基于动态边界层的水下航行器滑模轨迹跟踪

滑模控制方法的不变性和鲁棒性特性能够克服水下航行器轨迹跟踪过程中的参数不确定性以及摄动的影响,但在实际应用中存在执行器受限问题常常会导致滑动模态的丧失.为了抑制执行器的速率与幅值限制对滑模控制器的影响,采用二阶滑模控制的水下航行器轨迹跟踪控制,并用了边界层厚度动态控制的方法解决存在速率和幅值限制的有限带宽的执行器的滑模控制器的设计,通过增加边界层厚度,控制器的轨迹跟踪能力有所减弱.但是系统状态仍然保持在边界层内,保证了系统的稳定性.通过仿真证明了水下航行器的姿态角跟踪控制仿真证明了上述结论的正确性.     

Pendubot的一种分层滑模控制方法

针对Pendubot这类二阶欠驱动系统提出了一种分层滑模控制方法.该方法将系统状态分成两个子系统,分别构造滑动平面,采用Lyapunov方法求取总控制量,该控制量可以实现Pendubot的摆起控制,当系统接近平衡位置附近时,双层滑模控制器退化成单层控制器,这样又保证了Pendubot能够稳定在最终的平衡位置上.从理论上证明了各层滑动平面的渐近稳定性,并且通过仿真实验验证了该方法的有效性以及该控制器对各类扰动的自适应性.     

一类输入受限的不确定非仿射非线性系统二阶动态terminal 滑模控制

针对一类输入受限的不确定非仿射非线性系统跟踪控制问题, 提出一种二阶动态terminal 滑模控制策略. 在不损失模型精度, 并考虑系统输入饱和受限的前提下, 给出一种适用于全局的不确定非仿射非线性系统近似方法. 提出小波小脑模型干扰观测器设计方法, 实现复合扰动的有效逼近. 构造辅助系统分析输入饱和对跟踪误差的影响. 通过构造基于PI 滑模面的terminal 二阶滑模面, 给出二阶动态terminal 滑模控制器设计过程, 克服了传统滑模的抖振问题. 仿真结果验证了所提出方法的有效性.

     

悬臂式掘进机器人截割臂建模与二阶滑模控制器设计

根据悬臂式掘进机器人截割工艺和结构特点,建立了截割臂动力学模型.将一种基于有限状态结构的二阶滑模控制扩展到多输入多输出系统中,在无速度观测器的情况下,保证了滑模量及其导数在有限时间收敛到零.算法消弱了传统滑模控制中的抖动问题,提高了控制系统精度.利用提出的多输入多输出二阶滑模控制算法,设计了截割臂控制器.通过仿真和实验,证明了算法的有效性.     

基于模糊干扰观测器的自适应二阶动态滑模控制

针对一类存在不确定性和外干扰的非线性系统滑模控制的抖振问题,本文首先证明了以高斯函数为隶属度函数的模糊基向量对状态向量的偏导在任意情况下有界,解决了模糊辨识同二阶动态滑模结合的关键问题.然后设计了二阶动态Terminal滑模,有效克服了滑模抖振,且能保证滑模面上的滑动在有限时间内收敛.再基于模糊干扰观测器的输出设计自适应鲁棒补偿项.基于李雅普诺夫理论证明了系统稳定性.最后将本文提出的控制方案用于近空间飞行器姿态角跟踪仿真,并分析了高阶动态滑模收敛时间增加的问题.结果表明本文提出的控制方案跟踪速度快、精度高,且有效去除了抖振.与常规Terminal滑模相比,二阶动态Terminal滑模增加的收敛时间非常有限,适于工程应用.     

基于观测器的滑模控制非线性中立型时滞系统

针对一类状态不可测的非线性不确定中立型时滞系统,基于滑模控制理论,采用线性矩阵不等式的处理方法,提出了滑动模态鲁棒渐近稳定时滞相关的充分条件,设计了一类滑模观测器,同时给出了该观测器存在的充分条件;然后应用滑模控制的趋近率方法和基于观测器所得到的系统估计状态,综合了一类滑模控制器,该控制器同时保证了估计状态下滑模面和估计误差状态下滑模面的渐近可达性;最后通过数值实例证明了该控制方案的可行性.     

滑模控制一类非线性分布式时滞系统

针对一类状态不可测的非线性不确定分布式时滞系统, 给出了系统滑动模态鲁棒渐近稳定的充分条件. 设计了一类滑模观测器, 同时采用线性矩阵不等式的处理方法给出了该观测器存在的充分条件. 再应用滑模控制的趋近率方法和基于观测器所得到的估计状态, 综合了一类滑模控制器. 该控制器同时保证了估计状态下的滑模面和估计误差状态下的滑模面的渐近可达性.     

