Robust Stabilization of Uncertain Fuzzy Systems Using Variable Structure System Approach

Based on the variable structure system (VSS) theory, we develop a fuzzy control system design method for a class of uncertain nonlinear multivariable systems that can be represented by a Takagi-Sugeno fuzzy model. We make the first attempt to relax the restrictive assumption that each nominal local system model shares the same input channel, which is required in the traditional VSS-based fuzzy control design methods. As the local controller we use a sliding mode controller with a switching feedback control term. In terms of linear matrix inequalities (LMIs), we derive a sufficient condition for the existence of linear sliding surfaces guaranteeing asymptotic stability of the reduced-order equivalent sliding mode dynamics. We present an LMI characterization of such sliding surfaces. We also give an LMI-based algorithm to design the switching feedback control term so that a stable sliding motion is induced in finite time. Finally, we give a numerical design example.     

Control of a Class of Underactuated Mechanical Systems Using Sliding Modes

In this paper, we present a sliding mode control algorithm to robustly stabilize a class of underactuated mechanical systems that are not linearly controllable and violate Brockett's necessary condition for smooth asymptotic stabilization of the equilibrium, with parametric uncertainties. In defining the class of systems, a few simplifying assumptions are made on the structure of the dynamics; in particular, the damping forces are assumed to be linear in velocities. We first propose a switching surface design for this class of systems, and subsequently, a switched algorithm to reach this surface in finite time using conventional and higher order sliding mode controllers. The stability of the closed-loop system is investigated with an undefined relative degree of the sliding functions. The controller gains are designed such that the controller stabilizes the actual system with parametric uncertainty. The proposed control algorithm is applied to two benchmark problems: a mobile robot and an underactuated underwater vehicle. Simulation results are presented to validate the proposed scheme.     

基于滑模变结构控制的RBF神经元网络

针对高精度飞行仿真转台，设计一种基于滑模变结构控制的RBF神经元网络控制器。该控制器根据滑模变结构控制器的特点，将控制律分为等效控制律和到达控制律。等效控制律使系统运动于滑模面附近，由RBFN拟合而成，权值用自适应算法在线修正，确保了实时控制的可能性；到达控制律可使处于状态空间内任意初始位置的系统趋近于滑模面，由滑模控制器的可达性条件推出，其中用到了系统的不确定性参数的上下界。计算机仿真结果表明了该方法的鲁棒性和实际应用的可能性。     

小行星433 Eros本体悬停轨道的稳定控制

研究了近地小行星433 Eros本体悬停轨道的稳定控制问题.用三轴椭球体模型近似Eros引力场分布,建立了航天器在其引力场内的动力学模型,并且应用等加速度变截距时变滑模控制设计了悬停控制器.该方法的滑模面选取与常规滑模控制不同,且不存在到达阶段.仿真分析从不同的初始条件和悬停条件入手,验证控制器的有效性,并讨论了航天器的速度与控制加速度的幅值随滑模面切换时间的变化情况.     

New approaching condition for sliding mode control design with Lipschitz switching surface

In this paper, we concern the approaching condition of sliding mode control (SMC) with a Lipschitz switching surface that may be nonsmooth. New criteria on the relation between phase trajectories and an arbitrary Lipschitz continuous surface are examined firstly. Filippov’s differential inclusion is adopted to describe the dynamics of trajectories of the closed-loop system with SMC. Compared with Filippov’s criteria for only smooth surface, new criteria are proposed by utilizing the cone conditions that allow the surface to be nonsmooth. This result also yields a new approaching condition of SMC design. Based on the new approaching condition, we develop the sliding mode controller for a class of nonlinear single-input single-output (SISO) systems, of which the switching surface is designed Lipschitz continuous for the nonsmooth sliding motion. Finally, we provide a numerical example to verify the new design method.     

