# Robust Control of Electric Tail Reduction System: Uncertainty and Performance Index
## 1 Introduction  
In recent years, the application of unmanned aircraft systems (UAS) in the military and civil fields is attracting people's attention and interest [1]. Compared with fixed-wing unmanned aerial vehicles (UAVs), the rotor UAV has the characteristics of vertical take-off and landing, hovering, and flight at very low altitude, so it is used in a wider spectrum of applications [2]. With the rapid development of battery and motor technology, the advantages of unmanned electric helicopter have gradually been reflected [3]. On one hand, compared with the traditional fuel helicopter, the electric unmanned helicopter has the characteristics of lower noise, smaller vibration, higher reliability, and no pollution. On the other hand, the main flight performance algorithms and the design of autonomous flight control systems provide references for the development of electric helicopters. Therefore, unmanned electric helicopters with good mobility and low cost have recently been applied in various fields [4, 5]. Unmanned electric helicopters have significant dynamic coupling, which is an inherently unstable and highly nonlinear underactuated system. These factors lead to serious challenges in dealing with robustness, disturbance rejection, decoupling, and other control problems [5]. In the control of an unmanned helicopter, some scholars have undertaken relevant research such as robust control [6, 7], adaptive control [8, 9, 10, 11], nonlinear attitude control [12], finite-time control [13], fuzzy control [14, 15], and heading control of a composite helicopter [16]. Similar to the trend of aircraft electrification known as the \"More Electric Aircraft\" (MEA) approach, helicopter propulsion system and its flight control devices are undergoing a system optimization using electric actuators [3]. The electric tail reduction system of the unmanned helicopter is a typical electric actuator integrated system composed of a permanent magnet synchronous motor, reducer, and tail rotor, which is based on the background of independent speed control of the main rotor and the tail rotor. The speedof the tail rotor is variable, which could reduce the flight resistance of tail rotor when the helicopter flies forward, and improve the operational flexibility and efficiency reliability of the helicopter. In this way, the stagnation of the tail rotor when the main rotor speed suddenly drops can be avoided by decoupling the control of the main rotor and tail rotor. For these reasons, some scholars have undertaken related research. [PERSON] and [PERSON] studied variable tail rotor speed as a method to improve helicopter performance [17], and a dynamic response platform for collecting the thrust of an independent electric tail rotor was built by [PERSON] [3]. However, one of the main faults of a helicopter is the failure of the tail rotor, which occurs frequently and causes accidents [18]. The aerodynamic interference between the main rotor and the tail rotor will have a strong negative impact on the flight dynamics of conventional helicopters [19]. The electric tail reduction system is affected by uncertainty, aerodynamics, and dynamic coupling, which is determined by the inherent characteristics of the helicopter. Therefore, the research on its dynamic control is significant and challenging. To control such nonlinear uncertain systems, many outstanding works have been done. A fuzzy backstepping sliding mode control for a manipulator with nonlinear disturbance observer was proposed by [PERSON] [20]. A global fast sliding mode control to effectively compensate for the uncertain parameter variations and external disturbances was proposed by [PERSON] [21]. The servo constraint control based on the Udwadia-Kalaba theory is one of the most advanced research directions at present. [PERSON] proposed the tracking control of nonlinear mechanical systems based on the servo constraint control method [22; 23; 24; 25]. In addition, he completed precise trajectory control with the advantage of less computation [26].