Fuzzy-Lyapunov based controller for a quadrocopter

Quadrocopters are nonlinear and inherently unstable systems. To be able to account for the nonlinearities during more aggressive manoeuvres nonlinear control methods need to be utilized to obtain the desired position while at the same time guaranteeing stability. In the article, the quadrocopter dynamics is modelled using the Newton-Euler method. The propeller aerodynamics is modelled using a combination of momentum theory and blade element theory. There are two different control objectives; the 1st objective requires the quadrocopter to reach a desired attitude set point using, while the 2nd objective requires the quadrocopter to track an attitude trajectory. In both cases, Lyapunov stability criterion, in conjunction with LaSalle’s invariance principle, is used to guarantee the system becomes asymptotically stable. In the case of reaching the desired attitude set point, a direct Lyapunov control method is implemented with the control constants determined empirically. For the trajectory tracking, limited knowledge is assumed on the system dynamics and the Mamdani fuzzy controller is used with a rule base that satisfy the Lyapunov stability criterion. The fuzzy membership functions developed empirically and a centre of gravity defuzzification method is used. All simulations are done in MATLAB/Simulink. The results of the numerical simulation are presented in the article.