Backstepping Sliding Mode Control Based on Extended State Observer for Hydraulic Servo System

Hydraulic servo system plays an important role in industrial fields due to the advantages of high response,small size-to-power ratio and large driving force.However,inherent nonlinear behaviors and modeling uncertainties are the main obstacles for hydraulic servo system to achieve high tracking perfor-mance.To deal with these difficulties,this paper presents a backstepping sliding mode controller to improve the dynamic tracking performance and anti-interfer-ence ability.For this purpose,the nonlinear dynamic model is firstly established,where the nonlinear behaviors and modeling uncertainties are lumped as one term.Then,the extended state observer is introduced to estimate the lumped distur-bance.The system stability is proved by using the Lyapunov stability theorem.Finally,comparative simulation and experimental are conducted on a hydraulic servo system platform to verify the efficiency of the proposed control scheme.

Civil aircraft fault tolerant attitude tracking based on extended state observers and nonlinear dynamic inversion

For the problem of sensor faults and actuator faults in aircraft attitude control,this paper proposes a fault tolerant control(FTC)scheme based on extended state observer(ESO)and nonlinear dynamic inversion(NDI).First,two ESOs are designed to estimate sensor faults and actuator faults respectively.Second,the angular rate signal is reconstructed according to the estimation of sensor faults.Third,in angular rate loop,NDI is designed based on reconstruction of angular rate signals and estimation of actuator faults.The FTC scheme proposed in this paper is testified through numerical simulations.The results show that it is feasible and has good fault tolerant ability.

基于TNESO的PMSLM分数阶自抗扰控制

线性自抗扰控制(LADRC)以结构简单、易于实现且抗干扰能力强的特点在永磁同步直线电机(PMSLM)中得到广泛应用,但电机启动和负载突变会导致LADRC系统中的线性扩张状态观测器(LESO)扰动估计精度下降。为此,提出一种基于时变增益非线性扩张状态观测器(TNESO)的PMSLM分数阶自抗扰控制策略。结合LESO和非线性扰动观测器(NDOB),并根据误差与增益的关系构建动态增益函数,设计新型状态观测器TNESO;在此基础上,以分数阶PDμ控制律代替线性状态误差反馈控制律(LSEF),建立改进型自抗扰速度控制系统,以进一步提高电机控制的实时性和鲁棒性。仿真与实验结果表明:所设计的速度控制系统可以有效减少直线电机启动、负载突变时的观测响应时间,抑制观测初始时刻扰动峰值,从而满足高性能的PMSLM速度控制要求。

基于NESO-LFDC的四旋翼无人机滑模姿态控制

针对四旋翼无人机姿态控制中存在空气动力学特性复杂,易受干扰的特性,提出一种基于非线性扩张状态观测器(nonlinear extended state observer,NESO)和低频干扰补偿器(low-frequency disturbance compensator,LFDC)的非奇异快速终端滑模控制方法。该方法内环设计了NESO和LFDC结合,以获得干扰补偿值并补偿总干扰的低频分量。在外环设计了跟踪微分器和可变切换增益的非奇异快速终端滑模控制器,用于补偿虚拟干扰估计值的误差和总干扰的高频分量。仿真结果表明,该控制方法可以更好地估计总干扰的低频和高频分量,减少虚拟干扰估计值的误差对四旋翼无人机姿态控制的影响,并提升响应速度。

Enhanced adaptive nonlinear extended state observer for pure feedback systems with matched and mismatched disturbances

In this paper, an enhanced adaptive nonlinear extended state observer (EANESO) for single-input single-output pure feedback systems in the presence of external time-varying disturbances is proposed. In this paper, a nonlinear system with matched and mismatched disturbances is considered. The conventional extended state observer (ESO) can only be applied to systems that are in the form of integral chains. Moreover, this method has limitations in the face of mismatched disturbances. In the presence of time-varying disturbances, the traditional ESOs cannot estimate the disturbances accurately. To overcome this limitation, an EANESO is proposed in this paper. The main idea is to design the nonlinear ESO (NESO) to estimate the states of the system and multiple disturbances simultaneously. The observer gains are considered time-varying and adjusted with adaptation laws to improve the estimation accuracy and overcome the peaking phenomenon. Next, the proposed controller is designed based on output feedback to eliminate the effects of multiple disturbances and stabilize the closed-loop system. Subsequently, the stability analysis of the closed-loop system and convergence of the observer error are discussed. Finally, the proposed method is applied to the inverted pendulum system. The simulated results show good performance of the proposed method as compared with a recently published scheme in the related literature.

