Necessary and sufficient conditions for robust stability using modal intervals

In this paper, robustness of parametric systems is analyzed using a new approach to interval mathematics called Modal Interval Analysis. Modal Intervals are an interval extension that, instead of classic intervals, recovers some of the properties required by a numerical system. Modal Interval Analysis not only simplifies the computation of interval functions but allows semantic interpretation of their results. Necessary, sufficient and, in some cases, necessary and sufficient conditions for robust performance are presented

Necessary and sufficient conditions for robust stability using modal intervals

In this paper, robustness of parametric systems is analyzed using a new approach to interval mathematics called Modal Interval Analysis. Modal Intervals are an interval extension that, instead of classic intervals, recovers some of the properties required by a numerical system. Modal Interval Analysis not only simplifies the computation of interval functions but allows semantic interpretation of their results. Necessary, sufficient and, in some cases, necessary and sufficient conditions for robust performance are presented

Robust stability of sequential multi-input multi-output quantitative feedback theory designs

This paper re-examines the stability of multi-input multi-output (MIMO) control systems designed using sequential MIMO quantitative feedback theory (QFT). In order to establish the results, recursive design equations for the SISO equivalent plants employed in a sequential MIMO QFT design are established. The equations apply to sequential MIMO QFT designs in both the direct plant domain, which employs the elements of plant in the design, and the inverse plant domain, which employs the elements of the plant inverse in the design. Stability theorems that employ necessary and sufficient conditions for robust closed-loop internal stability are developed for sequential MIMO QFT designs in both domains. The theorems and design equations facilitate less conservative designs and improved design transparency.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 Elsevier Ltd. All rights reserved.

Robust and optimal adjustment of Power System Stabilizers through Linear Matrix Inequalities

This work presents the application of Linear Matrix Inequalities to the robust and optimal adjustment of Power System Stabilizers with pre-defined structure. Results of some tests show that gain and zeros adjustments are sufficient to guarantee robust stability and performance with respect to various operating points. Making use of the flexible structure of LMI's, we propose an algorithm that minimizes the norm of the controllers gain matrix while it guarantees the damping factor specified for the closed loop system, always using a controller with flexible structure. The technique used here is the pole placement, whose objective is to place the poles of the closed loop system in a specific region of the complex plane. Results of tests with a nine-machine system are presented and discussed, in order to validate the algorithm proposed. (C) 2012 Elsevier Ltd. All rights reserved.

Impedance-based stability and transient-performance assessment applying maximum peak criteria

The impedance-based stability-assessment method has turned out to be a very effective tool and its usage is rapidly growing in different applications ranging from the conventional interconnected dc/dc systems to the grid-connected renewable energy systems. The results are sometime given as a certain forbidden region in the complex plane out of which the impedance ratio--known as minor-loop gain--shall stay for ensuring robust stability. This letter discusses the circle-like forbidden region occupying minimum area in the complex plane, defined by applying maximum peak criteria, which is well-known theory in control engineering. The investigation shows that the circle-like forbidden region will ensure robust stability only if the impedance-based minor-loop gain is determined at the very input or output of each subsystem within the interconnected system. Experimental evidence is provided based on a small-scale dc/dc distributed system.

Performance metrics for small-signal stability assessment of DC-distributed power-system-architecture comparisons

The objective of this paper is to provide performance metrics for small-signal stability assessment of a given system architecture. The stability margins are stated utilizing a concept of maximum peak criteria (MPC) derived from the behavior of an impedance-based sensitivity function. For each minor-loop gain defined at every system interface, a single number to state the robustness of stability is provided based on the computed maximum value of the corresponding sensitivity function. In order to compare various power-architecture solutions in terms of stability, a parameter providing an overall measure of the whole system stability is required. The selected figure of merit is geometric average of each maximum peak value within the system. It provides a meaningful metrics for system comparisons: the best system in terms of robust stability is the one that minimizes this index. In addition, the largest peak value within the system interfaces is given thus detecting the weakest point of the system in terms of robustness.

