Generalized Extended State Observer Research Articles

Robust internal model control based on a novel generalized extended state observer and its application on a two-inertia system

Disturbance observer (DOB) and extended state observer (ESO) are extensively utilized to handle external disturbances and model uncertainties in the control system. Nevertheless, the integration of these two methods to improve disturbance suppression remains an open question. In this research, the disturbance compensation mechanism of DOB is employed to compensate the disturbance estimation error of ESO, thereby achieving an effective integration of DOB and ESO. Additionally, a generalized ESO (GESO) is proposed to replace ESO. A robust internal mode control (RIMC) scheme is then developed by incorporating GESO into a two-degree-of-freedom internal mode control (TDF-IMC) framework. Moreover, the equivalence of RIMC and classical TDF-IMC is given by a rigorous derivation under the frequency domain description. Finally, the RIMC is applied to the control of a two-inertia system to verify its superiority in terms of robustness, disturbance rejection, and resonance suppression.

Systematic Control Design for Adaptive Rejection of Narrow-Band Disturbances Based on a Novel Resonant Generalized Extended State Observer

In this paper, the adaptive rejection of multiple narrow-band disturbances with time-varying frequencies is investigated. A systematic control approach based on a resonant generalized extended state observer (RGESO) is proposed. The frequency response of the RGESO is shaped into a desired form to reject the total disturbance, including the wide-band uncertainties and the narrow-band disturbances. The state-space realization of the RGESO is also provided to estimate both the states and the total disturbance. To handle the time-varying frequencies of the narrow-band disturbances, a direct frequency estimation approach based on the Levenberg–Marquardt method and an online supervision strategy is presented to improve convergence and reliability, and the estimations are then used to adapt the RGESO parameters. Parameter tuning and stability robustness analysis methods are also developed for the proposed scheme to facilitate its application. Finally, extensive simulations are conducted to demonstrate the effectiveness of our method.

Decoupling control of radial 4 degree of freedom system of magnetic-liquid double suspension bearing based on generalized extended state observer.

As the novel suspension bearing, Magnetic-Liquid Double Suspension Bearing (MLDSB) is mainly supported by magnetic suspension and supplemented by a liquid hydrostatic bearing. Due to its great bearing capacity and stiffness, rapid response, great active control, and so on, MLDSB is suitable for medium speed heavy loads and has a large carrying capacity and high operating stability. In addition, the radial inertia coupling and gyroscopic coupling between radial 4-DOF control channels can reduce control precision, operation stability, and reliability of MLDSB. Therefore, a mathematical model of radial 4-DOF rotor-dynamics of MLDSB is established in this paper, and the inherent coupling mechanism is explored. Taking inertial coupling, gyroscopic coupling, and external disturbance loads as lumped disturbances, a decoupled controller based on Generalized Extended State Observer (GESO) is established. The influence of the GESO controller on the decoupling and control performance of radial 4-DOF control channels is simulated. The results indicate that the decoupling effect of the GESO controller is great. Under the action of step signal, the steady displacement, maximum displacement, adjustment time, and peak time of the rotor after decoupling are all reduced, among which the steady displacement and maximum displacement are the most obvious. Under the sinusoidal signal, the steady displacement and maximum displacement are reduced by 90%, which can effectively avoid the "gap-impact" fault. Under the pulse signal, the steady displacement, maximum displacement, adjustment time, and peak time are all reduced, among which the maximum displacement is the most obvious. The research in this paper can provide a theoretical reference for the stable support and decoupling control of MLDSB.

Generalized Active Disturbance Rejection With Reduced-Order Vector Resonant Control for PMSM Current Disturbances Suppression

A control strategy that combines a novel reduced-order vector resonant controller and a generalized active disturbance rejection control (ROVR-GADRC) is proposed in this paper to suppress the current disturbances containing periodic harmonics of permanent magnet synchronous motor (PMSM). Firstly, the ROVR controller is designed, which integrates the advantages of both the complex coefficient filter and the vector resonant controller. Compared with the existing resonant control methods, the proposed ROVR can separate and extract the positive and negative sequence harmonics, and avoid the phase delay and peak point simultaneously. Secondly, a generalized extended state observer (GESO) is introduced to enhance the suppression of low-frequency disturbance. Then, the composite control strategy is developed. Besides, the stability, disturbance rejection performance, parameters configuration, robustness and tracking performance of the proposed ROVR-GADRC are comprehensively analyzed. The proposed current controller simultaneously performs harmonics suppression of specific phase sequence and other unknown disturbances attenuation. Finally, the feasibility and effectiveness of the proposed method is verified on a PMSM platform through the experimental results.

