Distributed optimal and predictive control methods for networks of dynamic systems

Several recent approaches to distributed control design over networks of interconnected dynamic systems rely on certain assumptions, such as identical subsystem dynamics, absence of dynamical couplings, linear dynamics and undirected interaction schemes. In this thesis, we investigate systematic methods for relaxing a number of simplifying factors leading to a unifying approach for solving general distributed-control stabilization problems of networks of dynamic agents. We show that the gain-margin property of LQR control holds for complex multiplicative input perturbations and a generic symmetric positive definite input weighting matrix. Proving also that the potentially non-simple structure of the Laplacian matrix can be neglected for stability analysis and control design, we extend two well-known distributed LQR-based control methods originally established for undirected networks of identical linear systems, to the directed case. We then propose a distributed feedback method for tackling large-scale regulation problems of a general class of interconnected non-identical dynamic agents with undirected and directed topology. In particular, we assume that local agents share a minimal set of structural properties, such as input dimension, state dimension and controllability indices. Our approach relies on the solution of certain model matching type problems using local linear state-feedback and input matrix transformations which map the agent dynamics to a target system, selected to minimize the joint control effort of the local feedback-control schemes. By adapting well-established distributed LQR control design methodologies to our framework, the stabilization problem of a network of non-identical dynamical agents is solved. We thereafter consider a networked scheme synthesized by multiple agents with nonlinear dynamics. Assuming that agents are feedback linearizable in a neighborhood near their equilibrium points, we propose a nonlinear model matching control design for stabilizing networks of multiple heterogeneous nonlinear agents. Motivated by the structure of a large-scale LQR optimal problem, we propose a stabilizing distributed state-feedback controller for networks of identical dynamically coupled linear agents. First, a fully centralized controller is designed which is subsequently substituted by a distributed state-feedback gain with sparse structure. The control scheme is obtained byoptimizing an LQR performance index with a tuning parameter utilized to emphasize/deemphasize relative state difference between coupled systems. Sufficient conditions for stability of the proposed scheme are derived based on the inertia of a convex combination of two Hurwitz matrices. An extended simulation study involving distributed load frequency control design of a multi-area power network, illustrates the applicability of the proposed method. Finally, we propose a fully distributed consensus-based model matching scheme adapted to a model predictive control setting for tackling a structured receding horizon regulation problem

A geometric framework for constraints and data:from linear systems to convex processes

In part one of this thesis we develop the theory of analyis of convex processes. The results of this development can be directly applied to the analysis of discrete time, linear, time-invariant mathematical systems with conic constraints. Such constraints arise from physical properties of natural phenomena, and hence it is important that these are considered in the mathematical models thereof. In part two we focus determining whether a system has a given system theoretic property on the basis of measured data. For this, we develop the informativity framework, which allows us to consider and resolve a large number of such problems

Optimal Selection of Measurements and Manipulated Variables for Production Control

The main objective in a chemical plant is to improve profit while assuring products meet required specifications and satisfy environmental and operational constraints. A sub-objective that directly affects profit (main objective) is to improve the control performance of key economic variables in the plant, such as production rate and quality. An optimal control-based approach is proposed to determine a set of measurements and manipulated variables (dominant variables) and to structure them to improve plant profitability. This approach is model-based, and it uses optimal control theory to find the dominant variables that affect economic variables in the plant. First, the measurements and manipulated variables that affect product flow and quality are identified. Then, a decentralized control structure is designed to pair these measurements with the manipulated variables. Finally, a model predictive control (MPC) is built on top of the resulting control structure. This is done to manipulate the set point of these loops in order to change the production rate and product quality. Another sub-objective that affects the profit in the plant is to improve the control of inerts. In general, the inventory of the inerts is controlled using a purge. A new methodology to optimally control inerts is presented. This methodology aims to reduce the losses that occur throughout the purge by solving an optimization problem to determine the maximum amount of inert that can be handled in the plant without having shut down of the plant due to inert accumulation. The methodology is successfully applied to the Tennessee Eastman Plant where the operating cost was reduced approximately 4%. This methodology solves an approximation to an optimal economic problem. First, it improves the control performance of key economic variables in the plant. Therefore, tighter control of these economic variables is achieved and the plant can be operated closer to operational constraints. Second, it minimizes purge which is a variable that generally causes significant costs in the plant. This approach is applied to the Tennessee Eastman and the Vinyl Acetate Processes. Results demonstrating the effectiveness of this method are presented and compared with the results from other authors

Integrated design and control of chemical processes : part I : revision and clasification

[EN] This work presents a comprehensive classification of the different methods and procedures for integrated synthesis, design and control of chemical processes, based on a wide revision of recent literature. This classification fundamentally differentiates between “projecting methods”, where controllability is monitored during the process design to predict the trade-offs between design and control, and the “integrated-optimization methods” which solve the process design and the control-systems design at once within an optimization framework. The latter are revised categorizing them according to the methods to evaluate controllability and other related properties, the scope of the design problem, the treatment of uncertainties and perturbations, and finally, the type the optimization problem formulation and the methods for its resolution.[ES] Este trabajo presenta una clasificación integral de los diferentes métodos y procedimientos para la síntesis integrada, diseño y control de procesos químicos. Esta clasificación distingue fundamentalmente entre los "métodos de proyección", donde se controla la controlabilidad durante el diseño del proceso para predecir los compromisos entre diseño y control, y los "métodos de optimización integrada" que resuelven el diseño del proceso y el diseño de los sistemas de control a la vez dentro de un marco de optimización. Estos últimos se revisan clasificándolos según los métodos para evaluar la controlabilidad y otras propiedades relacionadas, el alcance del problema de diseño, el tratamiento de las incertidumbres y las perturbaciones y, finalmente, el tipo de la formulación del problema de optimización y los métodos para su resolución

MIT Space Engineering Research Center

The Space Engineering Research Center (SERC) at MIT, started in Jul. 1988, has completed two years of research. The Center is approaching the operational phase of its first testbed, is midway through the construction of a second testbed, and is in the design phase of a third. We presently have seven participating faculty, four participating staff members, ten graduate students, and numerous undergraduates. This report reviews the testbed programs, individual graduate research, other SERC activities not funded by the Center, interaction with non-MIT organizations, and SERC milestones. Published papers made possible by SERC funding are included at the end of the report

Control and Automation

Control and automation systems are at the heart of our every day lives. This book is a collection of novel ideas and findings in these fields, published as part of the Special Issue on Control and Automation. The core focus of this issue was original ideas and potential contributions for both theory and practice. It received a total number of 21 submissions, out of which 7 were accepted. These published manuscripts tackle some novel approaches in control, including fractional order control systems, with applications in robotics, biomedical engineering, electrical engineering, vibratory systems, and wastewater treatment plants. This Special Issue has gathered a selection of novel research results regarding control systems in several distinct research areas. We hope that these papers will evoke new ideas, concepts, and further developments in the field

Dynamics of aerospace vehicles

The focus of this research was to address the modeling, including model reduction, of flexible aerospace vehicles, with special emphasis on models used in dynamic analysis and/or guidance and control system design. In the modeling, it is critical that the key aspects of the system being modeled be captured in the model. In this work, therefore, aspects of the vehicle dynamics critical to control design were important. In this regard, fundamental contributions were made in the areas of stability robustness analysis techniques, model reduction techniques, and literal approximations for key dynamic characteristics of flexible vehicles. All these areas are related. In the development of a model, approximations are always involved, so control systems designed using these models must be robust against uncertainties in these models