L'objectif de ma thèse étant d'étudier certains systèmes linéaires continus à paramètres variant dans le temps (LPV), certains travaux sur l'analyse, synthèse et aussi études de performances relatives à ces systèmes ont pu être effectués. Les incertitudes peuvent avoir une structure qui varie, qui peut être polytopique, affine ou autre... Les conditions que l'on propose exigent de diminuer le conservatisme engendré au préalable par certaines conditions données dans ce contexte dans la littérature. Egalement, nous sommes appelés à mettre en place des représentations nouvelles de la dérivée temporelle du paramètre temps-variant et de l'intégrer dans nos conditions. En effet, il a été prouvé que le problème de commande robuste, peut être tourné en un ensemble d'inégalités matricielles linéaires. Les problèmes LMIs étant convexes, et nombreux algorithmes polynomiaux d'optimisation, sont disponibles pour les résoudre. Dans ce contexte, les études sur ces systèmes continus Linéaires à Paramètres temps Variant a pris de l'ampleur durant ces dernières années. C'est dans ce sens que j'ai essayé de présenter ma thèse. Les modèles qui ont été considérés dans mon mémoire sont à temps continu. Une étude bibliographique sur les systèmes admettant un modèle incertain linéaire à temps invariant (LTI) a été faite dans une première partie, puis tous les résultats relatifs aux systèmes LPV ont succédés dans des parties ultérieures.

State dependent Riccati equation (SDRE) plays an important role in nonlinear controller design. For autonomous nonlinear systems that can be expressed in linear form with state-dependent coefficients (SDC), SDRE-based controllers guarantee local asymptotic stability of the closed-loop system, under pointwise stabilizability and detectability conditions. Moreover, the optimal control for a quadratic cost function, when it exists, corresponds to an SDRE-based control design for a specific SDC parameterization of the associated nonlinear system. Unfortunately, the implementation of the SDRE-based controllers is computationally expensive. Various techniques have been developed for solving the SDRE, which are either computationally expensive or lack acceptable precision. In this dissertation, a modified state-dependent differential Riccati equation (MSDDRE) is proposed for approximating the solution of the SDRE, which is easy to implement with moderate computation power and its solution can be made arbitrarily close to that of the SDRE. Therefore, it can be used for real-time implementation of near-optimal controllers for nonlinear systems in state-dependent linear form. The proposed technique is then extended to SDRE-based filter design and its application to SDRE-based output feedback control technique. The proposed technique is also extended to state-dependent H-inf; robust control design for a constant noise attenuation bound, when the solution exists. To reduce the design conservativeness, the technique is further extended to state-dependent H-inf; robust control design with adaptive noise attenuation bound, using gain-scheduling technique and linear matrix inequality (LMI) optimization, to approximate H-inf; optimal control with state-dependent noise-attenuation bound. Local asymptotic stability of the closed-loop system is proven for all proposed techniques. Simulation results further confirm the validity of the development and demonstrate the efficiency of the proposed techniques.

The main objective of this work is to design robust, fast, and practical controllers for gantry and tower cranes. The controllers are designed to transfer the load from point to point as fast as possible and, at the same time, the load swing is kept small during the transfer process and completely vanishes at the load destination. Moreover, variations of the system parameters, such as the cable length and the load weight, are also included. Practical considerations, such as the control action power, and the maximum acceleration and velocity, are taken into account. In addition, friction effects are included in the design using a friction-compensation technique. The designed controllers are based on two approaches. In the first approach, a gain-scheduling feedback controller is designed to move the load from point to point within one oscillation cycle without inducing large swings. The settling time of the system is taken to be equal to the period of oscillation of the load. This criterion enables calculation of the controller feedback gains for varying load weight and cable length. The position references for this controller are step functions. Moreover, the position and swing controllers are treated in a unified way. In the second approach, the transfer process and the swing control are separated in the controller design. This approach requires designing two controllers independently: an anti-swing controller and a tracking controller. The objective of the anti-swing controller is to reduce the load swing. The tracking controller is responsible for making the trolley follow a reference position trajectory. We use a PD-controller for tracking, while the anti-swing controller is designed using three different methods: (a) a classical PD controller, (b) two controllers based on a delayed-feedback technique, and (c) a fuzzy logic controller that maps the delayed-feedback controller performance. To validate the designed controllers, an experimental setup was built. Although the designed controllers work perfectly in the computer simulations, the experimental results are unacceptable due to the high friction in the system. This friction deteriorates the system response by introducing time delay, high steady-state error in the trolley and tower positions, and high residual load swings. To overcome friction in the tower-crane model, we estimate the friction, then we apply an opposite control action to cancel it. To estimate the friction force, we assume a mathematical model and estimate the model coefficients using an off-line identification technique using the method of least squares. With friction compensation, the experimental results are in good agreement with the computer simulations. The gain-scheduling controllers transfer the load smoothly without inducing an overshoot in the trolley position. Moreover, the load can be transferred in a time near to the optimal time with small swing angles during the transfer process. With full-state feedback, the crane can reach any position in the working environment without exceeding the system power capability by controlling the forward gain in the feedback loop. For large distances, we have to decrease this gain, which in turn slows the transfer process. Therefore, this approach is more suitable for short distances. The tracking-anti-swing control approach is usually associated with overshoots in the translational and rotational motions. These overshoots increase with an increase in the maximum acceleration of the trajectories . The transfer time is longer than that obtained with the first approach. However, the crane can follow any trajectory, which makes the controller cope with obstacles in the working environment. Also, we do not need to recalculate the feedback gains for each transfer distance as in the gain-scheduling feedback controller. / Ph. D.

