Continuous Finite‐Time Sliding Mode Control for Uncertain Nonlinear Systems with Applications to DC‐DC Buck Converters

This paper investigates the continuous finite‐time control problem of high‐order uncertain nonlinear systems with mismatched disturbances through the terminal sliding mode control method. By constructing a novel dynamic terminal sliding manifold based on the disturbance estimations of high‐order sliding mode observers, a continuous finite‐time terminal sliding mode control method is developed to counteract mismatched disturbances. To avoid discontinuous control action, the switching terms of a dynamic terminal sliding manifold are designed to appear only in the derivative term of the control variable. To validate its effectiveness, the proposed control method is applied to a DC‐DC buck converter system. The experimental results show the proposed method exhibits better control performance than a chattering free controller, such as mismatched disturbances rejection and smaller steady‐state fluctuations.     

Practical adaptive fractional‐order nonsingular terminal sliding mode control for a cable‐driven manipulator

For the high precise tracking control purpose of a cable‐driven manipulator under lumped uncertainties, a novel adaptive fractional‐order nonsingular terminal sliding mode control scheme based on time delay estimation (TDE) is proposed and investigated in this paper. The proposed control scheme mainly has three elements, ie, a TDE element applied to properly compensate the lumped unknown dynamics of the system resulting in a fascinating model‐free feature; a fractional‐order nonsingular terminal sliding mode (FONTSM) surface element used to ensure high precision in the steady phase; and a combined reaching law with adaptive technique adopted to obtain fast convergence and high precision and chatter reduction under complex lumped disturbance. Stability of the closed‐loop control system is analyzed with the Lyapunov stability theory. Comparative simulations and experiments were performed to demonstrate the effectiveness of our proposed control scheme using 2‐DOF (degree of freedom) of a cable‐driven manipulator named Polaris‐I. Corresponding results show that our proposed method can ensure faster convergence, higher precision, and better robustness against complex lumped disturbance than the existing TDE‐based FONTSM and continuous FONTSM control schemes.     

Adaptive disturbance observer‐based finite‐time continuous fault‐tolerant control for reentry RLV

The control effectors of reusable launch vehicle (RLV) can produce significant perturbations and faults in reentry phase. Such a challenge imposes tight requirements to enhance the robustness of vehicle autopilot. Focusing on this problem, a novel finite‐time fault‐tolerant control strategy is proposed for reentry RLV in this paper. The key of this strategy is to design an adaptive‐gain multivariable finite‐time disturbance observer (FDO) to estimate the synthetical perturbation with unknown bounds, which is composed of model uncertainty, external disturbance, and actuator fault considered as the partial loss of actuator effectiveness in this work. Then, combined with the finite‐time high‐order observer and differentiator, a continuous homogeneous second‐order sliding mode controller based on the terminal sliding mode and super‐twisting algorithm is designed to achieve a fast and accurate RLV attitude tracking with chattering attenuation. The main features of the integrated control strategy are that the adaptation algorithm of FDO can achieve non‐overestimating values of the observer gains and the second‐order super‐twisting sliding mode approach can obtain a more elegant solution in finite time. Finally, simulation results of classical RLV (X‐33) are provided to verify the effectiveness and robustness of the proposed fault‐tolerant controller in tracking the guidance commands. Copyright © 2017 John Wiley & Sons, Ltd.     

Heterogeneous consensus of higher‐order multi‐agent systems with mismatched uncertainties using sliding mode control

A robust consensus controller is proposed for heterogeneous higher‐order nonlinear multi‐agent systems, when the agent dynamics are involved with mismatched uncertainties. A distributed consensus protocol based on a time‐varying nonhomogeneous finite‐time disturbance observer and sliding mode control is designed to realize the network consensus of higher‐order multi‐agent systems. The time‐varying finite‐time disturbance observer overcomes the problem of peaking value near the initial time caused by the constant gain one and is designed to estimate the uncertainties and to mitigate the effect of mismatched uncertainties during the sliding mode. To eliminate the chattering phenomenon and ensure finite‐time convergence to the sliding surface, the control law is designed by using the super twisting algorithm. Finally numerical simulations are given to illustrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

非匹配扰动干扰下的无人直升机轨迹跟踪控制

针对小型无人直升机在飞行过程中容易受到非匹配扰动影响的特点,本文设计了一种基于新型滑模控制方法的轨迹跟踪控制器.首先,建立了无人直升机系统的非线性数学模型,并对该模型进行近似反馈线性化处理,同时将模型分为位置和偏航两个子系统;然后,利用扩展扰动观测器对复合扰动以及非匹配扰动的各阶导数的估计值,设计新型时变滑模面,得到滑模控制律,并给出了控制系统的稳定性分析;最后,仿真结果验证了控制方法的有效性和优越性.该新型滑模控制方法的优越性主要体现在:对非匹配扰动具有较强的鲁棒性,以及能有效地抑制抖振现象.     

