A novel dynamic terminal sliding mode control of uncertain nonlinear systems

A new dynamic terminal sliding mode control （DTSMC） technique is proposed for a class of single-input and single-output （SISO） uncertain nonlinear systems. The dynamic terminal sliding mode controller is formulated based on Lyapunov theory such that the existence of the sliding phase of the closed-loop control system can be guaranteed, chattering phenomenon caused by the switching control action can be eliminated, and high precision performance is realized. Moreover, by designing terminal equation, the output tracking error converges to zero in finite time, the reaching phase of DSMC is eliminated and global robustness is obtained. The simulation results for an inverted pendulum are given to demonstrate the properties of the proposed method.

Synchronization of uncertain fractional-order chaotic systems with disturbance based on a fractional terminal sliding mode controller

This paper provides a novel method to synchronize uncertain fractional-order chaotic systems with external disturbance via fractional terminal sliding mode control. Based on Lyapunov stability theory, a new fractional-order switching manifold is proposed, and in order to ensure the occurrence of sliding motion in finite time, a corresponding sliding mode control law is designed. The proposed control scheme is applied to synchronize the fractional-order Lorenz chaotic system and fractional-order Chen chaotic system with uncertainty and external disturbance parameters. The simulation results show the applicability and efficiency of the proposed scheme.

Second order sliding mode control with back stepping approach for moving mass spinning missiles

An attitude controller using the second order sliding mode control methodology with a backstepping approach（SOSMCB）is designed and implemented for a spinning missile with two internal moving mass blocks.The system consists of a rigid body and two radial internal moving mass blocks and its mathematical model is established based on Newtonian mechanics.The control scheme integrates a second order sliding mode control algorithm into the last step of the backstepping approach,and its stability is proved by means of a Lyapunov function.The performance of the controller is demonstrated by numerical simulations,the results show that the attitude controller is stable and effective.

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.

Adaptive Differentiators via Second Order Sliding Mode for a Fixed Wing Aircraft

Safety automation of complex mobile systems is a current topic issue in industry and research laboratories,especially in aeronautics.The dynamic models of these systems are nonlinear,Multi-Input Multi-Output(MIMO)and tightly coupled.The nonlinearity resides in the dynamic equations and also in the aerodynamic coefficients’variability.This paper is devoted to developing the piloting law based on the combination of the robust differentiator with a dynamic adaptation of the gains and the robust controller via second order sliding mode,by using an aircraft in virtual simulated environments.To deal with the design of an autopilot controller,we propose an environment framework based on a Software In the Loop(SIL)methodology and we use Microsoft Flight Simulator(FS-2004)as the environment for plane simulation.The first order sliding mode control may be an appropriate solution to this piloting problem.However,its implementation generates a chattering phenomenon and a singularity problem.To overcome these problems,a new version of the adaptive differentiators for second order sliding modes is proposed and used for piloting.For the sliding mode algorithm,higher gains values may be used to improve accuracy;however this leads to an amplification of noise in the estimated signals.A good tradeoff between these two criteria(accuracy,robustness to noise ratio)is difficult to achieve.On the one hand,these values must increase the gains in order to derive a signal sweeping of some frequency ranges.On the other hand,low gains values have to be imposed to reduce noise amplification.So,our goal is to develop a differentiation algorithm in order to have a good compromise between error and robustness to noise ratio.To fit this requirement,a new version of differentiators with a higher order sliding modes and a dynamic adaptation of the gains,is proposed:the first order differentiator for the control of longitudinal speed and the second order differentiator for the control of the Euler angles.

Dynamic event-triggered finite-time control for multiple Euler-Lagrange systems using integral terminal sliding mode

The tracking control for multiple Euler-Lagrange systems with external disturbances in finite time under undirected topology is investigated in this paper.A dynamic model is established for the multi-EL systems to accurately describe the general mechanical system.Furthermore,an integral terminal sliding mode surface is devised to converge the tracking errors of the system state to a neighborhood of zero within finite time,and the designed finite-time controller ensures fast convergence and high steady-state accuracy.To reduce the controller update frequency and network transmission communication load,a dynamic event-triggered mechanism is introduced between the sensor and controller,and no Zeno behavior was observed.Therefore,the Lyapunov stability theory and finite-time stability criterion prove that all signals in the closed-loop system are uniformly ultimately bounded in finite time.Finally,the simulation results verified the effectiveness of the proposed control method.