The overall objective of the Wallenberg Laboratory for Information Technology and Autonomous Systems (WITAS) at Linköping University is the development of an intelligent command and control system, containing vision sensors, which supports the operation of a unmanned air vehicle (UAV) in both semi- and full-autonomy modes. One of the UAV platforms of choice is the APID-MK3 unmanned helicopter, by Scandicraft Systems AB. The intended operational environment is over widely varying geographical terrain with traffic networks and vehicle interaction of variable complexity, speed, and density. The present version of APID-MK3 is capable of autonomous take-off, landing, and hovering as well as of autonomously executing pre-defined, point-to-point flight where the latter is executed at low-speed. This is enough for performing missions like site mapping and surveillance, and communications, but for the above mentioned operational environment higher speeds are desired. In this context, the goal of this thesis is to explore the possibilities for achieving stable ‘‘aggressive’’ manoeuvrability at high-speeds, and test a variety of control solutions in the APID-MK3 simulation environment. The objective of achieving ‘‘aggressive’’ manoeuvrability concerns the design of attitude/velocity/position controllers which act on much larger ranges of the body attitude angles, by utilizing the full range of the rotor attitude angles. In this context, a flight controller should achieve tracking of curvilinear trajectories at relatively high speeds in a robust, w.r.t. external disturbances, manner. Take-off and landing are not considered here since APIDMK3 has already have dedicated control modules that realize these flight modes. With this goal in mind, we present the design of two different types of flight controllers: a fuzzy controller and a gradient descent method based controller. Common to both are model based design, the use of nonlinear control approaches, and an inner- and outer-loop control scheme. The performance of these controllers is tested in simulation using the nonlinear model of APID-MK3. / <p>Report code: LiU-Tek-Lic-2002:11. The format of the electronic version of this thesis differs slightly from the printed one: this is due mainly to font compatibility. The figures and body of the thesis are remaining unchanged.</p>