Generalized-Extended-State-Observer and Equivalent-Input-Disturbance Methods for Active Disturbance Rejection: Deep Observation and Comparison

Active disturbance-rejection methods are effective in estimating and rejecting disturbances in both transient and steady-state responses. This paper presents a deep observation on and a comparison between two of those methods: the generalized extended-state observer (GESO) and the equivalent input disturbance (EID) from assumptions, system configurations, stability conditions, system design, disturbance-rejection performance, and extensibility. A time-domain index is introduced to assess the disturbance-rejection performance. A detailed observation of disturbance-suppression mechanisms reveals the superiority of the EID approach over the GESO method. A comparison between these two methods shows that assumptions on disturbances are more practical and the adjustment of disturbance-rejection performance is easier for the EID approach than for the GESO method.

A Backstepping Controller Based on a Model-Assisted Extended State Observer for a Slice Rotor Supported by Active Magnetic Bearings

To improve the robustness of a slice rotor system supported by active magnetic bearings (AMBs), here, we propose a backstepping controller based on a model-assisted extended state observer (MESO-BC). Based on a generalized extended state observer (GESO), a model-assisted extended state observer is studied with consideration of the linear model of AMBs. The model-assisted extended state observer can estimate the unknown disturbances of the active magnetic bearing system, such as model inaccuracy and external disturbance, and is superior to the generalized extended state observer with respect to observation errors and the speed of convergence errors. In addition, it is compared with the backstepping controller based on a generalized extended state observer (GESO-BC) and conventional adaptive backstepping controller (ABC), and the simulation and experimental results verify the effectiveness of the proposed method. The experimental results demonstrate that the overshoot of the MESO-BC decrease by 5.94% and 13.2% as compared with the GESO-BC and ABC under the effect of pulse disturbance, respectively, and the rotor displacement of the MESO-BC reduce by 40.3% and 54.6% as compared with the GESO-BC and ABC under the effect of the sinusoidal disturbance, respectively.

Generalized Extended State Observer-Based Distributed Attack-Resilient Control for DC Microgrids

Due to the attack signal injection on the DC microgrid system, voltage regulation and current sharing cannot be guaranteed and the overall system may even be destabilized. To solve this problem, a generalized extended state observer (GESO)-based distributed attack-resilient control method is proposed for DC microgrids in this paper. The presented control scheme can detect and mitigate the unknown dc/low-frequency/grid-frequency attack signals while achieving voltage regulation and accurate current sharing among distributed generation (DG) units. In addition, benefiting from employing the proposed distributed control strategy, the information exchange among the DG units is updated in an aperiodic way. As a result, the communication burden of the DC microgrid communication network can be greatly reduced. The stability of the proposed method is verified by the Lyapunov function, and no Zeno behavior will exist. Finally, the experimental results are illustrated to validate the effectiveness of the proposed approach.

Novel resilient compensator design for FDI attack mitigation on AGC system

ABSTRACT For proper functioning and stability of a power system, it is of utmost importance that the system frequency is kept within permitted operating limits using the Automatic Generation Control (AGC) else stability is compromised. This may lead to disruption of system operation and/or damage of the power grid equipment. The AGC system must be protected against false data injection (FDI) attacks as the information required by AGC is transmitted to the control centre by the means of communication links which are vulnerable against cyber-attacks. Hence, to overcome this issue a Generalized Extended State Observer (GESO) based resilient sliding mode compensator is developed in this paper. GESO is used for the purpose of detecting FDI attacks against the AGC system. In order to mitigate the effect of the FDI attack in the system, sliding mode compensator is utilised. It not only mitigates the effect of attacks but also allows the control centre to make its decision based on the uncompromised sensor signals instead of the compromised signals. The proposed method is subjected to a variety of FDI attacks and the simulation results confirm its competency to successfully detect, estimate and compensate for FDI attacks regardless of the effect of AGC nonlinearities.

Sliding Mode Controller with Generalized Extended State Observer for Single Link Flexible Manipulator

This paper presents an enhanced generalized extended state observer (EGESO) based sliding mode control (SMC) technique for dealing with the disturbance attenuation problem for a class of non-integral chain systems with mismatched uncertainty. In the proposed control law, the robust SMC with reaching phase elimination is applied in the proposed control law, which uses the estimated states of a system. The stability analysis is thoroughly examined for both EGESO and SMC. The efficacy of the proposed controller is verified using specific examples, and later it is applied on a single-link flexible manipulator. Through simulation and experimentation analysis, it is observed that the proposed controller is giving a robust transient response as compared to existing GESO based controllers.

