Reduced‐order sliding function design for a class of nonlinear systems

In this paper, the design of first order sliding mode control (SMC) and twisting control based on the reduced order sliding function is proposed for the robust stabilization of an class of uncertain nonlinear single‐input system. This method greatly simplifies the control design as the sliding function is linear, which is based on reduced order state vector. The nonlinear system is represented as a cascade interconnection of two subsystems driving and driven subsystems. Sliding surface and SMC are designed for only the driving subsystem that guarantees the asymptotic stability of the entire system. To show the effectiveness of the proposed control schemes, the simulation results of translational oscillator with rotational actuator are illustrated.     

Control for Underactuated Systems Using Sliding Mode Observer

In this work, first we estimate all the system’s state vector, with guarantied precision, for a category of second order underactuated mechanical systems (UMS), exploiting the triangular observer (TO) model that suits to the structure of these systems. Then we propose a sliding mode controller (SMC). The latter uses the estimated states given by the observer. The underactuated system is decomposed into two subsystems, where the sliding surface is constructed in two levels for each subsystem. The proposed controller guaranties the tracking performances, with minimization of chattering phenomenon, due to the constructed observer, even for system with uncertainties. Simulation results show the effectiveness of this strategy of control.

     

The Trajectory Tracking Problem of Quadrotor UAV: Global Stability Analysis and Control Design Based on the Cascade Theory

This paper deals with the trajectory tracking problem of a six‐degree of freedom (6‐DOF) quadrotor unmanned aerial vehicle (UAV). The problem of simplified kinematics based on Euler angles is analyzed and the modified Rodrigues parameters (MRPs) technique is introduced to model the rotational dynamics of the rigid body. A nonlinear system error model is established based on the trajectory tracking problem, and, due to the coupling property between the translational and rotational dynamics, we divide the complete closed‐loop system into two reduced‐order subsystems and a coupling term. The Rodrigues theorem is applied to analyze the internal connections between the coupling term and MRPs. Therefore, the global stability conclusions, by which the trajectory tracking controller of the quadrotor UAV could be designed based on the subsystem directly in future works, are proved based on several assumptions of the subsystems. Thereafter, the controllers, using the backstepping approach and nonlinear disturbance observer/sliding mode control approach, which stabilize the quadrotor UAV globally ‐exponentially and globally uniformly bounded, are proposed based on the stability theorem proofs mentioned above. Numerical simulations are provided to show that the theoretical conclusions and the controller proposed are effective.     

基于模糊不确定观测器的四旋翼飞行器自适应动态面轨迹跟踪控制

针对具有未知外界扰动和系统不确定性的四旋翼飞行器,提出了一种基于模糊不确定观测器（Fuzzy uncertainty observer,FUO）的自适应动态面轨迹跟踪控制方法.通过将四旋翼飞行器系统分解为位置、姿态角和角速率三个动态子系统,使得各子系统虚拟控制器能够充分考虑欠驱动约束;采用一阶低通滤波器重构虚拟控制信号及其一阶导数,实现四旋翼跟踪控制设计的迭代解耦;设计了一种模糊不确定观测器,用以估计和补偿未知外界扰动与系统不确定性,从而确保闭环系统的稳定性和跟踪误差与其他系统信号的一致有界性.仿真研究验证了所提出的控制方法的有效性和优越性.     

Backstepping Sliding Mode Trajectory Tracking via Extended State Observer for Quadrotors with Wind Disturbance

To overcome nonlinear, underactuated and external wind disturbances problems for the 6-DOF (degrees of freedom) quadrotor unmanned aerial vehicle (UAV) system, a backstepping sliding mode control algorithm based on high-order extended state observer (ESO) is proposed. Based on the hierarchical control principle, the quadrotor UAV dynamic system is decomposed into position subsystem and attitude subsystem to facilitate the backstepping control design. Moreover, the EXO is used to estimate the remaining unmeasurable states and the external wind disturbances online. The advantages of the controllers are that they can not only ensure good tracking performance, but also deal with uncertain external disturbances. To imitate the real situation as much as possible, the external wind disturbances are composed of four basic wind models in this paper. The tracking error and estimate error of the design methods are shown to arbitrarily small by using Lyapunov theory. Finally, the effectiveness and superiority of the proposed control algorithm are proved by the simulation.

