Improved multi model predictive control for distillation column

Model predictive control (MPC) strategy is known to provide effective control of chemical processes including distillation. As illustration, when the control scheme was applied to three linear distillation columns, i.e., Wood-Berry (2x2), Ogunnaike-Lemaire-Morari-Ray (3x3) and Alatiqi (4x4), the results obtained proved the superiority of linear MPC over the conventional PI controller. This is however, not the case when nonlinear process dynamics are involved, and better controllers are needed. As an attempt to address this issue, a new multi model predictive control (MMPC) framework known as Representative Model Predictive Control (RMPC) is proposed. The control scheme selects the most suitable local linear model to be implemented in control computations. Simulation studies were conducted on a nonlinear distillation column commonly known as Column A using MATLAB® and SIMULINK® software. The controllers were compared in terms of their ability in tracking set points and rejecting disturbances. Using three local models, RMPC was proven to be more efficient in servo control. It was however, not able to cope with disturbance rejection requirement. This limitation was overcome by introducing two controller output configurations: Maximizing MMPC and PI controller output (called hybrid controller, HC), and a MMPC and PI controller output switching (called MMPCPIS). When compared to the PI controller, HC provided better control performances for disturbance changes of 1% and 20% with an average improvement of 12% and 20% of the integral square error (ISE), respectively. It was however, not able to handle large disturbance of + 50% in feed composition. This limitation was overcome by MMPCPIS, which provided improvements by 17% and 20% of the ISE for all of types and magnitudes of disturbance change. The application of MMPCPIS on a single model MPC strategy produced almost similar performance for both types of disturbances, while its application on MMPC yielded better results. Based on the results obtained, it can be concluded that the proposed HC and MMPCPIS deserve further detailed investigations to serve as linear control approaches for solving complex nonlinear control problems commonly found in chemical industr

Model Predictive Control Applications to Spacecraft Rendezvous and Small Bodies Exploration

