<p>This thesis has been conducted at Saab Bofors Dynamics AB. The purpose was to investigate if a non-linear missile model could be stabilized when the optimal control signal is computed considering constraints on the control input. This is particularly interesting because the missile is controlled with rudders that have physical bounds. This strategy is called Model Predictive Control. Simulations are conducted to compare this strategy with others; firstly simulations with step responses and secondly simulations when the missile is supposed to hit a moving target. The latter is performed to show that the missile can be stabilized in its whole area of operation. The simulations show that the controller indeed can stabilize the missile for the given scenarios. However, this control strategy does not show any obvious improvements in comparison with alternative ones.</p>

This thesis has been performed at SAAB Bofors Dynamics. The purpose was to derive a robust control design for a nonlinear missile using backstepping. A particularly interesting matter was to see how different design choices affect the robustness. Backstepping is a relatively new design method for nonlinear systems which leads to globally stabilizing control laws. By making wise decisions in the design the resulting closed loop can receive significant robustness. The method also makes it possible to benefit from naturally stabilizing aerodynamic forces and momentums. It is based on Lyapunov theory and the control laws and a Lyapunov function are derived simultaneously. This Lyapunov function is used to guarantee stability. In this thesis the control laws for the missile are first derived by using backstepping. The missile dynamics are described with aerodynamic coeffcients with corresponding uncertainties. The robustness of the design w.r.t. the aerodynamic uncertainties is then studied further in detail. One way to analyze how the stability is affected by the errors in the coeffcients is presented. To improve the robustness and remove static errors, dynamics are introduced in the control laws by adding an integrator. One conclusion that has been reached is that it is hard to immediately determine how a certain design choice affects the robustness. Instead it is at the point when algebraic expressions for the closed loop system have been obtained, that it is possible to analyze the affects of a certain design choice. The designed control laws are evaluated by simulations which shows satisfactory results.

This thesis has been conducted at Saab Bofors Dynamics AB. The purpose was to investigate if a non-linear missile model could be stabilized when the optimal control signal is computed considering constraints on the control input. This is particularly interesting because the missile is controlled with rudders that have physical bounds. This strategy is called Model Predictive Control. Simulations are conducted to compare this strategy with others; firstly simulations with step responses and secondly simulations when the missile is supposed to hit a moving target. The latter is performed to show that the missile can be stabilized in its whole area of operation. The simulations show that the controller indeed can stabilize the missile for the given scenarios. However, this control strategy does not show any obvious improvements in comparison with alternative ones.

<p>This thesis has been performed at SAAB Bofors Dynamics. The purpose was to derive a robust control design for a nonlinear missile using backstepping. A particularly interesting matter was to see how different design choices affect the robustness. Backstepping is a relatively new design method for nonlinear systems which leads to globally stabilizing control laws. By making wise decisions in the design the resulting closed loop can receive significant robustness. The method also makes it possible to benefit from naturally stabilizing aerodynamic forces and momentums. It is based on Lyapunov theory and the control laws and a Lyapunov function are derived simultaneously. This Lyapunov function is used to guarantee stability. In this thesis the control laws for the missile are first derived by using backstepping. The missile dynamics are described with aerodynamic coeffcients with corresponding uncertainties. The robustness of the design w.r.t. the aerodynamic uncertainties is then studied further in detail. One way to analyze how the stability is affected by the errors in the coeffcients is presented. To improve the robustness and remove static errors, dynamics are introduced in the control laws by adding an integrator. One conclusion that has been reached is that it is hard to immediately determine how a certain design choice affects the robustness. Instead it is at the point when algebraic expressions for the closed loop system have been obtained, that it is possible to analyze the affects of a certain design choice. The designed control laws are evaluated by simulations which shows satisfactory results.</p>

This master's thesis deals with the control design method called Non-linear Dynamic Inversion (NDI) and how it can be applied to Unmanned Aerial Vehicles (UAVs). In this thesis, simulations are conducted using a model for the unmanned aerial vehicle SHARC (Swedish Highly Advanced Research Configuration), which Saab AB is developing. The idea with NDI is to cancel the non-linear dynamics and then the system can be controlled as a linear system. This design method needs much information about the system, or the output will not be as desired. Since it is impossible to know the exact mathematical model of a system, some kind of robust control theory is needed. In this thesis integral action is used. A problem with NDI is that the mathematical model of a system is often very complex, which means that the controller also will be complex. Therefore, a controller that uses pure NDI is only discussed, and the simulations are instead based on approximations that use a cascaded NDI. Two such methods are investigated. One that uses much information from aerodata tables, and one that uses the derivatives of some measured outputs. Both methods generate satisfying results. The outputs from the second method are more oscillatory but the method is found to be more robust. If the signals are noisy, indications are that method one will be better.

