An algorithm is presented which computes a state feedback for a standard linear system which not only stabilizes, but also dampens the closed-loop system dynamics. In other words, a feedback gain vector is computed such that the eigenvalues of the closed-loop state matrix are within the region of the left half-plane where the magnitude of the real part of each eigenvalue is greater than the imaginary part. This may be accomplished by solving one periodic algebraic Riccati equation and one degenerate Riccati equation. The solution to these equations are computed using numerically robust algorithms. Finally, the periodic Riccati equation is unusual in that it produces one symmetric and one skew symmetric solution, and as a result two different state feedbacks. Both feedbacks dampen the system dynamics, but produce different closed-loop eigenvalues, giving the controller designer greater freedom in choosing a desired feedback.

Orientador: Mario Antonio Bernal Rodriguez / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-30T22:42:12Z (GMT). No. of bitstreams: 1 TelloCajiao_JohnJames_M.pdf: 2614936 bytes, checksum: e5bdfc91b42434b003cad0b5fa850afb (MD5) Previous issue date: 2016 / Resumo: O objetivo deste trabalho é estudar a influência da conformação do DNA na probabilidade de dano direto produzido por partículas ionizantes. Além disso, os fundamentos mecanicísticos do modelo Linear-Quadrático são investigadas através de um modelo biofísico desenvolvido neste trabalho, baseado na TADR (Teoria da Ação Dual da Radiação). Para este fim, três modelos geométricos do material genético foram construídos. Os modelos têm resolução atomística e levam em conta ? 10^9 pares de base (bps) nas configurações A,B e Z do DNA. A partir de um único bp, os diferentes níveis organizacionais no interior do núcleo da célula foram criados por meio de transformações lineares. Em seguida, o código Monte Carlo (MC) GEANT4-DNA foi usado para simular o transporte de prótons de 0.5, 1, 5, 7 e 10 MeV assim como de partículas alfa de 2, 5, 7 e 10M eV . O número de partículas em cada caso é de tal modo que as doses absorvidas estão entre 0.5 ? 16Gy. Os três modelos foram consistentes com as dimensões das estruturas reais. Em particular, os modelos foram compatíveis com a exigência de que o diâmetro da cromatina seja de 30 nm, bem como com os volumes bp reportados em outros trabalhos. Os rendimentos tanto das quebras totais quanto das quebras duplas (TSBY e DSBY) foram obtidos para cada qualidade de radiação. Além disso, a probabilidade de impacto (SHP) definida como a razão entre o volume do DNA e o volume núcleo, foi calculada teoricamente e a partir das simulações. O modelo biofísico em conjunto com as simulações MC forneceu o número de lesões letais (N_LL) em função da dose, para prótons de 0,5 e 10 MeV, e para partículas alfa de 2 e 10 MeV . Os N_LL puderam ser divididos em aqueles criados por uma única trajetória e aqueles originados pela interacção de duas trajetórias. Concluiu-se que o TSBY é praticamente determinada pela SHP e depende fracamente da qualidade de radiação incidente. No entanto, o DSBY mostrou forte dependência tanto da conformação do DNA quanto da qualidade de radiação. Isto é devido à relação entre a capacidade de agrupamento das deposições de energia para uma radiação dada e o empacotamento do DNA. Por outro lado, a análise dos mecanismos de produção de dano, baseada na TADR e testada com o modelo biofísico desenvolvido, mostraram que os efeitos de uma única trajetória (de primeira ordem) dependem linearmente com a dose. Além disso, os efeitos inter-trajetórias seguem um comportamento quadrático com a dose, com um termo linear que influencia o mecanismo de primeira ordem. Isto significa que o comportamento linear-quadrático do N_LL com a dose, tem fundamentos mecanicistas, pelo menos, na primeira fase do dano / Abstract: The aim of this work is to study the influence of the DNA conformation on the probability of direct damage induction by ionizing particles. Also, the mechanistic grounds of the Linear-Quadratic radiobiological model are investigated through the eyes of a home-made biophysical model based on the DRAT (Dual Radiation Action Theory). To this end, three geometrical models of the genetic material were constructed. The models have atomistic resolution and account for ? 10^9 base pairs (bps) in the A-, B- and Z-DNA configurations. Starting from a single bp, the different organizational levels inside the cell nucleus were created by means of linear transformations. Next, the Monte Carlo (MC) code GEANT4-DNA was used to simulate the transport of protons of 0.5, 1, 5, 7 and 10 MeV , and alpha particles of 2, 5, 7 and 10 MeV. The number of particles in each case is such that the absorbed doses range between 0.5 Gy and 16 Gy. The three models proved to be consistent with the dimensions of the real structures. In particular, the models were compatible with the 30 nm chromatin fiber diameter requirement as well as with the bp volumes reported in other works. The Total and Double Strand Break Yields (TSBY and DSBY) were obtained for every radiation quality. Also, the Site-Hit Probability (SHP) defined as the total target to the nucleus volume ratio, was computed theoretically and from the simulations. The biophysical model in conjunction with the MC simulations furnished the number of lethal lesions (N_LL) as a function of dose, for protons of 0.5 and 10 MeV , and for alpha particles of 2 and 10 MeV . The N_LL could be split into those created by a single track and those originated by interaction of two tracks. It is concluded that the TSBY is practically determined by the SHP and depends weakly on the incident radiation quality. Nevertheless, the DSBY showed strong dependence on both the DNA conformation and the radiation quality. This is due to the interplay between the energy deposition clustering capacity of a given radiation and the DNA spatial packing. On the other hand, the analysis of the mechanisms of damage production based on the DRAT and tested with the biophysical model developed, showed that single-track (first order) effects depend linearly on the dose. Moreover, inter-track effects follows a quadratic behavior with the dose, having a linear term that influences the first order mechanism. This means that the Linear-Quadratic behavior of the N_LL with the dose, has mechanistic groundings at least at the first stage of the damage / Mestrado / Física / Mestre em Física / 1370449/2014 / CAPES