The overarching goal of this thesis is the design of model predictive control algorithms for spacecraft proximity operations. These include, but it is not limited to, spacecraft rendezvous, hovering phases or orbiting in the vicinity of small bodies. The main motivation behind this research is the increasing demand of autonomy, understood as the spacecraft capability to compute its own control plan, in current and future space operations. This push for autonomy is fostered by the recent introduction of disruptive technologies changing the traditional concept of space exploration and exploitation. The development of miniaturized satellite platforms and the drastic cost reduction in orbital access have boosted space activity to record levels. In the near future, it is envisioned that numerous artificial objects will simultaneously operate across the Solar System. In that context, human operators will be overwhelmed in the task of tracking and commanding each spacecraft in real time. As a consequence, developing intelligent and robust autonomous systems has been identified by several space agencies as a cornerstone technology. Inspired by the previous facts, this work presents novel controllers to tackle several scenarios related to spacecraft proximity operations. Mastering proximity operations enables a wide variety of space missions such as active debris removal, astronauts transportation, flight-formation applications, space stations resupply and the in-situ exploration of small bodies. Future applications may also include satellite inspection and servicing. This thesis has focused on four scenarios: six-degrees of freedom spacecraft rendezvous; near-rectilinear halo orbits rendezvous; the hovering phase; orbit-attitude station-keeping in the vicinity of a small body. The first problem aims to demonstrate rendezvous capabilities for a lightweight satellite with few thrusters and a reaction wheels array. For near-rectilinear halo orbits rendezvous, the goal is to achieve higher levels of constraints satisfaction than with a stateof- the-art predictive controller. In the hovering phase, the objective is to augment the control accuracy and computational efficiency of a recent global stable controller. The small body exploration aims to demonstrate the positive impact of model-learning in the control accuracy. Although based on model predictive control, the specific approach for each scenario differs. In six-degrees of freedom rendezvous, the attitude flatness property and the transition matrix for Keplerian-based relative are used to obtain a non-linear program. Then, the control loop is closed by linearizing the system around the previous solution. For near-rectilinear halo orbits rendezvous, the constraints are assured to be satisfied in the probabilistic sense by a chance-constrained approach. The disturbances statistical properties are estimated on-line. For the hovering phase problem, an aperiodic event-based predictive controller is designed. It uses a set of trigger rules, defined using reachability concepts, deciding when to execute a single-impulse control. In the small body exploration scenario, a novel learning-based model predictive controller is developed. This works by integrating unscented Kalman filtering and model predictive control. By doing so, the initially unknown small body inhomogeneous gravity field is estimated over time which augments the model predictive control accuracy.El objeto de esta tesis es el dise˜no de algoritmos de control predictivo basado en modelo para operaciones de veh´ıculos espaciales en proximidad. Esto incluye, pero no se limita, a la maniobra de rendezvous, las fases de hovering u orbitar alrededor de cuerpos menores. Esta tesis est´a motivada por la creciente demanda en la autonom´ıa, entendida como la capacidad de un veh´ıculo para calcular su propio plan de control, de las actuales y futuras misiones espaciales. Este inter´es en incrementar la autonom´ıa est´a relacionado con las actuales tecnolog´ıas disruptivas que est´an cambiando el concepto tradicional de exploraci´on y explotaci´on espacial. Estas son el desarrollo de plataformas satelitales miniaturizadas y la dr´astica reducci´on de los costes de puesta en ´orbita. Dichas tecnolog´ıas han impulsado la actividad espacial a niveles de record. En un futuro cercano, se prev´e que un gran n´umero de objetos artificiales operen de manera simult´anea a lo largo del Sistema Solar. Bajo dicho escenario, los operadores terrestres se ver´an desbordados en la tarea de monitorizar y controlar cada sat´elite en tiempo real. Es por ello que el desarrollo de sistemas aut´onomos inteligentes y robustos es considerado una tecnolog´ıa fundamental por diversas agencias espaciales. Debido a lo anterior, este trabajo presenta nuevos resultados en el control de operaciones de veh´ıculos espaciales en proximidad. Dominar dichas operaciones permite llevar a cabo una gran variedad de misiones espaciales como la retirada de basura espacial, transferir astronautas, aplicaciones de vuelo en formaci´on, reabastecer estaciones espaciales y la exploraci ´on de cuerpos menores. Futuras aplicaciones podr´ıan incluir operaciones de inspecci´on y mantenimiento de sat´elites. Esta tesis se centra en cuatro escenarios: rendezvous de sat´elites con seis grados de libertad; rendezvous en ´orbitas halo cuasi-rectil´ıneas; la fase de hovering; el mantenimiento de ´orbita y actitud en las inmendiaciones de un cuerpo menor. El primer caso trata de proveer capacidades de rendezvous para un sat´elite ligero con pocos propulsores y un conjunto de ruedas de reacci´on. Para el rendezvous en ´orbitas halo cuasi-rectil´ıneas, se intenta aumentar el grado de cumplimiento de restricciones con respecto a un controlador predictivo actual. Para la fase de hovering, se mejora la precisi´on y eficiencia computacional de un controlador globalmente estable. En la exploraci´on de un cuerpo menor, se pretende demostrar el mayor grado de precisi´on que se obtiene al aprender el modelo. Siendo la base el control predictivo basado en modelo, el enfoque espec´ıfico difiere para cada escenario. En el rendezvous con seis grados de libertad, se obtiene un programa no-lineal con el uso de la propiedad flatness de la actitud y la matriz de transici´on del movimiento relativo Kepleriano. El bucle de control se cierra linealizando en torno a la soluci´on anterior. Para el rendezvous en ´orbitas halo cuasi-rectil´ıneas, el cumplimiento de restricciones se garantiza probabil´ısticamente mediante la t´ecnica chance-constrained. Las propiedades estad´ısticas de las perturbaciones son estimadas on-line. En la fase de hovering, se usa el control predictivo basado en eventos. Ello consiste en unas reglas de activaci´on, definidas con conceptos de accesibilidad, que deciden la ejecuci´on de un ´unico impulso de control. En la exploraci´on de cuerpos menores, se desarrolla un controlador predictivo basado en el aprendizaje del modelo. Funciona integrando un filtro de Kalman con control predictivo basado en modelo. Con ello, se consigue estimar las inomogeneidades del campo gravitario lo que repercute en una mayor precisi´on del controlador predictivo basado en modelo

