An extended state observer with adjustable bandwidth for measurement noise

In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.

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.

基于ESO分数阶滑模调节的PMSM模型预测转矩控制

为了提高永磁同步电机调速系统的性能,提出一种基于扩张状态观测器的分数阶滑模预测转矩控制策略。采用扩张状态观测器对电机的综合扰动项、定子电流和反电动势进行实时观测,可快速准确得到它们的估计值并进行补偿;利用估计值构建分数阶滑模控制器来削弱系统抖振并提高鲁棒性;利用转矩和磁链无差拍预测控制,减少了遍历次数并降低了计算复杂度。通过仿真和半实物平台进行了验证,所得结果表明,所提出的方法能有效提升系统的鲁棒性,使电机具有良好的动态和静态性能。

引入ESO的永磁超环面电机无模型预测电流控制

为改善无差拍预测电流控制(DPCC)对永磁超环面电机系统参数的依赖性,研究了引入扩张状态观测器(ESO)的永磁超环面电机无模型预测电流控制(MFPCC-ESO)策略。根据永磁超环面电机的复合转子结构,引入自转运动影响系数与磁势系数,在旋转坐标系下建立该电机的时变数学模型;利用永磁超环面电机系统的输入与输出,建立该电机具有时变比例因子的超局部模型,同时引入ESO对超局部模型的干扰部分进行实时估计,并利用朱利稳定判据证明了ESO的稳定性;结合延时补偿的DPCC预测得到参考电压矢量,从而实现永磁超环面电机的MFPCC-ESO策略。对参数匹配和失配下永磁超环面电机MFPCC-ESO策略与DPCC策略进行对比分析,仿真结果表明:MFPCC-ESO策略下的永磁超环面电机具有优越的动态和稳态性能及强鲁棒性,同时该控制策略还能有效降低永磁超环面电机的输出波动。

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ESO的PMSM无模型快速超螺旋滑模预测控制

为提高表贴式永磁同步电机(Surface permanent magnet synchronous motor,SPMSM)在参数变化和外部扰动下的鲁棒性,提出一种基于扩张状态观测器的无模型快速超螺旋滑模预测控制方法。首先,建立SPMSM参数摄动时的新型超局部模型。其次,采用改进的超螺旋算法作为辅助控制率设计转速环无模型超螺旋滑模反馈控制器,同时利用复合的扩张扰动观测器估计超局部模型中的未知部分,并通过Lyapunov稳定性理论证明了控制器和观测器的稳定性。电流环应用无差拍电流预测控制策略,结合扩张状态观测器对扰动量进一步估计并进行前馈补偿,使电流环具有更好的动态响应和更小的谐波分量。仿真试验结果表明,所提方法可有效提高系统响应速度,改善SPMSM在发生参数漂移和外部扰动下的暂稳态性能,降低电流总谐波畸变率,提升系统鲁棒性和抗干扰性能。

基于ESO的仿蝙蝠扑翼飞行器姿态控制仿真

针对仿蝙蝠扑翼飞行器的纵向气动特性不稳定、易受扰动的问题,设计了一种基于扩张状态观测器(ESO)的姿态控制方法,实现了扑翼飞行器姿态的稳定与抗干扰控制。首先建立仿蝙蝠扑翼飞行器的动力学模型;进而在该模型基础上分析了扑翼飞行器的纵向稳定性;然后将系统的不确定部分与各种未知的外界扰动作为系统的总扰动,引入ESO模块对总扰动进行实时观测与跟踪;最后在原有的PID控制器中加入扰动补偿环节。数值仿真结果表明,基于ESO的控制算法对于仿蝙蝠扑翼飞行器的控制效果显著优于基于PID的控制方法,阶跃响应的调节时间加快41.27%,对系统输入的白噪声干扰波动峰值从6.02%降低到2.82%,正弦扰动的波动峰值从11.56%降低到3.22%。

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。

基于LESO的PMSM转子位置估算误差补偿方法

高速永磁同步电机运行中,转子位置精确与否确定了系统运行性能优劣,对于只补偿一拍滞后和零阶保持器引起的角度误差,以及通过与前馈解耦做差获得误差角进行补偿的方法,在精度和动态性等方面性能欠佳。为此,通过分析转子位置估算误差产生原因,推导出误差角的通用型数学模型,提出一种基于线性扩张状态观测器(LESO)的转子位置估算误差补偿方法。基于推导模型设计出一种可提取转子位置误差角的LESO,并采用获得的转子位置误差角进行补偿。此转子位置误差角估算考虑了不同类型非理想因素的影响,以及动态过程中电感电压项对误差角的影响,精度高、动态性好。最后搭建系统实验平台,实验结果表明所提转子位置估算误差补偿方法在精度和动态性方面具有优势。

Stability analysis of the extended state observers by Popov criterion

The analysis and design of the extended state observer （ESO） involves a continuous non-smooth structure, thus the study of the ESO dynamic requires mathematical tools of the nonlinear systems analysis. This paper establishes the sufficient conditions for absolute stability of the ESO. Based on this study, a methodology to estimate several nonlinear functions in dy- namics systems is proposed.