基于RBF神经网络滑模控制的车辆横向控制研究

针对车辆横向控制系统中滑模控制器存在的抖振现象对转向机械结构带来的损耗问题,提出了一种基于RBF神经网络的滑模控制算法。利用RBF神经网络较强的自学习能力实时在线调节滑模控制器的切换项增益参数,增强系统的抗干扰能力与动态性能。将车辆实际参数代入仿真数学模型中,在Simulink仿真环境中进行对比仿真实验,仿真结果表明:该控制算法跟踪性能好,能够有效降低滑模控制器的抖振,满足车辆横向控制要求。     

陀螺仪系统同步控制的参数自适应滑模控制

针对带有内部不确定性及外部扰动的陀螺仪混沌系统的同步问题,提出了一种参数自适应滑模控制方法,并给出参数自适应律.该方法不依赖被控混沌系统的数学模型,可以快速跟踪主混沌系统.时域及复频域理论分析表明,由参数自适应滑模控制器组成的闭环控制系统是全局渐近稳定的,而且参数自适应滑模控制器具有良好的抗扰动鲁棒性.仿真结果表明该控制方法计算量小、响应速度快、控制精度高、抗扰动鲁棒性强,在非线性不确定系统控制领域具有广泛的应用价值.     

基于非线性模糊滑膜控制算法的多缸液压设备同步控制研究

为满足液压设备多缸同步操作的控制需求,提出一种非线性模糊滑膜控制算法研究。以多缸液压设备的控制特性为基础建模,并获取模型的切换函数；借助液压缸与负载力平衡方程,完成多级液压缸的换级处理,再联合液压设备同步速度计算结果,确定节流缓冲控制条件,实现对设备的同步控制。利用AMESim软件设计仿真实验,得到加速度、速度、位移差三项指标数值,结果显示非线性模糊滑膜控制算法能够更好第控制多缸液压设备的同步操作需求。     

坦克炮控系统的模糊滑模控制系统设计和分析

主要针对坦克炮控系统这一包含非线性和不确定性的复杂系统,提出了一种新的模糊滑模控制算法.该算法将模糊逻辑和变结构控制结合起来,利用模糊方法,在切换面临近的一个薄边界层内对控制的不连续性加以平滑,以减弱变结构控制产生的抖振.本文还对控制系统稳定性进行了分析,并给出了用MATLAB仿真的结果及实验结果.     

A singular system approach to robust sliding mode control for uncertain Markov jump systems

The robust sliding mode control for Markov jump systems with parameter uncertainties and an unknown nonlinear function is discussed. Based on a singular system approach and linear matrix inequality (LMI), a sufficient condition which guarantees the existence of linear switching surface and the stochastic stability of sliding mode dynamics is given. A sliding mode controller is designed such that the closed-loop system is convergent to the switching surface in finite time. A numerical example is given to show the effectiveness of the proposed method.     

时滞系统的输出反馈滑模控制的一种奇异系统方法

利用一种奇异系统方法讨论了时滞系统的输出反馈滑模控制问题. 时滞系统的非线性项满足范数有界约束.首先,将滑动模态与线性切换面作为一个奇异时滞系统,基于奇异时滞系统的稳定性理论, 给出滑动模态稳定及切换面存在的线性矩阵不等式(Linear matrix inequality, LMI)充分条件.然后,给出使得系统闭环渐近稳定的静态输出反馈滑模控制器的设计方法,此控制器保证闭环 系统有限时间到达切换面.最后,用数值算例验证本文方法的有效性和正确性.     

Hybrid control of synchronization of fractional order nonlinear systems

Under the existence of model uncertainties and external disturbance, finite‐time projective synchronization between two identical complex and two identical real fractional‐order (FO) chaotic systems are achieved by employing FO sliding mode control approach. In this paper, to ensure the occurrence of synchronization and asymptotic stability of the proposed methods, a sliding surface is designed and the Lyapunov direct method is used. By using integer and FO derivatives of a Lyapunov function, three different FO real and complex control laws are derived. A hybrid controller based on a switching law is designed. Its behavior is more efficient that if the individual controllers were designed based on the minimization of an appropriate cost function. Numerical simulations are implemented for verifying the effectiveness of the methods.     

基于模糊变结构的机械臂控制

现有的机械臂模糊变结构控制方法大都计算复杂或需要检测滑模面的微分信号.本文将机械臂模型分为确定部分和不确定部分进行研究,对确定部分采用一般反馈控制,对不确定部分采用变结构集中补偿控制,为了消除变结构控制器的抖震引入模糊控制方法,将滑模面作为模糊控制器的输入,补偿控制器权值作为输出.本方案不仅不需要检测滑模面微分信号,而且计算简单,易于实现.仿真结果表明,在存在模型误差和外部扰动的情况下,该方案既能达到快速跟踪,又能很好的消除控制器的抖震.     