Methodology for Dynamic Stability and Robustness Analysis of Commercial-Power-Module-Based DC-Distributed Systems

El propósito de esta tesis es presentar una metodología para realizar análisis de la dinámica en pequeña señal y el comportamiento de sistemas de alimentación distribuidos de corriente continua (CC), formados por módulos comerciales. Para ello se hace uso de un método sencillo que indica los márgenes de estabilidad menos conservadores posibles mediante un solo número. Este índice es calculado en cada una de las interfaces que componen el sistema y puede usarse para obtener un índice global que indica la estabilidad del sistema global. De esta manera se posibilita la comparación de sistemas de alimentación distribuidos en términos de robustez. La interconexión de convertidores CC-CC entre ellos y con los filtros EMI necesarios puede originar interacciones no deseadas que dan lugar a la degradación del comportamiento de los convertidores, haciendo el sistema más propenso a inestabilidades. Esta diferencia en el comportamiento se debe a interacciones entre las impedancias de los diversos elementos del sistema. En la mayoría de los casos, los sistemas de alimentación distribuida están formados por módulos comerciales cuya estructura interna es desconocida. Por ello los análisis presentados en esta tesis se basan en medidas de la respuesta en frecuencia del convertidor que pueden realizarse desde los terminales de entrada y salida del mismo. Utilizando las medidas de las impedancias de entrada y salida de los elementos del sistema, se puede construir una función de sensibilidad que proporciona los márgenes de estabilidad de las diferentes interfaces. En esta tesis se utiliza el concepto del valor máximo de la función de sensibilidad (MPC por sus siglas en inglés) para indicar los márgenes de estabilidad como un único número. Una vez que la estabilidad de todas las interfaces del sistema se han evaluado individualmente, los índices obtenidos pueden combinarse para obtener un único número con el que comparar la estabilidad de diferentes sistemas. Igualmente se han analizado las posibles interacciones en la entrada y la salida de los convertidores CC-CC, obteniéndose expresiones analíticas con las que describir en detalle los acoplamientos generados en el sistema. Los estudios analíticos realizados se han validado experimentalmente a lo largo de la tesis. El análisis presentado en esta tesis se culmina con la obtención de un índice que condensa los márgenes de estabilidad menos conservativos. También se demuestra que la robustez del sistema está asegurada si las impedancias utilizadas en la función de sensibilidad se obtienen justamente en la entrada o la salida del subsistema que está siendo analizado. Por otra parte, la tesis presenta un conjunto de parámetros internos asimilados a impedancias, junto con sus expresiones analíticas, que permiten una explicación detallada de las interacciones en el sistema. Dichas expresiones analíticas pueden obtenerse bien mediante las funciones de transferencia analíticas si se conoce la estructura interna, o utilizando medidas en frecuencia o identificación de las mismas a través de la respuesta temporal del convertidor. De acuerdo a las metodologías presentadas en esta tesis se puede predecir la estabilidad y el comportamiento de sistemas compuestos básicamente por convertidores CC-CC y filtros, cuya estructura interna es desconocida. La predicción se basa en un índice que condensa la información de los márgenes de estabilidad y que permite la obtención de un indicador de la estabilidad global de todo el sistema, permitiendo la comparación de la estabilidad de diferentes arquitecturas de sistemas de alimentación distribuidos. ABSTRACT The purpose of this thesis is to present dynamic small-signal stability and performance analysis methodology for dc-distributed systems consisting of commercial power modules. Furthermore, the objective is to introduce simple method to state the least conservative margins for robust stability as a single number. In addition, an index characterizing the overall system stability is obtained, based on which different dc-distributed systems can be compared in terms of robustness. The interconnected systems are prone to impedance-based interactions which might lead to transient-performance degradation or even instability. These systems typically are constructed using commercial converters with unknown internal structure. Therefore, the analysis presented throughout this thesis is based on frequency responses measurable from the input and output terminals. The stability margins are stated utilizing a concept of maximum peak criteria, derived from the behavior of impedance-based sensitivity function that provides a single number to state robust stability. Using this concept, the stability information at every system interface is combined to a meaningful number to state the average robustness of the system. In addition, theoretical formulas are extracted to assess source and load side interactions in order to describe detailed couplings within the system. The presented theoretical analysis methodologies are experimentally validated throughout the thesis. In this thesis, according to the presented analysis, the least conservative stability margins are provided as a single number guaranteeing robustness. It is also shown that within the interconnected system the robust stability is ensured only if the impedance-based minor-loop gain is determined at the very input or output of each subsystem. Moreover, a complete set of impedance-type internal parameters as well as the formulas according to which the interaction sensitivity can be fully explained and analyzed, is provided. The given formulation can be utilized equally either based on measured frequency responses, time-domain identified internal parameters or extracted analytic transfer functions. Based on the analysis methodologies presented in this thesis, the stability and performance of interconnected systems consisting of converters with unknown internal structure, can be predicted. Moreover, the provided concept to assess the least conservative stability margins enables to obtain an index to state the overall robust stability of distributed power architecture and thus to compare different systems in terms of stability.