     

基于终端滑模的四旋翼飞行器非线性轨迹跟踪控制

考虑到四旋翼飞行器的传统内外环控制策略依赖时标分离假设,稳定性分析复杂,并且控制参数选取困难的缺点,提出了一种与传统内外环控制策略不同的轨迹跟踪控制器;首先将四旋翼飞行器数学模型进行相应的变换,以分解为高度、偏航角和纵横向三个级联的子系统,再使用终端滑模控制方法设计高度和偏航角子系统的控制器,使两个子系统的状态误差可以在有限时间内收敛到原点,之后基于变量非线性变换设计纵横向子系统的控制器,分析了闭环系统稳定性,证明了所设计的轨迹跟踪控制器可以保证闭环系统跟踪误差渐近稳定到原点,最后仿真实验的结果验证了所设计的控制器的有效性。     

Robust Backstepping Control Based on Integral Sliding Modes for Tracking of Quadrotors

Modern non-inertial robots are usually underactuated, such as fix or rotary wing Unmanned Aerial Vehicles (UAVs), underwater or nautical robots, to name a few. Those systems are subject to complex aerodynamic or hydrodynamic forces which make the dynamic model more difficult, and typically are subject to bounded smooth time-varying disturbances. In these systems, it is preferred a formal control approach whose closed-loop system can predict an acceptable performance since deviations may produce instability and may lead to catastrophic results. Backstepping provides an intuitive solution since it solves underactuation iteratively through slaving the actuated subsystem so as to provide a virtual controller in order to stabilize the underactuated subsystem. However it requires a full knowledge of the plant and derivatives of the state, which it is prone to instability for any uncertainty; and although robust sliding mode has been proposed, discontinuities may be harmful for air- or water-borne nonlinear plants. In this paper, a novel robust backstepping-based controller that induces integral sliding modes is proposed for the Newton–Euler underactuated dynamic model of a quadrotor subject to smooth bounded disturbances, including wind gust and sideslip aerodynamics, as well as dissipative drag in position and orientation dynamics. The chattering-free sliding mode compensates for persistent or intermittent, and possible unmatched state dependant disturbances with reduced information of the dynamic model. Representative simulations are presented and discussed.     

欠驱动RTAC的滑模自抗扰镇定控制

针对欠驱动RTAC (rotational/translational actuator)的镇定问题,提出了一种滑模自抗扰控制方法,通过对总扰动的观测和补偿降低了未知扰动对RTAC的影响.为克服RTAC的欠驱动特性,所提方法通过将可驱动的摆球角度和无驱动的小车位置两个状态相结合,构建出虚拟被控量作为系统输出,从而使RTAC的动力学模型转换为非欠驱动模型.基于重建的模型设计线性扩张状态观测器(linear extended state observer, LESO)和滑模控制器,并采用Lyapunov方法证明RTAC的闭环稳定性,实现了RTAC的镇定控制,有效抑制了小车的振荡.最后,通过数值仿真和硬件实验验证了所提控制方法的有效性,与已有方法的对比分析证明该方法具有良好的控制性能.     

基于级联型具有旋转激励的平移振荡器系统的滑模控制

针对欠驱动具有旋转激励的平移振荡器(TORA)系统的控制问题,本文首次提出一种全局滑模控制方法,使闭环系统在整个控制过程对外界干扰均具有鲁棒性.相比已有控制方法,本文所提方法结构简单,便于实现;而且放宽了对外界干扰的假设条件,可实现闭环系统的全局滑模控制.具体而言,本文首先将系统模型变换为由两个子系统组成的级联形式;随后,针对内环子系统设计了一种虚拟控制输入,在此基础上构造了一种新颖的滑模面并设计了相应的滑模控制器;最后,通过严格的数学分析证明了闭环系统的稳定性及系统状态的渐近收敛性,利用数值仿真测试检验了本文所提方法的控制性能.通过与已有方法进行仿真对比可知,本文方法在镇定控制与鲁棒性方面均表现出良好的控制性能.     

一种球形移动机器人爬坡运动的自适应滑模控制

针对一种球形机器人爬坡运动的位置控制问题,提出了一种自适应滑模控制方法.基于对实际系统的合理简化,利用拉格朗日方法建立了球形机器人爬坡运动的动力学模型,并将动力学模型表示为状态空间形式.基于系统的状态空间模型,将整个系统划分为两个子系统,并分别定义各子系统的滑动面.将其中一个子系统的滑动面引入到另一个子系统的控制设计中,采用李亚普诺夫稳定性理论设计了滑模控制律,并通过自适应律在线调节其切换增益.从理论上分析了闭环控制系统的稳定性,并通过数值仿真和样机实验验证了所提控制方法的有效性.     