Robust backstepping global integral terminal sliding mode controller to enhance dynamic stability of hybrid AC/DC microgrids

In this paper,a Backstepping Global Integral Terminal Sliding Mode Controller(BGITSMC)with the view to enhancing the dynamic stability of a hybrid AC/DC microgrid has been presented.The proposed approach controls the switch-ing signals of the inverter,interlinking the DC-bus with the AC-bus in an AC/DC microgrid for a seamless interface and regulation of the output power of renewable energy sources(Solar Photovoltaic unit,PMSG-based wind farm),and Battery Energy Storage System.The proposed control approach guarantees the dynamic stability of a hybrid AC/DC microgrid by regulating the associated states of the microgrid system to their intended values.The dynamic stabil-ity of the microgrid system with the proposed control law has been proved using the Control Lyapunov Function.A simulation analysis was performed on a test hybrid AC/DC microgrid system to demonstrate the performance of the proposed control strategy in terms of maintaining power balance while the system’s operating point changed.Furthermore,the superiority of the proposed approach has been demonstrated by comparing its performance with the existing Sliding Mode Control(SMC)approach for a hybrid AC/DC microgrid.

Integrated guidance and control of guided projectile with multiple constraints based on fuzzy adaptive and dynamic surface

Based on fuzzy adaptive and dynamic surface(FADS),an integrated guidance and control(IGC)approach was proposed for large caliber naval gun guided projectile,which was robust to target maneuver,canard dynamic characteristics,and multiple constraints,such as impact angle,limited measurement of line of sight(LOS)angle rate and nonlinear saturation of canard deflection.Initially,a strict feedback cascade model of IGC in longitudinal plane was established,and extended state observer(ESO)was designed to estimate LOS angle rate and uncertain disturbances with unknown boundary inside and outside of system,including aerodynamic parameters perturbation,target maneuver and model errors.Secondly,aiming at zeroing LOS angle tracking error and LOS angle rate in finite time,a nonsingular terminal sliding mode(NTSM)was designed with adaptive exponential reaching law.Furthermore,combining with dynamic surface,which prevented the complex differential of virtual control laws,the fuzzy adaptive systems were designed to approximate observation errors of uncertain disturbances and to reduce chatter of control law.Finally,the adaptive Nussbaum gain function was introduced to compensate nonlinear saturation of canard deflection.The LOS angle tracking error and LOS angle rate were convergent in finite time and whole system states were uniform ultimately bounded,rigorously proven by Lyapunov stability theory.Hardware-in-the-loop simulation(HILS)and digital simulation experiments both showed FADS provided guided projectile with good guidance performance while striking targets with different maneuvering forms.

Second-order terminal sliding mode control for hypersonic vehicle in cruising flight with sliding mode disturbance observer

This paper focuses on the design of nonlinear robust controller and disturbance observer for the longitudinal dynamics of a hypersonic vehicle （HSV） in the presence of parameter uncertainties and external disturbances. First, by combining terminal sliding mode control （TSMC） and second-order sliding mode control （SOSMC） approach, the second- order terminal sliding control （2TSMC） is proposed for the velocity and altitude tracking control of the HSV. The 2TSMC possesses the merits of both TSMC and SOSMC, which can provide fast convergence, continuous control law and high- tracking precision. Then, in order to increase the robustness of the control system and improve the control performance, the sliding mode disturbance observer （SMDO） is presented. The closed-loop stability is analyzed using the Lyapunov technique. Finally, simulation results illustrate the effectiveness of the proposed method, as well as the improved overall performance over the conventional sliding mode control （SMC）.

