Fault-tolerant sliding mode attitude control for flexible spacecraft under loss of actuator effectiveness

In this paper, a novel fault-tolerant attitude control synthesis is carried out for a flexible spacecraft subject to actuator faults and uncertain inertia parameters. Based on the sliding mode control, a fault-tolerant control law for the attitude stabilization is first derived to protect against the partial loss of actuator effectiveness. Then the result is extended to address the problem that the actual output of the actuators is constrained. It is shown that the presented controller can accommodate the actuator faults, even while rejecting external disturbances. Moreover, the developed control law can rigorously enforce actuator-magnitude constraints. An additional advantage of the proposed fault-tolerant control strategy is that the control design does not require a fault detection and isolation mechanism to detect, separate, and identify the actuator faults on-line; the knowledge of certain bounds on the effectiveness factors of the actuator is not used via the adaptive estimate method. The associated stability proof is constructive and accomplished by the development of the Lyapunov function candidate, which shows that the attitude orientation and angular velocity will globally asymptotically converge to zero. Numerical simulation results are also presented which not only highlight the ensured closed-loop performance benefits from the control law derived here, but also illustrate its superior fault tolerance and robustness in the face of external disturbances when compared with the conventional approaches for spacecraft attitude stabilization control.     

Robust fault-tolerant control for flexible spacecraft against partial actuator failures

In this paper, we present a robust fault-tolerant control scheme to achieve attitude control of flexible spacecraft with disturbances and actuator failures. It is shown that the control algorithms are not only attenuate exogenous bounded disturbances with attenuation level, but also able to tolerate partial loss of actuator effectiveness. The proposed controller design is simple and can guarantee the faulty closed-loop system to be quadratically stable with a prescribed upper bound of the cost function. The design algorithms are obtained by combining free weighting matrices method with linear matrix inequality technique. The effectiveness of the proposed design method is demonstrated in a spacecraft attitude control system subject to loss of actuator effectiveness.     

航天器有限时间饱和姿态跟踪控制

针对刚体航天器系统,对存在模型不确定性、外界干扰力矩和控制器饱和等条件下的姿态跟踪控制问题进行了研究。首先,考虑未知模型不确定性和外界干扰,且总干扰上界为未知常数,结合快速非奇异终端滑模、快速终端滑模趋近律以及辅助系统构造了基本的鲁棒有限时间饱和控制器,并通过辅助系统直接补偿了控制器饱和;其次,针对系统总干扰具有多项式上界的情形,进一步结合自适应控制算法,对其上界函数中的未知参数进行在线估计,并设计了自适应有限时间饱和控制器。同时,基于Lyapunov稳定性理论证明了所提出控制算法的有限时间收敛特性。最后,通过数值仿真验证所提出控制算法的控制效果,在两种控制器作用下姿态的跟踪精度分别为5×10-5和1×10-5,证明了所提出控制算法的有效性。     

Model predictive control of rigid spacecraft with two variable speed control moment gyroscopes

In this paper, an attitude maneuver control problem is investigated for a rigid spacecraft using an array of two variable speed control moment gyroscopes(VSCMGs)with gimbal axes skewed to each other. A mathematical model is constructed by taking the spacecraft and the gyroscopes together as an integrated system, with the coupling interaction between them considered. To overcome the singular issues of the VSCMGs due to the conventional torque-based method, the first-order derivative of gimbal rates and the second-order derivative of the rotor spinning velocity, instead of the gyroscope torques, are taken as input variables. Moreover, taking external disturbances into account,a feedback control law is designed for the system based on a method of nonlinear model predictive control(NMPC). The attitude maneuver can be realized fast and smoothly by using the proposed controller in this paper.     