Price-based optimal control of electrical power systems

During the past decade, electrical power systems have been going through some major restructuring processes. From monopolistic, highly regulated and one utility controlled operation, a system is being restructured to include many parties competing for energy production and consumption, and for provision of many of the ancillary services necessary for system operation. With the emergence of competitive markets as central operational mechanisms, the prime operational objective has shifted from a centralized, utility cost minimization objective to decentralized, profit maximization objectives of competing parties. The market-based (price-based) operation is shown to be practically the only approach that is capable to simultaneously provide incentives to hold the prices at marginal costs and to minimize the costs. As a result, such an operational structure inherently tends to maximize the social welfare of the system during its operation, and to accelerate developments and applications of new technologies. Another major change that is taking place in today’s power systems is an increasing integration of small-scale distributed generation (DG) units. Since in future power systems, a large amounts of DG will be based on renewable, intermittent energy sources, e.g. wind and sun, these systems will be characterized by significantly larger uncertainties than those of the present power systems. Power markets significantly deviate from standard economics since the demand side is largely disconnected from the market, i.e. it is not price responsive, and it exhibits uncertain, stochastic behavior. Furthermore, since electrical energy cannot be efficiently stored in large quantities, production has to meet these rapidly changing demands in real-time. In future power systems, efficient real-time power balancing schemes will become crucial and even more challenging due to the significant increase of uncertainties by large-scale integration of renewable sources. Physical and security limits on the maximal power flows in the lines of power transmission networks represent crucial system constraints, which must be satisfied to protect the integrity of the system. Creating an efficient congestion management scheme for dealing with these constraints is one of the toughest problems in the electricity market design, as the line power flows are characterized by complex dependencies on nodal power injections. Efficient congestion control has to account for those limits by adequately transforming them into market signals, i.e. into electricity prices. One of the main contributions of this thesis is the development of a novel dynamic, distributed feedback control scheme for optimal real-time update of electricity prices. The developed controller (which is called the KKT controller in the thesis) reacts on the network frequency deviation as a measure of power imbalance in the system and on measured violations of line flow limits in a transmission network. The output of the controller is a vector of nodal prices. Each producer/consumer in the system is allowed to autonomously react on the announced price by adjusting its production/consumption level to maximize its own benefit. Under the hypothesis of global asymptotic stability of the closed-loop system, the developed control scheme is proven to continuously balance the system by driving it towards the equilibrium where the transmission power flow constraints are satisfied, and where the total social welfare of the system is maximized. One of the advantageous features of the developed control scheme is that, to achieve this goal, it requires no knowledge of marginal cost/benefit functions of producers/consumers in the system (neither is it based on the estimates of those functions). The only system parameters that are explicitly included in the control law are the transmission network parameters, i.e. network topology and line impedances. Furthermore, the developed control law can be implemented in a distributed fashion. More precisely, it can be implemented through a set of nodal controllers, where one nodal controller (NC) is assigned to each node in the network. Each NC acts only on locally available information, i.e. on the measurements from the corresponding node and on the information obtained from NC’s of the adjacent nodes. The communication network graph among NC’s is therefore the same as the graph of the underlying physical network. Any change is the network topology requires only simple adjustments in NC’s that are local to the location of the change. To impose the hard constraints on the level to which the transmission network lines are overloaded during the transient periods following relatively large power imbalances in the system, a novel price-based hybrid model predictive control (MPC) scheme has been developed. The MPC control action adds corrective signals to the output of the KKT controller, i.e. to the nodal prices, and acts only when the predictions indicate that the imposed hard constraint will be violated. In any other case, output of the MPC controller is zero and only the KKT controller is active. Under certain hypothesis, recursive feasibility and asymptotic stability of the closed-loop system with the hybrid MPC controller are proven. Next contribution of this thesis is formulation of the autonomous power networks concept as a multilayered operational structure of future power systems, which allows for efficient large-scale integration of DG and smallscale consumers into power and ancillary service markets, i.e. markets for different classes of reserve capacities. An autonomous power network (AN) is an aggregation of networked producers and consumers, whose operation is coordinated/controlled with one central unit (AN market agent). By performing optimal dispatching and unit commitment services, the main goals of an AN market agent is to efficiently deploy the AN’s internal resources by its active involvement in power and ancillary service markets, and to optimally account for the local reliability needs. An autonomous power network is further defined as a major building block of power system operation, which is capable of keeping track of its contribution to the uncertainty in the overall system, and is capable of bearing the responsibility for it. With the introduction of such entities, the conditions are created that allow for the emergence of novel, competitive ancillary service market structures. More precisely, in ANs based power systems, each AN can be both producer and consumer of ancillary services, and ancillary service markets are characterized by double-sided competition, what is in contrast to today’s single-sided ancillary service markets. One of the main implications of this novel operational structure in that, by facilitating competition, it creates the strong incentive for ANs to reduce the uncertainties and to increase reliability of the system. On a more technical side, the AN concept is seen as decentralization and modularization approach for dealing with the future, large scale, complex power systems. As additional contribution of this thesis, motivated by the KKT controller for price-based real-time power balancing and congestion management, the general KKT control paradigm is presented in some detail. The developed control design procedure presents a solution to the problem of regulating a general linear time-invariant dynamical system to a time-varying economically optimal operating point. The system is characterized with a set of exogenous inputs as an abstraction of time-varying loads and disturbances. Economic optimality is defined through a constrained convex optimization problem with a set of system states as decision variables, and with the values of exogenous inputs as parameters in the optimization problem. A KKT controller belongs to a class of dynamic complementarity systems, which has been recently introduced and which has, due to its wide applicability and specific structural properties, gained a significant attention in systems and control community. The results of this thesis add to the list of applications of complementarity systems in control