Reaction wheel fault‐tolerant finite‐time control for spacecraft attitude tracking without unwinding

This article proposes fault‐tolerant finite‐time attitude tracking control of a rigid spacecraft actuated by four reaction wheels without unwinding problem in the presence of external disturbances, uncertain inertia parameter, and actuator faults. First, a novel antiunwinding finite‐time attitude tracking control law is derived with a designed control signal which works within a known actuator‐magnitude constraint using a continuous nonsingular fast terminal sliding mode (NFTSM) concept. Second, a finite‐time disturbance observer (FTDO) is introduced to estimate a lumped disturbance due to external disturbances, uncertain inertia parameter, actuator faults, and input saturation. Third, a composite controller is developed which consists of a feedback control based on the continuous NFTSM method and compensation term based on the FTDO. The global finite‐time stability is proved using Lyapunov stability theory. Moreover, the singularity and unwinding phenomenon are avoided. Simulation results are conducted under actuator constraints in the presence of external disturbances, inertia uncertainty, and actuator faults and results are illustrated to show the effectiveness of the proposed method. In addition, to show the superiority of the proposed control method over the recently reported control methods, comparative analysis is also presented.     

Chattering‐free adaptive sliding mode control for continuous‐time systems with time‐varying delay and process disturbance

This paper concerns the controller design for continuous‐time linear systems with time‐varying delay and process disturbance. A novel adaptive sliding mode control law is mainly proposed to attract the sliding mode to first‐order sliding surface within a finite time; afterwards, the uniformly ultimately bounded stability of the closed‐loop system on the sliding surface is simultaneously guaranteed. In addition, the chattering phenomena can be conveniently excluded if the disturbance is a low‐intensity process. Once the high‐intensity disturbance is involved, the state variation can be significantly reduced as well. Furthermore, by the technique of a novel exponential free‐matrix technique, the convergence rate of the closed‐loop system can be conveniently preregulated. Numerical example is provided to demonstrate the effectiveness of the proposed method.     

Adaptive multivariable finite‐time continuous fault‐tolerant control of rigid spacecraft

The problem of fault‐tolerant attitude tracking control for rigid spacecraft in the presence of inertia uncertainties, actuator faults, and external disturbances is investigated in this paper. A novel adaptive finite‐time continuous fault‐tolerant control strategy is developed by combining the fast nonsingular terminal sliding mode surface and the adaptive multivariable super‐twisting algorithm, which improves the robustness while preserving high accuracy and finite‐time convergence. The main features of the control strategy are the double‐layer adaptive algorithm based on equivalent control, which ensures nonoverestimation of the control gain and the continuous controller, which maintains better property of chattering reduction. Finally, the efficiency of the proposed controller is illustrated by numerical simulations.     

Distributed fault‐tolerant control design for spacecraft finite‐time attitude synchronization

This paper develops two distributed finite‐time fault‐tolerant control algorithms for attitude synchronization of multiple spacecraft with a dynamic virtual leader in the presence of modeling uncertainties, external disturbances, and actuator faults. The leader gives commands only to a subset of the followers, and the communication flow between followers is directed. By employing a novel distributed nonsingular fast terminal sliding mode and adaptive mechanism, a distributed finite‐time fault‐tolerant control law is proposed to guarantee all the follower spacecraft that finite‐time track a dynamic virtual leader. Then utilizing three distributed finite‐time sliding mode estimators, an estimator‐based distributed finite‐time fault‐tolerant control law is proposed using only the followers' estimates of the virtual leader. Both of them do not require online identification of the actuator faults and provide robustness, finite‐time convergence, fault‐tolerant, disturbance rejection, and high control precision. Finally, numerical simulations are presented to evaluate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

非匹配不确定高阶非线性系统递阶Terminal滑模控制

对于高阶非线性系统,首先采用改进的高阶滑模微分器作为间接干扰观测器,获得前n-1个子系统中的非匹配复合干扰的估计值,证明了估计误差可任意小. 为避免代数环,设计了三种方案获得最后一个子系统中非匹配复合干扰的估计值,并证明了估计误差有界. 在此基础上设计递阶Terminal滑模控制器,证明了控制器参数非奇异及结构非奇异,并给出所需条件. 最后,证明了系统稳定,跟踪误差可任意小. 近空间飞行器姿态控制仿真验证了本文结论.     