<p>This master's thesis deals with the control design method called Non-linear Dynamic Inversion (NDI) and how it can be applied to Unmanned Aerial Vehicles (UAVs). In this thesis, simulations are conducted using a model for the unmanned aerial vehicle SHARC (Swedish Highly Advanced Research Configuration), which Saab AB is developing. </p><p>The idea with NDI is to cancel the non-linear dynamics and then the system can be controlled as a linear system. This design method needs much information about the system, or the output will not be as desired. Since it is impossible to know the exact mathematical model of a system, some kind of robust control theory is needed. In this thesis integral action is used. </p><p>A problem with NDI is that the mathematical model of a system is often very complex, which means that the controller also will be complex. Therefore, a controller that uses pure NDI is only discussed, and the simulations are instead based on approximations that use a cascaded NDI. Two such methods are investigated. One that uses much information from aerodata tables, and one that uses the derivatives of some measured outputs. Both methods generate satisfying results. The outputs from the second method are more oscillatory but the method is found to be more robust. If the signals are noisy, indications are that method one will be better.</p>

La propulsion aérobie à grande vitesse est depuis longtemps identifiée comme l'un des prochains sauts technologiques à franchir dans le domaine des lanceurs spatiaux. Cependant, les véhicules hypersoniques (HSV) fonctionnant dans des domaines de vitesse extrêmement élevées, de nombreuses contraintes et incertitudes entravent les garanties des propriétés des contrôleurs. L'objet de cette thèse est d'étudier la synthèse de commande d'un tel véhicule.Pour commencer, il s'agit de définir un modèle représentatif d'un HSV exploitable pour la commande. Dans ce travail, nous construisons deux modèles de HSV. Un pour la simulation en boucle fermée, et le second afin de poser précisément le problème de commande.Nous proposons ensuite une synthèse de commande de la dynamique longitudinale dans le plan vertical de symétrie. Celle-ci est robuste aux incertitudes de modélisation, tolérante à des saturations, et n'excite pas les dynamiques rapides négligées. Ses propriétés sont évaluées sur différents cas de simulation. Puis, une extension est proposée afin de résoudre le problème de commande simultanée des dynamiques longitudinale et latérale, sous les mêmes contraintes.Ce résultat est obtenu par une assignation de fonction de Lyapunov, suite à une étude des dynamiques longitudinale et latérale. Par ailleurs, pour traiter les erreurs de poursuite dues aux incertitudes de modélisation, nous nous intéressons au problème de régulation asymptotique robuste par retour d'état. Nous montrons que cette régulation peut être accomplie en stabilisant le système augmenté d'un intégrateur de la sortie. Ceci constitue une extension de la structure de contrôle proportionnel-intégral au cas des systèmes non linéaires. / High speed airbreathing thrust has been known for a long time as one of the next technological step to be overcome in space launchers domain. However, HyperSonic Vehicles (HSV) speed operating ranges being extremely high, numerous constraints and uncertainties restrict the ensuring of control properties. The purpose of this thesis is to study control synthesis for such a vehicle.First, it concern the definition of a HSV model for controlling purpose. In this work is constructed two HSV models. One in order to effect closed loop simulation, and the other in order to precisely establish the control problem.Then, is proposed a control synthesis for the longitudinal dynamics restricted to the symmetric vertical plane. It is robust to modelling uncertainties, allows saturation, and does not excite neglected fast dynamics. Its properties are evaluated on different cases of simulation. Next, an extension is proposed in order to solve the problem of controlling simultaneously longitudinal and lateral dynamics, under the same constraints.This result is obtained by the use of control Lyapunov functions, following the study of longitudinal and lateral dynamics. Furthermore, in order to solve tracking errors due to modelling uncertainties, the problem of robust asymptotic regulation by state feedback has been addressed. It is shown that such a regulation can be achieved by stabilizing the system augmented by an output integrator. This constitutes an extension for nonlinear systems of the proportional-integral control structure.