One of the challenges that satellites face is the interaction between control movement and vibration of flexible appendages such as solar arrays and antennas that can negatively affect the performance of the spacecraft. The aim of this thesis is to develop a numerical model of a solar panel structure for KNATTE, a frictionless platform developed by the Onboard Space Systems group at Luleå University of Technology, and develop a control law that reduces the flexible vibration of the solar arrays when attitude control manoeuvres are performed. A set of solar panel structures have been designed and tested, the mathematical model of the multibody system, which consists of KNATTE and two flexible solar panels, has been developed in MATLAB by applying the finite element method. A finite element analysis has been performed in MATLAB to extract the natural frequencies of the system. The model has been numerically verified using a commercial software, and experimentally verified by performing testing on the frictionless vehicle, KNATTE, equipped with the solar panel structures and a number of piezoelectric sensors. Once the model has been verified, a Linear Quadratic Gaussian (LQG) controller has been developed using the results from the finite element model in order to reduce the amplitude of the vibrations of the flexible solar panel structure. The behaviour of the system has been simulated when the spacecraft performs an attitude manoeuvre. The finite element model provides the modal behaviour of the multibody system, obtaining its natural frequencies with low relative error. The LQG controller reduces the amplitude of the vibrations of the flexible solar panel structure.

In this thesis, analysis and comparison of different attitude control systems of a satelliteusing different reaction wheel configurations were investigated. Three different reactionwheel configurations (e.g. tetrahedron configuration, pyramid configuration, standardorthogonal 3-wheel configuration) and three control algorithms (Linear Quadratic Regulator,Sliding Mode, Integrator Backstepping) were analyzed and compared in terms of settlingtimes, power consumptions and actuator failure robustness. / <p>Validerat; 20121205 (global_studentproject_submitter)</p>

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We study the behavior of numerical stabilization schemes in the context of linear quadratic regulator (LQR) control problems for convection diffusion equations. The motivation for this effort comes from the observation that when linearization is applied to fluid flow control problems the resulting equations have the form of a convection diffusion equation. This effort is focused on the specific problem of computing the feedback functional gains that are the kernels of the feedback operators defined by solutions of operator Riccati equations. We develop a stabilization scheme based on the Galerkin Least Squares (GLS) method and compare this scheme to the standard Galerkin finite element method. We use cubic B-splines in order to keep the higher order terms that occur in GLS formulation. We conduct a careful numerical investigation into the convergence and accuracy of the functional gains computed using stabilization. We also conduct numerical studies of the role that the stabilization parameter plays in this convergence. Overall, we discovered that stabilization produces much better approximations to the functional gains on coarse meshes than the unstabilized method and that adjustments in the stabilization parameter greatly effects the accuracy and convergence rates. We discovered that the optimal stabilization parameter for simulation and steady state analysis is not necessarily optimal for solving the Riccati equation that defines the functional gains. Finally, we suggest that the stabilized GLS method might provide good initial values for iterative schemes on coarse meshes. / Ph. D.

