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<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>

Robust control design has become a major research area during the last twenty years and there are nowadays several robust design methods available. One example of such a method is the robust loop shaping method that was developed by K. Glover and D. C. MacFarlane in the late 1980s. The idea of this method is to use decentralized controller design to give the singular values of the loop gain a desired shape. This step is called Loop Shaping and it is followed by a Robust Stabilization procedure, which aims to give the closed loop system a maximum degree of stability margins. In this thesis, the robust loop shaping method is used to design a gain scheduled controller for a missile. The report consists of three parts, where the first part introduces the Robust Loop Shaping theory and a Gain Scheduling approach. The second part discusses the missile and its characteristics. In the third part a controller is designed and a short analysis of the closed loop system is performed. A scheduled controller is implemented in a nonlinear environment, in which performance and robustness are tested. Robust Loop Shaping is easy to use and simulations show that the resulting controller is able to cope with model perturbations without considerable loss in performance. The missile should be able to operate in a large speed interval. There, it is shown that a single controller does not stabilize the missile everywhere. The gain scheduled controller is however able to do so, which is shown by means of simulations.

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>Robust control design has become a major research area during the last twenty years and there are nowadays several robust design methods available. One example of such a method is the robust loop shaping method that was developed by K. Glover and D. C. MacFarlane in the late 1980s. The idea of this method is to use decentralized controller design to give the singular values of the loop gain a desired shape. This step is called Loop Shaping and it is followed by a Robust Stabilization procedure, which aims to give the closed loop system a maximum degree of stability margins. In this thesis, the robust loop shaping method is used to design a gain scheduled controller for a missile. The report consists of three parts, where the first part introduces the Robust Loop Shaping theory and a Gain Scheduling approach. The second part discusses the missile and its characteristics. In the third part a controller is designed and a short analysis of the closed loop system is performed. A scheduled controller is implemented in a nonlinear environment, in which performance and robustness are tested. Robust Loop Shaping is easy to use and simulations show that the resulting controller is able to cope with model perturbations without considerable loss in performance. The missile should be able to operate in a large speed interval. There, it is shown that a single controller does not stabilize the missile everywhere. The gain scheduled controller is however able to do so, which is shown by means of simulations.</p>

DYNAMIC MODELING, GUIDANCE, AND CONTROL OF HOMING MISSILES &Ouml / ZKAN, B&uuml / lent Ph. D., Department of Mechanical Engineering Supervisor: Prof. Dr. M. Kemal &Ouml / ZG&Ouml / REN Co-Supervisor: Dr. G&ouml / kmen MAHMUTYAZICIOgLU September 2005, 236 pages In this study, the dynamic modeling, guidance, and control of a missile with two relatively rotating parts are dealt with. The two parts of the missile are connected to each other by means of a roller bearing. In the first part of the study, the governing differential equations of motion of the mentioned missile are derived. Then, regarding the relative rotation between the bodies, the aerodynamic model of the missile is constructed by means of the Missile Datcom software available in T&Uuml / BiTAK-SAGE. After obtaining the required aerodynamic stability derivatives using the generated aerodynamic data, the necessary transfer functions are determined based on the equations of motion of the missile. Next, the guidance laws that are considered in this study are formulated. Here, the Linear Homing Guidance and the Parabolic Homing Guidance laws are introduced as alternatives to the Proportional Navigation Guidance law. On this occasion, the spatial derivation of the Proportional Navigation Guidance law is also done. Afterwards, the roll, pitch and yaw autopilots are designed using the determined transfer functions. As the roll autopilot is constructed to regulate the roll angle of the front body of the missile which is the controlled part, the pitch and yaw autopilots are designed to realize the command signals generated by the guidance laws. The guidance commands are in the form of either the lateral acceleration components or the flight path angles of the missile. Then, the target kinematics is modeled for a typical surface target. As a complementary part of the work, the design of a target state estimator is made as a first order fading memory filter. Finally, the entire guidance and control system is built by integrating all the models mentioned above. Using the entire system model, the computer simulations are carried out using the Matlab-Simulink software and the proposed guidance laws are compared with the Proportional Navigation Guidance law. The comparison is repeated for a selected single-body missile as well. Consequently, the simulation results are discussed and the study is evaluated.