Finite-time Extended State Observer based fault tolerant output feedback control for attitude stabilization

This work addresses the challenging problem of finite-time fault tolerant attitude stabilization control for the rigid spacecraft attitude control system without the angular velocity measurements, in the presence of external disturbances and actuator failures. Consider the severe circumstances with above failures and uncertainties, a novel continuous finite-time Extended State Observer is first established to observe the attitude angular velocity and the synthetic failure simultaneously. Unlike the existing observers, the finite-time methodology and Extended State Observer are utilized, to achieve the finite-time uniformly ultimately bounded stability of the attitude angular velocity and extended state observation errors. Furthermore, a novel continuous finite-time attitude controller is developed by using the nonsingular terminal sliding mode control and super-twisting method. The main feature of this work stems from our use of multiply advanced techniques or methodologies that enables the finite-time stability of the closed-loop attitude control system and the designed control scheme is continuous with the property of chattering restraining. Finally, numerical simulation results are presented to illustrate the effectiveness and fine performances of the finite-time observer and controller for the attitude control system.     

Hybrid finite-time trajectory tracking control of a quadrotor

In this paper, accurate trajectory tracking control problem of a quadrotor with unknown dynamics and disturbances is addressed by devising a hybrid finite-time control (HFTC) approach. An adaptive integral sliding mode (AISM) control law is proposed for altitude subsystem of the quadrotor, whereby underactuated characteristics can decoupled. Backstepping technique is further deployed to control the horizontal position subsystem. To exactly attenuate external disturbances, a finite-time disturbance observer (FDO) combining with nonsingular terminal sliding mode (NTSM) control strategy is constructed for attitude subsystem, and thereby achieve finite-time stability. Using the compounded control scheme, trajectory tracking errors can be stabilized rapidly. Simulation results and comprehensive comparisons show that the proposed HFTC scheme has remarkably superior performance.     

Adaptive-gain fast super-twisting sliding mode fault tolerant control for a reusable launch vehicle in reentry phase

In this paper, a novel adaptive-gain fast super-twisting (AGFST) sliding mode attitude control synthesis is carried out for a reusable launch vehicle subject to actuator faults and unknown disturbances. According to the fast nonsingular terminal sliding mode surface (FNTSMS) and adaptive-gain fast super-twisting algorithm, an adaptive fault tolerant control law for the attitude stabilization is derived to protect against the actuator faults and unknown uncertainties. Firstly, a second-order nonlinear control-oriented model for the RLV is established by feedback linearization method. And on the basis a fast nonsingular terminal sliding mode (FNTSM) manifold is designed, which provides fast finite-time global convergence and avoids singularity problem as well as chattering phenomenon. Based on the merits of the standard super-twisting (ST) algorithm and fast reaching law with adaption, a novel adaptive-gain fast super-twisting (AGFST) algorithm is proposed for the finite-time fault tolerant attitude control problem of the RLV without any knowledge of the bounds of uncertainties and actuator faults. The important feature of the AGFST algorithm includes non-overestimating the values of the control gains and faster convergence speed than the standard ST algorithm. A formal proof of the finite-time stability of the closed-loop system is derived using the Lyapunov function technique. An estimation of the convergence time and accurate expression of convergence region are also provided. Finally, simulations are presented to illustrate the effectiveness and superiority of the proposed control scheme.     

Rotation matrix based finite-time attitude synchronization control for spacecraft with external disturbances

This paper investigates the anti-unwinding finite-time attitude synchronization control problem for Spacecraft formation flying with external disturbances. Two finite-time controllers are designed based on rotation matrix and terminal sliding mode method. By designing a novel sliding mode surface, the first controller is developed when the upper bound of the external disturbances can be exactly known. However, this value is not always available in reality. In addition, the direct use of the upper bound of the external disturbances can result in the chattering problem. For the purpose of overcoming the disadvantage of the first controller, a modified control law is proposed, in which the adaptive law is applied to estimate the unknown value online. Theoretical analysis and numerical simulations are presented to demonstrate the validity of the proposed controllers.     

