Quaternion-based linear quadratic regulator and integral controller design for a fixed-wing aircraft

In literature, lots of works that build on Euler-based aircraft models dwell on regulation and tracking problems. However, quaternions are rarely used for solving those problems for fixed-wing aircraft though they have nice features such as avoidance of singularities and ease of algebraic properties. Moreover, quaternions prevent gimbal lock which means the loss of a three-dimensional degree of freedom caused by Euler angles and provide advantages in many ways. In numerous works, quaternions are preferred for spacecraft, satellite vehicles, or drones. In this work, for the purpose of extending the current state of research, the Euler-based aircraft model provided by Airlib library has been transformed into a quaternion-based aircraft model. Additionally, quaternion-based linear quadratic regulator and quaternion-based linear quadratic integral controller are synthesized and implemented for the Cessna 172 aircraft. The design of the controller and the simulation of the whole system was done in the MATLAB/Simulink environment. In control theory, the regulation problem is an important class of optimal control problems. The aim of solving regulator problems is to drive the state vectors as close as possible to the origin of the state vector from any nonzero initial values of states. Furthermore, it is desired to perform that without excessive control effort. In this thesis, different kinds of regulation problems for different systems and their solutions are touched on. The linear quadratic regulator aims to minimize the performance index (i.e. the cost function) with an optimal state feedback control law by solving the optimization problem with the selection of appropriate weight matrices. The selection of weight matrices is used to identify two conflicting criteria for the optimization problem. First, the system regulation should be fast, while the second criterion requires the controller input to be low. According to the needs of the system, it is decided which of these two criteria is more important and the coefficients for the weight matrices are selected. In this thesis, the aim of the designed regulator and controller is to avoid saturation by using less control. It is observed from the simulation results, obtained with the quaternion-based linear quadratic regulator designed for the Cessna 172 aircraft, that the system states successfully go fromthe initial values to the desired values and that the system inputs and quaternion values are regulated.Reference tracking is aimed with the quaternion-based linear quadratic integral approach obtained by adding an integral action in quaternion-based linear quadratic regulator design. Also, by adding the integral action to the feedback controller, the steady-state error has been improved with an accumulation of the integrator state. The simulation results show that the objectives are fulfilled. This study has expanded the research area by addressing the application of quaternion-based controllers, which are rarely found in the literature, to fixed wing aircraft. In future studies, in addition to the studies in the thesis, a state observer can be added to predict system states and surpass process and measurement noise. The results can be verified twice by performing a flight simulation using X-plane, a highly realistic simulation program. Lastly, both designs in this thesis is adaptable to all aircraft, they can be updated and applied to different aircraft models.