A Novel Disturbance Observer Based Fixed-Time Sliding Mode Control for Robotic Manipulators With Global Fast Convergence

This paper proposes a new global fixed-time sliding mode control strategy for the trajectory tracking control of uncertain robotic manipulators.First,a fixed-time disturbance observer(FTDO) is designed to deal with the adverse effects of model uncertainties and external disturbances in the manipulator systems.Then an adaptive scheme is used and the adaptive FTDO(AFTDO) is developed,so that the priori knowledge of the lumped disturbance is not required.Further,a new non-singular fast terminal sliding mode(NFTSM) surface is designed by using an arctan function,which helps to overcome the singularity problem and enhance the robustness of the system.Based on the estimation of the lumped disturbance by the AFTDO,a fixed-time non-singular fast terminal sliding mode controller(FTNFTSMC)is developed to guarantee the trajectory tracking errors converge to zero within a fixed time.The settling time is independent of the initial state of the system.In addition,the stability of the AFTDO and FTNFTSMC is strictly proved by using Lyapunov method.Finally,the fixed-time NFESM(FTNFTSM) algorithm is validated on a 2-link manipulator and comparisons with other existing sliding mode controllers(SMCs) are performed.The comparative results confirm that the FTNFTSMC has superior control performance.

Fixed-Time Sliding Mode Control With Varying Exponent Coefficient for Modular Reconfigurable Flight Arrays

The modular system can change its physical structure by self-assembly and self-disassembly between modules to dynamically adapt to task and environmental requirements. Recognizing the adaptive capability of modular systems, we introduce a modular reconfigurable flight array(MRFA) to pursue a multifunction aircraft fitting for diverse tasks and requirements,and investigate the attitude control and the control allocation problem by using the modular reconfigurable flight array as a platform. First, considering the variable and irregular topological configuration of the modular array, a center-of-mass-independent flight array dynamics model is proposed to allow control allocation under over-actuated situations. Secondly, in order to meet the stable, fast and accurate attitude tracking performance of the MRFA, a fixed-time convergent sliding mode controller with state-dependent variable exponent coefficients is proposed to ensure fast convergence rate both away from and near the system equilibrium point without encountering the singularity. It is shown that the controller also has fixed-time convergent characteristics even in the presence of external disturbances. Finally,simulation results are provided to demonstrate the effectiveness of the proposed modeling and control strategies.

Revised barrier function-based adaptive finite-and fixed-time convergence super-twisting control

This paper presents an adaptive gain,finite-and fixedtime convergence super-twisting-like algorithm based on a revised barrier function,which is robust to perturbations with unknown bounds.It is shown that this algorithm can ensure a finite-and fixed-time convergence of the sliding variable to the equilibrium,no matter what the initial conditions of the system states are,and maintain it there in a predefined vicinity of the origin without violation.Also,the proposed method avoids the problem of overestimation of the control gain that exists in the current fixed-time adaptive control.Moreover,it shows that the revised barrier function can effectively reduce the computation load by obviating the need of increasing the magnitude of sampling step compared with the conventional barrier function.This feature will be beneficial when the algorithm is implemented in practice.After that,the estimation of the fixed convergence time of the proposed method is derived and the impractical requirement of the preceding fixed-time adaptive control that the adaptive gains must be large enough to engender the sliding mode at time t=0 is discarded.Finally,the outperformance of the proposed method over the existing counterpart method is demonstrated with a numerical simulation.

Some Remarks on the Boundedness and Convergence Properties of Smooth Sliding Mode Controllers

Conventional sliding mode controllers are based on the assumption of switching control, but a well-known drawback of such controllers is the chattering phenomenon. To overcome the undesirable chattering effects, the discontinuity in the control law can be smoothed out in a thin boundary layer neighboring the switching surface. In this paper, rigorous proofs of the boundedness and convergence properties of smooth sliding mode controllers are presented. This result corrects flawed conclusions previously reached in the literature. An illustrative example is also presented in order to confirm the convergence of the tracking error vector to the defined bounded region.

