桥吊时变滑模控制过程的优化建模仿真研究

利用传统方法对桥吊时变滑模控制策略中会产生收敛速度慢,控制作用不连续,误差大等诸多缺憾.针对这一问题,提出基于螺旋算法的桥吊时变滑模控制模型,在二阶超螺旋算法的基础上引入了新的高阶滑模控制律,跟踪了误差的高阶导数,建立滑动量,保证了控制的精度.仿真结果证明利用改进后的模型对桥吊时变滑模控制,具有控制过程收敛速度快、控制作用平滑连续等优势.     

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.     

二阶滑模控制在直流无刷电机转速调节中的应用

针对受参数不确定和负载扰动影响的直流无刷电机的鲁棒速度控制问题,采用二阶滑模控制中的超螺旋算法设计速度控制器。控制器将不连续控制作用在滑模量的二阶微分上,不但保持了传统一阶滑模的性能,而且消弱了系统抖振。仿真结果表明,算法对负载和参数的变化具有很强的鲁棒性,有效地消弱了传统滑模的抖振现象。     

基于过零检测的Buck变换器自适应连续滑模控制

为提高Buck变换器的输出电压品质,本文提出一种基于在线过零检测自适应机制的连续滑模控制方法,可有效抑制抖振问题,且可保证系统稳态误差收敛到给定范围.本文建立变换器的数学模型,从滑模面和控制律两方面改进传统滑模控制算法,即有目的地将系统状态的积分项引入到滑模面的设计中,并将其收敛轨迹分成两阶段,实时测量其过零点的个数;将期望的稳态误差纳入到滑模控制律的设计中,引入由系统状态过零点个数决定的自适应变增益,在收敛轨迹的约束下,分阶段推导出其变增益的连续控制律,并给出相应的稳定性分析.最后,通过与传统一阶和二阶滑模的理论和仿真性能对比,证明所提方法在抖振抑制、响应速度和控制精度方面的优越性.     

基于积分滑动流形的高阶滑模控制器设计

滑模变结构控制方法因其易实现,鲁棒性强等优点广泛应用于实际控制系统中,讨论了具有积分滑动流形的高阶滑模控制器的设计方法.通过设计含积分滑动流形的高阶滑模面,使系统状态在一阶乃至高阶滑模面上均能达到滑动模态.同时利用高阶滑模面为状态变量设计新的状态空间系统,将原先促使系统状态接近并停留在滑模面上的控制目标,拓展为使高阶滑模状态变量趋近于零的控制目标,并结合最优控制方法来设计等效控制量,利用积分流形设计切换控制的切换面,通过严格证明来证实控制器设计的稳定性.在仿真验证部分采用了一阶倒立摆模型,通过比较常规趋近律滑模控制方法和本文方法的仿真结果,可以得出本文方法在减小系统控制量抖振方面的重要作用和优异效果.     

高阶滑模控制理论综述

滑模控制方法因其结构简单且对系统不确定及外部扰动具有良好的鲁棒性受到人们的广泛关注. 因此, 目前正处于飞速发展阶段. 首先, 本文回顾了滑模控制理论的起源, 简单介绍了传统一阶滑模控制方法的发展; 其次, 列举了几种常用的二阶滑模控制方法, 并介绍了其工作原理; 接着, 总结了高阶滑模控制理论的研究现状, 主要包括齐次性算法和继电–多项式算法的研究成果; 最后, 结合高阶滑模控制方法中需要克服的问题, 讨论了未来可能的研究方向.     

