Robust H∞ Sliding Mode Control for a Class of Singular Stochastic Nonlinear Systems

This paper concerns the problem of robust H_∞ sliding mode control for a class of singular stochastic nonlinear systems. Integral sliding mode control is developed to deal with this problem. Based on the integral sliding surface of the design and linear matrix inequality, a sufficient condition which guarantees the sliding mode dynamics is asymptotically mean square admissible and has a prescribed H_∞ performance for a class of singular stochastic nonlinear systems is proposed. Furthermore, a sliding mode control law is synthesized such that the singular stochastic nonlinear system can be driven to the sliding surface in finite time. Finally, a numerical example is proposed to illustrate the effectiveness of the given theoretical results.     

Design of an adaptive tracker for n-link rigid robotic manipulators based on super-twisting global nonlinear sliding mode control

This paper develops an adaptive super-twisting global nonlinear sliding mode control technique for n-link rigid robotic manipulators. A novel control law is designed to guarantee elimination of the reaching phase and existence of the sliding mode around the surface right from the initial time. Furthermore, the adaptive tuning law eliminates requirement of the knowledge about the upper bounds of external disturbances. By using the proposed method, a robust controller is designed so that the tracking error of rigid manipulator is convergent to the global nonlinear sliding surface in a finite time, and strong robustness with respect to large uncertainties and disturbances is guaranteed. Illustrative simulations on a two-link elbow robot manipulator and a three degree of freedom rigid manipulator are presented to show the robustness and effectiveness of the suggested design compared to other method. Moreover, a simulation as well as experimental study of a rotary inverted pendulum system demonstrates the applicability of the proposed method.     

Uncertain Saturated Discrete‐Time Sliding Mode Control for A Wind Turbine Using A Two‐Mass Model

The aim of this paper is to propose a new design variable speed wind turbine control by discrete‐time sliding mode approach. The control objective is to obtain a maximum extraction of wind energy, while reducing mechanical loads and rotor speed tracking combined with an electromagnetic torque. For this application, we designed a discrete time sliding mode control using the equivalent discrete time reaching law. Furthermore, a systematic and improved design procedure for uncertainties discrete‐time sliding mode control (SMC) with saturation problem is provided in this paper. The saturation constraint is reported on inputs vector. LMI technique and polytopic models are used in the design of the switching surface. To achieve some performance requirements and good robustness, in the sliding mode, the pole clustering method is investigated. Based on the unit vector control approach, a robust control is developed, then, to direct and maintain the system states onto the sliding manifold in finite time. Finally, a systematic design procedure for DSMC required to achieve a given performance level is provided and its effectiveness is varied by applying it to variable speed wind turbine systems.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

不确定多智能体系统的鲁棒量化一致性研究

采用滑模控制设计方法考虑了多智能体系统的鲁棒量化一致性问题。将多智能体系统的滑模面设计由考虑匹配不确定的情形推广到同时带有匹配和不匹配不确定性的情形,并采用线性矩阵不等式技术给出滑模面参数的求解方法。针对数字通信通道编解码的特点,充分考虑了量化参数不匹配和外部干扰等多种不利因素的影响,提出一种新的滑模到达控制律确保闭环系统能在有限时间到达设计的滑模面,实现量化一致性的目标。经计算机仿真实验比较验证了本设计方法的有效性。     

On nonlinear H ∞ sliding mode control for a class of nonlinear cascade systems

In this work two main robust control strategies, the sliding mode control (SMC) and nonlinear H ^∞ control, are integrated to function in a complementary manner for tracking control tasks. The SMC handles matched L ^∞[0,∞) type system uncertainties with known bounding functions. H ^∞ control deals with unmatched disturbances of L ₂[0,∞) type where the upper-bound knowledge is not available. The new control method is designed for a class of nonlinear uncertain systems with two cascade subsystems. Nonlinear H ^∞ control is applied to the first subsystem in the presence of unmatched disturbances. Through solving a Hamilton-Jacoby inequality, the nonlinear H ^∞ control law for the first subsystem well defines a nonlinear switching surface. By virtue of nonlinear H ^∞ control, the resulting sliding manifold in the sliding phase possesses the desired L ₂ gain property and to a certain extend the optimality. Associated with the new switching surface, the SMC is applied to the second subsystem to accomplish the tracking task, and ensure the L ₂ gain robustness in the reaching phase. Two illustrative examples are given to show the effectiveness of the proposed robust control scheme.     

