Model reference fractional order control using type-2 fuzzy neural networks structure: Implementation on a 2-DOF helicopter

In this paper, an adaptive learning algorithm is proposed for an interval type-2 fuzzy fractional order controller. The use of fractional order controller adds more degrees of freedom which makes it possible to obtain superior performance in comparison with ordinary differential controllers. A fractional order reference model is used to define the desired trajectory of the nonlinear dynamic system. The structure of the system is based on the feedback error learning method. The stability of the adaptation laws is proved using Lyapunov theory. In order to test the efficiency and efficacy of the proposed learning and the control algorithm, the trajectory tracking problem of a magnetic rigid spacecraft is studied. The simulation results show that the proposed control algorithm outperforms the case when ordinary differential fuzzy controller is used. Furthermore, it is shown that it is possible to define a master chaotic system as a reference model and obtain synchronization between the two chaotic systems using the proposed approach. In the simulation part the synchronization between two Duffing–Holmes system is also achieved. In order to show the implementability of the proposed method, it is used to control a real time laboratory setup 2-DOF helicopter. It is shown that the proposed fractional order controller can be implemented in a low cost embedded system and can successfully control a highly nonlinear dynamic system.