Event-triggered model-free adaptive control for a class of surface vessels with time-delay and external disturbance via state observer

This paper provides an improved model-free adaptive control(IMFAC)strategy for solving the surface vessel trajectory tracking issue with time delay and restricted disturbance.Firstly,the original nonlinear time-delay system is transformed into a structure consisting of an unknown residual term and a parameter term with control inputs using a local compact form dynamic linearization(local-CFDL).To take advantage of the resulting structure,use a discrete-time extended state observer(DESO)to estimate the unknown residual factor.Then,according to the study,the inclusion of a time delay has no effect on the linearization structure,and an improved control approach is provided,in which DESO is used to adjust for uncertainties.Furthermore,a DESO-based event-triggered model-free adaptive control(ET-DESO-MFAC)is established by designing event-triggered conditions to assure Lyapunov stability.Only when the system’s indicator fulfills the provided event-triggered condition will the control input signal be updated;otherwise,the control input will stay the same as it is at the last trigger moment.A coordinate compensation approach is developed to reduce the steady-state inaccuracy of trajectory tracking.Finally,simulation experiments are used to assess the effectiveness of the proposed technique for trajectory tracking.

Differential geometric guidance command with finite time convergence using extended state observer

For improving the performance of differential geometric guidance command(DGGC), a new formation of this guidance law is proposed, which can guarantee the finite time convergence(FTC) of the line of sight(LOS) rate to zero or its neighborhood against maneuvering targets in three-dimensional(3D) space. The extended state observer(ESO) is employed to estimate the target acceleration, which makes the new DGGC more applicable to practical interception scenarios. Finally, the effectiveness of this newly proposed guidance command is demonstrated by the numerical simulation results.

Extended state observer-based control with an adjustable parameter for a large ground-based telescope

The high-precision requirements will always be constrained due to the complicated operating conditions of the ground-based telescope. Owing to various internal and external disturbances, it is necessary to study a control method, which should have a good ability on disturbance rejection and a good adaptability on system parameter variation. The traditional proportional-integral(PI) controller has the advantage of simple and easy adjustment, but it cannot deal with the disturbances well in different situations. This paper proposes a simplified active disturbance rejection control law, whose debugging is as simple as the PI controller, and with better disturbance rejection ability and parameter adaptability. It adopts a simplified second-order extended state observer(ESO) with an adjustable parameter to accommodate the significant variation of the inertia during the different design stages of the telescope. The gain parameter of the ESO can be adjusted online with a recursive least square estimating method once the system parameter has changed significantly. Thus, the ESO can estimate the total disturbances timely and the controller will compensate them accordingly. With the adjustable parameter of the ESO, the controller can always achieve better performance in different applications of the telescope. The simulation and experimental verification of the control law was conducted on a 1.2-meter ground based telescope. The results verify the necessity of adjusting the parameter of the ESO, and demonstrate better disturbance rejection ability in a large range of speed variations during the design stages of the telescope.

PMSM speed control using adaptive sliding mode control based on an extended state observer

In this study,a composite strategy based on sliding-mode control( SMC) is employed in a permanent-magnet synchronous motor vector control system to improve the system robustness performance against parameter variations and load disturbances. To handle the intrinsic chattering of SMC,an adaptive law and an extended state observer( ESO) are utilized in the speed SMC controller design. The adaptive law is used to estimate the internal parameter variations and compensate for the disturbances caused by model uncertainty. In addition,the ESO is introduced to estimate the load disturbance in real time. The estimated value is used as a feed-forward compensator for the speed adaptive sliding-mode controller to further increase the system's ability to resist disturbances. The proposed composite method,which combines adaptive SMC( ASMC) and ESO,is compared with PI control and ASMC. Both the simulation and experimental results demonstrate that the proposed method alleviates the chattering of SMC systems and improves the dynamic response and robustness of the speed control system against disturbances.

Extended state observer based smooth switching control for tilt-rotor aircraft

A tilt-rotor aircraft has three flight modes: helicopter mode, airplane mode and conversion mode. Unlike the traditional aircraft, the tilt-rotor aircraft, which combines the characteristics of helicopters and fixed-wing aircraft, is a complex multi-body system with the violent variation of the aerodynamic parameters. For these characteristics, a new smooth switching control scheme is provided for the tilt-rotor aircraft. First, the reference commands for airspeed and nacelle angles are calculated by analyzing the conversion corridor and the conversion path. Subsequently, based on the finite-time switching theorem, an average dwell time condition is designed to guarantee the stability in the switching process. Besides, considering the state vibrations and bumps may appear in switching points, the fuzzy weighted logic is employed to improve the system transient performance. For disturbance rejection, three extended state observers are designed separately to estimate the disturbances in the switched systems. Compared with the traditional auto disturbance rejection control and proportion integration differentiation control, this method overcomes the conservatism of wasting the whole model information. The control performances of robustness and smoothness are verified with simulation, which shows that the new smooth switching control scheme is more targeted and superior than the traditional design method.