基于稳定性分析的一类欠驱动系统的滑模控制器设计

从稳定分析的角度提出了一种欠驱动系统的新型滑模控制方法．该方法将各个子系统的一个变量进行组合定义成一个中间变量，然后从这个中间变量出发构造滑模函数，通过求取总的控制量保证中间变量在有限时间内收敛到平衡点；进一步利用LaSalle不变性原理证明该收敛域内只有一个平衡点且是渐近稳定的．仿真实验进一步验证了该结论．     

Composite Hierarchical Anti-Disturbance Control of a Quadrotor UAV in the Presence of Matched and Mismatched Disturbances

Quadrotor helicopter is an unstable system subject to matched and mismatched disturbances. To stabilize the quadrotor dynamics in the presence of these disturbances, the application of a composite hierarchical anti-disturbance controller, combining a sliding mode controller and a disturbance observer, is presented in this paper. The disturbance observer is used to attenuate the effect of constant and slow time-varying disturbances. Whereas, the sliding mode controller is used to attenuate the effect of fast time-varying disturbances. In addition, sliding mode control attenuates the effect of the disturbance observer estimation errors of the constant and slow time-varying disturbances. In this approach, the upper bounds of the disturbance observer estimation errors are required instead of the disturbances’ upper bounds. The disturbance observer estimation errors are found to be bounded when the disturbance observer dynamics are asymptotically stable and the disturbance derivatives and initial disturbances are bounded. Moreover, due to the highly nonlinear nature of the quadrotor dynamics, the upper bounds of a part of the quadrotor states and disturbance estimates are required. The nonlinear terms in the rotational dynamics are considered as disturbances, part of which is mismatched. This assumption simplifies the control system design by dividing the quadrotor’s model into a position subsystem and a heading subsystem, and designing a controller for each separately. The stability analysis of the closed loop system is carried out using Lyapunov stability arguments. The effectiveness of the developed control scheme is demonstrated in simulations by applying different sources of disturbances such as wind gusts and partial actuator failure.     

A multitask sliding mode control for mismatched uncertain large-scale systems

A new sliding mode control (SMC) approach, output variables only, single phase only and chattering phenomenon free, is presented for a class of mismatched uncertain large-scale systems. For a new multitask SMC, it is not required that the system states are available. Moreover, the sliding function in this study just depends on output variables. Using an exponential type sliding surface, the system states are always in the sliding mode at the beginning time t = 0. Using a newly appropriate linear matrix inequality stability conditions by the Lyapunov method are derived such that each subsystem in the new sliding mode is completely invariant to matched uncertainties. As a result, robustness of the mismatched uncertain large-scale systems can be assured throughout an entire response of the system starting from the initial time t = 0. In every subsystem, a scheme of decentralised control using only output states is proposed. In addition, a continuous controller is finally designed for chattering removal. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.     

四旋翼飞行器自适应动态面轨迹跟踪控制

针对具有未知外界扰动和系统不确定性集总未知非线性的四旋翼飞行器,提出了一种采用自适应不确定性补偿器的自适应动态面轨迹跟踪方法.通过将四旋翼飞行器系统分解为位置、欧拉角和角速率3个动态子系统,使各子系统虚拟控制器设计能充分考虑欠驱动约束;结合动态面控制技术,通过采用一阶低通滤波器,避免对虚拟控制信号求导;进而设计自适应不确定性补偿器,处理未知外界扰动和系统不确定性,最终确保闭环控制系统的稳定性、跟踪误差一致最终有界和系统所有状态信号有界.仿真研究和实验结果验证了本文提出控制方法的有效性和优越性.     

Fuzzy sliding mode control for an under-actuated system with mismatched uncertainties

This article presents a robust fuzzy sliding mode controller. The methodology of sliding mode control provides an easy way to control under-actuated nonlinear systems with uncertainties. The structure of the sliding surface is designed as follows. First, decouple the entire system into second-order systems so that each subsystem has a separate control target expressed in terms of a sliding surface. Second, from the sliding surface of subsystems, organize the main sliding surface system. Third, generate a control input for the main sliding surface to make whole subsystems move toward their sliding surface. A fuzzy controller is used to obtain a smooth boundary layer to the sliding surface. Finally, the fuzzy sliding mode controller presented is used to control an under-actuated nonlinear system, and confirms the validity of the proposed approach and its robustness to uncertainties.     