基于对数型障碍Lyapunov函数的俯仰驾驶仪设计

相控阵雷达制导拦截弹在拦截高速大机动目标时,弹体气动参数剧烈非线性变化影响控制系统对大攻角的响应效果,应设计考虑攻角指令跟踪误差约束的鲁棒自动驾驶仪控制律。基于双幂次趋近律和对数型障碍李雅普诺夫函数设计了鲁棒非线性自动驾驶仪控制律,可将攻角指令的跟踪误差快速收敛于约束范围内。通过降阶扩张状态观测器对系统中存在的气动参数不确定性和系统外部扰动进行在线估计和补偿。稳定性分析和数值仿真表明,攻角可在1 s内达到稳态且攻角响应的稳态误差<10-4°,所提出的自动驾驶仪控制律具有较强的鲁棒性,能够准确稳定地跟踪攻角指令,控制导弹产生所需过载进而精准拦截目标。

基于扩张状态观测器的伺服加载模糊滑模控制

针对电动伺服加载测试台存在的间隙、摩擦等非线性控制问题,以滑模变结构控制(SMC)为主体进行了加载控制器设计。分析伺服加载测试台整体结构,提出一种基于扩张状态扰动观测器(ESO)的模糊滑模控制(FSMC)策略。该策略在使用ESO针对伺服加载系统的外部干扰进行观测的基础上,设计了模糊控制对滑动模态面和滑模趋近律进行自适应调节,提高了系统的动态实时跟随能力和干扰补偿能力,并减小SMC控制器稳定时的抖振现象。仿真结果表明:所设计的基于扩张状态观测器的模糊滑模控制器(FSMC-ESO)对比传统SMC及PID控制具有更好的快速响应性和鲁棒性。

高空舱进气环境压力模拟新型自抗扰控制

高空舱进气环境压力模拟控制系统在发动机开展过渡态试验中存在强气流扰动及大量随机噪声干扰,为此,提出新型非线性状态误差反馈函数xal及在结构上引入总扰动状态变量反馈环节来设计扩张状态观测器算法(记作xal-ESO),并以此提出基于xal-ESO的高空舱进气环境压力模拟新型自抗扰控制方法。借助数值仿真对比所提出的xal-ESO与常见ESO在状态与总扰动方面的估计能力,结果表明xal-ESO能有效抑制系统输出噪声并取得较好的估计品质。基于系统核心设备模型搭建高空舱进气环境压力模拟仿真平台并进行工程试验,对比了基于xal-ESO的自抗扰控制与当前工程中使用的线性自抗扰控制的进气环境压力控制效果,试验结果显示线性自抗扰控制方法受噪声影响明显,而所提出的新型自抗扰控制方法在发动机过渡态试验中跟踪进气压力时超调量降低了58.70%,稳态误差降低了95.71%,表明该方法能够有效提升高空舱进气环境压力模拟效果,提升发动机过渡态性能评价的准确性。

轮式移动机器人复合分层抗干扰轨迹跟踪控制

针对存在多种不同类型干扰的非完整轮式移动机器人,提出了一种复合分层抗干扰跟踪控制策略。通过引入直流电机模型,分别设计了非线性干扰观测器(nonlinear disturbance observer,NDO)和扩张状态观测器(extended state observer,ESO)来估计摩擦、空气阻力以及负载变化引起的参数不确定等不同类型扰动。随后,基于观测器估计值设计反馈控制器来跟踪期望速度。在整体控制方案中,运动学控制器位于外环,为轮式移动机器人的内环控制器提供所需的期望速度指令。最后,仿真验证了所提方法的有效性。

A guidance and control design with reduced information for a dual-spin stabilized projectile

In this paper,an integrated guidance and control method based on an adaptive path-following controller is proposed to control a spin-stabilized projectile with only translational motion information under the constraint of an actuator,uncertainties in aerodynamic parameters and measurements,and control system complexity.Owing to the fairly high rotation speed,the dynamic model of this missile is strongly nonlinear,uncertain and coupled in pitch,yaw and roll channels.A theoretical equivalent resultant force and uncertainty compensation method are comprehensively used to realize decoupling of pitch and yaw.In response to the strong nonlinear and time-varying characteristics of the dynamic system,the quasi-linear model whose parameters are obtained by interpolation of points selected as the segmentation points in the trajectory envelope,is used for calculation in each step.To cope with the system uncertainty caused by model approximation,parameter uncertainty and ballistic interference,an extended state estimator is used to compensate the output feedback according to the test ballistic angle.In order to improve the tracking efficiency and ensure the tracking error convergence with only translational motion information,the virtual guide point,whose derivative is deduced according to the Lyapunov principle,is calculated in real time according to the projection relationship between the real-time position and the reference trajectory,and a virtual line-of-sight angle and the backstepping method are used for the design of the guidance and control system.In order to avoid the influence of control input saturation on the guidance and control performance due to the actuator limitation and improve the robustness of the system,an anti-saturation compensator is designed according to the two-step method.The feasibility and effectiveness of the path-following controller is verified through closed-loop flight simulations with measurement,control,and condition uncertainties.The results indicate that the designed controller can converge to the reference path and evidently decrease the distance between the impact point and target under different uncertainties.