Unmanned aerial systems have been widely used for variety of civilian applications over the past few years. Some of these applications require accurate guidance and control. Consequently, Unmanned Aerial Vehicle (UAV) guidance and control attracted many researchers in both control theory and aerospace engineering. Flying wings, as a particular type of UAV, are considered to have one of the most efficient aerodynamic structures. It is however difficult to design robust controller for such systems. This is due to the fact that flying wings are highly sensitive to control inputs. The focus of this thesis is on modeling and control design for a UAV system. The platform understudy is a flying wing developed by SmartPlanes Co. located in Skellefteå, Sweden. This UAV is particularly used for topological mapping and aerial photography. The novel approach suggested in this thesis is to use two controllers in sequence. More precisely, Linear Quadratic Regulator (LQR) is suggested to provide robust stability, and Proportional, Integral, Derivative (PID) controller is suggested to provide reference signal regulation. The idea behind this approach is that with LQR in the loop, the system becomes more stable and less sensitive to control signals. Thus, PID controller has an easier task to do, and is only used to provide the required transient response. The closed-loop system containing the developed controller and a UAV non-linear dynamic model was simulated in Simulink. Simulated controller was then tested for stability and robustness with respect to some parametric uncertainty. Obtained results revealed that the LQR successfully managed to provide robust stability, and PID provided reference signal regulation.

As inverter-based distributed energy resources (DERs) such as photovoltaic (PV) and battery energy storage system (BESS) penetrate within the distribution system. New challenges regarding how to utilize these devices to improve power quality arises. Before, PV systems were required to disconnect from the grid during a large disturbance, but now smart inverters are required to have dynamically controlled functions that allows them to remain connected to the grid. Monitoring power flow at the point of common coupling is one of the many functions the controller should perform. Smart inverters can inject active power to pick up critical load or inject reactive power to regulate voltage within the electric grid. In this context, this thesis focuses on a high level and local control design that incorporates DERs. Different controllers are implemented to stabilize the microgrid in an Islanding and resiliency mode. The microgrid can be used as a resiliency source when the distribution is unavailable. An average model in the D-Q frame is calculated to analyze the inherent dynamics of the current controller for the point of common coupling (PCC). The space vector approach is applied to design the voltage and frequency controller. Secondly, using inverters for Volt/VAR control (VVC) can provide a faster response for voltage regulation than traditional voltage regulation devices. Another objective of this research is to demonstrate how smart inverters and capacitor banks in the system can be used to eliminate the voltage deviation. A mixed-integer quadratic problem (MIQP) is formulated to determine the amount of reactive power that should be injected or absorbed at the appropriate nodes by inverter. The Big M method is used to address the nonconvex problem. This contribution can be used by distribution operators to minimize the voltage deviation in the system. / Master of Science / Reliable power supply from the electric grid is an essential part of modern life. This critical infrastructure can be vulnerable to cascading failures or natural disasters. A solution to improve power systems resilience can be through microgrids. A microgrid is a small network of interconnected loads and distributed energy resources (DERs) such as microturbines, wind power, solar power, or traditional internal combustion engines. A microgrid can operate being connected or disconnected from the grid. This research emphases on the potentially use of a Microgrid as a resiliency source during grid restoration to pick up critical load. In this research, controllers are designed to pick up critical loads (i.e hospitals, street lights and military bases) from the distribution system in case the electric grid is unavailable. This case study includes the design of a Microgrid and it is being tested for its feasibility in an actual integration with the electric grid. Once the grid is restored the synchronization between the microgrid and electric must be conducted. Synchronization is a crucial task. An abnormal synchronization can cause a disturbance in the system, damage equipment, and overall lead to additional system outages. This thesis develops various controllers to conduct proper synchronization. Interconnecting inverter-based distributed energy resources (DERs) such as photovoltaic and battery storage within the distribution system can use the electronic devices to improve power quality. This research focuses on using these devices to improve the voltage profile within the distribution system and the frequency within the Microgrid.

This thesis project aims to model a quadcopter and design a linear quadratic regulator (LQR) by means of Matlab/Simulink. To this purpose, the LQR-based optimal control theory for controllinga quadcopter is first studied which includes state-space representation (SSR) of a dynamicprocess or system, cost function, LQR, quadcopter flight dynamics and system linearization. A quadcopter model is developed in Matlab/Simulink, followed by the implementation of a LQR-based control system. The LQR parameters are tuned and the system is tested under various flight conditions (wind disturbance, in the simulation, specific/simplified model, etc.). The simulation results show that the LQR is an effective controller for maintaining stable hover at a height straight up and compensating for wind disturbances. However, when the quadcopter moves to a new position, oscillations occur, highlighting the limitations of the LQR due to its reliance on a simplified and linearized model. Additionally, modifications to the model parameters, such as mass and inertia, impact the system performance, indicating potential robustness issues with the controller. It can be concluded that Matlab/Simulink is an effective tool for quadcopter modeling, LQR designing and LQR performance analyzing. In this thesis project, only the LQR method is used for controlling a quadcopter and the LQR tuning process is not efficient. In future work other techniques such as regional linearization and alternative non-linear controllers, like model predictive control (MPC) or sliding mode control (SMC), can be explored. Development of optimization algorithms for LQR tuning in the LQR method is highly recommended.