Poles and zeros – examples of the behavioral approach applied to discrete linear repetitive processes

In this paper the behavorial approach is applied to discrete linear repetitive processes, which are class of 2D systems of both systems theoretic and applications interest. The main results are on poles and zeros for these processes, which have exponential trajectory interpretations

Linear Algebra Methods for the Control of Multidimensional Systems

The purpose of the thesis is to develop a comprehensive theory of the geometric control for N-dimensional systems. Two possible representations and their structural invariance properties of 2-D systems will be considered and generalised to the N-dimensional case: the Fornasini-Marchesini first order model and Fornasini-Marchesini second order model. In addition, necessary and sufficient conditions for the existence of solutions for the implicit 2-D Fornasini-Marchesini models will be provided, and generalised to the N-dimensional case

Model based fault detection for two-dimensional systems

Fault detection and isolation (FDI) are essential in ensuring safe and reliable operations in industrial systems. Extensive research has been carried out on FDI for one dimensional (1-D) systems, where variables vary only with time. The existing FDI strategies are mainly focussed on 1-D systems and can generally be classified as model based and process history data based methods. In many industrial systems, the state variables change with space and time (e.g., sheet forming, fixed bed reactors, and furnaces). These systems are termed as distributed parameter systems (DPS) or two dimensional (2-D) systems. 2-D systems have been commonly represented by the Roesser Model and the F-M model. Fault detection and isolation for 2-D systems represent a great challenge in both theoretical development and applications and only limited research results are available. In this thesis, model based fault detection strategies for 2-D systems have been investigated based on the F-M and the Roesser models. A dead-beat observer based fault detection has been available for the F-M model. In this work, an observer based fault detection strategy is investigated for systems modelled by the Roesser model. Using the 2-D polynomial matrix technique, a dead-beat observer is developed and the state estimate from the observer is then input to a residual generator to monitor occurrence of faults. An enhanced realization technique is combined to achieve efficient fault detection with reduced computations. Simulation results indicate that the proposed method is effective in detecting faults for systems without disturbances as well as those affected by unknown disturbances.The dead-beat observer based fault detection has been shown to be effective for 2-D systems but strict conditions are required in order for an observer and a residual generator to exist. These strict conditions may not be satisfied for some systems. The effect of process noises are also not considered in the observer based fault detection approaches for 2-D systems. To overcome the disadvantages, 2-D Kalman filter based fault detection algorithms are proposed in the thesis. A recursive 2-D Kalman filter is applied to obtain state estimate minimizing the estimation error variances. Based on the state estimate from the Kalman filter, a residual is generated reflecting fault information. A model is formulated for the relation of the residual with faults over a moving evaluation window. Simulations are performed on two F-M models and results indicate that faults can be detected effectively and efficiently using the Kalman filter based fault detection. In the observer based and Kalman filter based fault detection approaches, the residual signals are used to determine whether a fault occurs. For systems with complicated fault information and/or noises, it is necessary to evaluate the residual signals using statistical techniques. Fault detection of 2-D systems is proposed with the residuals evaluated using dynamic principal component analysis (DPCA). Based on historical data, the reference residuals are first generated using either the observer or the Kalman filter based approach. Based on the residual time-lagged data matrices for the reference data, the principal components are calculated and the threshold value obtained. In online applications, the T2 value of the residual signals are compared with the threshold value to determine fault occurrence. Simulation results show that applying DPCA to evaluation of 2-D residuals is effective.Doctoral These

Iterative learning control: algorithm development and experimental benchmarking

This thesis concerns the general area of experimental benchmarking of Iterative Learning Control (ILC) algorithms using two experimental facilities. ILC is an approach which is suitable for applications where the same task is executed repeatedly over the necessarily finite time duration, known as the trial length. The process is reset prior to the commencement of each execution. The basic idea of ILC is to use information from previously executed trials to update the control input to be applied during the next one. The first experimental facility is a non-minimum phase electro-mechanical system and the other is a gantry robot whose basic task is to pick and place objects on a moving conveyor under synchronization and in a fixed finite time duration that replicates many tasks encountered in the process industries. Novel contributions are made in both the development of new algorithms and, especially, in the analysis of experimental results both of a single algorithm alone and also in the comparison of the relative performance of different algorithms. In the case of non-minimum phase systems, a new algorithm, named Reference Shift ILC (RSILC) is developed that is of a two loop structure. One learning loop addresses the system lag and another tackles the possibility of a large initial plant input commonly encountered when using basic iterative learning control algorithms. After basic algorithm development and simulation studies, experimental results are given to conclude that performance improvement over previously reported algorithms is reasonable. The gantry robot has been previously used to experimentally benchmark a range of simple structure ILC algorithms, such as those based on the ILC versions of the classical proportional plus derivative error actuated controllers, and some state-space based optimal ILC algorithms. Here these results are extended by the first ever detailed experimental study of the performance of stochastic ILC algorithms together with some modifications necessary to their configuration in order to increase performance. The majority of the currently reported ILC algorithms mainly focus on reducing the trial-to-trial error but it is known that this may come at the cost of poor or unacceptable performance along the trial dynamics. Control theory for discrete linear repetitive processes is used to design ILC control laws that enable the control of both trial-to-trial error convergence and along the trial dynamics. These algorithms can be computed using Linear Matrix Inequalities (LMIs) and again the results of experimental implementation on the gantry robot are given. These results are the first ever in this key area and represent a benchmark against which alternatives can be compared. In the concluding chapter, a critical overview of the results presented is given together with areas for both short and medium term further researc