Unmanned aircraft systems (UAS) often encounter turbulent fields that perturb the aircraft from its desired target trajectory, or in a manner that increases the load factor. The aircraft's fixed dihedral angle, providing passive roll-stiffness, is often selected based on lateral-directional stability requirements for the vehicle. A study to predict the effect of an active dihedral system on lateral-directional stability and vertical gust rejection capability was conducted to assess the performance and feasibility of the system. Traditionally, the dihedral location begins at the root to maintain wing structural requirements, however, the active dihedral system was also evaluated for dynamic stability and gust rejection performance at alternative dihedral breakpoint locations. Simulations were completed using linear parameter-varying (LPV) models, derived from traditional Newtonian aircraft dynamics and associated kinematic equations, to improve the modeling of the nonlinear active dihedral system. The stability of the LPV system was evaluated using Lyapunov stability theory applied to switched linear systems, assessing bounds of operation for the dihedral angle and flapping rate. An ideal feedback controller was developed using a linear–quadratic regulator (LQR) for both a discrete gust model and a continuous gust model, and a gain scheduled LQR controller was implemented to show the benefits of gain scheduling with a parameter varying state and input model. Finally, a cost analysis was conducted to investigate the real-world benefit of altering the dihedral breakpoint location. The effects of the active dihedral system on battery capacity and consumption efficiency were observed and compared with the gust rejection authority. / Master of Science / Unmanned aircraft systems (UAS) often encounter wind disturbances that perturb the aircraft from its desired target trajectory, or in a manner that increases the force encountered on the vehicle. The aircraft's fixed dihedral angle, providing stiffness to roll rotations, is often selected based on stability and control requirements for the vehicle. A study to predict the effect of a flapping wing (active dihedral) system on the stability, control, and wind gust rejection capability is completed to assess the performance and feasibility of such a system. Traditionally, the dihedral location begins at the root to maintain wing structural requirements, however, the active dihedral system was also evaluated for stability and wind gust rejection performance at alternative locations along the wing where the dihedral could begin, with intention of finding the best location. Simulations were completed using a varying set of simplified models, obtained from traditional aircraft mechanics, to improve the modeling of the true complex active dihedral system. The stability of the system was evaluated using various theories applied to the linear systems in attempt to define a bounded operating region for the dihedral angle and flapping motion. An ideal controller for the system was developed using ideas from well documented linear control theory for both a single wind gust and a continuous wind gust model. A controller that varies with vehicle flapping motion was implemented to show the benefits of scheduling the controller with a parameter varying state and input model. Finally, a cost analysis was conducted to investigate the real-world benefit of altering the dihedral starting location. The effects of the active dihedral system on battery capacity and consumption efficiency were observed and compared with the total gust rejection capability.

Orientador: Edvaldo Assunção / Resumo: Neste trabalho são propostas metodologias com base na teoria de estabilidade segundo Lyapunov para projetar controladores gain scheduling usando realimentação de estado ou derivativa e o conceito de D-estabilidade. As condições de projeto são dadas por desigualdades matriciais lineares (do inglês, Linear Matrix Inequalities - LMIs). A metodologia é aplicada em sistemas lineares sujeitos a parâmetros variantes no tempo (do inglês, Linear Parameter Varying - LPV). A utilização do Lema de Finsler eliminou a necessidade de inverter uma matriz literal para projetar o ganho de realimentação. Com o objetivo de satisfazer requisitos práticos, foi feito uso da restrição de D-estabilidade no projeto de um controlador para um sistema de suspensão ativa. A implementação prática mostra a eficiência da metodologia proposta. / Abstract: In this work are proposed methologies based on Lyapunov stability theory for designing gain scheduling controller using state-derivative feedback or state feedback and considering D-stability constraint. The design conditions are given by Linear Matrix Inequalities. The methodology is applied on system with time-variant parameter. The use of Finsler’s Lemma eliminated the problem of inverting a symbolic matrix to calculate the feedback gain. The theory of D-stability allowed to get implementable controllers for an active suspension system. The practical implementation showed the efficiency of the proposed methodology. / Mestre