Second-order terminal sliding mode control of uncertain multivariable systems

A second-order terminal sliding mode controller for uncertain multivariable systems is proposed in this paper. The controller adopts the hierarchical control structure. The paper derives the state transform matrices which are used to transform a multivariable linear system to the block controllable form consisting of two subsystems, an input–output subsystem and a stable internal dynamic subsystem. The proposed controller utilizes a non-singular terminal sliding mode manifold for the input–output subsystem to realize fast convergence and better tracking precision. Meanwhile, a chattering-free second-order terminal sliding mode control law is presented. The stability of uncertain multivariable systems can be realized using the proposed controller. A derivative estimator is utilized in the paper to estimate the derivatives of the sliding mode functions for the controller. The simulation results are presented to validate the design method.     

四旋翼无人飞行器的轨迹跟踪与滑模事件驱动控制

四旋翼飞行器作为一个典型的欠驱动的系统,具有强耦合、非线性等特性.针对飞行器外部干扰、和通信资源受限条件下的轨迹跟踪控制问题,进行滑模事件驱动控制方法的研究.首先,分析动力学特性,通过时间尺度分解方法将系统解耦成位置子系统和姿态子系统.其次,将位置子系统转化为严格反馈形式,设计反步滑模控制器,实现位置轨迹稳定跟踪;针对姿态子系统存在时变有界扰动及通信受限,设计滑模事件驱动控制律,在抑制干扰的同时实现对虚拟姿态跟踪指令的跟踪.根据Lyapunov分析方法证明了所设计控制器的稳定性,并通过理论分析证明闭环控制系统不会出现Zeno现象.最后,仿真结果验证了滑模事件驱动控制律在存在外部扰动和通信受限时四旋翼无人飞行器轨迹跟踪的鲁棒性.     

四旋翼飞行器的轨迹跟踪抗干扰控制

针对四旋翼飞行器轨迹跟踪问题中系统存在模型不确定和易受到外界扰动的情况,提出了基于切换函数的扩张状态观测器设计方法来对系统中的扰动进行估计,并将估计值与滑模控制器的设计相结合,实现了对系统中非匹配不确定性和匹配不确定性的抑制且实现了系统跟踪误差的一致最终有界.首先,根据变量间的耦合关系将飞行器系统模型分解为两个子系统模型,设计扩张状态观测器对子系统中的非匹配不确定性进行估计,并将估计值作为变量加入到切换函数的设计中;进而基于切换函数设计扩张状态观测器以估计经切换函数重构系统中的扰动,并在控制器中对扰动进行补偿.最后通过李雅普诺夫理论证明了控制系统的稳定性.通过仿真验证了本文提出的方法能够有效实现飞行器轨迹跟踪控制且能够抑止传统滑模控制的抖振现象.     

基于干扰观测器的解耦快速终端滑模控制

针对一类欠驱动系统跟踪控制问题,提出了一种基于非线性干扰观测器的全局解耦快速终端滑模控制(NDODGFTSMC)策略.将欠驱动系统分解成两个子系统分别设计全局快速终端滑模面,利用其中一个子系统滑模面的符号函数来构造中间变量,并将该变量引入到另一个子系统的滑模面中,构造出整个系统的滑模面,采用等效控制法和模糊双幂次趋近律...     

A nonholonomic control method for stabilizing an X4-AUV

A nonholonomic control method is considered for stabilizing all attitudes and positions (x, y, or z) of an underactuated X4 autonomous underwater vehicle (AUV) with four thrusters and six degrees of freedom (DOF), in which the positions are stabilized according to the Lyapunov stability theory. A dynamic model is first derived, and then a sequential nonlinear control strategy is implemented for the X4-AUV which is composed of translational and rotational subsystems. A controller for the translational subsystem stabilizes one position out of the x-, y-, and z-coordinates, whereas controllers for the rotational subsystems generate the desired roll, pitch, and yaw angles. Thus, the rotational controllers stabilize all the attitudes of the X4-AUV at the desired (x-, y-, or z-) position of the vehicle. Some numerical simulations are conducted to demonstrate the effectiveness of the proposed controllers.