Composite fault-tolerant and anti-disturbance control for switched fuzzy stochastic systems

This paper investigates the issue of fault-tolerant and anti-disturbance attenuation for a two-dimensional modified repetitive control system (2D MRCS) which is described by switched fuzzy systems with multiple disturbances. In particular, the multiple disturbances contain an exogenous disturbance and standard Wiener noise. Specifically, a generalized extended state observer (GESO) is incorporated with the 2D MRCS to estimate both fault and exogenous multiple disturbances so that the disturbances and faults can be attenuated in the control input. Further, the improved 2D MRCS relaxes the stability condition and provides an enhanced tracking performance. Based on the Lyapunov function approach, pole placement technique and average dwell time approach, the stability criteria for the considered system is developed in terms of linear matrix inequality (LMI). Then an algorithm for designing a GESO-based 2D MRC design is developed based on the obtained LMIs. Further, the results developed are validated in the simulation section through three numerical examples.

Load Frequency Control for Power System using Generalized Extended State Observer

This study investigates load frequency control based generalized extended state observer (GESO) for interconnected power systems subject to multi-kind of the power plant. First, the mathematical model of the interconnected power system is proposed based on the dynamic model of thermal power plant with reheat turbine and hydropower plant. Second, the GESO is designed to estimate the system states and disturbances. In addition, the problem of unmeasurable system states in the interconnected power network due to lack of sensor has been solved by using the proposed load frequency control based GESO. The numerical experiments are carried out by using MATLAB/ SIMULINK simulation. The simulation results point out that the proposed control approach has the capacity to handle the uncertainties and disturbances in the interconnected power system with better transient performances in comparison with the existing control approach. The relevant dynamic models have already been used for the simulation of the physical constraints of the governor dead band (GDB) and generation rate constraint (GRC) effect in the power plants. It is evident that the robustness of the suggested controller in terms of stability and effectiveness of the system. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Counteractive control against cyber‐attack uncertainties on frequency regulation in the power system

In this study, an observer based control strategy is proposed for load frequency control (LFC) scheme against cyber-attack uncertainties. Most of research work focused on detection scheme or delay estimation scheme in presence of cyber-attack vulnerabilities and paid less attention on design of counteractive robust control scheme for LFC problem. Thus, observer based control scheme is designed here and provides robust performance against unknown input attack uncertainty and communication time-delay attack uncertainty. The generalized extended state observer (GESO) is used not only for state and disturbance estimation but also for disturbance rejection of the system. The said observer ensures accurate estimation of the actual states leading to convergence of estimation error to zero. So, the observer based linear quadratic regulator (LQR) is used to regulate the closed-loop damping ratio against cyber-attack uncertainty. In addition to fast response in terms of settling time and reduced over/undershoots, the proposed control scheme satisfactorily compensates the cyber-attack uncertainties in power system cyber physical networks and also compared with existing traditional PI and PID controllers. The simulation results demonstrate the robustness in terms of stability and effectiveness in terms of system security with proposed controller when subjected to cyber-attack uncertainties and load disturbances.

Low Impedance-Guaranteed Gain-Scheduled GESO for Torque-Controlled VSA With Application of Exoskeleton-Assisted Sit-to-Stand

This article investigates a closed-loop torque-controlled variable stiffness actuator (VSA) combined with a disturbance observer for enhancing low output impedance. We implement the generalized extended state observer (GESO) for conveniently testing the stability of the time-varying VSA system. In our application, the GESO is also required to serve the operation of the low- and high-impedance task. Here, the most important aspect is to consider the influence of the physical stiffness on the output impedance, because the VSA has been regulated with the closed-loop torque control. Through the interaction-torque experiments, we verify that using the fast dynamics GESO with the low-stiffness actuator can achieve low output impedance and stable interaction under the reachable frequency of a human. These properties contribute to perform the low-impedance task. When performing the high-impedance task, where a large torque command is needed, the high-stiffness actuator and the slow dynamics GESO are implemented to achieve high bandwidth and proper tracking performance. The continuously variable observer responses in accordance with the stiffness values are achieved via the gain-scheduling control. Moreover, the present closed-loop linear parameter varying system can be verified to be quadratically stable. The VSA system is then implemented on a knee exoskeleton for a sit-to-stand application. The reference command of the exoskeleton is a joint torque, calculated from the inverse dynamics. This torque signal is also used as the reference command of the stiffness motor of the VSA. The effectiveness of the exoskeleton system is experimentally verified with one healthy volunteer. Subsequently, another two healthy volunteers also successfully experienced the system.