Robust multivariable control of complex biological processes

This paper addresses advanced control of a biological nutrient removal (BNR) activated sludge process. Based on a previously validated distributed parameter model of the BNR activated sludge process, we present robust multivariable controller designs for the process, involving loop shaping of plant model, robust stability and performance analyses. Results from three design case studies showed that a multivariable controller with stability margins of 0.163, 0.492 and 1.062 measured by the normalised coprime factor, multiplicative and additive uncertainties respectively give the best results for meeting performance robustness specifications. The controller robustly stabilises effluent nutrients in the presence of uncertainties with the behaviour of phosphorus accumulating organisms as well as to effectively attenuate major disturbances introduced as step changes. This study also shows that, performance of the multivariable robust controller is superior to multi-loops SISO PI controllers for regulating the BNR activated sludge process in terms of robust stability and performance and controlling the process using inlet feed flowrate is infeasible. (C) 2003 Elsevier Ltd. All rights reserved.

On stability in nonsequential MIMO QFT designs

This paper reexamines the stability of uncertain closed-loop systems resulting from the nonsequential (NS) MIMO QFT design methodology. By combining the effect of satisfying both the robust stability and robust performance specifications in a NS MIMO QFT design, a proof for the stability of the uncertain closed-loop system is derived. The stability theorem proves that, subject to the satisfaction of a critical necessary and sufficient condition, the original NS MIMO QFT design methodology will provide a robustly stable closed-loop system. This necessary and sufficient condition provides a useful existence test for a successful NS MIMO QFT design. The results expose the salient features of the NS MIMO QFT design methodology. Two 2 x 2 MIMO design examples are presented to illustrate the key features of the stability, theorem.

Persistence of EBV Antigen-Specific CD8 T Cell Clonotypes during Homeostatic Immune Reconstitution in Cancer Patients.

Persistent viruses are kept in check by specific lymphocytes. The clonal T cell receptor (TCR) repertoire against Epstein-Barr virus (EBV), once established following primary infection, exhibits a robust stability over time. However, the determinants contributing to this long-term persistence are still poorly characterized. Taking advantage of an in vivo clinical setting where lymphocyte homeostasis was transiently perturbed, we studied EBV antigen-specific CD8 T cells before and after non-myeloablative lympho-depleting chemotherapy of melanoma patients. Despite more advanced T cell differentiation, patients T cells showed clonal composition comparable to healthy individuals, sharing a preference for TRBV20 and TRBV29 gene segment usage and several co-dominant public TCR clonotypes. Moreover, our data revealed the presence of relatively few dominant EBV antigen-specific T cell clonotypes, which mostly persisted following transient lympho-depletion (TLD) and lymphocyte recovery, likely related to absence of EBV reactivation and de novo T cell priming in these patients. Interestingly, persisting clonotypes frequently co-expressed memory/homing-associated genes (CD27, IL7R, EOMES, CD62L/SELL and CCR5) supporting the notion that they are particularly important for long-lasting CD8 T cell responses. Nevertheless, the clonal composition of EBV-specific CD8 T cells was preserved over time with the presence of the same dominant clonotypes after non-myeloablative chemotherapy. The observed clonotype persistence demonstrates high robustness of CD8 T cell homeostasis and reconstitution.

Estudo comparativo do desempenho de controladores robustos aplicados a um sistema de tanques acoplados.

Currently the uncertain system has attracted much academic community from the standpoint of scientific research and also practical applications. A series of mathematical approaches emerge in order to troubleshoot the uncertainties of real physical systems. In this context, the work presented here focuses on the application of control theory in a nonlinear dynamical system with parametric variations in order and robustness. We used as the practical application of this work, a system of tanks Quanser associates, in a configuration, whose mathematical model is represented by a second order system with input and output (SISO). The control system is performed by PID controllers, designed by various techniques, aiming to achieve robust performance and stability when subjected to parameter variations. Other controllers are designed with the intention of comparing the performance and robust stability of such systems. The results are obtained and compared from simulations in Matlab-simulink.

Controle robusto com realimentação derivativa de sistemas não lineares via LMI

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Controle robusto chaveado de sistemas lineares variantes no tempo com aplicação em falhas estruturais

Pós-graduação em Engenharia Elétrica - FEIS

Flutter analysis including structural uncertainties

The common practice in industry is to perform flutter analyses considering the generalized stiffness and mass matrices obtained from finite element method (FEM) and aerodynamic generalized force matrices obtained from a panel method, as the doublet lattice method. These analyses are often reperformed if significant differences are found in structural frequencies and damping ratios determined from ground vibration tests compared to FEM. This unavoidable rework can result in a lengthy and costly process of analysis during the aircraft development. In this context, this paper presents an approach to perform flutter analysis including uncertainties in natural frequencies and damping ratios. The main goal is to assure the nominal system’s stability considering these modal parameters varying in a limited range. The aeroelastic system is written as an affine parameter model and the robust stability is verified solving a Lyapunov function through linear matrix inequalities and convex optimization