Tracking control of uncertain Euler–Lagrange systems with finite‐time convergence

A unified solution is presented to the tracking control problem of Euler–Lagrange systems with finite‐time convergence. A reconstruction module is designed to estimate the overall of unmodeled dynamics, disturbance, actuator misalignment, and multiple actuator faults. That reconstruction is accomplished in finite time with zero error. A nonsingular terminal sliding mode controller is then synthesized, and the resultant closed‐loop system is also shown to be finite‐time stable with the reference trajectory followed in finite time. Unlike most sliding mode control methods to handle system uncertainties, the designed control has less conservativeness and stronger fault tolerant capability. A rigid spacecraft system is used to demonstrate the effectiveness and potential of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐Time Fault‐Tolerant Control for a Class of Non‐Affine Nonlinear System Using Sliding Mode Disturbance Observer

This study investigates a finite‐time fault‐tolerant control scheme for a class of non‐affine nonlinear system with actuator faults and unknown disturbances. A global approximation method is applied to non‐affine nonlinear system to convert it into an affine‐like expression with accuracy. An adaptive terminal sliding mode disturbance observer is proposed to estimate unknown compound disturbances in finite time, including external disturbances and system uncertainties, which enhances system robustness. Controllers based on finite‐time Lyapunov theory are designed to force tracking errors to zero in finite time. Simulation results demonstrate the effectiveness of proposed method.     

一类3阶非线性系统的非奇异终端滑模控制

针对传统非奇异终端滑模控制方法不适用于3阶系统的问题,提出一类具有不确定和外干扰的3阶非线性系统的新型非奇异终端滑模控制方法.该方案首先结合backstepping控制中的动态面方法和传统2阶非奇异终端滑模控制构造非奇异3阶终端滑模面,首次提出采用高阶滑模微分器估计值代替控制器中的负指数项.采用非线性干扰观测器任意精度地估计不确定和干扰,设计控制器中的补偿项.采用终端吸引子函数做趋近律避免抖振的同时能保证有限时间趋近滑模面.基于有限时间稳定李雅普诺夫定理证明了被控状态将在有限时间内收敛到任意小的闭球内.所提出方案快于传统的递阶线性滑模控制和其他非奇异终端滑模控制.仿真中与其他滑模控制方案对比,总误差减小18%以上,超调及收敛时间也显著下降.     

A novel fixed-time fractional order nonsingular terminal sliding mode control

In order to reduce the convergence time of permanent magnet linear synchronous motor (PMLSM) and improve the robustness of system, a fixed-time fractional order nonsingular terminal sliding mode control (FTFONTSMC) strategy is designed to realize the rapidity and accuracy of PMLSM position tracking response. Firstly, an improved fixed-time terminal sliding mode (FTTSM) reaching law is proposed to reduce the time of convergence. Secondly, due to the uncertainty of the disturbance in PMLSM system, an exponential convergent disturbance observer (DO) is designed to observe the disturbance. Further, finite time stability of the control system is proved by Lyapunov stability theory. Finally, the above control algorithm is applied to PMLSM, and the proposed control method's effectiveness and superiority are validated by comparing with existing control methods.     

Synchronization and Tracking of Multi‐Spacecraft Formation Attitude Control Using Adaptive Sliding Mode

This paper presents the finite‐time attitude synchronization and tracking control method of undirected multi‐spacecraft formation with external disturbances. First, a modified adaptive nonsingular fast terminal sliding mode surface (ANFTSMS) is designed by introducing a user‐defined function, both of which avoid the singularity problem and continuous sliding surface, and, therefore, can freely adjust relative weighting between angular velocity error and attitude error adaptively, such that the controller can provide sufficient maneuvers and precision. This provides designers with a new technique to adjust and improve formation control performance. Second, by applying the ANFTSMS associated with adaptation, two proposed decentralized ANFTSM‐controllers provide finite‐time convergence, robustness to disturbance, and chattering free for continuous design. Finally, simulation results validate the proposed algorithms.     

