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.

Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control 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.

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.

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.

Retraction control of motorized seat belt system with linear state observer

A design and verification of linear state observers which estimate state information such as angular velocity and load torque for retraction control of the motorized seat belt (MSB) system were described. The motorized seat belt system provides functions to protect passengers and improve passenger's convenience. Each MSB function has its own required belt tension which is determined by the function's purpose. To realize the MSB functions, state information, such as seat belt winding velocity and seat belt tension are required. Using a linear state observer, the state information for MSB operations can be estimated without sensors. To design the linear state observer, the motorized seat belt system is analyzed and represented as a state space model which contains load torque as an augmented state. Based on the state space model, a linear state observer was designed and verified by experiments. Also, the retraction control of the MSB algorithm using linear state observer was designed and verified on the test bench. With the designed retraction control algorithm using the linear state observer, it is possible to realize various types of MSB functions.

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.

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.

An observer based asymptotic trajectory control using a scalar state for chaotic systems

A state-observer based full-state asymptotic trajectory control （OFSTC） method requiring a scalar state is presented to asymptotically drive all the states of chaotic systems to arbitrary desired trajectories. It is no surprise that OFSTC can obtain good tracking performance as desired due to using a state-observer. Significantly OFSTC requires only a scalar state of chaotic systems. A sinusoidal wave and two chaotic variables were taken as illustrative tracking trajectories to validate that using OFSTC can make all the states of a unified chaotic system track the desired trajectories with high tracking accuracy and in a finite time. It is noted that this is the first time that the state-observer of chaotic systems is designed on the basis of Kharitonov＇s Theorem.

Fault detection based on H_∞ states observer for networked control systems

The influence of random short time-delay to networked control systems （NCS） is changed into an unknown bounded uncertain part. Without changing the structure of the system, an Hoo states observer is designed for NCS with short time-delay. Based on the designed states observer, a robust fault detection approach is proposed for NCS. In addition, an optimization method for the selection of the detection threshold is introduced for better tradeoff between the robustness and the sensitivity. Finally, some simulation results demonstrate that the presented states observer is robust and the fault detection for NCS is effective.

Generalized projective synchronization via the state observer and its application in secure communication

Based on the improved state observer and the pole placement technique, by adding a constant which extends the scope of use of the original system, a new design method of generalized projective synchronization is proposed. With this method, by changing the projective synchronization scale factor, one can achieve not only complete synchronization, but also anti-synchronization, as well as arbitrary percentage of projective synchronization, so that the system may attain arbitrary synchronization in a relatively short period of time, which makes this study more meaningful. By numerical simulation, and choosing appropriate scale factor, the results of repeated experiments verify that this method is highly effective and satisfactory. Finally, based on this method and the relevant feedback concept, a novel secure communication project is designed. Numerical simulation verifies that this secure communication project is very valid, and moreover, the experimental result has been greatly improved in decryption time.

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.

Integrated guidance and control design method based on finite-time state observer

A composited integrated guidance and control(IGC) algorithm is presented to tackle the problem of the IGC design in the dive phase for the bank-to-turn(BTT) vehicle with the inaccuracy information of the line-of-sight(LOS) rate. For the sake of theoretical derivation, an IGC model in the pitch plane is established. The high-order finite-time state observer(FTSO), with the LOS angle as the single input, is employed to reconstruct the states of the system online. Besides, a composited IGC algorithm is presented via the fusion of back-stepping and dynamic inverse. Compared with the traditional IGC algorithm, the proposed composited IGC method can attenuate effectively the design conservation of the flight control system, while the LOS rate is mixed with noise. Extensive experiments have been performed to demonstrate that the proposed approach is globally finite-time stable and strongly robust against parameter uncertainty.

Soft Sensor for Inputs and Parameters Using Nonlinear Singular State Observer in Chemical Processes

Chemical processes are usually nonlinear singular systems.In this study,a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes,which are augmented as state variables.Based on the observability of the singular system,this paper presents a simplified observability criterion under certain conditions for unknown inputs and uncertain model parameters.When the observability is satisfied,the unknown inputs and the uncertain model parameters are estimated online by the soft sensor using augmented nonlinear singular state observer.The riser reactor of fluid catalytic cracking unit is used as an example for analysis and simulation.With the catalyst circulation rate as the only unknown input without model error,one temperature sensor at the riser reactor outlet will ensure the correct estimation for the catalyst circulation rate.However,when uncertain model parameters also exist,additional temperature sensors must be used to ensure correct estimation for unknown inputs and uncertain model parameters of chemical processes.

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.

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.

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.