Command filtered integrated estimation guidance and control for strapdown missiles with circular field of view

In this paper,an integrated estimation guidance and control(IEGC)system is designed based on the command filtered backstepping approach for circular field-of-view(FOV)strapdown missiles.The threedimensional integrated estimation guidance and control nonlinear model with limited actuator deflection angle is established considering the seeker's FOV constraint.The boundary time-varying integral barrier Lyapunov function(IBLF)is employed in backstepping design to constrain the body line-of-sight(BLOS)in IEGC system to fit a circular FOV.Then,the nonlinear adaptive controller is designed to estimate the changing aerodynamic parameters.The generalized extended state observer(GESO)is designed to estimate the acceleration of the maneuvering targets and the unmatched time-varying disturbances for improving tracking accuracy.Furthermore,the command filters are used to solve the"differential expansion"problem during the backstepping design.The Lyapunov theory is used to prove the stability of the overall closed-loop IEGC system.Finally,the simulation results validate the integrated system's effectiveness,achieving high accuracy strikes against maneuvering targets.

一类欠驱动系统的变结构自抗扰控制

为提高一类欠驱动系统的控制精度和抗扰动能力,提出一种变结构自抗扰控制策略。构建了一种新型的qal函数,解决了传统非线性函数在原点处不够平滑导致的抖振现象和误差增益较大的问题。设计了2个线性跟踪微分器用于精确跟踪欠驱动倒立摆系统位移和速度的实时信号和参考的信号。基于新型非线性qal函数设计了观测性能较好的改进型扩张状态观测器,对欠驱动系统的输出角度及角速度进行实时估计,设计了线性控制率将2个输出量组合成控制量,实现对2个输出量的良好控制。以欠驱动系统的控制电机和欠驱动系统倒立摆为实验对象进行了实验,并将实验结果与传统自抗扰控制和差分进化算法ADRC进行了对比分析,验证了欠驱动系统的变结构自抗扰控制方法的优越性和可行性。

侧滑和打滑下的轮式移动机器人轨迹跟踪控制

针对未知侧滑和打滑干扰下轮式移动机器人(WMR)轨迹控制中,存在模型不确定性、外部干扰等扰动导致传统滑模控制易出现收敛精度不足、控制输入抖振的问题,提出一种基于非线性扩展状态观测器的自适应二阶滑模跟踪控制方法(ASOSMC-NESO)。首先建立了侧滑与打滑条件下的轮式移动机器人运动学和动力学模型;其次,由反步法设计运动学控制器,为动力学提供虚拟速度;接着,针对外部干扰设计了非线性扩展状态观测器,以估计总扰动;然后,基于二阶积分滑模的思想将积分滑模和非奇异快速终端滑模面相结合,设计了动力学控制器,并给出了控制器稳定性分析。实验结果表明,对比一阶滑模控制方法,该控制方法误差最大值在线性和非线性轨迹下,分别下降约89.53%和16.28%,而且控制输入基本不受干扰影响。由此可见,ASOSMC-NESO能有效提高WMR在未知侧滑和打滑下的控制精度,并有效削减抖振和提升WMR轨迹跟踪鲁棒性。

基于NESO的潜艇航向滑模控制器设计

[目的]潜艇在复杂海况下进行水面航行时,为实现低噪操舵控制,[方法]采用潜艇水平面线性运动模型,并利用基于双幂次趋近律的滑模控制对参数变化和外部干扰不敏感、响应速度快、容易实现等优点,设计航向控制器。针对海浪干扰问题,利用非线性扩张状态观测器(NESO)设计海浪滤波器,用以补偿系统外部干扰。[结果]理论推导结果证明了航向滑模控制器的稳定性,并通过Matlab仿真结果验证了其良好的滤波效果。[结结论]研究结果表明,该航向滑模控制器在不同航速、不同海况、不同浪向下均可实现低噪、快速、高精度的航向控制性能。

Full-Order Sliding Mode Control for High-Order Nonlinear System Based on Extended State Observer

In this paper, a full-order sliding mode control based on extended state observer(FSMC+ESO) is proposed for high-order nonlinear system with unknown system states and uncertainties.The extended state observer(ESO) is employed to estimate both the unknown system states and uncertainties so that the restriction that the system states should be completely measurable is relaxed,and a full-order sliding mode controller is designed based on the ESO estimation to overcome the chattering problem existing in ordinary reduced-order sliding mode control. Simulation results show that the proposed method facilitates the practical application with respect to good tracking performance and chattering elimination.