Robust adaptive fixed‐time tracking control of 6‐DOF spacecraft fly‐around mission for noncooperative target

The fixed‐time relative position tracking and attitude synchronization control problem of a spacecraft fly‐around mission for a noncooperative target in the presence of parameter uncertainties and external disturbances is investigated. Firstly, a novel and coupled relative position and attitude motion model for a noncooperative fly‐around mission is established. Subsequently, a novel nonsingular fast terminal sliding mode (NFTSM) surface is developed, and the explicit estimation of the convergence time independent of initial states is provided. Fair and systematic comparisons among several typical terminal sliding modes show that the designed NFTSM has faster convergence performance than the fast terminal sliding mode. Then, a robust integrated adaptive fixed‐time NFTSM control law with no precise knowledge of the mass and inertia matrix and disturbances by combining the nonsingular terminal sliding mode technique with an adaptive methodology is proposed, which can eliminate the chattering phenomenon and guarantee that the relative position and attitude tracking errors can converge into the small regions containing the origin in fixed time. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control schemes.     

A new practical robust control of cable‐driven manipulators using time‐delay estimation

In this paper, a new practical robust control scheme is proposed and investigated for the cable‐driven manipulators under lumped uncertainties. There are three parts in the proposed method, ie, a time‐delay estimation (TDE) part, a modified super‐twisting algorithm (STA) part, and a fractional‐order nonsingular terminal sliding mode (FONTSM) error dynamics part. The TDE uses intentionally time‐delayed system signals to estimate the lumped dynamics of the system and ensures an attractive model‐free control structure. The STA is applied to guarantee high performance and chattering suppression simultaneously in the reaching phase. The FONTSM error dynamics is utilized to obtain fast convergence and strong robustness in the sliding mode phase. Thanks to the above three parts, the proposed control scheme is model free and can ensure high control performance under lumped uncertainties. The stability considering the FONTSM error dynamics and modified STA scheme is analyzed. Comparative simulation and experiments were conducted to demonstrate the effectiveness and superiorities of the newly proposed control scheme. Corresponding experimental results show that our newly proposed control scheme can provide more than 20% improvement of the steady control accuracy under three different reference trajectories.     

Adaptive terminal angle constraint interception against maneuvering targets with fast fixed‐time convergence

In this paper, a modified adaptive fast nonsingular terminal sliding mode guidance law is proposed based on the theory of fixed‐time convergence, which is applied for intercepting maneuvering targets considering terminal angle constraint. The proposed guidance law achieves system stabilization within bounded settling time independent on initial conditions and provides no singularity and globally rapid convergence property by accelerating the convergence rate when the system is close to the origin. The upper bound of settling time can be obtained in advance by the controller's parameters. Besides, in order to achieve chattering‐free property, a continuous adaptive switching control is introduced and the achieved acceleration‐magnitude constraints are rigorously enforced. Finally, the fixed‐time convergence of the sliding mode manifold and the system states is demonstrated by Lyapunov stability theory. Extensive numerical simulations are presented to validate the efficiency and superiority of the proposed guidance law.     

Attitude Tracking Control of A Quad‐Rotor with Partial Loss of Rotation Effectiveness

This paper investigates the attitude control problem of a quad‐rotor unmanned helicopter. In response to adverse factors, including the lumped disturbance, inertia parameter uncertainties, and the partial loss of rotation effectiveness, an adaptive compensation control strategy combining the terminal sliding mode technique and the input shaping method is proposed. Specifically, a group of updating laws using an adaptive mechanism is added to adjust the control strategy in a manner conductive to attitude stability and performance preservation in the presence of adverse factors. The key features of the proposed control strategy are that it is independent from the knowledge of actuator faults, and adaptive compensation control is achieved without the need for online identification of rotor failure. The finite time convergence and stability of the attitude tracking errors are proved by using Lyaponov's method. Finally, the simulation results demonstrate the effectiveness of the proposed control strategy.     

Nonsingular terminal sliding mode control of nonlinear second‐order systems with input saturation

This paper considers the nonsingular terminal sliding mode (TSM) controller design for a nonlinear second‐order system subject to input saturation. A new nonsingular TSM manifold is constructed by integrating the conventional nonsingular TSM manifold with a saturation function. When the bound of the uncertainty is known, based on the designed TSM manifold, a saturated controller can be designed directly for the nonlinear system. When the bound of the uncertainty is unknown, a disturbance observer is first employed to estimate the uncertainty, followed by constructing a composite controller consisting of a bounded feedback controller and a forward compensator. Theoretical analysis shows that under the proposed two control methods, the states of the closed‐loop system will both converge to zero in finite time. Simulation results demonstrate the effectiveness of the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.