On-line RNN compensated second order nonsingular terminal sliding mode control for hypersonic vehicle

Purpose–The purpose of this paper is to design a robust control scheme to achieve robust tracking of velocity and altitude commands for a general hypersonic vehicle(HSV)in the presence of parameter variations and external disturbances.Design/methodology/approach–The robust control scheme is composed of nonsingular terminal sliding mode control(NTSMC),super twisting control algorithm(STC)and recurrent neural network(RNN).First,by combing a novel NTSMC and STC algorithm,a second order NTSMC approach for HSV is proposed to provide fast,continuous and high precision tracking control.Second to relax the requirements for the bounds of the lumped uncertainties in control design,a RNN disturbance observer is presented to increase the robustness of the control system.The weights of RNN are updated by adaptive laws based on Lyapunov theorem,thus the closed-loop stability can be guaranteed.Findings–Simulation results demonstrate that the proposed method is effective,leading to promising performance.Originality/value–The main contributions of this work are:first,both parameter variations and external disturbances are considered in control design for the longitudinal dynamic model of HSV;and second,the proposed controller can remove chattering and achieve more favorable tracking performances than conventional sliding mode control.

无人机舵面故障高阶滑模重构观测器设计及主动容错控制

针对无人机舵面损伤故障容错问题,提出了基于二阶非奇异终端滑模重构观测器及主动容错设计方法。在分析舵面正常偏转运动学和动力学特性基础上,构建了无人机典型舵面故障非线性特性模型。提出无人机舵面故障的高阶滑模重构滑模观测器设计方案;引入线性变换降维简化观测器设计程式;将终端滑模和非奇异终端滑模结合起来,实现滑模运动有限时间快速收敛;综合自适应律、线性矩阵不等式设计观测器系数矩阵,确保状态估计偏差有界稳定。提出集状态与故障重构于一体的主动容错控制方案,并通过仿真算例检验所提方案的有效性。

基于扰动观测器和改进自适应二阶快速终端滑模的PMLSM伺服系统控制

针对永磁直线同步电动机(PMLSM)在运行时易受到摩擦力、负载扰动及环境变化等不确定影响,设计一种基于扰动观测器和自适应二阶快速终端滑模控制方法。首先,该方法在高阶滑模的基础上结合了快速终端滑模控制,有效加快了系统响应速度。其次,在二阶滑模面的基础上引入条件积分项,该项仅作用于边界层内部,能够有效避免滑模到达阶段由于积分饱和现象导致的超调量过大及响应时间过慢的问题。此外,设计自适应切换控制律,使切换增益在合理的区间内,并根据系统状态进行实时更新,从而削弱抖振现象。最后,为进一步提升系统的鲁棒性,采用扰动观测器对PMLSM系统的集总不确定性进行补偿。经实验验证,该控制方法具有良好的位置跟踪精度和强鲁棒性,且对系统抖振现象有明显削弱作用。

基于超螺旋二阶滑膜的汽车主动悬架控制方法研究

汽车悬架的控制效果直接影响汽车的稳定性和舒适性,针对一阶滑模控制在主动悬架控制中存在的抖振和控制精度问题,基于汽车二自由度1/4主动悬架模型,提出了一种基于超螺旋二阶滑模控制的汽车主动悬架控制方法。在控制器前端串联一个负加速度反馈回路来调节悬架性能,并使用扩展的超螺旋观测器实时补偿系统的未知内部动态。为了验证控制方法的可行性,通过仿真进行对比分析。仿真结果表明,相比于一阶滑膜控制,该方法解决了悬架未知非线性动态的多目标控制问题,能更有效地改善汽车稳定性和舒适性。

Second Order Sliding Mode Control for Discrete Decouplable Multivariable Systems via Input-output Models

The problem of the chattering phenomenon is still the main drawback of the classical sliding mode control. To resolve this problem, a discrete second order sliding mode control via input-output model is proposed in this paper. The proposed control law is synthesized for decouplable multivariable systems. A robustness analysis of the proposed discrete second order sliding mode control is carried out. Simulation results are presented to illustrate the effectiveness of the proposed strategy.

