An adaptive reaching law of chattering-free discrete-time sliding mode control for systems with external disturbance

An adaptive reaching law of chattering-free discrete-time sliding mode control is proposed for the systems with external disturbance. An adaptive function is proposed in the reaching law which can increase reaching speed as sliding variable is far away from zero and avoid undesired chattering when sliding variable is close to origin. Moreover, a third-order backward difference of disturbance is added to obtain a narrower quasi-sliding mode band (QSMB). Both the closed-loop system performance and finite reaching steps to achieve the desired QSMB are theoretically analyzed. The simulation results verify the effectiveness of the proposed control strategy.     

飞翼布局无人机分数阶积分滑模姿态控制

针对存在复合干扰的飞翼布局无人机(UAV)姿态控制问题,提出了一种基于分数阶积分滑模与双幂次趋近律的姿态跟踪控制方案.结合分数阶微积分及滑模变结构控制理论,设计了分数阶积分滑模面.为解决传统趋近律收敛时间长和抖振严重等不足,提出一种具有二阶滑模特性且有限时间收敛的双幂次趋近律.在名义控制律的基础上,设计super twisting滑模干扰观测器,实现对复合干扰的估计和补偿,增强内外环控制器应对复合干扰的鲁棒性.为充分利用冗余操纵面与解决非线性舵效问题,在飞行控制系统中引入了非线性控制分配环节.仿真结果验证了所提方案的有效性.     

Closed-form solutions to discrete-time LQ optimal control and disturbance attenuation

This paper presents straightforward derivations of closed-form solutions to two discrete-time problems: linear-quadratic optimal control and disturbance attenuation. Then, as the main results, it shows how to reduce directly the closed-form solutions to their recursive forms. These recursive solutions are in the form of Riccati equation and, hence, establish a close relation between the closed-form solutions and the Riccati equations used in both problems.     

Robust tracking and model following of uncertain dynamic systems via discrete-time integral sliding mode control

A discrete-time integral sliding mode control scheme is proposed to realize the problem of robust tracking and modeling following for a class of uncertain linear systems. It will be shown that the proposed scheme guarantees the stability of closed-loop system and achieves zero-tracking error in the presence of parameter uncertainties and external disturbances. The selection of switching surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against system uncertainties and disturbances. Chattering phenomenon and reaching phase are eliminated. Moreover, the knowledge of upper bound of uncertainties is not required. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme. Recommended by Editorial Board member Ju Hyun Park under the direction of Editor Young IL Lee. Ming-Chang Pai received the M.S. and Ph.D. degrees in Mechanical Engineering in 1994 and 1998 from Pennsylvania State University, State College, P.A.. He is currently an Associate Professor in the Department of Automation Engineering at Nan-Kai University of Technology. His research interests are in mechatronics, robots, robust control and nonlinear control.     

离散时间系统变结构控制的趋近律问题

针对离散系统变结构控制，提出了两个新的滑模趋近律．应用该趋近设计变结构控制系统，其原点的稳定性和系统的平稳性都优于指数趋近律和比例-等速-变速趋近律．通过仿真例子对此进行了验证．     

基于扰动补偿趋近律的准滑模控制

针对不确定离散时间系统,提出了一种基于扰动补偿趋近律的准滑模控制方法.该方法不仅能够加快系统趋近模态的趋近速度,缩短到达时间,而且能够缩窄系统的准滑动模态带宽,增强系统鲁棒性,有效改善系统动态品质,并无控制抖振和稳态抖振产生.仿真结果表明了该方法的有效性.     

全景式航空相机的离散滑模控制

为了提高全景式航空相机镜筒速度控制系统的动态特性,使其具有响应速度快且超调小的特点,本文提出一种基于降维状态观测器的离散滑模控制方法,对镜筒角速度、角加速度进行观测,并对其速度系统进行控制.针对高氏趋近律带来的控制抖振和稳态抖振问题,本文采用幂次函数趋近律的方法,并对这种方法进行了无抖振理论分析以及稳定性证明.最后以某全景式航空相机作为实验平台,将基于幂次函数趋近律的离散滑模控制应用到镜筒速度控制系统中.实验结果表明,本文提出的控制方法能够有效地减小系统的抖振,使镜筒速度控制系统表现出良好的动态品质.     