Robust adaptive sliding mode attitude maneuvering and vibration damping of three-axis-stabilized flexible spacecraft with actuator saturation limits

This paper presents a dual-stage control system design method for flexible spacecraft attitude maneuvering control by use of on-off thrusters and active vibration suppression by embedded smart material as actuator. As a stepping stone, an adaptive sliding mode controller with the assumption of knowing the upper bounds of the lumped perturbation is designed that ensures exponential convergence or uniform ultimate boundedness (UUB) of the attitude control system in the presence of bounded parameter variation/disturbances and control input saturation as well. Then this adaptive controller is redesigned such that the need for knowing the upper bound in advance is eliminated. Lyapunov analysis shows that this modified adaptive controller can also guarantee the exponential convergence or UUB of the system. For actively suppressing the induced vibration, linear quadratic regulator (LQR) based positive position feedback control method is presented. Numerical simulations are performed to show that rotational maneuver and vibration suppression are accomplished in spite of the presence of disturbance torque/parameter uncertainty and saturation input.     

Passivity-based control for a flexible spacecraft in the presence of disturbances

The attitude regulation control problem for flexible spacecraft is investigated in this paper. Two extended PD+variable structure controllers are proposed using passivity-based control technique instead of sliding mode control approach. The first controller is a basic one, while the second one is an extension of the first one which relaxes the bound requirement for the external disturbances. In the presence of model uncertainties and external disturbances, both controllers presented in this research can make the flexible spacecraft UGAS (uniformly globally asymptotically stable). By virtue of related analysis tools, stability of the proposed controllers is proven theoretically. Numerical simulations are also included to demonstrate the performance of the developed controllers.     

Resilient anti-disturbance dynamic surface control of uncertain strict-feedback systems subject to partial loss of actuator effectiveness

This paper is concerned with the tracking control of a class of uncertain strict-feedback systems subject to partial loss of actuator effectiveness, in addition to uncertain model dynamics and unknown disturbances. A resilient anti-disturbance dynamic surface control method is proposed to achieve stable tracking regardless of partial actuator faults. First, data-driven adaptive extended state observers are designed based on memory-based identifiers, such that the uncertain model dynamics, external disturbances and the unknown input gains due to actuator faults can be estimated. Next, a resilient anti-disturbance dynamic surface controller is developed based on recovered information from the data-driven adaptive extended state observers. After that, it is proven that the cascade system formed by the observer and controller is input-to-state stable. Finally, comparative studies are performed to validate the efficacy of the resilient anti-disturbance dynamic surface control method for nonlinear strict-feedback systems subject to partial loss of actuator effectiveness.

     

An anti-disturbance PD control scheme for attitude control and stabilization of flexible spacecrafts

This paper studies the attitude control problem of spacecrafts with flexible appendages. It is well known that the unwanted vibration modes, model uncertainty and space environmental disturbances may cause degradation of the performance of attitude control systems for a flexible spacecraft. In this paper, the vibration from flexible appendages is modeled as a derivative-bounded disturbance to the attitude control system of the rigid hub. A disturbance-observer-based control (DOBC) is formulated for feedforward compensation of the elastic vibration. The model uncertainty and space environmental disturbances as well as other noises are merged into an “equivalent” disturbance. We design a composite controller with a hierarchical architecture by combining DOBC and PD control, where DOBC is used to reject the vibration effect from the flexible appendages. Numerical simulations are performed to demonstrate that by using the composite hierarchical control law, disturbances can be effectively attenuated and the robust dynamic performances be enhanced.     

非自旋航天器混沌姿态运动及其参数开闭环控制

研究万有引力场中受大气阻力且存在结构内阻尼的非自旋航天器在椭圆轨道上平面天平动的混沌及其参数开闭环控制问题．在建立数学模型的基础上确定出现混沌的必要条件并数值验证混沌的存在性，提出非线性振动系统混沌运动的参数开闭环控制并应用于控制航天器的混沌姿态运动．     

AIRSHIP ATTITUDE TRACKING SYSTEM

The attitude tracking control problem for an airship with parameter uncertainties and external disturbances was considered in this paper. The mathematical model of the airship attitude is a multi-input/multi-output uncertain nonlinear system. Based on the characteristics of this system, a design method of robust output tracking controllers was adopted based on the upper-bounds of the uncertainties. Using the input/output feedback linearization approach and Liapunov method, a control law was designed, which guarantees that the system output exponentially tracks the given desired output. The controller is easy to compute and complement. Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties and external disturbances in the system.     