基于二阶滑模扰动观测的PMSM电流预测控制研究

针对无差拍电流预测控制(DPCC)对电机参数的依赖性,系统性能尤其易受电感参数影响的问题,研究基于二阶滑模扰动观测的永磁同步电机(PMSM)电流预测控制方法。首先,根据滑模控制原理分析电感参数失配对系统参数鲁棒性的影响,及传统滑模控制的不连续函数导致的系统“抖振”;然后,在DPCC中引入一种基于二阶趋近律的滑模扰动观测器(SMDO),实时补偿电感参数失配造成的扰动,同时通过二阶趋近律加速扰动误差的收敛;最后,将该方法与DPCC、SMDO+DPCC进行对比仿真实验。实验结果表明,在电感参数失配的情况下,该方法降低了电流稳态误差,提高了系统参数的鲁棒性,减少了传统滑模控制带来的系统“抖振”现象。

不确定非线性系统快速终端滑模控制

针对界未知的非匹配不确定非线性系统轨迹快速跟踪控制,设计非线性干扰观测器(NDO)的反演自适应终端滑模控算法。首先设计子系统干扰观测器来确定界未知非匹配项补偿量,并结合子系统的Lyapunov函数求出反演控制中虚拟控制律,并运用指令滤波器解决虚拟项求导所带来的微分膨胀缺陷;再设计系统的非奇异快速终端滑模面并给出建模误差不确定性的自适应律,继而求出系统总控制律以确保总闭环系统有限时间全局渐近稳定;最后机器人动力学仿真案例表明,所设计的控制器能实现对指定轨迹的快速稳定跟踪,控制量光滑弱抖振,并对非匹配干扰具有较强的鲁棒性。

基于增强型扩张状态观测器的永磁同步电机低抖振高抗扰二阶终端滑模电流控制

永磁同步电机电流滑模控制具有较好的参数鲁棒性,但控制精度受到滑模抖振的影响,且抖振抑制与抗扰性之间存在矛盾。为此,该文提出一种基于增强型扩张状态观测器的二阶终端滑模电流控制方案,可以有效提升电流控制性能。通过二阶终端滑模控制器的设计,将一阶积分快速终端滑模嵌套在二阶非奇异终端滑模面中,使得滑模抖振得到较好的抑制,同时实现电流无稳态误差的快速收敛。通过引入扩张状态观测器对扰动信号的集总估计与补偿,缓解了抖振与抗扰性之间的矛盾,进一步提升了电流精度。针对数字控制的延迟影响,设计了Smith预估器,提升了扰动补偿精度。最后,通过实验对该文所设计的电流控制方案进行验证,并通过对比展示了该方案的有效性。

基于二阶动态Terminal滑模的近空间飞行器控制

针对近空间飞行器飞行速度极高,气动参数变化剧烈,外界扰动大,控制精度要求高等特点,设计了基于二阶动态Terminal滑模的控制方案。Terminal滑模能在有限时间内收敛的特性加快了系统跟踪速度;二阶动态滑模的引入,使得滑模面及其部分阶导数为零,并且得到在时间本质上连续的控制器,有效克服了传统滑模的抖振问题。最后,仿真结果表明了二阶动态滑模去除抖振的优越性和整体控制方案的有效性。

大攻角条件下制导弹滚转稳定控制方法

制导弹跨域飞行过程中,伴随着大攻角下的涡流非对称以及跨音速气动转捩,这些干扰将引起控制失稳,进一步增大脱靶量。针对以上问题,考虑气动模型强非线性、强参数不确定性及强外界干扰,建立制导弹滚转通道动力学模型,进而提出一种基于滑模观测器与非奇异终端滑模的滚转姿态组合控制方法。以此为基础框架,结合微分跟踪器设计一种反步控制方法,以补偿执行机构动力学。利用Lyapunov稳定性理论证明了闭环系统稳定性及有限时间收敛特性。通过仿真实验验证了所设计控制方法的优越性及普适性。