基于准连续高阶滑模的可重复使用运载器再入姿态控制

针对可重复使用运载器再入段的姿态控制问题,提出一种基于准连续高阶滑模的控制方法。将姿态控制系统分为两个回路,分别为角度控制回路与角速度控制回路。角度回路作为外回路产生角速度指令,角速度回路作为内回路跟踪外回路产生的角速度控制指令。为了提高系统的鲁棒性,对两个回路分别设计滑模控制器。外回路中设计基于低通滤波的终端滑模控制方法,以获得平滑的控制量作为角速度指令。内回路设计增加系统相对阶的准连续高阶滑模方法,使控制律中不直接含有符号函数项,保证系统稳定的同时减弱控制器抖振。在具有外界干扰与参数不确定的情况下,使用本文提出的方法进行仿真试验,仿真结果证明了所提出方法的有效性。     

不确定欠驱动系统的高阶自适应Super-Twisting滑模控制

为实现一类不确定欠驱动系统在未知干扰情况下的鲁棒控制,针对传统滑模控制中存在的抖振问题,提出一种基于二次型Lyapunov函数的二阶Super-Twisting自适应滑模控制策略.首先,控制器的不连续项采用二阶Super-Twisting算法,将不连续控制作用在滑模量的二阶导数.然后,针对滑模面受不确定干扰影响的情况,为调节参数设计一种自适应律方法,该方法不受传统二阶滑模控制中干扰项的一阶导数边界已知的条件限制,保证滑模面在有干扰情况下的收敛,削弱控制器输入的抖振现象.最后,以两轮自平衡车为实验对象验证该方法,并与传统滑模及普通二阶滑模方法做仿真对比.仿真结果表明文中所提的二阶自适应滑模控制方法在控制效果和降低抖振方面表现更优.     

永磁同步直线电机的分数阶超螺旋滑模控制

为了提高永磁同步直线电机的跟踪性能,增强系统的鲁棒性,本文提出了分数阶超螺旋滑模控制策略.首先,针对外部扰动以及系统的未知状态设计广义超螺旋观测器,其能够精确估计永磁同步直线电机的速度和外部扰动.其次,将分数阶理论和终端滑模控制理论相结合,提出有限时间收敛的分数阶超螺旋滑模控制器,以实现永磁同步直线电机的跟踪控制.最后,通过仿真对比验证所提方案的有效性.     

一类非线性采样系统高阶迭代学习控制

迭代学习控制能够实现期望轨迹的完全跟踪而被广泛关注,但是采样迭代学习控制成果目前还比较少。针对一类有相对阶和输出延迟的非线性采样系统,研究了高阶迭代学习控制算法。利用Newton-Leibniz公式、贝尔曼引理和Lipschiz条件证明了当系统的采样周期足够小,迭代学习初态严格重复,且学习增益满足要求的条件,那么系统输出在采样点上收敛于期望输出。对一阶和二阶学习算法的仿真表明高阶算法在收敛速度上比一阶有明显改善。     

Impulsive second‐order sliding mode control in reduced information environment

The perturbed system with input‐output dynamics of arbitrary and well‐defined relative degree is considered in a reduced information environment. A novel impulsive second‐order sliding mode control in the reduced information environment is proposed. The almost instantaneous convergence to the origin is achieved via impulsive control acting in a concert with second‐order sliding mode control, specifically supertwisting and twisting algorithms. The impulsive actions are implemented in a piecewise constant format. Numerical examples illustrate the efficiency of the proposed control algorithms.     

Adaptive backstepping impact angle control with autopilot dynamics and acceleration saturation consideration

This paper presents a robust impact angle constraint guidance law for maneuvering target interception in the presence of autopilot dynamics and input saturation. The presented guidance law is designed on the basis of a combination of adaptive backstepping control technique and higher‐order sliding mode differentiator. Different from existing impact angle constraint guidance law using sliding mode control, the line‐of‐sight angular rate and impact angle tracking error are regulated by two different virtual control laws. Because the future course of action of the target, an independent entity, cannot be predicted beforehand, adaptive laws are introduced in guidance law derivation for disturbance rejection. Unlike dynamic surface control approach, higher‐order sliding mode differentiator is adopted here as an alternative way to obtain the derivatives of the virtual control laws, thus leading to the exact tracking performance of backstepping control. Detailed stability analysis shows that both the line‐of‐sight angular rate and impact angle error can be stabilized in a small region around zero asymptotically. Simulation results explicitly show that accurate interception is achieved with a wide range of impact angles. Copyright © 2017 John Wiley & Sons, Ltd.     

