Robust Backstepping Control of Wing Rock Using Disturbance Observer
Wing rock is a highly nonlinear phenomenon when the aircraft suffers undesired roll-dominated oscillatory at high angle of attack (AOA). Considering the strong nonlinear and unsteady aerodynamic characteristics, an uncertain multi-input and multi-output (MIMO) nonlinear wing rock model is studied, and system uncertainties, unsteady aerodynamic disturbances and external disturbances are considered in the design of wing rock control law. To handle the problem of multiple disturbances, a robust
... bances, a robust control scheme is proposed based on the extended state observer (ESO) and the radial basis function neural network (RBFNN) technique. Considering that the effectiveness of actuators are greatly decreased at high AOA, the input saturation problem is also handled by constructing a corresponding auxiliary system. Based on the improved ESO and the auxiliary system, a robust backstepping control law is proposed for the wing rock control. In addition, the dynamic surface control (DSC) technique is introduced to avoid the tedious computations of time derivatives for the virtual control laws in the backstepping method. The stability of the closed-loop system is guaranteed via rigorously Lyapunov analysis. Finally, simulation results are presented to illustrate the effectiveness of the ESO and the proposed wing rock control approach. or traditional extended state observer (ESO) was adopted in the design of robust wing rock control law. However, the yaw oscillation was often ignored in the design of wing rock controller for the convenience of research. Considering the serious coupling effect between the roll and yaw motion, multi-degree-of-freedom wing rock models should be further studied. In this paper, an uncertain multi-input and multi-output (MIMO) nonlinear wing rock model is studied, and the coupling effect between the roll oscillation and yaw oscillation will be fully considered in the design of the wing rock controller. Meanwhile, to enhance the system robustness, the ESO and radial basis function neural network (RBFNN) techniques are combined to tackle the external disturbances and system uncertainties, respectively. Up to now, more and more researchers have paid attention to the study of the ESO or RBFNN based control techniques    . In  , an adaptive neural network based control law was developed for an uncertain MIMO system with unknown control coefficient matrices and input nonlinearities. In , the observer and adaptive neural network (NN) techniques were combined to tackle the uncertainties. To tackle the state constraint problem, the adaptive neural network technique was employed for an uncertain robot system  . And the ESO technique was firstly proposed in the active disturbance rejection control (ADRC)  . It has been successfully used in many challenging engineering problems [26, 27] . The main advantage of the traditional ESO is that it can handle various disturbances with little model information, and it takes both structured and unstructured uncertainties as generalized disturbances. Hence, considering the satisfactory uncertainty estimation performance, the ESO and RBFNN are fully combined in the design of the robust wing-rock control law. Meanwhile, except for uncertainties, the input saturation problem will also cause adverse effects on the performance of the wing rock control. Input saturation is a challenging problem in the wing rock control. With the increase of AOA, the aircraft will lose the control efficiency gradually, which severely degrades the closed-loop system performance. During the past decades, there exist extensive researches on the control of mechanical systems with input saturation    . In  , an adaptive neural tracking control was considered for a class of stochastic nonlinear systems with input saturation, and a smooth nonaffine function of the control input signal was designed to approximate the input saturation function. In , a modified fault tolerant control law was designed to handle the input saturation problem. Constrained adaptive backstepping control was proposed based on the command filters in  . Inspired by , the auxiliary system is designed to weaken the influence of the input saturation based on the backstepping technique in this paper. The backstepping design method has been widely employed in the control of nonlinear systems. In recent years, many robust control methods have been introduced to combine with backstepping technique for the uncertain MIMO nonlinear systems      . However, the ESO-based robust backstepping technique should be further developed for the wing-rock motion due to the relatively easy realization. Inspired by the above discussions, a robust attitude tracking control law is proposed for the wing-rock motion in the presence of unsteady aerodynamic disturbances, external disturbances, system uncertainties and input saturation. In this paper, considering the characters of different disturbances, efficient processing methods are adopted. The system uncertainty is estimated online by adaptive RBFNN. By taking full advantage of the output of the RBFNN and the known model information of the unsteady aerodynamic disturbance, the ESO is employed to estimate the compounded disturbance, which consists of the unsteady aerodynamic disturbance, external disturbance, and the unknown neural network approximation error. By making full use of the known information of the system, the disturbance estimation performance will be greatly improved. In addition, it is meaningful in the wing rock control at high AOA. The paper is organized as follows. Problem formulation and preliminaries are described in Section 2. Section 3 presents the detailed design process of the disturbance observers. In Section 4, the robust backstepping wing rock control law is developed considering the input saturation. In Section 5, simulation results are given to demonstrate the effectiveness of the proposed robust tracking control scheme, followed by concluding remarks in Section 6.