Finite time convergent control using terminal sliding mode

A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control desin methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples.

Precise trajectory tracking of mecanum-wheeled omnidirectional mobile robots via a novel fixed-time sliding mode control approach

This paper proposes a novel fixed-time sliding mode control approach for trajectory-tracking tasks of a mecanum-wheeled omnidirectional mobile robot.First,the idea of two-phase attractors is introduced into the domain of sliding mode control,and a new fixed-time sliding surface is proposed.Then,according to this sliding surface,a new type of nonsingular fast terminal sliding mode control algorithm is designed for the omnidirectional mobile robot,which can realize a fast fixed-time convergence property.The stability of the control system is proven scrupulously,and a guideline for control-parameter tuning is expounded.Finally,experiments are implemented to test the trajectory-tracking performance of the robot.Experimental results demonstrate the superiority of the proposed sliding surface and the corresponding control scheme in comparison with benchmark controllers.

Adaptive backstepping finite-time sliding mode control of spacecraft attitude tracking

This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con- trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se- cond control law is also designed by combining the second or- der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya- punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers.

An Overview of Finite/Fixed-Time Control and Its Application in Engineering Systems

The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability,the finite-time stability possesses the better control performance and disturbance rejection property. Different from the finite-time stability, the fixed-time stability has a faster convergence speed and the upper bound of the settling time can be estimated. Moreover, the convergent time does not rely on the initial information.This work aims at presenting an overview of the finite/fixed-time stabilization and tracking control and its applications in engineering systems. Firstly, several fundamental definitions on the finite/fixed-time stability are recalled. Then, the research results on the finite/fixed-time stabilization and tracking control are reviewed in detail and categorized via diverse input signal structures and engineering applications. Finally, some challenging problems needed to be solved are presented.

Adaptive terminal sliding mode control for high-order nonlinear dynamic systems

An adaptive terminal sliding mode control (SMC) technique is proposed to deal with the tracking problem for a class of high-order nonlinear dynamic systems. It is shown that a function augmented sliding hyperplane can be used to develop a new terminal sliding mode for high-order nonlinear systems. A terminal SMC controller based on Lyapunov theory is designed to force the state variables of the closed-loop system to reach and remain on the terminal sliding mode, so that the output tracking error then converges to zero in finite time which can be set arbitrarily. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated. It is also shown that the stability of the closed-loop system can be guaranteed with the proposed control strategy. The simulation of a numerical example is provided to show the effectiveness of the new method.

Robust controller design for compound control missile with fixed bounded convergence time

A robust controller for bank to turn(BTT) missiles with aerodynamic fins and reaction jet control system(RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties. The fixed time convergence theory is incorporated with the sliding mode control technique to ensure that the system tracks the desired command within uniform bounded time under different initial conditions. Unlike previous terminal sliding mode approaches, the bound of settling time is independent of the initial state, which means performance metrics like convergence rate can be predicted beforehand. To reduce the burden of control design in terms of robustness, extended state observer(ESO) is introduced for uncertainty estimation with the output substituted into the controller as feedforward compensation. Cascade control structure is employed with the proposed control law and therein the compound control signal is obtained.Afterwards, control inputs for two kinds of actuators are allocated on the basis of their inherent characteristics. Finally, a number of simulations are carried out and demonstrate the effectiveness of the designed controller.

