90 research outputs found
Min–max MPC using a tractable QP problem
Min–max model predictive controllers (MMMPC) suffer from a great computational burden that is often circumvented by using approximate solutions or upper bounds of the worst possible case of a performance index. This paper proposes a computationally efficient MMMPC control strategy in which a close approximation of the solution of the min–max problem is computed using a quadratic programming problem. The overall computational burden is much lower than that of the min–max problem and the resulting control is shown to have a guaranteed stability. A simulation example is given in the paper
Composite control Lyapunov functions for robust stabilization of constrained uncertain dynamical systems
This work presents innovative scientific results on the robust stabilization of constrained uncertain dynamical systems via Lyapunov-based state feedback control.
Given two control Lyapunov functions, a novel class of smooth composite control Lyapunov functions is presented. This class, which is based on the R-functions theory, is universal for the stabilizability of linear differential inclusions and has the following property. Once a desired controlled invariant set is fixed, the shape of the inner level sets can be made arbitrary close to any given ones, in a smooth and non-homothetic way. This procedure is an example of ``merging'' two control Lyapunov functions.
In general, a merging function consists in a control Lyapunov function whose gradient is a continuous combination of the gradients of the two parents control Lyapunov functions.
The problem of merging two control Lyapunov functions, for instance a global control Lyapunov function with a large controlled domain of attraction and a local one with a guaranteed local performance, is considered important for several control applications. The main reason is that when simultaneously concerning constraints, robustness and optimality, a single Lyapunov function is usually suitable for just one of these goals, but ineffective for the others.
For nonlinear control-affine systems, both equations and inclusions, some equivalence properties are shown between the control-sharing property, namely the existence of a single control law which makes simultaneously negative the Lyapunov derivatives of the two given control Lyapunov functions, and the existence of merging control Lyapunov functions.
Even for linear systems, the control-sharing property does not always hold, with the remarkable exception of planar systems.
For the class of linear differential inclusions, linear programs and linear matrix inequalities conditions are given for the the control-sharing property to hold.
The proposed Lyapunov-based control laws are illustrated and simulated on benchmark case studies, with positive numerical results
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 diseËśno 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
Nonlinear constrained and saturated control of power electronics and electromechanical systems
Power electronic converters are extensively adopted for the solution of timely issues, such
as power quality improvement in industrial plants, energy management in hybrid electrical
systems, and control of electrical generators for renewables. Beside nonlinearity, this systems
are typically characterized by hard constraints on the control inputs, and sometimes
the state variables. In this respect, control laws able to handle input saturation are crucial
to formally characterize the systems stability and performance properties. From a practical
viewpoint, a proper saturation management allows to extend the systems transient
and steady-state operating ranges, improving their reliability and availability.
The main topic of this thesis concern saturated control methodologies, based on modern
approaches, applied to power electronics and electromechanical systems. The pursued
objective is to provide formal results under any saturation scenario, overcoming the
drawbacks of the classic solution commonly applied to cope with saturation of power converters,
and enhancing performance. For this purpose two main approaches are exploited
and extended to deal with power electronic applications: modern anti-windup strategies,
providing formal results and systematic design rules for the anti-windup compensator, devoted
to handle control saturation, and “one step” saturated feedback design techniques,
relying on a suitable characterization of the saturation nonlinearity and less conservative
extensions of standard absolute stability theory results.
The first part of the thesis is devoted to present and develop a novel general anti-windup
scheme, which is then specifically applied to a class of power converters adopted for power
quality enhancement in industrial plants. In the second part a polytopic differential inclusion
representation of saturation nonlinearity is presented and extended to deal with a
class of multiple input power converters, used to manage hybrid electrical energy sources.
The third part regards adaptive observers design for robust estimation of the parameters
required for high performance control of power systems
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