Fixed‐time adaptive sliding mode trajectory tracking control of uncertain mechanical systems

An adaptive fixed‐time trajectory tracking controller is proposed for uncertain mechanical systems in this study. The polynomial reference trajectory is planned for trajectory tracking error. Fractional power of linear sliding mode is applied to design the nonlinear controller, adaptive laws are used to adjust controller parameters. Trajectory planning and fractional power are combined to ensure the tracking‐error convergence in a fixed time. The boundary layer technique is used to suppress the model uncertainties and decrease the chattering phenomenon. The closed‐loop system stability is proved strictly in the Lyapunov framework to show that the trajectory tracking errors and adaptive parameters tend to zero in a fixed time set in advance. Numerical simulation results of robotic manipulators illustrate the effectiveness of the proposed controller.     

Robust trajectory tracking control for unmanned tail‐sitters in aggressive flight mode transitions

In this paper, the trajectory tracking control problem is investigated for a new typical tail‐sitter. A robust hierarchical control method is proposed to achieve aggressive flight mode transitions. The proposed control method results in a composite controller including a translational controller and a rotational controller to control the position and attitude respectively. Continuous aggressive flight mode transitions can be achieved without switching on the coordinate systems or the controller structures. It is proven that the tracking errors of the designed closed‐loop system can converge into a given neighborhood of the origin in a finite time. Simulation results show the effectiveness of the proposed control strategy.     

Nonlinear control with integral sliding properties for circular aerial robot trajectory tracking: Real‐time validation

A nonlinear control algorithm for tracking dynamic trajectories using an aerial vehicle is developed in this work. The control structure is designed using a sliding mode methodology, which contains integral sliding properties. The stability analysis of the closed‐loop system is proved using the Lyapunov formalism, ensuring convergence in a desired finite time and robustness toward unknown and external perturbations from the first time instant, even for high frequency disturbances. In addition, a dynamic trajectory is constructed with the translational dynamics of an aerial robot for autonomous take‐off, surveillance missions, and landing. This trajectory respects the constraints imposed by the vehicle characteristics, allowing free initial trajectory conditions. Simulation results demonstrate the good performance of the controller in closed‐loop system when a quadrotor follows the designed trajectory. In addition, flight tests are developed to validate the trajectory and the controller behavior in real time.     

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.     

一种基于指数趋近律的非线性系统变结构轨迹跟踪控制新方法

针对多输入多输出二阶不确定非线性机械系统中轨迹跟踪控制的问题,提出一种新的基于指数趋近律的滑模变结构控制方法,用于提高系统的平稳性和快速性。在滑模变结构控制器设计过程中采用一种新的指数趋近律以改进闭环系统的暂态和稳态响应性能,使系统跟踪误差收敛速度加快,特别是减少轨迹跟踪误差到达滑模面的时间,同时提高了系统轨迹跟踪过程的平稳性。通过采用边界层方法消除滑模控制输入抖振问题,避免控制过程中执行器的频繁切换,进一步提高所提出滑模控制器在实际系统中的实用性。基于李雅普诺夫稳定性理论证明了闭环系统的稳定性和跟踪误差的收敛性。数值仿真验证了所提出的控制方法的有效性。     

Switched Second‐Order Sliding Mode Control with Partial Information: Theory and Application

This paper proposes a novel switched second order sliding mode (S‐SOSM) control strategy in a partial information setting, i.e., when only the sliding variable is accessible for measurements. Such a control approach allows one to deal with systems characterised by different levels of uncertainties associated with different regions of the state space and to accommodate different control objectives in the different regions by switching among appropriate SOSM controllers. The proposed approach is shown to ensure global finite‐time convergence to the origin of the closed‐loop system trajectory. The braking control of two‐wheeled vehicles is considered as a case‐study to test the controller performance.     

Adaptive Terminal Sliding Mode Control for Motion Tracking of a Micropositioning System

This paper presents the design of a novel adaptive terminal sliding mode controller (ATSMC) and its application to motion tracking control of a piezoelectric‐driven micropositioning system. A nonsingular terminal sliding surface is used to achieve fast and finite‐time convergence for the trajectory tracking, and also to avoid the singularity phenomenon in traditional terminal sliding mode design. An adaptive gain law is developed to update the gain of the proposed controller and to provide stable and chattering‐free control action. The stability of the control system has been demonstrated in the sense of Lyapunov. The ATSMC scheme is established based on the output feedback only, which does not require a state observer and facilitates an easy implementation. The proposed controller is implemented on a field‐programmable gate array (FPGA) platform. Comparison study with three conventional controllers has been conducted. Experimental results show the feasibility and effectiveness of the proposed control strategy.     

A simplified version of adaptive super‐twisting control

In this paper, a simplified super‐twisting control with adaptive gain is proposed for a class of nonlinear uncertain systems. A strong Lyapunov function is constructed to design a sliding mode controller with adaptive gain. Furthermore, the analysis of the finite time convergence towards the equilibrium point of the closed‐loop system is detailed. Regarding previous works from literature, the main contribution of this approach is the simplification of the gain tuning process by maintaining a high level of performance. Finally, simulation results for tracking control of a quadrotor are given to show the performance of the proposed algorithm.     