Improved Fixed-Time Convergence Guidance Scheme Design and Its Application to Missile

This study presents a fixed-time convergence guidance scheme for impact time and angle control.First,two improved fixed-time stable systems are presented,which have smaller initial control command and better terminal convergence.16 An improved fixed-time extended state observer is proposed to provide accurate estimation of system states and disturbance,which effectively solves peaking value problem.Furthermore,an improved fixed-time sliding mode controller is derived,which avoids the singular problem and achieves faster convergence rate with smaller initial control command.Second,a new guidance scheme with impact angle and impact time constraints is proposed for intercepting a stationary target.By introducing a virtual target,the guidance process is divided into two stages.The proposed fixed-time controller is employed in the first stage.The method with a virtual leader ensures that the missile intercept the virtual target with desired line-of-sight angles at a specific time.By using the proportional navigation guidance law,the missile keeps travelling with desired flight-path angles to hit the real target in the second stage,17 so as to achieve the impact time and angle control.Finally,the feasibility and effectiveness of the proposed guidance scheme in different engagement scenarios are verified by numerical simulations with comparisons.

Fixed-time adaptive model reference sliding mode control for an air-to-ground missile

This paper addresses the fixed-time adaptive model reference sliding mode control for an air-to-ground missile associated with large speed ranges, mismatched disturbances and un-modeled dynamics. Firstly, a sliding mode surface is developed by the tracking error of the state equation and the model reference state equation with respect to the air-to-ground missile. More specifically,a novel fixed-time adaptive reaching law is presented. Subsequently, the mismatched disturbances and the un-modeled dynamics are treated as the model errors of the state equation. These model errors are estimated by means of a fixed-time disturbance observer, and they are also utilized to compensate the proposed controller. Therefore, the fixed-time controller is obtained by an adaptive reaching law and a fixed-time disturbance observer. Closed-loop stability of the proposed controller is established. Finally, simulation results including Monte Carlo simulations, nonlinear six-DegreeOf-Freedom(6-DOF) simulations and different ranges are presented to demonstrate the efficacy of the proposed control scheme.

基于二阶滑模扰动观测的PMSM电流预测控制研究

针对无差拍电流预测控制(DPCC)对电机参数的依赖性,系统性能尤其易受电感参数影响的问题,研究基于二阶滑模扰动观测的永磁同步电机(PMSM)电流预测控制方法。首先,根据滑模控制原理分析电感参数失配对系统参数鲁棒性的影响,及传统滑模控制的不连续函数导致的系统“抖振”;然后,在DPCC中引入一种基于二阶趋近律的滑模扰动观测器(SMDO),实时补偿电感参数失配造成的扰动,同时通过二阶趋近律加速扰动误差的收敛;最后,将该方法与DPCC、SMDO+DPCC进行对比仿真实验。实验结果表明,在电感参数失配的情况下,该方法降低了电流稳态误差,提高了系统参数的鲁棒性,减少了传统滑模控制带来的系统“抖振”现象。

具有角度和时间约束的固定时间协同制导律

针对多飞行器协同打击机动目标问题,提出一种具有终端角度约束和时间一致性约束的固定时间收敛协同中制导方法。建立二维场景下飞行器-目标视线(LOS)坐标系,将加速度分解为沿视线方向和与视线垂直方向。首先,基于代数图论和分布式合作协议算法,对飞行器的沿视线方向加速度进行设计,以保证多个飞行器的剩余飞行时间在固定时间内收敛至一致。其次,基于滑模控制理论和固定时间到达算法,构建飞行器视线法线方向加速度计算方法,使得视线角在固定时间内收敛到期望值。此外,针对目标加速度未知的问题,采用固定时间观测器进行估计,并在制导指令中进行补偿。仿真结果表明所提出的协同制导方法能够在固定时间内实现剩余飞行时间和视线角度的收敛。

同步BUCK电路中的新型非奇异终端滑模控制性能研究

针对传统滑模控制趋近速度较慢、抖振较大,应用在同步Buck变换器中响应速度较慢、精度较低等问题,提出了一种新型非奇异终端滑模控制的方法。首先对传统的滑模面函数进行了修改,通过引入非线性函数并附上积分项,可以迫使系统快速收敛,从而缩短响应时间。其次在传统趋近律的基础上引入了形式为sigmoid的函数,并用饱和函数来替代符号函数,避免了符号函数在零附近高频切换,因此降低了传统滑模控制带来抖振影响。最后在MATLAB/Simulink仿真平台搭建相应的模型,结果显示,其调整时间为90μs,突加负载后恢复时间为20μs。并通过实验验证,在转速指令发生改变时,所设计的方法调整时间更快,在突加负载后,抗干扰能力更强。

