Small aerial vehicles such as quad-rotors have been widely used commercially, for research and for hobby for the last decade with use still growing. The high interest is mainly due to the vehicles being small, simple, cheap and versatile. Among rigid body dynamics fast dynamics exist cohering to motors and other fast actuators. A linear quadratic control design technique is here investigated. The design technique suggests that the linear quadratic controller can be designed with penalties on the slow states only. The fast dynamics are modeled but the states are not penalised in the linear quadratic design. The design technique is here applied and evaluated. The results show that this in several cases is a suitable design technique for linear quadratic control design. MATLAB and Simulink have been widely used for design and implementation of control systems. With additional toolboxes these control systems can be compiled to and run on remote computers. Small, lightweight computers with high computational capacity are now easily accessible. In this thesis an avionics solution based on a small, powerful computer is presented. Simulink models can be compiled and transferred to the computer from the Simulink environment. The result is a user friendly way of rapid prototyping and evaluation of control systems.

In this thesis, we give a mathematical background of solving a linear quadratic control problem for the heat equation, which involves noise on the boundary, in a concise way. We use the semigroup approach for the solvability of the problem. To obtain optimal controls, we use optimization techniques for convex functionals. Finally we give a feedback form for the optimal control. In order to enhance understanding of linear quadratic problem, we first present the methods in deterministic cases and then extend to noisy systems.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / A cyber physical system (CPS) is an intelligent integration of computation and communication infrastructure for monitoring and/or control of an underlying physical system. In this dissertation, we consider a specific class of CPS architectures where state of the system is spatially distributed in physical space. Examples that fit this category of CPS include, smart distribution gird, smart highway/transportation network etc. We study state estimation and control process in such systems where, (1) multiple sensors and actuators are arbitrarily deployed to jointly sense and control the system; (2) sensors directly communicate their observations to a central estimation and control unit (ECU) over communication links; and, (3) the ECU, on computing the control action, communicates control actions to actuators over communication links. Since communication links are susceptible to random failures, the overall estimation and control process is subjected to: (1) partial observation updates in estimation process; and (2) partial actuator actions in control process. We analyze stochastic stability of estimation and control process, in this scenario by establishing the conditions under which estimation accuracy and deviation from desired state trajectory is bounded. Our key contribution is the derivation of a new fundamental result on bounds for critical probabilities of individual communication link failure to maintain stability of overall system. The overall analysis illustrates that there is trade-off between stability of estimation and control process and quality of underlying communication network. In order to demonstrate practical implication of our work, we also present a case study in smart distribution grid as a system example of spatially distributed CPSs. Voltage/VAR support via distributed generators is studied in a stochastic nonlinear control framework.

Uma câmera pan-tilt é capaz de se movimentar em torno de dois eixos de rotação (pan e tilt), permitindo que sua lente possa ser apontada para um ponto qualquer no espaço. Uma aplicação possível dessa câmera é mantê-la apontada para um determinado alvo em movimento, através de posicionamentos angulares pan e tilt adequados. Este trabalho apresenta uma técnica de controle servo visual, em que, inicialmente, as imagens capturadas pela câmera são utilizadas para determinar a posição do alvo. Em seguida, calculam-se as rotações necessárias para manter a projeção do alvo no centro da imagem, em um sistema em tempo real e malha fechada. A técnica de rastreamento visual desenvolvida se baseia em comparação de uma região de referência, utilizando a soma dos quadrados das diferenças (SSD) como critério de correspondência. Sobre essa técnica, é adicionada uma extensão baseada no princípio de estimação incremental e, em seguida, o algoritmo é mais uma vez modificado através do princípio de estimação em multiresolução. Para cada uma das três configurações, são realizados testes para comparar suas performances. O sistema é modelado através do princípio de fluxo óptico e dois controladores são apresentados para realimentar o sistema: um proporcional integral (PI) e um proporcional com estimação de perturbações externas através de um filtro de Kalman (LQG). Ambos são calculados utilizando um critério linear quadrático e os desempenhos deles também são analisados comparativamente. / A pan-tilt camera can move around two rotational axes (pan and tilt), allowing its lens to be pointed to any point in space. A possible application of the camera is to keep it pointed to a certain moving target, through appropriate angular pan-tilt positioning. This work presents a visual servoing technique, which uses first the images captured by the camera to determinate the target position. Then the method calculates the proper rotations to keep the target position in image center, establishing a real-time and closed-loop system. The developed visual tracking technique is based on template region matching, and makes use of the sum of squared differences (SSD) as similarity criterion. An extension based on incremental estimation principle is added to the technique, and then the algorithm is modified again by multiresolution estimation method. Experimental results allow a performance comparison between the three configurations. The system is modeled through optical flow principle and this work presents two controllers to accomplish the system feedback: a proportional integral (PI) and a proportional with external disturbances estimation by a Kalman filter (LQG). Both are determined using a linear quadratic method and their performances are also analyzed comparatively.