Design of Second Order Sliding Mode and Sliding Mode Algorithms: A Practical Insight to DC-DC Buck Converter

This paper presents a simple and systematic approach to design second order sliding mode controller for buck converters. The second order sliding mode control (SOSMC) based on twisting algorithm has been implemented to control buck switch mode converter. The idea behind this strategy is to suppress chattering and maintain robustness and finite time convergence properties of the output voltage error to the equilibrium point under the load variations and parametric uncertainties. In addition, the influence of the twisting algorithm on the performance of closed-loop system is investigated and compared with other algorithms of first order sliding mode control such as adaptive sliding mode control (ASMC), nonsingular terminal sliding mode control (NTSMC).In comparative evaluation, the transient response of the output voltage with the step change in the load and the start-up response of the output voltage with the step change in the input voltage of buck converter were compared. Experimental results were obtained from a hardware setup constructed in laboratory. Finally, for all of the surveyed control methods, the theoretical considerations, numerical simulations, and experimental measurements from a laboratory prototype are compared for different operating points. It is shown that the proposed twisting method presents an improvement in steady state error and settling time of output voltage during load changes.      

Higher order sliding mode control based on integral sliding mode

A higher order sliding mode control scheme for uncertain nonlinear systems is proposed in the present paper. It is shown that the problem is equivalent to the finite time stabilization of higher order input-output dynamics with bounded uncertainties (r∈N). The controller uses integral sliding mode concept and contains two parts. A part achieves finite time stabilization of the higher order input-output dynamics without uncertainties. The other part rejects bounded uncertainties throughout the entire response of the system. As a result, a higher order sliding mode is established. The advantages of the method are that its implementation is easy, the time convergence is chosen in advance and the robustness is ensured. An illustrative example of a car control shows the applicability of the method.     

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer, for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements. A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains, which will give enough flexibility in the choice of initial estimates. Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.      

Passivity‐based sliding mode controller/observer for second‐order nonlinear systems

A passivity‐based sliding mode control for a class of second‐order nonlinear systems with matched disturbances is proposed in this paper. Firstly, a nonlinear sliding surface is designed using feedback passification, in which the passivity is employed to guarantee the closed‐loop system's stability. The passivity‐based controller comprising a discontinuous term guarantees globally asymptotical convergence to the sliding surface. A sliding mode‐based control law that satisfies the reaching and sliding condition is also developed. Moreover, the passivity‐based sliding mode observer is also developed to effectively estimate the system states. Compared with conventional sliding mode control, the proposed control scheme has a shorter reaching time; and hence, the system performance is less affected by disturbances, thus eliminating the need to increase the control input gain. Finally, simulation results demonstrate the validity of the proposed method.     

Reduced‐order design of high‐order sliding mode control system

To design an rth (r>2) order sliding mode control system, a sliding variable and its derivatives of up to (r ? 1) are in general required for the control implementation. This paper proposes a reduced‐order design algorithm using only the sliding variable and its derivatives of up to (r ? 2) as the extension of the second‐order asymptotic sliding mode control. For a linear time‐invariant continuous‐time system with disturbances, it is found that a high‐order sliding mode can be reached locally and asymptotically by a reduced‐order sliding mode control law if the sum of the system poles is less than the sum of the system zeros. The robust stability of the reduced‐order high‐order sliding mode control system, including the convergence to the high‐order sliding mode and the convergence to the origin is proved by two Lyapunov functions. Simulation results show the effectiveness of the proposed control algorithm. Copyright © 2010 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.     

Discrete‐time higher‐order sliding mode control of systems with unmatched uncertainty

The research on discrete‐time higher‐order sliding mode has received a considerable attention recently. Systems with unmatched uncertainties are common in practice; however, the existing discrete‐time higher‐order sliding mode control algorithms are designed considering only matched uncertainty. This paper proposes a technique to design discrete‐time higher‐order sliding mode control for an uncertain LTI system in the presence of unmatched uncertainty. The proposed technique is numerically simulated and experimentally validated on an electromechanical rectilinear plant. Various experiments are conducted considering the several operational conditions of electromechanical systems in industries to verify the performance of the proposed controller.