一类不确定混沌系统的模糊滑模控制与同步

针对一类具有不确定项的二阶连续时间混沌系统的定值跟踪控制和自混沌同步及异结构混沌同步问题,提出了一种模糊滑模变结构控制方法,设计了模糊滑模变结构控制器,并从理论上证明了控制系统的稳定性.在该控制器的作用下,可以实现两个相同或不同结构的混沌系统的控制与同步,且不受不确定性的影响,具有很强的鲁棒性.定值跟踪和同步控制的仿真结果表明,该控制器是有效的.     

二阶动态滑模控制在磁悬浮控制系统中的应用

磁悬浮是典型的非线性、不稳定系统.为了实现其控制,本文采用了一种结合二阶滑模和动态滑模两种设计思想的二阶动态滑模控制器的设计方法,首先推导了磁悬浮系统的线性化状态空间模型;然后针对被控对象设计了二阶动态滑模控制器;最后与普通滑模控制器进行对比仿真试验.仿真结果表明,所设计的二阶动态滑模控制器在使小球快速稳定到达平衡点的同时,大大削弱了普通滑模控制器中存在的严重抖振现象.     

考虑执行器动态和输入受限的近空间飞行器鲁棒可重构跟踪控制

针对多变量、不稳定的近空间飞行器姿态系统,在系统存在参数不确定和外部干扰的情况下,并考虑执行器动态和输入受限,提出一种鲁棒可重构跟踪控制策略.首先,利用二阶滑模干扰观测器分别重构姿态、角速率回路的复合干扰;其次,采用鲁棒二阶滑模积分滤波器的反推(backstepping)方法避免了控制器设计中微分项膨胀问题,利用鲁棒项抵消重构误差对系统的影响,以实现姿态控制器设计.然后,在考虑执行器动态、输入受限及舵面卡死故障下,给出一种线性矩阵不等式的在线优化舵面分配算法,以实现飞行器的姿态角渐近跟踪期望的制导指令.最后,仿真结果表明所提出的方法具有良好的跟踪控制性能.     

Second‐order sliding mode controller design subject to mismatched unbounded perturbations

The dynamics of the second‐order sliding mode (SOSM) can be obtained by directly taking the second derivative on the sliding variable when it has a relative degree of 2 with respect to the control input. However, there will always appear some state‐dependent certain or uncertain terms in the first derivative of the sliding variable, and the derivative directly imposed on these terms could enlarge the uncertainties in the control channel. One method to reduce the uncertainties in the control channel is to hold this information in the dynamics of the first derivative of the sliding variable, while the original SOSM dynamics could be transformed to be a SOSM system with a mismatched unbounded perturbation. This paper focuses on the controller design problem for SOSM dynamics subject to mismatched unbounded perturbation. By using Lyapunov analysis, a novel backstepping‐like design methodology will be proposed. The rigorous mathematical proof will show that under the derived SOSM controller, the closed‐loop sliding mode dynamics is globally finite‐time stable. Meanwhile, the frequently used constant upper bound assumptions for the standard SOSM system can also be extended to the state‐dependent hypotheses in this paper. An academic example is illustrated to verify the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

Global second‐order sliding mode control for nonlinear uncertain systems

Second‐order sliding mode (SOSM) control is used to keep exactly a constraint σ of the second relative degree or to avoid chattering phenomenon. Yet, the traditional SOSM controllers are designed based upon the assumption that the uncertainties or their derivatives are bounded by positive constants. In this paper, a global SOSM controller is designed for a general class of single‐input–single‐output nonlinear systems with uncertainties bounded by positive functions. Moreover, a variable‐gain robust exact differentiator is developed such that the SOSM controllers with finite‐time convergence can also be implemented even when the derivative of the constraint σ is unavailable. Simulation results are given to show the effectiveness of the proposed method.     

On frequency-domain criterion of finite-time convergence of second-order sliding mode control algorithms

Transient processes in the systems controlled by the twisting second-order sliding mode (SOSM) control algorithm and certain generic SOSM given by the describing function are analyzed in the frequency domain. The analysis is based on the approximate describing function method. The relationship between the frequency response (Nyquist plot) of the plant, the shape of the negative reciprocal describing function of the controller, and the transient process convergence rate is investigated. A simple criterion of the existence of finite-time convergence is proposed. It is shown that the convergence rate in a system controlled by a SOSM controller depends on the angle between the high-frequency asymptote of the Nyquist plot of the plant and the low-amplitude asymptote of the negative reciprocal of the describing function of the controller, which is named the phase deficit.     