Extended state observer for uncertain lower triangular nonlinear systems subject to stochastic disturbance

The extended state observer （ESO） is the most important part of an emerging control technology known as active disturbance rejection control to this day, aiming at estimating ＂total disturbance＂ from observable measured output. In this paper, we construct a nonlinear ESO for a class of uncertain lower triangular nonlinear systems with stochastic disturbance and show its convergence, where the total disturbance includes internal uncertain nonlinear part and external stochastic disturbance. The numerical experiments are carried out to illustrate effectiveness of the proposed approach.

Sampled-data extended state observer for uncertain nonlinear systems

In this paper, we present a sampled-data nonlinear extended state observer （NLESO） design method for a class of nonlinear systems with uncertainties and discrete time output measurement. To accommodate the inter-sample dynamics, an inter-sample output predictor is employed in the structure of the NLESO to estimate the system output in the sampling intervals, where the prediction is used in the proposed observer instead of the system output. The exponential convergence of the sampled-data NLESO is also discussed and a sufficient condition is given by the Lyapunov method. A numerical example is provided to illustrate the performance of the proposed observer.

Active Disturbance Rejection Control for Uncertain Nonlinear Systems With Sporadic Measurements

This paper deals with the problem of active disturbance rejection control(ADRC)design for a class of uncertain nonlinear systems with sporadic measurements.A novel extended state observer(ESO)is designed in a cascade form consisting of a continuous time estimator,a continuous observation error predictor,and a reset compensator.The proposed ESO estimates not only the system state but also the total uncertainty,which may include the effects of the external perturbation,the parametric uncertainty,and the unknown nonlinear dynamics.Such a reset compensator,whose state is reset to zero whenever a new measurement arrives,is used to calibrate the predictor.Due to the cascade structure,the resulting error dynamics system is presented in a non-hybrid form,and accordingly,analyzed in a general sampled-data system framework.Based on the output of the ESO,a continuous ADRC law is then developed.The convergence of the resulting closed-loop system is proved under given conditions.Two numerical simulations demonstrate the effectiveness of the proposed control method.

An Improved Nonlinear Dynamic Inversion Method for Altitude and Attitude Control of Nano Quad-Rotors under Persistent Uncertainties

Nonlinear dynamic inversion(NDI)has been applied to the control law design of quad-rotors mainly thanks to its good robustness and simplicity of parameter tuning.However,the weakness of relying on accurate model greatly restrains its application on quad-rotors,especially nano quad-rotors(NQRs).NQRs are easy to be influenced by uncertainties such as model uncertainties(mainly from complicated aerodynamic interferences,strong coupling in roll-pitch-yaw channels and inaccurate aerodynamic prediction of rotors)and external uncertainties(mainly from winds or gusts),particularly persistent ones.Therefore,developing accurate model for altitude and attitude control of NQRs is difficult.To solve this problem,in this paper,an improved nonlinear dynamic inversion(INDI)method is developed,which can reject the above-mentioned uncertainties by estimating them and then counteracting in real time using linear extended state observer(LESO).Comparison with the traditional NDI(TNDI)method was carried out numerically,and the results show that,in coping with persistent uncertainties,the INDI-based method presents significant superiority.

基于扩张状态观测器的有限时间船舶编队控制

[目的]为了解决大多数船舶编队控制算法控制周期长和时效性差的问题,提出一种基于扩张状态观测器(ESO)的有限时间控制策略。[方法]采用一种非线性终端滑模算法,通过对控制律分区域设计,克服传统终端滑模存在的奇异性问题;将非线性终端滑模与图论结合,实现有限时间的船舶编队控制;利用扩张状态观测器观测并补偿船舶模型中的不确定性及外界的干扰,以保证船舶编队控制的精确性;运用Lyapunov理论验证船舶编队控制律的稳定性。[结果]仿真结果表明,采用所提控制策略使整个编队系统误差在5 s左右趋近于0,从而实现了稳定。[结论]该控制策略能有效控制船舶编队,且控制速度快、时效性好。