Structural invariants of two-dimensional systems

In this paper, some fundamental structural properties of two-dimensional (2-D) systems which remain invariant under feedback and output-injection transformation groups are identified and investigated for the first time. As is well known, structural invariants that follow from the definition of controlled and conditioned invariance, output-nulling, input-containing, self-bounded and self-hidden subspaces play pivotal roles in many theoretical studies of systems theory and in the solution of several control/estimation problems. These concepts are developed and studied within a 2-D context in this paper

Relaxing Fundamental Assumptions in Iterative Learning Control

Iterative learning control (ILC) is perhaps best decribed as an open loop feedforward control technique where the feedforward signal is learned through repetition of a single task. As the name suggests, given a dynamic system operating on a finite time horizon with the same desired trajectory, ILC aims to iteratively construct the inverse image (or its approximation) of the desired trajectory to improve transient tracking. In the literature, ILC is often interpreted as feedback control in the iteration domain due to the fact that learning controllers use information from past trials to drive the tracking error towards zero. However, despite the significant body of literature and powerful features, ILC is yet to reach widespread adoption by the control community, due to several assumptions that restrict its generality when compared to feedback control. In this dissertation, we relax some of these assumptions, mainly the fundamental invariance assumption, and move from the idea of learning through repetition to two dimensional systems, specifically repetitive processes, that appear in the modeling of engineering applications such as additive manufacturing, and sketch out future research directions for increased practicality: We develop an L1 adaptive feedback control based ILC architecture for increased robustness, fast convergence, and high performance under time varying uncertainties and disturbances. Simulation studies of the behavior of this combined L1-ILC scheme under iteration varying uncertainties lead us to the robust stability analysis of iteration varying systems, where we show that these systems are guaranteed to be stable when the ILC update laws are designed to be robust, which can be done using existing methods from the literature. As a next step to the signal space approach adopted in the analysis of iteration varying systems, we shift the focus of our work to repetitive processes, and show that the exponential stability of a nonlinear repetitive system is equivalent to that of its linearization, and consequently uniform stability of the corresponding state space matrix.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133232/1/altin_1.pd

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area

Improvement of detection and tracking techniques in multistatic passive radar systems. (Mejora de técnicas de detección y seguimiento en sistemas radar pasivos multiestáticos)

Esta tesis doctoral es el resultado de una intensa actividad investigadora centrada en los sensores radar pasivos para la mejora de las capacidades de detección y seguimiento en escenarios complejos con blancos terrestres y pequeños drones. El trabajo de investigación se ha llevado a cabo en el grupo de investigación coordinado por la Dra. María Pilar Jarabo Amores, dentro del marco diferentes proyectos: IDEPAR (“Improved DEtection techniques for PAssive Radars”), MASTERSAT (“MultichAnnel paSsive radar receiver exploiting TERrestrial and SATellite Illuminators”) y KRIPTON (“A Knowledge based appRoach to passIve radar detection using wideband sPace adapTive prOcessiNg”) financiados por el Ministerio de Economía y Competitividad de España; MAPIS (Multichannel passive ISAR imaging for military applications) y JAMPAR (“JAMmer-based PAssive Radar”), financiados por la Agencia Europea de Defensa (EDA) . El objetivo principal es la mejora de las técnicas de detección y seguimiento en radares pasivos con configuraciones biestáticas y multiestaticas. En el documento se desarrollan algoritmos para el aprovechamiento de señales procedentes de distintos iluminadores de oportunidad (transmisores DVB-T, satélites DVB-S y señales GPS). Las soluciones propuestas han sido integradas en el demostrador tecnológico IDEPAR, desarrollado y actualizado bajo los proyectos mencionados, y validadas en escenarios reales declarados de interés por potenciales usuarios finales (Direccion general de armamento y material, instituto nacional de tecnología aeroespacial y la armada española). Para el desarrollo y evaluación de cadenas de las cadenas de procesado, se plantean dos casos de estudio: blancos terrestres en escenarios semiurbanos edificios y pequeños blancos aéreos en escenarios rurales y costeros. Las principales contribuciones se pueden resumir en los siguientes puntos: • Diseño de técnicas de seguimiento 2D en el espacio de trabajo rango biestático-frecuencia Doppler: se desarrollan técnicas de seguimiento para los dos casos de estudio, localización de blancos terrestres y pequeños drones. Para es último se implementan técnicas capaces de seguir tanto el movimiento del dron como su firma Doppler, lo que permite implementar técnicas de clasificación de blancos. • Diseño de técnicas de seguimiento de blancos capaces de integrar información en el espacio 3D (rango, Doppler y acimut): se diseñan técnicas basadas en procesado en dos etapas, una primera con seguimiento en 2D para el filtrado de falsas alarmas y la segunda para el seguimiento en 3D y la conversión de coordenadas a un plano local cartesiano. Se comparan soluciones basadas en filtros de Kalman para sistemas tanto lineales como no lineales. • Diseño de cadenas de procesado para sistemas multiestáticos: la información estimada del blanco sobre múltiples geometrías biestáticas es utilizada para incremento de las capacidades de localización del blanco en el plano cartesiano local. Se presentan soluciones basadas en filtros de Kalman para sistemas no lineales explotando diferentes medidas biestáticas en el proceso de transformación de coordenadas, analizando las mejoras de precisión en la localización del blanco. • Diseño de etapas de procesado para radares pasivos basados en señales satelitales de las constelaciones GPS DVB-S. Se estudian las características de las señales satelitales identificando sus inconvenientes y proponiendo cadenas de procesado que permitan su utilización para la detección y seguimiento de blancos terrestres. • Estudio del uso de señales DVB-T multicanal con gaps de transmisión entre los diferentes canales en sistemas radares pasivos. Con ello se incrementa la resolución del sistema, y las capacidades de detección, seguimiento y localización. Se estudia el modelo de señal multicanal, sus efectos sobre el procesado coherente y se proponen cadenas de procesado para paliar los efectos adversos de este tipo de señales