Finite-time sliding mode controller for perturbed second-order systems

This paper presents a novel finite-time sliding mode controller applied to perturbed second order systems. The proposed scheme employs a disturbance observer that can identify growing in time disturbances. Then, the observer is combined with a sliding mode controller to achieve finite-time stabilization of the second-order system. The convergence of the observer as well as the finite-time stability of the closed-loop system is theoretically demonstrated. Besides, it is also shown that the finite-time convergence properties of a given controller can be enhanced when using a compensation term based on the disturbance observer. The proposed controller is compared with a twisting algorithm and a finite-time sliding mode controller with disturbance estimation. Also, a conventional proportional integral derivative (PID) controller is combined with the proposed disturbance observer in a trajectory tracking task. Numerical simulations indicate that the proposed controller attains finite-time stabilization of the second order system by requiring a less amount of power than that demanded by the other control schemes and without being affected by the peaking phenomenon. Besides, the performance of the PID technique is enhanced by applying the proposed control methodology.     

Output-feedback super-twisting control for line-of-sight angles tracking of non-cooperative target spacecraft

Without the line-of-sight (LOS) angles rate information, this paper investigates the LOS angles tracking problem of non-cooperative target in chaser’s body frame with the external disturbance force and torque via chaser’s control torque. By integrating with the attitude dynamics of the chaser, a novel coupled LOS-based relative motion model is firstly established, which reveals the redundancy relationship between the LOS angles motion with two Degree-of-Freedom (DOF) and three dimensional control torque. More specially, the LOS angles tracking control problem is formulated as an output-feedback control problem of an uncertain nonlinear system with the actuator redundancy. As a stepping-stone, a fourth order high order sliding mode observer (HOSMO) is proposed to estimate the system state and uncertain terms. A combination of modified super twisting algorithm (STA) with nonsingular fast terminal sliding mode (NFTSM) and control allocation is proposed, the main novelty of modified STA is that the NFTSM is introduced to replace the linear sliding mode (LSM), and the original STA cannot be applied directly, a modified STA is proposed, which can guarantee the fast finite-time convergence. Finally, simulations are conducted to show fine performance of the proposed control scheme.     

Adaptive fast sliding mode fault tolerant control integrated with disturbance observer for spacecraft attitude stabilization system

In this paper, the problem of fault-tolerant control (FTC) for spacecraft attitude stabilization system with actuator fault and mismatched disturbance is investigated. A novel fault tolerant control strategy based on adaptive fast terminal sliding mode control (AFTSMC) is proposed. Firstly, a novel composite observer is proposed to estimate the disturbance, actuator efficiency factor and partial states of the system. By introducing a sliding mode observer, the bias actuator fault is reconstructed. Subsequently, in accordance with the estimated information, a novel sliding mode fault tolerant controller is designed. The proposed control scheme contains two compensators and two adaptive parameters to attenuate the mismatched disturbance, to compensate actuator fault, and to guarantee fast convergence of the system. Furthermore, the reachability of sliding motion is proved. The simulation results for the spacecraft system illustrate the effectiveness of the proposed method.     

Disturbance observer-based backstepping sliding mode fault-tolerant control for the hydro-turbine governing system with dead-zone input

This paper investigates a backstepping sliding mode fault-tolerant tracking control problem for a hydro-turbine governing system with consideration of external disturbances, actuator faults and dead-zone input. To reduce the effects of the unknown random disturbances, the nonlinear disturbance observer is designed to identify and estimate the disturbance term. To drastically decrease the complexity of stability functions selection and controller design, the recursive processes of the backstepping technique are employed. Additionally, based on the nonlinear disturbance observer and the backstepping technique, the sliding mode fault-tolerant tracking control approach is developed for the hydro-turbine governing system (HTGS). The stability of HTGS is rigorously demonstrated through Lyapunov analysis which is capable to satisfy a tracking control performance. Finally, comprehensive simulation results are presented to illustrate the effectiveness and superiority of the proposed control scheme.     

Attitude output feedback control for rigid spacecraft with finite-time convergence

The main problem addressed is the quaternion-based attitude stabilization control of rigid spacecraft without angular velocity measurements in the presence of external disturbances and reaction wheel friction as well. As a stepping stone, an angular velocity observer is proposed for the attitude control of a rigid body in the absence of angular velocity measurements. The observer design ensures finite-time convergence of angular velocity state estimation errors irrespective of the control torque or the initial attitude state of the spacecraft. Then, a novel finite-time control law is employed as the controller in which the estimate of the angular velocity is used directly. It is then shown that the observer and the controlled system form a cascaded structure, which allows the application of the finite-time stability theory of cascaded systems to prove the finite-time stability of the closed-loop system. A rigorous analysis of the proposed formulation is provided and numerical simulation studies are presented to help illustrate the effectiveness of the angular-velocity observer for rigid spacecraft attitude control.     