<p>In this master thesis, control algoritms using arm side sensors are investigated for an industrial robot. The sensors can be position encoders placed after the gearbox and accelerometers on the robot arms. Control strategies are discussed and evaluated for different models of the robot, after which chosen strategies are applied to a realistic model. </p><p>Control algoritms using arm side sensors (LQ, dual-loop and PD-PID) are compared to a PID-controller that only uses measurements of motor position for feedback control. The comparison are done with respect to disturbance rejection, oscillation damping, robustness and tracking performance of a reference trajectory. </p><p>Results from tests with the realistic robot modell shows that disturbance rejection was improved a factor 2 to 5 while tracking performance was improved a factor 4 to 5 according to maximum deviation from the reference path. At the same time good re-sults are achieved regarding oscillation damping and robustness.</p>

In this master thesis, control algoritms using arm side sensors are investigated for an industrial robot. The sensors can be position encoders placed after the gearbox and accelerometers on the robot arms. Control strategies are discussed and evaluated for different models of the robot, after which chosen strategies are applied to a realistic model. Control algoritms using arm side sensors (LQ, dual-loop and PD-PID) are compared to a PID-controller that only uses measurements of motor position for feedback control. The comparison are done with respect to disturbance rejection, oscillation damping, robustness and tracking performance of a reference trajectory. Results from tests with the realistic robot modell shows that disturbance rejection was improved a factor 2 to 5 while tracking performance was improved a factor 4 to 5 according to maximum deviation from the reference path. At the same time good re-sults are achieved regarding oscillation damping and robustness.

Modern industrial control systems use a multitude of spatially distributed sensors and actuators to continuously monitor and control physical processes. Information exchange among control system components is traditionally done through physical wires. The need to physically wire sensors and actuators limits flexibility, scalability and reliability, since the cabling cost is high, cable connectors are prone to wear and tear, and connector failures can be hard to isolate. By replacing some of the cables with wireless communication networks, costs and risks of connector failures can be decreased, resulting in a more cost-efficient and reliable system. Integrating wireless communication into industrial control systems is challenging, since wireless communication channels introduce imperfections such as stochastic delays and information losses. These imperfections deteriorate the closed-loop control performance, and may even cause instability. In this thesis, we aim at developing design frameworks that take these imperfections into account and improve the performance of closed-loop control systems. The thesis first considers the joint design of packet forwarding policies and controllers for wireless control loops where sensor measurements are sent to the controller over an unreliable and energy-constrained multi-hop wireless network. For a fixed sampling rate of the sensor, the co-design problem separates into two well-defined and independent subproblems: transmission scheduling for maximizing the deadline-constrained reliability and optimal control under packet losses. We develop optimal and implementable solutions for these subproblems and show that the optimally co-designed system can be obtained efficiently. The thesis continues by examining event-triggered control systems that can help to reduce the energy consumption of the network by transmitting data less frequently. To this end, we consider a stochastic system where the communication between the controller and the actuator is triggered by a threshold-based rule. The communication is performed across an unreliable link that stochastically erases transmitted packets. As a partial protection against dropped packets, the controller sends a sequence of control commands to the actuator in each packet. These commands are stored in a buffer and applied sequentially until the next control packet arrives. We derive analytical expressions that quantify the trade-off between the communication cost and the control performance for this class of event-triggered control systems. The thesis finally proposes a supervisory control structure for wireless control systems with time-varying delays. The supervisor has access to a crude indicator of the overall network state, and we assume that individual upper and lower bounds on network time-delays can be associated to each value of the indicator. Based on this information, the supervisor triggers the most appropriate controller from a multi-controller unit. The performance of such a supervisory controller allows for improving the performance over a single robust controller. As the granularity of the network state measurements increases, the performance of the supervisory controller improves at the expense of increased computational complexity. / <p>QC 20150504</p>

