This paper proposes a new control structure containing polynomial-fuzzy-model-based (PFMB) control and variable speed control (VSC) for the quadcopter unmanned aerial vehicle (UAV). In the proposed structure, the PFMB control is applied to regulate the attitude (roll-pitch-yaw) and altitude. Moreover, the VSC dominates the horizontal movement. In the PFMB control part, the error state vector is first utilized to construct an error dynamic system for regulation. Then, the error dynamic system is transformed into a polynomial fuzzy model. Applying the transformed polynomial fuzzy model, a polynomial control is designed to stabilize the error dynamic system. Furthermore, for disturbance rejection and fast settling time, another polynomial control design considering \(H_{\infty }\) performance and decay rate maximization is also proposed. The polynomial control design is represented as sum-of-squares (SOS) conditions which can be efficiently solved by some available SOS tools. The parameters of a quadcopter UAV from the previous study are considered in a design example of attitude and altitude control. The result shows that the proposed \(H_{\infty }\) control design with the decay rate maximization method has the fastest settling time with excellent disturbance rejection performance. In the VSC part, the flying speed is scheduled according to the horizontal moving distance. Initially, a proportional-integral (PI) controller is used to generate the reference attitude, allowing the polynomial controller to manage the quadcopter UAV’s speed for tracking the scheduled speed. When the quadcopter UAV nears its target, an additional proportional–derivative (PD) controller is employed to ensure that it reaches the destination accurately. Finally, the simulation result of a real-world quadcopter UAV application is provided to show the value and utility of the proposed control structure.