具有输出/全状态约束的固定时间滑模控制

本文主要解决具有约束的二阶系统的固定时间跟踪控制问题,分别讨论了具有输出约束与具有全状态约束的控制算法设计.首先,为解决输出约束下的固定时间控制问题,本文构建了具有输出约束的新型终端滑模变量,并设计了具有扰动抑制能力的固定时间滑模控制律,保证系统输出始终满足约束条件,同时跟踪误差在固定时间内收敛到原点的充分小的邻域内.进一步,为了处理具有全状态约束的控制问题,本文构建了具有全状态约束的终端滑模变量并设计了相应的固定时间滑模控制律.鉴于系统控制律的不连续性,文章采用非光滑分析及Lyapunov稳定性理论证明了闭环控制系统的稳定性.最后,在数值仿真中,将本文提出的方法与传统固定时间滑模方法进行对比,验证了所建立算法的有效性.     

An adaptive full order sliding mode controller for mismatched uncertain systems

In this paper, an adaptive full order sliding mode (FOSM) controller is proposed for strict feedback nonlinear systems with mismatched uncertainties. The design objective of the controller is to track a specified trajectory in presence of significant mismatched uncertainties. In the first step the dynamic model for the first state is considered by the desired tracking signal. After the first step the desired dynamic model for each state is defined by the previous one. An adaptive tuning law is developed for the FOSM controller to deal with the bounded system uncertainty. The major advantages offered by this adaptive FOSM controller are that advanced knowledge about the upper bound of the system uncertainties is not a necessary requirement and the proposed method is an effective solution for the chattering elimination from the control signal. The controller is designed considering the full-order sliding surface. System robustness and the stability of the controller are proved by using the Lyapunov technique. A systematic adaptive step by step design method using the full order sliding surface for mismatched nonlinear systems is presented. Simulation results validate the effectiveness of the proposed control law.     

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.     

考虑攻击角度和视场角约束的自适应终端滑模制导律

针对导弹拦截机动目标的末制导问题,基于有限时间滑模控制理论设计一种带有攻击角度和导弹视场角约束的制导律.首先,将导弹末制导问题转化为带有状态约束的制导系统稳定问题,设计一种新型的非奇异终端滑模面和时变的障碍Lyapunov函数,给出一种终端滑模制导律的设计方法,并针对目标机动的不确定性设计一种对目标机动上界的自适应估计;然后,通过稳定性理论证明制导系统的状态变量最终是有限时间收敛的,并且结合时变的障碍Lyapunov函数和滑模面的设计特性证明在末制导过程中视场角约束条件始终不会被违背,相比于现有的考虑视场角约束的制导律,该制导律不存在指令转换,能够加快制导系统收敛速率,增强制导系统的抗干扰能力;最后,通过仿真实验验证所提出制导方法的有效性.     

农用拖拉机的自适应二阶滑模路径跟踪控制

针对农用拖拉机在未知扰动影响下的路径跟踪控制问题,本文提出了基于自适应二阶滑模和扰动观测技术的路径跟踪控制策略.首先,建立含有未知扰动项的路径跟踪偏差模型,通过利用自适应控制和改进的加幂积分技术,构造自适应二阶滑模路径跟踪控制方法,该控制方法削弱了滑模控制中存在的抖振影响.其次,为了解决大扰动下控制增益调整过度的问题,通过将鲁棒精确微分器和自适应二阶滑模控制结合,构造复合的路径跟踪控制方法.严格的Lyapunov分析表明横向偏差和航向偏差均在有限时间内稳定到原点.最后,仿真结果验证了本文设计的制导方法能够保证农用拖拉机快速且稳定地跟踪上任意弯曲的参考路径.     

不确定Willis脑动脉瘤系统的自适应模糊滑模控制

研究了具有不确定项的非线性Willis环上脑动脉瘤系统的混沌控制和同步问题,提出了一种自适应模糊滑模变结构控制方法,设计了模糊滑模变结构控制器及自适应控制律,并从理论上证明了控制系统的稳定性。在该控制器的作用下,受控Willis脑动脉瘤系统能够达到任意目标轨道,且不受不确定性的影响,具有很强的鲁棒性。定值跟踪和同步控制的仿真结果表明了控制器的有效性。