Neural network disturbance observer-based distributed finite-time formation tracking control for multiple unmanned helicopters

The distributed finite-time formation tracking control problem for multiple unmanned helicopters is investigated in this paper. The control object is to maintain the positions of follower helicopters in formation with external interferences. The helicopter model is divided into a second order outer-loop subsystem and a second order inner-loop subsystem based on multiple-time scale features. Using radial basis function neural network (RBFNN) technique, we first propose a novel finite-time multivariable neural network disturbance observer (FMNNDO) to estimate the external disturbance and model uncertainty, where the neural network (NN) approximation errors can be dynamically compensated by adaptive law. Next, based on FMNNDO, a distributed finite-time formation tracking controller and a finite-time attitude tracking controller are designed using the nonsingular fast terminal sliding mode (NFTSM) method. In order to estimate the second derivative of the virtual desired attitude signal, a novel finite-time sliding mode integral filter is designed. Finally, Lyapunov analysis and multiple-time scale principle ensure the realization of control goal in finite-time. The effectiveness of the proposed FMNNDO and controllers are then verified by numerical simulations.     

Finite-time tracking control of nth-order chained-form non-holonomic systems in the presence of disturbances

This paper addresses the problem of finite-time tracking controller design for nth-order chained-form non-holonomic systems in the presence of unknown disturbances. To this aim, a generalized disturbance observer based controller is proposed and combined with a recursive terminal sliding mode approach which guarantees finite-time convergence of the disturbance observer dynamic. By introducing a time-varying transformation and introducing a new control law, the existence of the sliding around the recursive terminal sliding mode surfaces is guaranteed. Finally, the proposed approach is applied for a wheeled mobile robot with a fourth-order chained-form non-holonomic model. The simulation results demonstrate the desirable and robust tracking performance of the proposed approach in the presence of unknown disturbance.     

Global fast dynamic terminal sliding mode control for a quadrotor UAV

A control method based on global fast dynamic terminal sliding mode control (TSMC) technique is proposed to design the flight controller for performing the finite-time position and attitude tracking control of a small quadrotor UAV. Firstly, the dynamic model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. Secondly, the dynamic flight controllers of the quadrotor are formulated based on global fast dynamic TSMC, which is able to guarantee that the position and velocity tracking errors of all system state variables converge to zero in finite-time. Moreover, the global fast dynamic TSMC is also able to eliminate the chattering phenomenon caused by the switching control action and realize the high precision performance. In addition, the stabilities of two subsystems are demonstrated by Lyapunov theory, respectively. Lastly, the simulation results are given to illustrate the effectiveness and robustness of the proposed control method in the presence of external disturbances.     

Extended observer based on adaptive second order sliding mode control for a fixed wing UAV

This paper addresses the design of attitude and airspeed controllers for a fixed wing unmanned aerial vehicle. An adaptive second order sliding mode control is proposed for improving performance under different operating conditions and is robust in presence of external disturbances. Moreover, this control does not require the knowledge of disturbance bounds and avoids overestimation of the control gains. Furthermore, in order to implement this controller, an extended observer is designed to estimate unmeasurable states as well as external disturbances. Additionally, sufficient conditions are given to guarantee the closed-loop stability of the observer based control. Finally, using a full 6 degree of freedom model, simulation results are obtained where the performance of the proposed method is compared against active disturbance rejection based on sliding mode control.     

A novel adaptive sliding mode control with application to MEMS gyroscope

This paper presents a new adaptive sliding mode controller for MEMS gyroscope; an adaptive tracking controller with a proportional and integral sliding surface is proposed. The adaptive sliding mode control algorithm can estimate the angular velocity and the damping and stiffness coefficients in real time. A proportional and integral sliding surface, instead of a conventional sliding surface is adopted. An adaptive sliding mode controller that incorporates both matched and unmatched uncertainties and disturbances is derived and the stability of the closed-loop system is established. The numerical simulation is presented to verify the effectiveness of the proposed control scheme. It is shown that the proposed adaptive sliding mode control scheme offers several advantages such as the consistent estimation of gyroscope parameters including angular velocity and large robustness to parameter variations and external disturbances.     

