This paper proposes a design method for a wind-disruption-resistant position controller for small unmanned helicopters based on the Lyapunov redesign framework. In this paper, wind disturbances are no longer considered as disturbances near the equilibrium state, but rather as additional force/torque inputs to the state equations, which can be estimated using experimental data obtained from the wind tunnel.
1 Introduction
In recent years, autonomous flight technology for unmanned helicopters has developed rapidly and has been widely applied in various fields. In particular, autonomous flight control technology in complex environments has attracted continuous attention from scholars in industry and academia.
Numerous controller design methods have been proposed over the past few decades. Most controller design methods are model-based, and these can be further divided into linear and nonlinear control methods. For example, the LQG controller and PD-PID controller, proposed in recent years, belong to linear control methods. These methods typically require linearization at certain equilibrium points, resulting in unsatisfactory stability and robustness. Other researchers employ model-based nonlinear control methods, such as sliding mode control, fuzzy gain control, nonlinear model predictive control, and inversion methods. Notably, inversion methods can effectively facilitate systematic and structured controller design, particularly suitable for unmanned helicopter models with upper triangular state equation characteristics.
In addition, some research groups have attempted to employ model-free control strategies. Examples include neural network-based position controllers and reinforcement learning-based controllers. These controller design methods do not require precise system models but rely heavily on extensive training data from pilots, making them unsuitable for controller design in complex environments such as high winds.
Wind interference resistance, a core challenge that unmanned helicopters (UHV) must face and overcome in outdoor flights, has attracted attention from scholars both domestically and internationally. However, compared to UHV control and modeling methods, research on wind interference resistance methods is still in its early stages. Some literature uses sensors to estimate wind disturbances and designs nonlinear feedforward controllers to achieve wind resistance. Others employ constrained finite-time optimal controllers (CFTOC) to control quadcopter UHVs in strong winds. Furthermore, some researchers use active interference rejection controllers (AICs) to compensate for wind interference, with interference information obtained from various interference observers, such as high-gain state observers, extended state observers, and Kalman state observers. However, these observation-based methods may introduce inaccurate observations, leading to suboptimal control results. One literature proposes a novel hybrid control structure that directly compensates for wind interference using force/torque, but due to the diversity of real-world scenarios, force and torque may not be calculated correctly. This paper proposes a new wind disturbance resistance control structure. First, an inversion controller is designed for the nominal system, and then a wind disturbance resistance controller is designed using nonlinear damping techniques to achieve the desired wind disturbance resistance.
2 Control System Design
2.1 Nonlinear Model of UAV
The six-degree-of-freedom rigid body dynamics model of an unmanned helicopter can be described by the following equations:
To suppress horizontal wind interference, we improved upon the hybrid control framework in the literature and proposed a new control framework, the overall control block diagram of which is shown in Figure 1.
The force/torque vectors include uncertain disturbances caused by wind interference, which are treated as additional inputs to the system rather than small disturbances caused by wind interference. Since the entire system satisfies the Lyapunov redesign framework, we design the overall controller in two parts: first, the nominal system without wind interference, which can be designed using the inversion method; and second, the system with disturbances caused by wind interference, for which the control law is designed to suppress disturbances by combining the inversion method with nonlinear damping. After obtaining the control law of the entire system, we can analyze it using Lyapunov stability to prove that the overall system outputs uniformly bounded under this controller.
2.3 Wind Transfer Function
The amount of disturbance caused by wind can be estimated using the following wind transfer function:
2.4 Design of Inversion Controller with Nonlinear Damping
In this section, the control law for the nominal system without wind interference is first designed using the inversion method, and then the wind-resistant controller for the case of uncertain strong wind interference is designed using the nonlinear damping method.
First, disregarding the nominal system under wind conditions, the external forces and torques acting on the unmanned helicopter are equal to the forces and torques generated by the helicopter itself through the rotor. We can use an inversion algorithm and select a Lyapunov candidate function to derive the expressions for the forces and torques required to reach the desired position under the nominal system.
The first Lyapunov candidate function can be:
This indicates that the solution to the state is uniformly bounded near the origin, so the position, linear velocity, and angular velocity of the unmanned helicopter can approach the target point within a finite amount of time.
After obtaining the required force and torque, we can deduce the servo control input through the dynamic model of the main rotor, the stabilizer bar, and the servo dynamic model of the servo.
Simulation results
In this chapter, the control system proposed in this paper was simulated in MATLAB/SIMULINK. The initial position was set to (-0.5m, 0.5m, 0.5m), and the target position was the origin (0m, 0m, 0m). The control performance of the controller under 0° (longitudinal) and 270° (lateral) gusts was simulated respectively. Case A: There is no wind disturbance in the first 10s and the last 10s, and there is wind disturbance with constant wind speed (ranging from 2m/s to 8m/s) from 10s to 20s. Figure 2 shows the control effect of the helicopter position controller under longitudinal horizontal gust disturbance. The selected parameters are 2.5 and 3. Figure 3 shows the control effect of the position controller under lateral horizontal gust disturbance, with controller parameters 2.5 and 3. Figure 4 shows the control input of the servo motor under longitudinal horizontal gust (6m/s) disturbance. Scenario B: Wind interference occurs throughout the entire simulation period (30s), with constant wind speeds of 2m/s, 4m/s, 6m/s, and 8m/s respectively. Figure 6 shows the control effect of the position controller under longitudinal horizontal constant wind interference. Selected parameters = 2.5, = 3. Figure 5 shows the control effect of the position controller under lateral horizontal constant wind interference, with selected parameters = 2.5, = 3. Figure 7 shows the control input of the servo motor under lateral horizontal constant wind (6m/s) interference.
in conclusion
The wind-disruption-resistant position controller for unmanned helicopters proposed in this paper comprises a theoretically designed controller and a force/torque compensator based on wind tunnel experimental data. In this paper, the experimentally obtained force/torque is considered an uncertain disturbance and cannot be directly compensated; instead, it requires nonlinear damping. Simulation results show that the proposed control method effectively suppresses horizontal wind disturbances. Compared with previously proposed hybrid control structures, the novel control system designed in this paper still functions normally when the force and torque cannot be calculated correctly or accurately. Future work will attempt to apply the proposed controller design method to actual unmanned helicopter flights for experimental testing.
