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.

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.

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.

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.

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.

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.

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.

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。

Observer-Based Control for a Cable-Driven Aerial Manipulator under Lumped Disturbances

With the increasing demand for interactive aerial operations,the application of aerial manipulators is becoming more promising.However,there are a few critical problems on how to improve the energetic efficiency and pose control of the aerialmanipulator forpractical application.In this paper,a novel cable-drivenaerialmanipulatorused for remote water sampling is proposed and then its rigid-flexible coupling dynamics model is constructed which takes joint flexibility into account.To achieve high precision joint position tracking under lumped disturbances,a newly controller,which consists of three parts:linear extended state observer,adaptive super-twisting strategy,and fractional-order nonsingular terminal sliding mode control,is proposed.The linear extended state observer is adopted to approximate unmeasured states and unknown lumped disturbances and achieve model-free control structure.The adaptive super-twisting strategy and fractional-order nonsingular terminal sliding mode control are combined together to achieve good control performance and counteract chattering problem.The Lyapunovmethod is utilized to prove the overall stability and convergence of the system.Lastly,various visualization simulations and ground experiments are conducted,verifying the effectiveness of our strategy,and all outcomes demonstrate its superiorities over the existing control strategies.

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。

An Improved Deadbeat Predictive Current Control Method for SPMSM Drives with a Novel Adaptive Disturbance Observer

To improve the dynamic performance of conventional deadbeat predictive current control(DPCC)under parameter mismatch,especially eliminate the current overshoot and oscillation during torque mutation,it is necessary to enhance the robustness of DPCC against various working conditions.However,the disturbance from parameter mismatch can deteriorate the dynamic performance.To deal with the above problem,firstly,traditional DPCC and the parameter sensitivity of DPCC are introduced and analyzed.Secondly,an extended state observer(ESO)combined with DPCC method is proposed,which can observe and suppress the disturbance due to various parameter mismatch.Thirdly,to improve the accuracy and stability of ESO,an adaptive extended state observer(AESO)using fuzzy controller based on ESO,is presented,and combined with DPCC method.The improved DPCC-AESO can switch the value of gain coefficients with fuzzy control,accelerating the current response speed and avoid the overshoot and oscillation,which improves the robustness and stability performance of SPMSM.Finally,the three methods,as well as conventional DPCC method,DPCC-ESO method,DPCC-AESO method,are comparatively analyzed in this paper.The effectiveness of the proposed two methods are verified by simulation and experimental results.

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。