A contractive sliding-mode MPC algorithm for nonlinear discrete-time systems

This paper investigates a sliding-mode model predictive control (MPC) algorithm with auxiliary contractive sliding vector constraint for constrained nonlinear discrete-time systems. By adding contractive constraint into the optimization problem in regular sliding-mode MPC algorithm, the value of the sliding vector is decreased to zero asymptotically, which means that the system state is driven into a vicinity of sliding surface with a certain width. Then, the system state moves along the sliding surface to the equilibrium point within the vicinity. By applying the proposed algorithm, the stability of the closed-loop system is guaranteed. A numerical example of a continuous stirred tank reactor (CSTR) system is given to verify the feasibility and effectiveness of the proposed method.     

Synthesis of the sliding-mode neural network controller for unknown nonlinear discrete-time systems

This paper develops a sliding-mode neural network controller for a class of unknown nonlinear discrete-time systems using a recurrent neural network (RNN). The control scheme is based on a linearized expression of the nonlinear system using a linear neural network (LNN). The control law is proposed according to the discrete L yapunov theory. With a modified real-time recurrent learning algorithm, the RNN as an estimator is used to estimate the unknown part in the control law in on-line fashion. The stability of the control system is guaranteed owing to the on-line learning ability of the RNN algorithm. The proposed control scheme is applied to numerical problems and simulation results that it is very effective.     

一类不确定离散时间系统的积分滑模控制

针对一类同时存在匹配和非匹配不确定性的离散时间系统,提出一种基于幂次函数的离散积分滑模控制方法.理论分析表明,所提出的方法可以消除离散积分滑模控制系统的抖振,而且能够保证对系统的匹配和非匹配不确定性具有强鲁棒性.在系统不确定性的界未知的情况下,通过引入一步延时干扰估计完成了控制器的设计,并给出了闭环系统稳定性证明.仿真结果验证了所提出方法的有效性.     

A nonlinear sliding surface to improve performance of a discrete-time input-delay system

A sliding mode controller is proposed for an uncertain input-delay system to enhance performance. A nonlinear sliding surface is proposed to achieve better transient response for general uncertain discrete SISO linear systems with input delay. Both matched and unmatched perturbations are considered and ultimate boundedness of motion is proved. The step tracking problem is analysed. The proposed surface increases the damping ratio of the transformed system (delay free) as the output moves nearer to the setpoint. To simplify the surface design, a linear matrix inequality based tuning procedure is proposed. The control law is designed based on an equivalent control approach which guarantees one step reaching. The scheme is able to achieve low overshoot and low settling time simultaneously which is not possible with a linear sliding surface. Simulation results verify the effectiveness of the proposed nonlinear surface over different linear surfaces.     

Event-triggered adaptive control based on integral sliding mode surface for a class of linear systems with matched disturbance

In this paper, we propose an event-triggered adaptive integral sliding mode control scheme for a class of linear systems with external disturbance. In this method, the controller is designed using a triggered-state-dependent integral sliding mode, which can ensure the robustness and avoid the shortcomings of traditional sliding mode arrival stage. The triggering mechanism utilizes a time-varying trigger threshold instead of a traditional fixed threshold, which not only realizes the dynamic update of the control law, reduces the overhead of network communication but also ensures that the system trajectory enters the bounded area. The lower bound of inter event time guarantees the avoidance of the Zeno phenomenon. Next, in order to reduce the impact of high-frequency chattering of the control signal effectively and allow the gain of the discontinuous control term to be adjusted automatically according to the rate of change of the disturbance, a dual-layer nested adaptive gain scheme based on equivalent control is considered. This scheme does not require a priori boundedness of the disturbance and its rate of change. Through Lyapunov stability analysis, the event-triggered adaptive sliding mode controller can make the system trajectory converge in finite time and ensure the robustness of the control. Finally, the simulation results verify the effectiveness and simplicity of this method.     

非匹配不确定离散系统的无抖振积分滑模控制

针对一类非匹配不确定离散系统, 设计一种无抖振离散积分滑模控制器. 为了抑制非匹配不确定性对系统的影响, 采用线性矩阵不等式方法设计一种新型的切换函数和对应的滑模控制律, 并证明了闭环系统的Lyapunov 稳定性. 同时, 引入饱和函数设计控制器, 使系统状态在积分滑模面的某个小邻域内做准滑模运动, 并通过合理选择饱和函数的边界层厚度, 使控制信号不含任何抖振. 理论分析和数值仿真验证了所提出方法的有效性.