When introducing autonomous functionality in personal vehicles the ability to control the quality of the ride is transferred from the driver to the vehicle control system. In this context, a reference method for quantifying ride quality may be a useful tool in the development and tuning process. This master’s thesis investigates whether general quantitative measures of ride quality can be of value in the tuning of motion controllers for autonomous vehicles. A set of tools is built for a specific case study, analysing a lateral path planning algorithm, based on a finite horizon linear quadratic tracking controller, and how its tuning affects ride quality performance. A graphical user interface is built, with functionality for frequency domainanalysis of the path planning algorithm, individually and in combination with the remaining lateral control system, as well as ride quality evaluation based on lateral acceleration data, from logged test runs and simulation results. In addition, a simulation environment for the lateral control system is modified to be used in combination with the evaluation tool. Results of the case study indicate a measurable difference in ride quality performance when comparing manual and autonomous driving with the current implementation. Attempts were made to improve ride quality by re-tuning the path planning algorithm but little or no improvement from the previous tuning was made. The work has recognized the potential of using ride quality measures in the development and tuning process for autonomous vehicles as well as devising a tuning strategy incorporating frequency analysis and ride quality evaluation through simulation for the lateral control system. To further increase ride quality performance via the path planning algorithm an altered controller structure, such as a frequency weighted linear quadratic controller is suggested.

Uma câmera pan-tilt é capaz de se movimentar em torno de dois eixos de rotação (pan e tilt), permitindo que sua lente possa ser apontada para um ponto qualquer no espaço. Uma aplicação possível dessa câmera é mantê-la apontada para um determinado alvo em movimento, através de posicionamentos angulares pan e tilt adequados. Este trabalho apresenta uma técnica de controle servo visual, em que, inicialmente, as imagens capturadas pela câmera são utilizadas para determinar a posição do alvo. Em seguida, calculam-se as rotações necessárias para manter a projeção do alvo no centro da imagem, em um sistema em tempo real e malha fechada. A técnica de rastreamento visual desenvolvida se baseia em comparação de uma região de referência, utilizando a soma dos quadrados das diferenças (SSD) como critério de correspondência. Sobre essa técnica, é adicionada uma extensão baseada no princípio de estimação incremental e, em seguida, o algoritmo é mais uma vez modificado através do princípio de estimação em multiresolução. Para cada uma das três configurações, são realizados testes para comparar suas performances. O sistema é modelado através do princípio de fluxo óptico e dois controladores são apresentados para realimentar o sistema: um proporcional integral (PI) e um proporcional com estimação de perturbações externas através de um filtro de Kalman (LQG). Ambos são calculados utilizando um critério linear quadrático e os desempenhos deles também são analisados comparativamente. / A pan-tilt camera can move around two rotational axes (pan and tilt), allowing its lens to be pointed to any point in space. A possible application of the camera is to keep it pointed to a certain moving target, through appropriate angular pan-tilt positioning. This work presents a visual servoing technique, which uses first the images captured by the camera to determinate the target position. Then the method calculates the proper rotations to keep the target position in image center, establishing a real-time and closed-loop system. The developed visual tracking technique is based on template region matching, and makes use of the sum of squared differences (SSD) as similarity criterion. An extension based on incremental estimation principle is added to the technique, and then the algorithm is modified again by multiresolution estimation method. Experimental results allow a performance comparison between the three configurations. The system is modeled through optical flow principle and this work presents two controllers to accomplish the system feedback: a proportional integral (PI) and a proportional with external disturbances estimation by a Kalman filter (LQG). Both are determined using a linear quadratic method and their performances are also analyzed comparatively.

O objetivo do trabalho é apresentar dois algoritmos para a solução de problemas de controle ótimo quadrático robusto com restrições, dentro de um contexto de controladores preditivos (MPC do inglês Model Predictive Control). Inicialmente apresentamos uma breve introdução aos algoritmos MPC, com ênfase na abordagem do controlador linear quadrático. Em seguida são apresentados os dois algoritmos de interesse, que utilizam técnicas de otimização LMI. Dessa forma as restrições e as incertezas podem ser colocadas em formas computacionalmente tratáveis. Por fim são realizadas simulações e comparações entre esses algoritmos, bem como com técnicas de MPC encontradas na literatura atual. / The goal of the work is to present two algorithms for the solution of robust quadratic optimal control problems with restrictions, within a model predictive control (MPC) setup. Initially we present a brief introduction of the MPC algorithms, emphasizing the linear quadratic controller approach. Next the two algorithms of interest, using LMI optimization techniques, are presented. By using this technique the restrictions and uncertainties can be written in a computational way. Finally some simulations and comparisons between these algorithms, as well as with MPC techniques found in the current literature, are performed.