Submitted by CARLOS ALEXIS ALVARADO SILVA (carlosalvaradosilva@gmail.com) on 2016-09-14T17:46:58Z No. of bitstreams: 1 dissertação final CARLOS ALVARADO.pdf: 3455623 bytes, checksum: 4fe5a62f068f2bf001ce3b1fdc1681ef (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-09-14T21:51:44Z (GMT) No. of bitstreams: 1 silva_caa_me_guara.pdf: 3455623 bytes, checksum: 4fe5a62f068f2bf001ce3b1fdc1681ef (MD5) / Made available in DSpace on 2016-09-14T21:51:44Z (GMT). No. of bitstreams: 1 silva_caa_me_guara.pdf: 3455623 bytes, checksum: 4fe5a62f068f2bf001ce3b1fdc1681ef (MD5) Previous issue date: 2016-07-04 / Agencia Nacional de Petróleo (ANP) / Controlar a pressão de poços petrolíferos durante a perfuração pode ser um dos processos mais complexos e perigosos da etapa de exploração. O sistema de perfuração varia constantemente e aleatoriamente, isto principalmente, devido à mudança da profundidade de perfuração, a qual faz variar outros parâmetros do processo. Assim, a aplicação de um controle variante no tempo torna-se necessário. Este estudo propõe o projeto de um controlador Gain Scheduling (GS) no controle da pressão no fundo de poços durante a perfuração. Este controlador GS consiste na sintonia dos ganhos relacionados aos diferentes pontos operacionais, para este caso, a profundidade do poço. Primeiro, apresentam-se as teorias a serem utilizadas durante o desenvolvimento do trabalho. Segundo, obtém-se o modelo matemático do processo o qual se fundamenta na mecânica dos fluidos. Da linearização do modelo, a função de transferência resultante apresenta um elemento integrador o que faz que a dinâmica do processo seja difícil de manipular. Também se adiciona um tempo de atraso, o que torna mais complexo o controle do processo. Na terceira parte, utilizaram-se três tipos de metodologias IMC (Internal Model Control) para sintonizar os ganhos do controlador PID (Proporcional, Integral e Derivativo) para diferentes profundidades de perfuração procurando o melhor desempenho, estabilidade e robustez do sistema. Finalmente, escolhe-se a estratégia de melhor desempenho (IMC de dois graus de liberdade) para especificar e montar a tabela do controlador GS, o qual é avaliado mediante simulações de problemas que geralmente ocorrem durante a perfuração, considerados como distúrbios, que verificam a sua viabilidade. Também, os resultados do sistema controlado por GS são comparados com os resultados de um outro controlador do tipo adaptativo de modelo de referência (CAMR). Verificando também melhor desempenho o controlador GS diante do CAMR. / Controlling the pressure of oil wells during drilling can be one of the most complex and dangerous processes of exploration stage. The drilling system is constantly end randomly changing due, among other things, the drilling depth, which varies other process parameters, accordingly to apply a time variant control becomes necessary. This study proposes the design of a Gain Scheduling controller to control the pressure at the bottom of wells during drilling. The GS controller is based on the corresponding tuning gains at different operating points in this case, the depth. First, presents the theories that will be used during development work. In the second part, was obtained a mathematical model of the process which is based on fluid mechanics. In the linearization of the, the final transfer function presents an integrating element which makes the process dynamics more difficult to handle. It becomes even more complex in the presence of time delay. In the third part, three IMC controllers’ types were used to tuning the PID (Proportional, Integral and Derivative) controller gains for different depths of drilling looking for the best performance, stability and robustness. Finally, was chose the best performing strategy (IMC of two degrees of freedom) to specify and assemble the GS controller table, which is evaluated by simulations of problems that usually occur during drilling, considered as disturbances, which check its viability. Also, the results of the controlled GS system are compared with the results of another adaptive controller model of model reference (MRAC). Also verifying that the GS controller presents better performance than MRAC. / PRH48/ANP: 48610.009725/2013

Submitted by MARIO ROLANDO RODRIGUEZ CADALSO null (mario.cadalso@gmail.com) on 2017-07-12T16:08:35Z No. of bitstreams: 1 Tese_Final.pdf: 2137231 bytes, checksum: 15875414251123bb7429e0efb684604c (MD5) / Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-07-14T17:05:32Z (GMT) No. of bitstreams: 1 rodriguez_cadalso_mr_me_ilha.pdf: 2137231 bytes, checksum: 15875414251123bb7429e0efb684604c (MD5) / Made available in DSpace on 2017-07-14T17:05:32Z (GMT). No. of bitstreams: 1 rodriguez_cadalso_mr_me_ilha.pdf: 2137231 bytes, checksum: 15875414251123bb7429e0efb684604c (MD5) Previous issue date: 2016-08-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho são propostas metodologias com base na teoria de estabilidade segundo Lyapunov para projetar controladores gain scheduling usando realimentação de estado ou derivativa e o conceito de D-estabilidade. As condições de projeto são dadas por desigualdades matriciais lineares (do inglês, Linear Matrix Inequalities - LMIs). A metodologia é aplicada em sistemas lineares sujeitos a parâmetros variantes no tempo (do inglês, Linear Parameter Varying - LPV). A utilização do Lema de Finsler eliminou a necessidade de inverter uma matriz literal para projetar o ganho de realimentação. Com o objetivo de satisfazer requisitos práticos, foi feito uso da restrição de D-estabilidade no projeto de um controlador para um sistema de suspensão ativa. A implementação prática mostra a eficiência da metodologia proposta. / In this work are proposed methologies based on Lyapunov stability theory for designing gain scheduling controller using state-derivative feedback or state feedback and considering D-stability constraint. The design conditions are given by Linear Matrix Inequalities. The methodology is applied on system with time-variant parameter. The use of Finsler’s Lemma eliminated the problem of inverting a symbolic matrix to calculate the feedback gain. The theory of D-stability allowed to get implementable controllers for an active suspension system. The practical implementation showed the efficiency of the proposed methodology.