A non-contact spacecraft architecture with extended stochastic state observer based control for gravity mission

A novel non-contact spacecraft architecture with the extended stochastic state observer for disturbance rejection control of the gravity satellite is proposed.First,the precise linear driving non-contact voice-coil actuators are used to separate the whole spacecraft into the non-contact payload module and the service module,and to build an ideal loop with precise dynamics for disturbance rejection control of the payload module.Second,an extended stochastic state observer is enveloped to construct the overall nonlinear external terms and the internal coupled terms of the payload module,enabling the controller design of the payload module turned into the linear form with simple bandwidth-parameterization tuning in the frequency domain.As a result,the disturbance rejection control of the payload module can be explicitly achieved in a timely manner without complicated tuning in actual implementation.Finally,an extensive numerical simulation is conducted to validate the feasibility and effectiveness of the proposed approach.

基于双层CESO的电液伺服系统线性自抗扰控制

针对含高频噪声的阀控非对称缸不确定扰动抑制问题,采用扰动频率分层技术,利用线性扩张状态观测器低通滤波特性以及扰动估计速度和精度与带宽取值正相关性的特点,提出一种基于双层级联扩张状态观测器的阀控非对称缸电液伺服系统线性自抗扰方法。在分析双层级联线性扩张状态观测器稳定性基础上,与传统线性自抗扰控制方法进行了仿真对比研究。仿真结果表明:该控制方法继承了传统自抗扰控制优点,提高了不确定扰动估计速度和精度,有效抑制了含高频测量噪声不确定扰动带来的不利影响,可实现阀控非对称缸电液伺服系统的高性能控制。

Intelligent Process Fault Diagnosis for Nonlinear Systems with Uncertain Plant Model via Extended State Observer and Soft Computing

There have been many studies on observer-based fault detection and isolation (FDI), such as using unknown input observer and generalized observer. Most of them require a nominal mathematical model of the system. Unlike sensor faults, actuator faults and process faults greatly affect the system dynamics. This paper presents a new process fault diagnosis technique without exact knowledge of the plant model via Extended State Observer (ESO) and soft computing. The ESO’s augmented or extended state is used to compute the system dynamics in real time, thereby provides foundation for real-time process fault detection. Based on the input and output data, the ESO identifies the un-modeled or incorrectly modeled dynamics combined with unknown external disturbances in real time and provides vital information for detecting faults with only partial information of the plant, which cannot be easily accomplished with any existing methods. Another advantage of the ESO is its simplicity in tuning only a single parameter. Without the knowledge of the exact plant model, fuzzy inference was developed to isolate faults. A strongly coupled three-tank nonlinear dynamic system was chosen as a case study. In a typical dynamic system, a process fault such as pipe blockage is likely incipient, which requires degree of fault identification at all time. Neural networks were trained to identify faults and also instantly determine degree of fault. The simulation results indicate that the proposed FDI technique effectively detected and isolated faults and also accurately determine the degree of fault. Soft computing (i.e. fuzzy logic and neural networks) makes fault diagnosis intelligent and fast because it provides intuitive logic to the system and real-time input-output mapping.

基于STESO的PMSM非奇异快速终端滑模控制

为了提高永磁同步电机驱动系统速度控制器的跟踪性能和鲁棒性,提出了一种基于超螺旋扩张状态观测器的非奇异快速终端滑模复合控制器。首先,采用一种基于新型变指数趋近律的非奇异快速终端滑模控制算法设计速度控制器,该趋近律在常规指数趋近律中引入系统状态变量,加快系统收敛到滑模面的速度,同时保持较小的抖振;其次,提出了一种超螺旋扩张状态观测器来观测系统的扰动,并补偿给速度控制器,提高了速度控制系统的鲁棒性;最后,通过仿真和实验证明所提方法的有效性。

基于ESO与改进滑模控制的交流电子负载研究

针对能馈型交流电子负载中负载模拟单元输入电流跟踪精度差以及抗扰能力弱的问题,研究一种扩张状态观测器(ESO)结合改进滑模控制的复合控制策略。为削弱滑模控制的抖振问题,根据幂次趋近率与指数趋近率各自优点提出新型趋近率,设计改进滑模控制器以削减电流稳定时的抖振,同时通过扩张状态观测器对电路参数摄动以及外界扰动进行观测并补偿滑模控制率。最后,仿真实验结果表明本文所提控制方法相较传统PI控制方案具备更好的电流跟踪能力以及抗扰能力。