基于两相幂次趋近律的航天器姿态控制

针对带有系统不确定性的航天器姿态控制系统,提出一种基于两相幂次趋近律的姿态控制方法.在趋近律设计中,根据滑模变量值的变化调整趋近律的幂次值,确保滑模变量在远离滑模面和接近滑模面时均具有更快的收敛速度.同时,通过分别计算两个趋近阶段的收敛时间,可直接获得较为准确的滑模变量收敛时间表达式.此外,在控制器设计中采用鲁棒项补偿...     

Sliding mode variable structure control for visual servoing system

A visual servoing tracking controller is proposed based on the sliding mode control theory in order to achieve strong robustness against parameter variations and external disturbances. A sliding plane with time delay compensation is presented by the pre-estimate of states. To reduce the chattering of the sliding mode controller, a modified exponential reaching law and hyperbolic tangent function are applied to the design of visual controller and robot joint controller. Simulation results show that the visual servoing control scheme is robust and has good tracking performance.     

Dynamic output feedback integral sliding mode control design for uncertain systems

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm for linear MIMO systems with mismatched parameter uncertainties along with disturbances and matched nonlinear perturbations. Once the system is in the sliding mode, the proposed output‐dependent integral sliding surface can robustly stabilize the closed‐loop system and obtain the desired system performance. Two types of mismatched disturbances are considered and their effects on the sliding mode are explored. By introducing an additional dynamics into the controller design, the developed control law can guarantee that the system globally reaches and is maintained on the sliding surface in finite time. Finally, the feasibility of the proposed method is illustrated by numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

一类不确定切换中立型系统的鲁棒滑模控制

针对一类不确定切换中立型系统, 设计相应的积分型滑模面. 基于平均驻留时间方法和线性矩阵不等式技术, 给出滑模动力学系统鲁棒指数渐近稳定的时滞相关性判据. 通过设计滑模控制器, 使闭环系统的状态满足到达条件. 数值仿真表明, 所提出的方法是有效可行的.

     

ℋ︁∞ sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis

This paper presents a scheme to design robust sliding mode observers(SMO) with ??_∞ performance for uncertain nonlinear Lipschitz systems where both faults and disturbances are considered. We study the necessary conditions to achieve insensitivity of the proposed sliding mode observer to the unknown input(fault). The objective is to derive a sufficient condition using linear matrix inequality(LMI) optimization for minimizing the ??_∞ gain between the estimation error and disturbances, while at the same time the design method guarantees that the solution of the LMI optimization satisfies the so‐called structural matching condition. The sliding motion affects only a part of the system through a novel reduced‐order sliding mode controller. Furthermore, the so‐called equivalent control concept is discussed for fault estimation. Finally, a numerical example of MCK chaos demonstrates the high performance of the results compared with a pure SMO. Copyright © 2010 John Wiley & Sons, Ltd.     

Output Feedback Sliding Mode Controller Design Via H∞ THEORY

For a linear system with mismatched disturbances, a sliding mode controller using only output feedback is developed in this paper. Through application of the H∞ control theory, the designed switching surface can achieve robust stabilization and guarantee a level of disturbance rejection during sliding mode. Although the system exhibits disturbances, a state estimator is used which, using only measured outputs, can asymptotically estimate the system states. The control law is designed with respect to the estimated signals. Finally, a numerical example is presented to demonstrate the proposed control scheme.     

线性电机伺服系统的自适应鲁棒控制

通过对一类音圈电机直驱式精密伺服系统运动控制问题的研究,在只考虑系统标称模型的情况下,采用分数阶形式的趋近律,得到了一种有限时间滑模控制算法;与此同时,当系统存在参数不确定和外界干扰的情况下,将有限时间滑模控制方法和自适应控制理论相结合,构造了一种自适应滑模控制律.另一方面,本文还考虑了系统具有输入饱和约束的情况,通过引入一个辅助系统,进而设计了一种自适应抗饱和控制律.而且,文中对闭环系统的稳定性进行了证明.最后,仿真和实验对所提出控制策略的有效性和伺服精度进行了对比、分析和验证.     