多输入多输出非线性不确定系统连续高阶滑模控制

针对一类MIMO非线性不确定系统,提出一种新的连续高阶滑模控制算法.引入状态反馈使得系统高阶滑模控制问题等效转换为多变量不确定积分链的有限时间稳定问题,首先针对标称系统设计有限时间到达连续控制律,实现系统状态快速收敛,然后采用多变量非解耦形式超螺旋算法克服系统不确定性,实现鲁棒性,最终使得系统控制作用连续、滑模抖振得以大大抑制.基于二次型Lyapunov函数证明系统的有限时间稳定性.针对三阶不确定系统有限时间稳定和气垫船圆形航迹跟踪问题分别进行了仿真,验证了所提算法的有效性、鲁棒性.     

Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

This paper presents a fast terminal sliding‐mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time‐varying disturbances. Fast terminal sliding‐mode finite‐time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite‐time control effort, the fast terminal sliding‐mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high‐precision output tracking performance in uncertain nonlinear systems.     

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。     

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

This paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication ?ow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors

This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under‐actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non‐singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed‐loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach. Copyright © 2016 John Wiley & Sons, Ltd.     

High‐order sliding mode control design based on adaptive terminal sliding mode

High‐order sliding mode control techniques are proposed for uncertain nonlinear SISO systems with bounded uncertainties based on two different terminal sliding mode approaches. The tracking error of the output converges to zero in finite time by designing a terminal sliding mode controller. In addition, the adaptive control method is employed to identify bounded uncertainties for eliminating the requirement of boundaries needed in the conventional design. The controllers are derived using Lyapunov theory, so the stability of the closed‐loop system is guaranteed. In the first technique, the developed procedure removes the reaching phase of sliding mode and realizes global robustness. The proposed algorithms ensure establishment of high‐order sliding mode. An illustrative example of a car control demonstrates effectiveness of the presented designs. Copyright © 2011 John Wiley & Sons, Ltd.     

自适应模糊滑模控制器的设计与分析

研究一类非线性系统的自适应模糊控制问题,根据滑模控制原理并利用I型模糊系 统的逼近能力,提出了一种自适应模糊滑模控制器的设计方案.通过理论分析,证明了闭环模 糊控制系统的全局稳定的,跟踪误差可收敛到零的一个领域内.     

Path‐Tracking Control of a Riderless Bicycle Via Road Preview and Speed Adaptation

In this study, a genetic‐fuzzy control system is used to control a riderless bicycle where control parameters can adapt to the speed change of the bicycle. The equations of motion are developed for a bicycle with constraints of rolling‐without‐slipping contact condition between the wheels and ground. This controller consists of two loops: the inner is a roll‐angle‐tracking controller which generates steering torque to control the roll angle while guaranteeing the stability, and the outer is a path‐tracking controller which generates the reference roll angle for the inner loop. The inner loop is a sliding‐mode controller (SMC) designed on the basis of a linear model obtained from a system identification process. By defining a stable sliding surface of error dynamics and an appropriate Lyapunov function, the bicycle can reach the roll‐angle reference in a finite time and follow that reference without chattering. The outer loop determines the proper reference roll‐angle by using a fuzzy‐logic controller (FLC) in which previewing and tracking errors are taken into consideration. The robustness of the proposed controller against speed change and external disturbances is verified by simulations.     

High‐order mismatched disturbance rejection control for small‐scale unmanned helicopter via continuous nonsingular terminal sliding‐mode approach

In this paper, the problem of finite‐time control for small‐scale unmanned helicopter system with high‐order mismatched disturbance is investigated via continuous nonsingular terminal sliding‐mode control approach. The key idea is to design a novel nonlinear dynamic sliding‐mode surface based on finite‐time disturbance observer. Then, the finite‐time convergence and chattering attenuation capability is guaranteed by the continuous nonsingular terminal sliding‐mode control law. Additionally, rigorous finite‐time stability analysis for the closed‐loop helicopter system is given by means of the Lyapunov theory. Finally, some simulation results demonstrate the effectiveness and predominant properties of the proposed control method for the small‐scale unmanned helicopter even in the presence of high‐order mismatched disturbance.     

Decentralized adaptive fuzzy sliding mode control for reconfigurable modular manipulators

A stable decentralized adaptive fuzzy sliding mode control scheme is proposed for reconfigurable modular manipulators to satisfy the concept of modular software. For the development of the decentralized control, the dynamics of reconfigurable modular manipulators is represented as a set of interconnected subsystems. A first‐order Takagi–Sugeno fuzzy logic system is introduced to approximate the unknown dynamics of subsystem by using adaptive algorithm. The effect of interconnection term and fuzzy approximation error is removed by employing an adaptive sliding mode controller. All adaptive algorithms in the subsystem controller are derived from the sense of Lyapunov stability analysis, so that resulting closed‐loop system is stable and the trajectory tracking performance is guaranteed. The simulation results are presented to show the effectiveness of the proposed decentralized control scheme. Copyright © 2009 John Wiley & Sons, Ltd.     

基于函数滑模控制器的机械手轨迹跟踪控制

提出一种基于函数滑模控制器(FSMC)的控制策略,用于不确定机械手的轨迹跟踪控制。首先,由动力学模型和滑模函数得到系统的不确定项;然后,利用RBF神经网络逼近系统不确定项,由于神经网络逼近存在误差,而且在初始阶段误差较大,设计函数滑模控制器和鲁棒补偿项对神经网络逼近误差进行补偿,以克服普通滑模控制器容易引起的抖振问题,同时提高系统的跟踪控制性能。基于李亚普诺夫理论证明了闭环系统的全局稳定性,仿真实验也验证了方法的有效性。