Tracking control methodologies for a quadrotor UAV

This thesis deals with the problem of designing linear and nonlinear controllers for unmanned quadrotor system stabilization and path tracking. Highly nonlinear and strongly coupling structure of quadrotor makes "Inverse Optimal Control (IOC)" a suitable method for the quadrotor nonlinear position and attitude control. This method is applied to the quadrator using a discrete-time nonlinear affine system model. PID controllers and linear quadratic regulator (LQR) are also applied the system as wellknown linear control strategies. All control methods used in the thesis are compared with each other on a highly nonlinear quadrotor model. Firstly, a highly nonlinear system model with both rigid body dynamics and aerodynamics is introduced. This nonlinear model of quadrotor is linearized around an equilibrium point which is hovering. This linearized model of the quadrotor is represented in state space in order to design LQR for altitude and attitude tracking of the quadrator. In this thesis, IOC also known as Inverse Reinforcement Learning (ILR) formulation is used to solve the reference tracking problem relying on the use of control lyapunov function (CLF) in the establishment of the control law for discrete-time nonlinear quadrotor system. Inverse optimal control approach is beneficial when compared to traditional nonlinear optimal control approach because IOC approach does not bring heavy computational burden as there is no need to solve Hamilton-Jacobi-Bellman (HJB) equation. At first, a stabilizing feedback control law is constructed such that Control Lyapunov Function (CLF) is known a priori. After this stability examination and determination of a meaningful cost functional, this respective cost functional is optimized. Then, a matrix which will minimize a tracking error function is searched by using PSO algorithm. Apart from trajectory error consideration, the control effort limitations based on not exceeding the actuation force limits were also taken into account. While using linear controllers in a nonlinear system, the influence of saturation limits of the actuator are obvious in the output. The inability of the quadrotor especially in following attitude commands is one of the drawbacks of using a linear controllers. The limitations of control effort that are considered during closed loop operation are brought by means of a penalty factor in the cost function only if control inputs go beyond the allowable minimum or maximum values. Subsequently, in the light of all comparative results of different controllers (proportional integral derivative, linear quadratic regulator, nonlinear method), it seems there is a variety of design specifications which require specific execution strategies. The strongest advantage of nonlinear controller design is that it gives the best possible results by enhancing performance based on parameter optimization using evolutionary algorithm. Finally, three different control approaches have been compared in this thesis. The feasibility and effectiveness of designed controllers has been verified based upon dynamic performance of the system as demonstrated in simulation results.