Observer-based prescribed performance attitude control for flexible spacecraft with actuator saturation

This paper investigates the prescribed performance attitude control problem for flexible spacecraft subject to external disturbances and actuator constraints. By using a new performance function and an error transformation, the attitude control system is transformed into an error system which will be kept bounded to ensure expected dynamic and steady-state responses. Compared with the commonly used performance function, the modified one has an explicit prespecified terminal time which determines the maximum convergence time of the attitude control system. A modal observer and a disturbance observer are designed to deal with the flexible vibration and disturbances, respectively. Furthermore, when considering actuator saturation, an improved control strategy is developed with an auxiliary system utilized to compensate the saturation. The stability of the closed-loop system is analyzed by Lyapunov theory. Simulation results show the effectiveness and performance of the proposed methods.     

基于改进扩展状态观测器的四旋翼无人机轨迹鲁棒跟踪控制

针对四旋翼无人机在轨迹跟踪过程中会受到内外部扰动、模型误差等不确定性因素的影响,本文提出了一种基于改进型扩展状态观测器的积分滑模控制方案。具体来讲,首先,将四旋翼无人机系统存在的模型误差以及内外部扰动等不确定性因素视作集总干扰,通过借鉴的改进扩展状态观测器对其进行观测;进而,在此基础上,进一步考虑四旋翼无人机系统控制的连续性,基于四旋翼无人机轨迹误差、速度误差、姿态角误差和姿态角速度误差设计积分滑模控制器,分析了系统的稳定性并分别进行了数值仿真和实机实验。结果表明,采用本文算法时,在数值仿真中,各状态跟踪误差不超过1%,跟踪精度最高;在实机实验中,位置跟踪误差总体上能控制在20%以下。因此,本文方法具备有效性和可行性。     

仅利用位置测量信息的机械手鲁棒滑模跟踪控制

针对机械手的鲁棒控制问题 ,提出了一种仅利用位置测量信息的机械手鲁棒滑模跟踪控制器设计方案。通过引入滑模观测器 ,避免了对关节角速度信号的测量 ,该控制器不仅能保证闭环系统所有信号全局有界 ,且能使跟踪误差以指数速度收敛到零的小邻域内。计算机仿真验证了该控制方案的可行性和有效性     

Robust control of post-stall pitching maneuver based on finite-time observer

This article presents a robust finite-time maneuver control scheme for the longitudinal attitude dynamic of the aircraft with unsteady aerodynamic disturbances and input saturation. To efficiently eliminate the influence of unsteady aerodynamic disturbances, nonlinear finite-time observers are developed. Despite the existence of the nonlinearity and the coupling between aircraft states and unsteady aerodynamic disturbances, the proposed observers can still precisely estimate the unmeasurable unsteady aerodynamic disturbances in finite time. To attenuate the effect caused by input saturation, a finite-time auxiliary system is constructed. With the error between the desired control input and saturation input as the input of the auxiliary system, the additional signals are generated to compensate for the effect of input saturation. Combined with the finite-time observers and the finite-time auxiliary system, a robust finite-time backstepping attitude control design is developed. The finite-time convergence of all closed-loop system signals is rigorously proved via Lyapunov analysis method under the developed robust attitude control schemes. Finally, simulation results are presented to illustrate the effectiveness of the proposed attitude control approaches.     

Robust state estimation based on sliding mode observer for aeroelastic system

This paper concerns the application and demonstration of sliding mode observer for aeroelastic system, which is robust to model uncertainty including mass and stiffness of the system and various disturbances The performance of a sliding mode observer is compared with that of a conventional Kalman filter to demonstrate robustness and disturbance decoupling characteristics. Aeroelastic instability may occur when an elastic structure is moving even in subcritical flow speed region Simulation results using sliding mode observer are presented to control aeroelastic response of flapped wing system due to various external excitations as well as model uncertainty and sinusoidal disturbances in subcritical incompressible flow