Attitude control of a rigid spacecraft with one variable-speed control moment gyro

Nonlinear controllability and attitude stabilization are studied for the underactuated nonholonomic dynamics of a rigid spacecraft with one variable-speed control moment gyro(VSCMG), which supplies only two internal torques.Nonlinear controllability theory is used to show that the dynamics are locally controllable from the equilibrium point and thus can be asymptotically stabilized to the equilibrium point via time-invariant piecewise continuous feedback laws or time-periodic continuous feedback laws. Specifically,when the total angular momentum of the spacecraft-VSCMG system is zero, any orientation can be a controllable equilibrium attitude. In this case, the attitude stabilization problem is addressed by designing a kinematic stabilizing law, which is implemented through a nonlinear proportional and derivative controller, using the generalized dynamic inverse(GDI)method. The steady-state instability inherent in the GDI controller is elegantly avoided by appropriately choosing control gains. In order to obtain the command gimbal rate and wheel acceleration from control torques, a simple steering logic is constructed to accommodate the requirements of attitude stabilization and singularity avoidance of the VSCMG. Illustrative numerical examples verify the efcacy of the proposed control strategy.     

Decentralized adaptive attitude synchronization control for spacecraft formation using nonsingular fast terminal sliding mode

This paper studies the attitude synchronization control problem for a group of spacecraft. Considering inertia uncertainties and external disturbances with unknown bounds, a decentralized adaptive control scheme is developed using nonsingular fast terminal sliding mode (NFTSM). A multispacecraft NFTSM is firstly designed, which contains the advantages of the nonsingular terminal sliding mode and the traditional linear sliding mode together. Then, the continuous decentralized adaptive NFTSM control laws with boundary layer by employing NFTSM associated with novel adaptive architecture are proposed, which can eliminate the chattering, and guarantee the attitude tracking errors converge to the regions containing the origin in finite time. At last, numerical simulations are presented to demonstrate the performance of the proposed control strategy.     

Control of Chaotic Motion in a Spinning Spacecraft with a Circumferential Nutational Damper

Control of chaotic vibrations in a simplified model of a spinning spacecraft with a circumferential nutational damper is achieved using two techniques. The control methods are implemented on a realistic spacecraft parameter configuration which has been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Such a torque, in practice, may arise in the platform of a dual-spin spacecraft under malfunction of the control system or from an unbalanced rotor or from vibrations in appendages. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude and consequently could have disastrous affects on its operation. The two control methods, recursive proportional feedback (RPF) and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamical systems. Each technique is outlined and the effectiveness of the two strategies in controlling chaotic motion exhibited by the present system is compared and contrasted. Numerical simulations are performed and the results are studied by means of time history, phase space, Poincaré map, Lyapunov characteristic exponents and bifurcation diagrams.     

Robust reliable sampled-data control for offshore steel jacket platforms with nonlinear perturbations

In this article, we consider the robust reliable sample-data control problem for an offshore steel jacket platform with input time-varying delay and possible occurrence of actuator faults subject to nonlinear self-exited hydrodynamic forces. The main objective of this work is to design a state feedback reliable sample-data controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly exponentially stable. By constructing an appropriate Lyapunov–Krasovskii functional and using linear matrix inequality (LMI) approach, a new set of sufficient condition is derived in terms of LMIs for the existence of robust reliable sample-data control law. In particular, the uncertainty under consideration in system parameters includes linear fractional norm-bounded uncertainty. Further, Schur complement and Jenson’s integral inequality are used to substantially simplify the derivation in the main results. More precisely, the controller gain matrix for the nonlinear offshore steel jacket platform can be achieved by solving the LMIs, which can be easily facilitated by using some standard numerical packages. Finally, a numerical example with simulation result is provided to illustrate the applicability and effectiveness of the proposed reliable sampled-data control scheme.     

Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters简

A dynamics-based adaptive control approach is proposed for a planar dual-arm space robot in the presence of closed-loop constraints and uncertain inertial parameters of the payload. The controller is capable of controlling the po- sition and attitude of both the satellite base and the payload grasped by the manipulator end effectors. The equations of motion in reduced-order form for the constrained system are derived by incorporating the constraint equations in terms of accelerations into Kane＇s equations of the unconstrained system. Model analysis shows that the resulting equations perfectly meet the requirement of adaptive controller design. Consequently, by using an indirect approach, an adaptive control scheme is proposed to accomplish position/attitude trajectory tracking control with the uncertain parameters be- ing estimated on-line. The actuator redundancy due to the closed-loop constraints is utilized to minimize a weighted norm of the joint torques. Global asymptotic stability is proven by using Lyapunov＇s method, and simulation results are also presented to demonstrate the effectiveness of the proposed approach.     

Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

This paper is concerned with the stabilization problem of uncertain chaotic systems with input nonlinearity. The slope parameters of this nonlinearity are unmeasured. A new sliding function is designed, then an adaptive sliding mode controller is established such that the trajectory of the system converges to the sliding surface in a finite time and finite-time reachability is theoretically proved. Using a virtual state feedback control technique, sufficient condition for the asymptotic stability of sliding mode dynamics is derived via linear matrix inequality (LMI). Then the results can be extended to uncertain chaotic systems with disturbances and adaptive sliding mode H _∞ controllers are designed. Finally, a simulation example is presented to show the validity and advantage of the proposed method.     

Adaptive finite time distributed 6-DOF synchronization control for spacecraft formation without velocity measurement

Nonlinear Dynamics - In this paper, the problem of distributed finite time six-degree-of-freedom (6-DOF) synchronization control for spacecraft formation flying (SFF) with the external disturbances...     

基于浸入与不变原理的四旋翼姿态系统反步滑模控制

针对较大幅度外部不确定扰动下的四旋翼姿态稳定问题,设计了一种基于浸入与不变原理(ⅠⅠ)的自适应反步滑模控制器(ABSMC)。首先建立了未知大扰动下四旋翼姿态系统动力学模型,然后以横滚角子系统搭建为例,设计并应用了反步法和基于趋进率的滑模控制策略。在扰动估计误差流型设计中,融合了ⅠⅠ原理,即自适应率的选取实现了误差流型的不变和吸引,确保估计误差收敛到0。最后,对系统进行了稳定性分析和数字仿真。结果表明,在较大未知扰动情况下,融合ⅠⅠ原理方法后,经10 s所测跟踪误差平方的累加和仅为传统ABSMC方法的11.2%,控制精度大幅提高。     

Robust fixed-time attitude stabilization control of flexible spacecraft with actuator uncertainty

Nonlinear Dynamics - A robust fixed-time control framework is presented to stabilize flexible spacecraft’s attitude system with external disturbance, uncertain parameters of inertia, and...     

A switching fractional calculus-based controller for normal non-linear dynamical systems

In this paper, a fractional calculus-based terminal sliding mode controller is introduced for finite-time control of non-autonomous non-linear dynamical systems in the canonical form. A fractional terminal switching manifold which is appropriate for canonical integer-order systems is firstly designed. Then some conditions are provided to avoid the inherent singularities of the conventional terminal sliding manifolds. A non-smooth Lyapunov function is adopted to prove the finite time stability and convergence of the sliding mode dynamics. Afterward, based on the sliding mode control theory, an equivalent control and a discontinuous control law are designed to guarantee the occurrence of the sliding motion in finite time. The proposed control scheme uses only one control input to stabilize the system. The proposed controller is also robust against system uncertainties and external disturbances. Two illustrative examples show the effectiveness and applicability of the proposed fractional finite-time control strategy. It is worth noting that the proposed sliding mode controller can be applied for control and stabilization of a large class of non-autonomous non-linear uncertain canonical systems.