基于干扰估计的非对称运动下飞机刹车系统模型预测控制

针对飞机在非对称运动下的双侧机轮协调控制问题, 提出一种基于滑模干扰估计的模型预测控制方法. 首先, 通过对飞机制动过程横纵方向力矩机理分析并分别考虑左右机轮对刹车性能的影响, 建立全面刻画系统动态的地面滑跑动力学模型. 在此基础上, 设计滑模观测器对侧风干扰进行实时估计, 利用补偿机制实现对侧风扰动的有效抑制. 此外, 提出基于前轮荷载状态门限特征和结合系数阈值范围特征的分析方法, 解决切换跑道环境辨识问题. 设计非线性模型预测算法, 实现飞机纵向防滑刹车和横向跑道纠偏的协调控制. 最后, 在侧风干扰、跑道切换以及不对称着陆等情况下进行仿真实验, 验证了所提出的控制策略能够有效提升刹车系统的防滑效率及纠偏性能.     

基于模糊双线性模型的连续搅拌反应釜滑模控制

主要对连续搅拌反应釜系统(CSTR)的滑模控制问题进行研究;该系统的模型可由Takagi-Sugeno (T-S)模糊双线性模型进行描述,基于该模糊双线性模型,给出滑模控制方法;在之前学者的研究成果上对线性滑模面进行改进,构造积分滑模面,由此设计出的等效控制量与切换控制量,可以保证系统的控制精度;通过对其进行稳定性研究,得到全局稳定的充分条件,并求出滑模面的控制器参数;同时,构造7条模糊规则,采用模糊化方法对切换增益项进行模糊推理,使整体控制量平滑化,也避免系统状态出现抖振现象,实现实际可操作性;最后,连续搅拌反应釜的仿真验证了控制方法的有效性.     

Passivity-based sliding mode control of uncertain singular time-delay systems

In this paper the problem of sliding mode control (SMC) with passivity of a class of uncertain nonlinear singular time-delay systems is studied. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain singular time-delay system. By introducing some slack matrices, a delay-dependent sufficient condition is proposed in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive. The passification solvability condition is then established. Moreover, a SMC law and an adaptive SMC law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.     

Design of decentralised variable structure observer for mismatched nonlinear uncertain large-scale systems

Although the state feedback approach is quite popular in control engineering, it cannot be used while the system states cannot be measured. The state observer approach may be used to overcome such a shortcoming. Also, most control systems have become larger and more complicated; therefore, based on the variable structure control theory, a new decentralised variable structure observer (DVSO) for a class of nonlinear large-scale systems with mismatched uncertainties will be considered in this article. The switching surface function is determined such that the equivalent system will have the desired behaviour once the system reaches the switching surface. And then a new DVSO is designed such that the estimated states will approach the system states. Using the Lyapunov stability theory and using the generalised matrix inverse concept, the uncertain nonlinear error system trajectories can be driven onto the sliding manifold and then the existence of a sliding mode and the attractiveness to the sliding surface is ensured. With the proposed DVSO, the estimation errors asymptotically tend to zero if the matching condition is satisfied, and the effects of the mismatched parts can be uniformly ultimately bounded if the matching condition is not satisfied. Finally, a numerical example with a succession of computer simulations is given to demonstrate the effectiveness of the proposed approach.     

高维网机系统失稳振荡的分岔研究

应用机电耦联动力学理论和电路理论,建立了统一的发电机组并网发电的数学模型．该模型为27维非线性微分动力系统,包括机械扭振方程、同步发电机瞬变过程基本方程、原动机力矩分配及调速控制方程、励磁调节控制方程和并网线路串补电容方程5大部分．本文选择线路串补电容的容抗、线路电阻作为分岔参数,计算并得到了失稳参数区域图．对满足两对纯虚特征值的参数点,利用中心流形定理对原系统方程做了降维．再利用多参数稳定性理论及归一化技术,对约化方程进行求解,得到了分岔方程．由此得到分岔参数图、4个参数区的动力学特性,并得到了数值验证．     

观测器基于自适应滑模控制的半马尔科夫跳变系统

在许多工业系统中都存在时滞的现象,会使得系统控制性能降低,影响系统的稳定,在实际系统中,滑模依赖时变时滞更值得研究,而滑模控制对于外界干扰,非线性和参数不确定具有很好的鲁棒性,并且控制结构简单,视如上情况,针对观测器基于滑模控制的Markov切换系统,设计积分滑模面,并通过估计变量得到误差系统,通过解线性矩阵不等式使得...