Decentralized sliding mode control for a class of nonlinear interconnected systems by static state feedback

In this paper, a class of interconnected systems is considered, where the nominal isolated systems are fully nonlinear. A robust decentralized sliding mode control based on static state feedback is developed. By local coordinate transformation and feedback linearization, the interconnected system is transformed to a new regular form. A composite sliding surface which is a function of the system state variables is proposed and the stability of the corresponding sliding mode dynamics is analyzed. A new reachability condition is proposed and a robust decentralized sliding mode control is then designed to drive the system states to the sliding surface in finite time and maintain a sliding motion thereafter. Both uncertainties and interconnections are allowed to be unmatched and are assumed to be bounded by nonlinear functions. The bounds on the uncertainties and interconnections have more general forms when compared with existing work. A MATLAB simulation example is used to demonstrate the effectiveness of the proposed method.     

Robust sliding mode control using adaptive switching gain for induction motors

A robust sliding mode approach combined with a field oriented control （FOC） for induction motor （IM） speed control is presented. The proposed sliding mode control （SMC） design uses an adaptive switching gain and an integrator. This approach guarantees the same robustness and dynamic performance of traditional SMC algorithms. And at the same time, it attenuates the chattering phenomenon, which is the main drawback in actual implementation of this technique. This approach is insensitive to uncertainties and permits to decrease the requirement for the bound of these uncertainties. The stability and robustness of the closed- loop system are proven analytically using the Lyapunov synthesis approach. The proposed method attenuates the effect of both uncertainties and external disturbances. Experimental results are presented to validate the effectiveness and the good performance of the developed method.     

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。     

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.     

Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.     

Sliding mode control of uncertain systems with distributed time-delay： parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.     

Nonlinear observer based control for travelling wave nuclear reactors based on the Lyapunov approach during load following operation

Power control of the nuclear reactor is one of the most important subjects in each nuclear power plant. In this paper, a nonlinear controller using sliding mode method which is a robust nonlinear controller is designed to control a Traveling Wave Nuclear Reactor (TWR) power. The reactor core is simulated based on the point kinetics equations and six delayed neutron groups. Considering the limitations of the delayed neutron precursors densities measurement, a sliding mode observer is designed to estimate their values and finally a sliding mode control based on the sliding mode observer is presented to control the reactor core power. The stability analysis is given by means Lyapunov approach, thus the control system is guaranteed to be stable within a large range. Sliding Mode Control (SMC) is one of the robust and nonlinear methods which have several advantages such as robustness against matched external disturbances and parameter uncertainties. Since it has systematic design procedure, it is one of the most powerful solutions to design many practical control systems. The designed control system is evaluated in the presence of disturbances and uncertainties. The results show the robustness and performance of the used control system.     

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。     

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.     

Robust formation control of electrically driven nonholonomic mobile robots via sliding mode technique

This paper proposes a sliding mode formation control method for electrically driven nonholonomic mobile robots in the presence of model uncertainties and disturbances. We use the kinematic model based on the leader-following approach for the formation control of multiple robots. Unlike many researches considering only the kinematic model, we also consider the dynamic model including actuator dynamics to obtain the voltage input because it is more realistic to use the voltage as input than the velocity. Then, the sliding mode control method is used to deal with model uncertainties and disturbances acting on the mobile robots. The stability of the proposed control system is proven using Lyapunov stability theory. Finally, we perform computer simulations to demonstrate the performance of the proposed control system.     

非匹配不确定系统的自适应反步非奇异快速终端滑模控制

针对一类n阶非匹配不确定系统,提出一种自适应反步非奇异快速终端滑模控制方法.控制的前n-1步采用自适应反步控制策略,消除非匹配不确定性的影响;最后一步利用误差的积分构造非奇异快速终端滑模面,设计控制律使系统第n个状态有限时间收敛.该方法对系统中匹配和非匹配不确定项均具有鲁棒性,比自适应反步终端滑模方法具有更快的收敛速度.理论分析证明了闭环系统的稳定性,仿真结果验证了该方法的有效性.     

ROBUST VIBRATION CONTROL FOR FLEXIBLE ARMS USING THE SLIDING MODE METHOD

The vibration control of flexible arms is accomplished here using the sliding mode method, where the traditional discontinuous approach is modified by a differentiable one. The higher order modes of the flexible arm are treated as disturbances and are compensated by introducing a disturbance observer. Simplified expressions of the motor angular and the strain moment for the flexible arm with a disturbance observer are obtained, where the remaining disturbance and the model uncertainties are considered as system uncertainties. The robustness of the sliding mode control is effectively employed to cope with the system uncertainties, where the bounds of the uncertainties are adaptively updated. The proposed control law simultaneously causes the motor angular to track a desired signal and the strain moment to approach zero. The stability of the controlled flexible arm is analyzed based on the obtained important fact that a part of the control input is the approximate estimate of a special signal generated by the uncertainty. The motor angular tracking error and the converging speed of the controlled signals are determined by means of design parameters. Experimental results demonstrate the robustness of the proposed method.     

