalization number)are investigated individually. First﹐the learning rates for the displacement signal and velocity signal are selected with the same value. It is shown that the displacement accuracy is good enough but the velocity tracking has large error during the transition of different friction phenomena. This is because the displacement and velocity have different dynamic characteristics in the system with varying friction characteristics. Hence﹐the selection of different learning rates for the displacement signal and velocity signal leads to better accuracy of displacement and velocity tracking. In order to further reduce the velocity error during the transition of different friction phenomena﹐a saturator device is added to the output of CMAC controller. This saturator device can limit the output of CMAC controller. Using this saturator device and carefully selecting the learning rates and memory size can yield excellent control performance. The results are verified by numerical simulations. Finally﹐a CMAC toolbox has been developed in MATLAB in this research. This toolbox provides a useful tool for the simulations of CMAC control systems. Furthermore﹐this toolbox can be implemented in the experimental work by using real-time workshop toolbox in MATLAB. It is convenient for user to develop his/her own prototype of CMAC control systems. Keyword：CMAC, PID controller, Precision motion control

One critical step to successfully integrate wireless data networks to the high-speed wired backbone is the design of network control policies that efficiently utilize resources to provide Quality of Service (QoS) to the users in the integrated networks. Such a design has remained a challenge since wireless networks are time-varying in nature, not only in terms of user/packet arrivals but also in terms of physical channel conditions and access opportunities. In this thesis, we study the stochastic control of time-varying networks to design efficient scheduling and resource allocation policies. In particular, in Chapter 3, we focus on a broad class of control policies that work based on a pick-and-compare principle for networks with time-varying channels. By trading the throughput for complexity and memory requirement, these policies require less complexity compared to the well-investigated throughput-optimal Generalized Maximum Weight Matching (GMWM) policy and also require only linear-memory storage with the number of data-flows. Through Lyapunov analysis tools, we characterize the stability region and delay performance of the studied policies and show how they vary in response to the channel variations. In Chapter 4, we go into further detail and consider the problem of network control from a new perspective through which we carefully incorporate the time-efficiency of underlying scheduling algorithms. Specifically, we develop a policy that dynamically adjusts the time given to the available scheduling algorithms according to queue-backlog and channel correlations. We study the resulting stability region of developed policy and show that the region is at least as large as the one for any static policy. Finally, motivated by the current under-utilization of wireless spectrum, in Chapter 5, we investigate the control of cognitive radio networks as a special example of networks that provide time-varying access opportunities. We assume that users dynamically join and leave the network and may have different utility functions, or could collaborate for a common purpose. We develop a policy that performs joint admission and resource control and works for any user load, either inside or outside the capacity region. Through Lyapunov Optimization techniques, we show that the developed policy can achieve a utility performance arbitrarily close to the optimality with a tradeoff in the average service delay of admitted users.