     

Guaranteed-cost active disturbance rejection control for uncertain systems with an integral controller

Guaranteed-cost active disturbance rejection control (ADRC) for uncertain systems is investigated in this study. Firstly, an integral action is introduced in the framework of ADRC to measure and reduce the tracking error. Then, a robust stability condition is presented, and a quadratic cost function where the tracking error is appearing explicitly is used for ADRC performance assessment. The cost bound is formulated by linear matrix inequality and optimised to obtain controller parameters. Full-dimension extended state observer is used, and thus, the proposed strategy is applicable to an uncertain system that allows relative-degree varying or right-half-plane zero. Finally, the validity of the proposed method and its advantages is demonstrated through the simulations of comparative examples and experiments on a motor speed control system.     

Stabilization of ODE with hyperbolic equation actuator subject to boundary control matched disturbance

ABSTRACT

In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation with external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By ADRC approach, the disturbance is estimated through a disturbance estimator with both time-varying high gain and constant high gain, and the disturbance is canceled online in the feedback loop. It is shown that the resulting closed-loop system with time-varying high gain is asymptotically stable and is practically stable with constant high gain. By SMC approach, the existence and uniqueness of the solution for the closed loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented. The resulting closed-loop system is shown to be exponentially stable. The numerical experiments are carried out to illustrate effectiveness of the proposed control law.     

Novel sliding mode control for multi‐input–multi‐output discrete‐time system with disturbance

This paper investigates sliding mode control for multi‐input–multi‐output discrete‐time system with disturbances. First of all, a novel nonlinear sliding surface, named as hyperbolic hybrid switching sliding surface, is proposed. Two different types of hyperbolic functions are introduced into the proposed sliding surface. Due to the changing of values of the hyperbolic functions, sliding surface switching occurs during the control process, which ensures that both settling time and overshoot can be decreased. The sliding mode controller is obtained based on a novel nonlinear reaching law. The nonlinear reaching law contains several parameters, and by properly designing these parameters, we can decrease the bounds of the sliding variables to small values. The stability analysis of the sliding motion is carried out from singular system viewpoint. Finally, simulation examples and comparison examples are presented to illustrate that the system performance is improved obviously by proposed novel sliding mode control, and the system is robust to the disturbances.     

Binary ABR flow control over ATM networks with uncertainty using discrete-time variable structure controller

A binary available bit rate （ABR） scheme based on discrete-time variable structure control （DVSC） theory is proposed to solve the problem of asynchronous transfer mode （ATM） networks congestion in this paper. A discrete-time system model with uncertainty is introduced to depict the time-varying ATM networks. Based on the system model, an asymptotically stable sliding surface is designed by linear matrix inequality （LMI）. In addition, a novel discrete-time reaching law that can obviously reduce chatter is also put forward. The proposed discrete-time variable structure controller can effectively constrain the oscillation of allowed cell rate （ACR） and the queue length in a router. Moreover, the controller is self-adaptive against the uncertainty in the system. Simulations are done in different scenarios. The results demonstrate that the controller has better stability and robustness than the traditional binary flow controller, so it is good for adequately exerting the simplicity of binary flow control mechanisms.     

考虑输入饱和的离散最优积分滑模控制

针对含有匹配有界干扰的线性离散系统, 提出一类最优积分滑模控制算法. 在系统开环极点位于单位圆内(上) 的前提下, 考虑输入饱和, 可以实现系统状态的半全局稳定. 该算法是低增益反馈和积分滑模的有益结合, 通过低增益反馈使输入饱和得到满足, 通过滑模控制增强了系统对干扰的鲁棒性; 另外, 该算法可以使特定的性能指标达到最优, 使系统稳态误差达到??(??²) 的量级. 仿真结果验证了所提出算法的有效性.

     

Output tracking with disturbance attenuation for cascade control systems subject to network constraint

In this paper, we investigate the output tracking control and disturbance attenuation for a class of cascade control systems subject to network‐induced delays. In order to indicate the time‐varying characteristics and uncertainty of network‐induced delays, a switched system approach is applied to the cascade architecture. This leads to the simultaneous design of controllers and switching signals in terms of the network transmission. Unlike the traditional cascade control design approach, which needs to first tune the secondary controller and then the primary one, we can provide a simultaneous design method of the double‐loop controllers and switching signals to make the networked cascade control system achieve the output tracking performance with disturbance attenuation. Finally, two examples are proposed to demonstrate the feasibility and the effectiveness of the approach.