Discrete-time sliding mode control for uncertain systems with state and input delays

This article presents a discrete-time sliding mode control method for the robust stabilisation of linear uncertain multi-input discrete-time systems with state and input delays. The systems are assumed to have structured mismatched time-varying parameter uncertainties. A specified switching surface is proposed and a sliding mode controller is derived to ensure the existence of the quasi-sliding mode. Based on the improved Lyapunov function and linear matrix inequality technique, delay-independent sufficient conditions for the design of a stable switching surface are given and the stability of the overall closed-loop system is guaranteed. Neither chattering phenomenon will occur nor the knowledge of upper bound of uncertainties is required. Finally, simulation results demonstrate the efficacy of the proposed control methodology.     

一种基于反步法的鲁棒自适应终端滑模控制

针对不确定严格反馈块控非线性系统, 提出了一种基于反步法的鲁棒自适应终端滑模变结构控制方法. 系统的未知不确定及外界干扰由模糊系统在线逼近, 利用反步法设计了变结构控制的终端滑模面, 并由此得到了鲁棒自适应终端滑模控制器, 使系统的跟踪误差在有限时间内趋于给定轨迹的任意小的邻域内. 通过Lyapunov定理证明了闭环系统所有信号最终有界. 对某战斗机6自由度机动仿真结果表明, 该方法具有强鲁棒性.     

Observer-based adaptive sliding mode control for robust tracking and model following

This paper presents a methodological approach to design an observer-based adaptive sliding mode control to realize the problem of robust tracking and modeling following for a class of uncertain linear systems. Only partial information of the system states is known. Based on Lyapunov stability theorem, 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 proposed observer-based adaptive sliding mode control scheme can be implemented without requiring a priori knowledge of upper bounds on the norm of the uncertainties and external disturbances. This scheme assures robustness against system uncertainties and disturbances. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme.     

Robust attitude control for tail‐sitter unmanned aerial vehicles in flight mode transitions

Tail‐sitter unmanned aerial vehicles (UAVs) can flight as rotorcrafts as well as fixed‐wing aircrafts, but it is hard to control the flight mode transition. The vehicle dynamics involves serious parametric uncertainties, highly nonlinear dynamics, and is easy to be affected by external disturbances, especially during the mode transition. This paper presents a robust control method for a kind of tail‐sitter UAVs to achieve the flight mode transition. The robust controller is proposed based on the state‐feedback control scheme and the robust compensation method. The proposed control method does not need to switch the coordinate system, the controller structure, or the controller parameters during the mode transitions. Theoretical analysis is given to guarantee the robustness stability of the designed flight control system. Numerical simulation results are presented to show the advantages of the proposed control method compared with the state‐feedback control method and the sliding mode control approach.     

Robust adaptive controller with disturbance observer for vehicular radar servo system

In vehicular radar servo system, parameter variations of the executive motor and external disturbance uncertainties have great effects on the position tracking precision of the system. In this paper, a robust adaptive controller with disturbance observer is designed for vehicular radar servo system, which combines the merits of disturbance observer, adaptive backstepping method and sliding mode control. The system is modeled, and a disturbance observer is employed to observe and compensate for the unknown uncertainties. Adaptive backstepping method is used to design the sliding model controller to guarantee the global stability of the overall system. Simulation results show that the proposed robust adaptive controller has good performance in position tracking and enhances the robustness of vehicular radar servo system while observing the uncertainties precisely and quickly.     

基于自适应神经网络的分数阶混沌系统滑模同步

针对一类异结构不确定分数阶混沌系统的同步问题,基于Lyapunov稳定性理论和分数阶系统稳定性理论,提出一种神经网络结合干扰观测器的主动反馈控制方法. 设计一种非线性干扰观测器对干扰进行观测,通过滑模控制对未观测出的部分干扰进行补偿,最终实现分数阶混沌系统的同步.与现有方法相比,采用的模型更符合工程应用实际,且不需要已知不确定项上界.数值仿真验证了所提出方法的有效性和正确性.     

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.      

电液伺服系统的多滑模鲁棒自适应控制

针对一类参数与外负载非匹配不确定的非线性高阶系统,提出了一种基于逐步递推方法的多滑模鲁棒自适应控制策略.应用逐步递推的多滑模控制方法简化了高阶系统的控制问题,同时在自适应控制中加入鲁棒控制的方法,以消除不确定性对控制性能的影响.首先利用逐步递推方法与状态反馈精确线性化理论,得出确定系统的多滑模控制器设计方法;然后基于Lyapunov稳定性分析方法,给出不确定系统的参数自适应律,及鲁棒自适应控制器的设计方法.本文把该控制策略应用到电液伺服系统的位置跟踪控制中,仿真结果显示,该控制方法具有较强的鲁棒性及良好的跟踪效果.