系统收敛时间和攻击角度控制的滑模导引律

针对打击机动目标带攻击角度约束的导引律设计问题,采用滑模控制理论、任意收敛时间控制方法和干扰观测器,设计了一种攻击角度和收敛时间控制的导引律。根据弹目相对运动关系,将目标机动和建模误差等视为干扰,构建了考虑攻击角度约束的制导系统状态方程。分析了任意收敛时间控制方法在干扰情况下的性能,采用滑模控制和干扰观测器对任意收敛时间控制方法进行改进,提升鲁棒性。将该方法用于滑模面和趋近律设计中,采用干扰观测器对系统扰动进行估计,基于滑模控制理论,结合制导控制系统状态方程,推导出了收敛时间和攻击角度可控的滑模导引律。相比有限时间收敛导引律,该导引律的收敛时间和攻击角度可直接设定,无需根据制导参数计算。设置不同的目标机动方式以及不同的攻击角度和收敛时间,进行了多场景的数值仿真。结果表明,所提导引律能够有效实现攻击角度和收敛时间控制,并精确命中目标,同时相比现有导引律其制导性能更佳。

Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

指向约束下有限时间航天器姿态重定向控制

针对指向约束下的航天器姿态重定向控制问题,提出一种解析的有限时间滑模控制器.与现有渐进收敛控制算法相比,该算法具有更快的收敛速度.根据姿态机动目标和姿态指向约束建立相应的导航势函数,并在滑模面上引入势函数及其梯度信息,使得航天器机动到目标姿态的过程中可以满足姿态指向约束.为严格保证滑模面外指向约束的可行性,结合滑模函数以及人工势场函数建立了新的李雅普诺夫函数.接着,基于该李雅普诺夫函数和有限时间收敛定理,设计一种控制器以实现指向约束下有限时间航天器姿态重定向控制.数值仿真表明所提控制器可以实现姿态快速收敛并确保航天器姿态指向约束的可行性.

跷跷板系统干扰补偿的分层滑模控制策略研究

为提高跷跷板系统在外部干扰下的平衡控制性能,提出一种基于指数收敛干扰观测器与切换增益模糊自适应分层滑模控制相结合的复合控制策略。首先,设计一种指数收敛干扰观测器,对系统受到的外部扰动等不确定因素进行估计补偿,以改善控制器鲁棒性。该观测器不需要状态变量二阶导的信息,可以应对实际工程中难以通过求导的方式获取加速度信号的问题。然后,针对跷跷板这类强耦合欠驱动系统提出一种分层滑模控制算法,并进一步针对滑模控制算法在未知大干扰下切换增益过大的问题,通过模糊规则的设计将切换增益模糊化,以降低系统抖振。最后,仿真和试验结果表明,相较于传统的滑模控制算法,该分层滑模控制算法抗干扰能力更强、切换增益更低。该策略可应用于类跷跷板平衡控制的实际系统。

基于FxTSMC-ESO的永磁同步电机调速系统滑模控制

针对永磁同步电机速度环中存在的外部负载扰动问题,为了提高速度环控制系统的动态性和鲁棒性,提出一种基于新型固定时间滑模控制器与扩张状态观测器的控制方法。所提出的滑模控制器简化了收敛时间公式,解决了快速响应与抑制抖振的矛盾。为了进一步提升调速系统的鲁棒性,采用固定时间收敛的扩张状态观测器对控制器的扰动进行前馈补偿,该观测器不仅可以减小趋近律的开关函数增益,还能实现扰动的精准观测。仿真验证了所提滑模控制方法的有效性。