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.

Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

Full-order sliding mode control of uncertain chaos in a permanent magnet synchronous motor based on a fuzzy extended state observer

A full-order sliding mode control based on a fuzzy extended state observer is proposed to control the uncertain chaos in the permanent magnet synchronous motor. Through a simple coordinate transformation, the chaotic PMSM model is transformed into the Brunovsky canonical form, which is more suitable for the controller design. Based on the fuzzy control theory, a fuzzy extended state observer is developed to estimate the unknown states and uncertainties, and the restriction that all the system states should be completely measurable is avoided. Thereafter, a full-order sliding mode controller is designed to ensure the convergence of all system states without any chattering problem. Comparative simulations show the effectiveness and superior performance of the proposed control method.

Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and E1-Nabulsi-Hamilton＇s canoni- cal equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of E1-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of E1-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Fi- nally, Noether＇s theorems for the non-conservative Hamilton system under the E1-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.

Carreau-Extended非牛顿流体圆管层流流动的摄动解

非牛顿流体在工业生产中应用广泛。文中基于同时包含屈服应力、时间常数和幂律指数的Carreau-Extended(简称Carreau-E)复杂流变方程及剪切应力与压降平衡关系,建立了圆管内充分发展的稳定Carreau-E流体层流管流的运动方程,并采用摄动方法推导出相应运动方程的一阶渐近解,获得了不同类型流体管流的速度分布以及压力梯度、流核宽度、屈服应力和时间常数对Carreau-E流体管流流场分布的影响规律,该研究对Carreau-E流体及其他复杂非牛顿流体管流特性研究具有参考价值。

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.

Overview of extended release tacrolimus in solid organ transplantation

Tacrolimus(Prograf?, Astellas Pharma Europe Ltd, Staines, United Kingdom; referred to as tacrolimusBID) is an immunosuppressive agent to prevent and treat allograft rejection in kidney transplant recipients in combination with mycophenolate mofetil, corticosteroids,with or without basiliximab induction. The drug has also been studied in liver, heart and lung transplant; however, these are currently off-label indications. An extended release tacrolimus formulation(Advagraf?, Astagraf XL?) allows for once-daily dosing, with the potential to improve adherence. Extended release tacrolimus has similar absorption, distribution, metabolism and excretion to tacrolimus-BID. Phase Ⅰ pharmacokinetic trials comparing extended release tacrolimus and tacrolimus-BID have demonstrated a decreased maximum concentration(C max) and delayed time to maximum concentration(t max) with the extended release formulation; however, AUC0-24 was comparable between formulations. Overall extended release tacrolimus has a very similar safety and efficacy profile to tacrolimus-BID. It is not recommended in the use of liver transplant patient's due to the increased risk of mortality in female recipients. There has been minimal data regarding the use of extended release tacrolimus in heart and lung transplant recipients. With the current data available for all organ groups the extended release tacrolimus should be dosed in a 1:1 fashion, the exception may be the cystic fibrosis population where their initial dose may need to be higher.

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 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.

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.

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.

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.

Hierarchical Modeling by Recursive Unsupervised Spectral Clustering and Network Extended Importance Measures to Analyze the Reliability Characteristics of Complex Network Systems

The complexity of large-scale network systems made of a large number of nonlinearly interconnected components is a restrictive facet for their modeling and analysis. In this paper, we propose a framework of hierarchical modeling of a complex network system, based on a recursive unsupervised spectral clustering method. The hierarchical model serves the purpose of facilitating the management of complexity in the analysis of real-world critical infrastructures. We exemplify this by referring to the reliability analysis of the 380 kV Italian Power Transmission Network (IPTN). In this work of analysis, the classical component Importance Measures (IMs) of reliability theory have been extended to render them compatible and applicable to a complex distributed network system. By utilizing these extended IMs, the reliability properties of the IPTN system can be evaluated in the framework of the hierarchical system model, with the aim of providing risk managers with information on the risk/safety significance of system structures and components.

Nonlinear Control of an Induction Motor Using a Reduced-Order Extended Sliding Mode Observer for Rotor Flux and Speed Sensorless Estimation

This article proposes an innovative strategy to the problem of non-linear estimation of states for electrical machine systems. This method allows the estimation of variables that are difficult to access or that are simply impossible to measure. Thus, as compared with a full-order sliding mode observer, in order to reduce the execution time of the estimation, a reduced-order discrete-time Extended sliding mode observer is proposed for on-line estimation of rotor flux, speed and rotor resistance in an induction motor using a robust feedback linearization control. Simulations results on Matlab-Simulink environment for a 1.8 kW induction motor are presented to prove the effectiveness and high robustness of the proposed nonlinear control and observer against modeling uncertainty and measurement noise.

Nonlinear cascade control of single-rod pneumatic actuator based on an extended disturbance observer

Precise position tracking control of the single-rod pneumatic actuator is considered and a nonlinear cascade controller is developed.The proposed controller comprises an extended disturbance observer(EDOB)and a nonlinear robust control law synthesized by the backstepping method.The EDOB is designed to estimate not only the influence of disturbances but also the parameter uncertainties.With the use of parameter and disturbance estimates,the nonlinear cascade controller,which consists of an outer position tracking loop and an inner load pressure loop,is further designed to attenuate the effects of parameter and disturbance estimation errors.The stability of the closed-loop system is proven by means of Lyapunov theory.Extensive comparative experimental results obtained verify the effectiveness of the proposed nonlinear cascade controller and its performance robustness to parameter and external disturbance variations in practical implementation.

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.

Simulation on model predictive control for PMSM drive system based on double extended state observer

A novel double extended state observer(DESO)based on model predictive torque control(MPTC)strategy is developed for three-phase permanent magnet synchronous motor(PMSM)drive system without current sensor.In general,to achieve high-precision control,two-phase current sensors are necessary for successful implementation of MPTC.For this purpose,two ESOs are used to estimate q-axis current and stator resistance respectively,and then based on this,d-axis current is estimated.Moreover,to reduce torque and flux ripple and to improve the performance of the torque and speed,MPTC strategy is designed.The simulation results validate the feasibility and effectiveness of the proposed scheme.

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.

Federal extended Kalman filter based on reconstructed observation in incomplete observations

In the estimation and identification of nonlinear system state,aiming at the adverse effect of observation missing randomly caused by detection probability of used sensor which is less than 1,a novel federal extended Kalman filter( FEKF) based on reconstructed observation in incomplete observations( ROIO) is proposed in this paper. On the basis of multi-sensor observation sets,the observation is exchanged at different times to construct a new observation set. Based on each observation set,an extended Kalman filter algorithm is used to estimate the state of the target,and then the federal filtering algorithm is used to solve the state estimation based on the multi-sensor observation data. The effect of the sensor probing probability on the filtering result and the effect of the number of sensors on the filtering result are obtained by the simulation experiment,respectively. The simulation results demonstrate effectiveness of the proposed algorithm.

An Extended Sliding Mode Observer for Speed, Position and Torque Sensorless Control for PMSM Drive Based Stator Resistance Estimator

This paper presents a robust sixth-order Discrete-time Extended Sliding Mode Observer (DESMO) for sensorless control of PMSM in order to estimate the currents, speed, rotor position, load torque and stator resistance. The satisfying simulation results on Simulink/Matlab environment for a 1.6 kW PMSM demonstrate the good performance and stability of the proposed ESMO algorithm against parameter variation, modeling uncertainty, measurement and system noises.