Adaptive Sliding Mode Control for Re-entry Attitude of Near Space Hypersonic Vehicle Based on Backstepping Design

Combining sliding mode control method with radial basis function neural network (RBFNN), this paper proposes a robust adaptive control scheme based on backstepping design for re-entry attitude tracking control of near space hypersonic vehicle (NSHV) in the presence of parameter variations and external disturbances. In the attitude angle loop, a robust adaptive virtual control law is designed by using the adaptive method to estimate the unknown upper bound of the compound uncertainties. In the angular velocity loop, an adaptive sliding mode control law is designed to suppress the effect of parameter variations and external disturbances. The main benefit of the sliding mode control is robustness to parameter variations and external disturbances. To further improve the control performance, RBFNNs are introduced to approximate the compound uncertainties in the attitude angle loop and angular velocity loop, respectively. Based on Lyapunov stability theory, the tracking errors are shown to be asymptotically stable. Simulation results show that the proposed control system attains a satisfied control performance and is robust against parameter variations and external disturbances.      

用于离散滑模重复控制的新型趋近律

针对不确定离散时间系统, 提出一种新型的离散趋近律, 构造理想切换动态, 并基于理想切换动态设计离散滑模重复控制器. 在消除系统颤振的同时, 完全抑制周期扰动带来的影响, 改善控制品质. 分别推导了切换函数的绝对收敛层、单调收敛层和拟滑模带的边界, 用于刻画在不同控制器参数下闭环系统的趋近过程和拟滑模运动. 数值仿真和在伺服装置上的实验结果证实了所提出控制方法的有效性.     

Sliding mode control of drum water level in an industrial boiler unit with time varying parameters: A comparison with H∞-robust control approach

In steam power-plants, to prevent over-heating of drum components or flooding of steam lines, perfect control of drum water level is of great importance. But during the operation, disturbances affecting water level, model uncertainties and parameter mismatch due to variant operating conditions lead to the variation of model parameters. In this paper, under transient conditions and in the presence of model uncertainties, two control strategies are implemented to achieve desired tracking of drum water level: robust sliding mode and H_∞ control. Two transfer functions between drum water level (output variable); feed-water and steam mass rates (input variables) are considered. For the dynamic system with time varying characteristic and parametric uncertainties, a sliding mode controller is developed and an optimal H_∞ controller is designed based on μ-synthesis with DK-iteration algorithm. For different desired commands of drum water level (including a sequence of steps and ramps-steps); it is observed that both control strategies guarantee robust stability and performance of the system without actuators saturation (control signals are bounded). However, using the sliding mode controller leads to the more smooth and rapid time responses of drum water level with less oscillatory behaviour of control efforts (and consequently less energy consumption). In addition, for tracking objectives in short command times, sliding mode controller performs more appropriately.     

Design of uncertain multi-input systems with state delay and input deadzone nonlinearity via sliding mode control

The problem of robust stabilization of a class of uncertain multi-input time-delayed systems with deadzone nonlinearity in the actuator is considered. To achieve a stable uncertain multi-input system, sliding mode control (SMC) is adopted in the controller design. The proposed controller guarantees the global reaching condition of the sliding mode in the uncertain multi-input system. In the sliding mode, the investigated time-delayed systems with deadzone nonlinearity still possess the insensitivity to the uncertainties and/or disturbances, which can be seen in the systems with linear inputs. In addition, the proposed controller can work effectively for systems no matter whether sector nonlinearity and/or deadzone exists in the actuator or not. However, such property cannot be obtained by the controller design through traditional SMC for the systems without input nonlinearity. Besides, the traditional SMC controller might produce limit cycles once the system contains deadzone in the input. Furthermore, the presented controller ensures the system trajectories globally exponentially converged in the sliding mode. Finally, two examples are illustrated to demonstrate the effectiveness of the proposed sliding mode controller.     

不确定线性2-D离散系统的鲁棒滑模控制

针对不确定线性离散二维（2-D）系统,研究了其鲁棒稳定性、鲁棒镇定和鲁棒滑模控制问题.基于线性矩阵不等式的方法推导了该系统鲁棒渐近稳定的充分条件,并给出了系统状态反馈镇定器和理想滑动模态存在的充分条件.改进了离散时间滑模控制系统的趋近律方法,使得状态能够到达滑模面上产生理想的滑动模态,并将其推广应用到2-D离散系统中,综合了一类滑模控制器保证闭环系统鲁棒渐近稳定.仿真实例证实了该设计方法的有效性.