The Permanent Magnet Synchronous Motor (PMSM, also known as the servo motor) is a crucial component within robotic servo systems. To optimally respond to the torque demands sent from the high-level motion controller, the PMSM current controller must track the reference with speed and precision. Nevertheless, the operation of servo motors could be compromised due to the nonlinearity of flux linkage and inaccuracies in parameters induced by unpredictable fluctuations in temperature. This Master’s thesis proposes a novel Robust Nonlinear Deadbeat Predictive Current Control (RN-DPCC) scheme to counter these challenges effectively. The nonlinear mappings between flux linkage and current on the dq-axis are established using polynomial fitting based on experimental data. Furthermore, the Nonlinear Deadbeat Predictive Current Control (N-DPCC) is derived using nonlinear feedforward. Meanwhile, Delayed Integral Action (DIA) is introduced as a robustness-enhancing measure for N-DPCC, thus evolving it into the Robust N-DPCC (RN-DPCC). Compared to conventional Integral Action (IA), DIA effectively curtails overshoot triggered by integral error and accelerates the current transient without incorporating additional tunable parameters. Numerical simulations that leverage the mathematical modeling of the converter and nonlinear PMSM are implemented using fundamental blocks in Simulink, which replicates the actual experimental setup employed within the Motor Control Lab at ABB Corporate Research. The effectiveness of employing nonlinear feedforward compensation is confirmed through a comparative analysis of the simulation results from N-DPCC and conventional Deadbeat Predictive Current Control (DPCC). The enhancements in transient response brought about by DIA are demonstrated through a comparison of RNDPCC and N-DPCC with IA. The robustness of RN-DPCC is demonstrated by comparing it with N-DPCC under conditions where parameter inaccuracies are present. / Den permanenta magnet-synkronmotorn (PMSM, även känd som servomotorn) är en avgörande komponent inom robotiserade servosystem. För att optimalt kunna reagera på momentkraven som skickas från högnivårörelsekontrollern måste PMSM-strömregulatorn följa referensen med hastighet och precision. Trots detta kan driften av servomotorer påverkas av ickelinjäriteter i flödeslänkningen och felaktigheter i parametrar som orsakas av oförutsägbara temperaturfluktuationer. Denna magisteravhandling föreslår en ny robust icke-linjär deadbeat-prediktiv strömreglering (RN-DPCC) för att effektivt hantera dessa utmaningar. De icke-linjära avbildningarna mellan flödeslänkning och ström på dq-axeln etableras med hjälp av polynomisk anpassning baserat på experimentella data. Dessutom härleds den ickelinjära deadbeat-prediktiva strömregleringen (N-DPCC) med hjälp av Ickelinjär feedforward. Samtidigt introduceras fördröjd integralåtgärd (DIA) som en robusthetsförbättrande åtgärd för N-DPCC, vilket förvandlar den till Robust N-DPCC (RN-DPCC). Jämfört med konventionell integralåtgärd (IA) minskar DIA effektivt överhäng som utlöses av integralfel och accelererar strömövergången utan att införa ytterligare justerbara parametrar. Numeriska simuleringar som utnyttjar den matematiska modelleringen av omvandlaren och den icke-linjära PMSM implementeras med hjälp av grundläggande block i Simulink, vilket återskapar den faktiska experimentella uppställningen som används i Motor Control Lab vid ABB Corporate Research. Effektiviteten i att använda icke-linjär framåtmatningskompensation bekräftas genom en jämförande analys av simulationsresultaten från N-DPCC och konventionell deadbeat-prediktiv strömreglering (DPCC). Förbättringarna i transientrespons som DIA medför demonstreras genom en jämförelse av RN-DPCC och NDPCC med IA. Robustheten hos RN-DPCC demonstreras genom att jämföra den med N-DPCC under förhållanden där parameterfel förekommer.