Pour synthétiser un correcteur robuste pour un système linéaire incertain, il existe de nombreuses méthodes linéaires. Cependant, bien souvent, le gain en robustesse se fait au détriment de la performance. Aussi, dans cette thèse, on s'intéresse à la situation où la plage des valeurs possibles des paramètres est "très grande" par rapport à la "faible" variation du niveau de performance souhaité. Dans cette situation, il peut alors s'avérer intéressant d'utiliser des correcteurs séquencés. Seulement, la mise en place de cette solution nécessite que le correcteur ait à sa disposition les paramètres sur lesquels il sera séquencé. Et il peut arriver que l'on ne souhaite pas (à cause de considérations de réalisation pratique), ou que l'on ne puisse pas disposer de la mesure de ces paramètres. On est alors amené à estimer ces paramètres et donc à utiliser le paradigme de la commande adaptative. Dans cette thèse, on cherche à proposer une méthodologie de synthèse d'un correcteur auto-adaptatif afin de résoudre un problème de commande robuste d'un procédé linéaire incertain. Après une étude théorique ayant pour objectif de proposer une telle méthodologie, le cas d'un avion instable est traité à titre d'application, permettant ainsi de mettre en évidence le bénéfice que la stratégie proposée peut apporter à la commande d'un système incertain. / Many linear methods exist to design a robust controller for an uncertain linear system. This thesis considered the situation where the range of possible values of parameters is "very large" in relation to "small" variations in the desired level of performance. Frequently, an increase in robustness is obtained at the expense of a performance loss. The use of scheduled controllers may be an innovative way to address this problem. The implementation of this solution requires the controller has at its disposal the parameters on which the scheduling is done. However, it may occur that making the measure of the parameters available is not desired (for example, because of practical implementation aspects) or not possible. In these situations, the designer of the controller is led to estimate these parameters and then to use the paradigm of adaptive control. This thesis explored a methodology for designing an adaptive controller in which to solve the problem of robust control for an uncertain linear plant. A theoretical study was first undertaken which aimed to propose such a methodology; followed by, a study of the case of an unstable airplane as an application. Such an analysis highlighted the benefits that the proposed strategy can bring to the control for an uncertain plant.

This thesis work contains a stabilization and a motion planning strategy for a truck and trailer system. A dynamical model for a general 2-trailer with two rigid free joints and a kingpin hitching has been derived based on previous work. The model holds under the assumption of rolling without slipping of the wheels and has been used for control design and as a steering function in a probabilistic motion planning algorithm. A gain scheduled Linear Quadratic (LQ) controller with a Pure pursuit path following algorithm has been designed to stabilize the system around a given reference path. The LQ controller is only used in backward motion and the Pure pursuit controller is split into two parts which are chosen depending on the direction of motion. A motion planning algorithm called Closed-Loop Rapidly-exploring Random Tree (CL-RRT) has then been used to plan suitable reference paths for the system from an initial state configuration to a desired goal configuration with obstacle-imposed constraints. The motion planning algorithm solves a non-convex optimal control problem by randomly exploring the input space to the closed-loop system by performing forward simulations of the closed-loop system. Evaluations of performance is partly done in simulations and partly on a Lego platform consisting of a small-scale system. The controllers have been used on the Lego platform with successful results. When the reference path is chosen as a smooth function the closed-loop system is able to follow the desired path in forward and backward motion with a small control error. In the work, it is shown how the CL-RRT algorithm is able to plan non-trivial maneuvers in simulations by combining forward and backward motion. Beyond simulations, the algorithm has also been used for planning in open-loop for the Lego platform. / <p>Links to movies:</p><p>Reference tracking on Lego platform:</p><p>https://www.dropbox.com/s/ebtfgfo7aq9ij8w/reference_tracking.m4v?dl=0</p><p></p><p>Motion planning simulation with CL-RRT:</p><p>https://www.dropbox.com/s/z9kk27cxdxc1llp/CL_RRT_motion_planning.wmv?dl=0</p>