Adaptive sliding mode control based on a combined state/disturbance observer for the disturbance rejection control of PMSM

An improved adaptive sliding mode controller (ASMC) based on a combined state/disturbance observer (CSO) is proposed for the high-performance control of permanent magnet synchronous motor (PMSM). In order to estimate the unknown state and the disturbance including the parameter uncertainty and the external disturbance, the CSO is proposed. Different from the extended state observer (ESO) or generalized ESO (GESO), the CSO uses the linear combination of the extended high-order states to construct the new estimation. The CSO resolves the contradiction between the estimation accuracy and the noise insensitivity, so it is more applicable to time-varying disturbances. Then, the CSO and the ASMC are integrated in the PMSM speed controller by the feed-forward compensation to enhance the system robustness. A simple nonlinear adaptive law is presented to solve the unknown upper bound of the estimation error and minimize the chattering. The theoretical analysis shows that the global stability of the closed-loop system is strictly guaranteed. The simulation and experimental results are presented to demonstrate the effectiveness of the proposed control method.

Generalized-extended-state-observer-based Repetitive Control for DC Motor Servo System with Mismatched Disturbances

This paper presents a generalized-extended-state-observer (GESO)-based repetitive control (RC) method for a direct-current motor servo system (DCMSS) subject to parameter perturbation and load torque variation, which are mismatched. A GESO is constructed to estimate the lumped disturbance in real time fashion. Incorporating the estimate into a state-feedback RC law yields a composite controller with a dynamical compensation gain, which ensures that the suppression of the mismatched total disturbance and the tracking of periodic signal are achieved simultaneously. The stability criterion and design procedure of the system are developed. Finally, simulation results show that the GESO-RC based DCMSS effectively eliminates the influences on the output of the parameter variation and the load disturbance and has both satisfactory dynamical performance and robustness. Comparisons with conventional PID control, PID-RC, and standard extended-state-observer based RC demonstrate the superiority of this method.

Modified GESO based Control for Systems with Sinusoidal Disturbances

This work addresses the problem of handling sinusoidal disturbances by proposing a modified Generalized Extended State Observer (GESO) designated as Higher order GESO (HGESO). The HGESO simultaneously estimates the mismatched disturbances along with their derivatives and matched disturbance. This work basically analyzes and extends the work in Li et al. (2012) for the generalized nth order system where a GESO based Control (GESOBC) is proposed for handling a constant type of mismatched disturbance only. The practical stability of the overall system in HGESO is proved and the results are verified through simulation of an illustrative example.

Wind Field Disturbance Analysis and Flight Control System Design for a Novel Tilt-Rotor UAV

The wind field has a great influence on the control stability of Tilt-rotor unmanned aerial vehicle (UAV), especially during the take-off and landing phase. The airspeed of UAV is so small during these phases that it cannot generate stable aerodynamic forces, which will significantly reduce the wind robustness of Tilt-rotor UAV. In this article, the disturbance of wind field is analyzed from two perspectives: the wind field acting on the UAV fuselage, which is regarded as external interference, and the wind acting on the propeller, which is considered as modeling error. After analyzing the interference mechanism of wind field, a generalized extended state observer (GESO) and a $H\infty $ robust control method with mixed sensitivity are proposed, which could empower the Tilt-rotor UAV with good interference suppression ability as well as better performance tracking ability. Finally, the laboratory simulation and flight experiment are studied. The results validate the theory and prove that the proposed method could resist the interference of wind field and shows excellent control effect.

GESO-Based Position Synchronization Control of Networked Multiaxis Motion System

This paper studies the position synchronization control problem for networked multiaxis motion systems (NMAMSs). First, a position synchronization error model is established for the multiaxis motion system, and the uncertainty induced by the network-induced delay is modeled as an additive disturbance of the system. Second, the delay-induced uncertainty and the external disturbances such as load torque variation are lumped together as a total disturbance in the system model. Based on the established position synchronization error model, a generalized extended state observer (GESO) is designed to estimate the lumped disturbance and system states simultaneously. Then, the GESO-based synchronization controller is designed to achieve the objective of position synchronization and disturbance rejection, and the effect of the network-induced delay in the synchronization performance is significantly reduced. Moreover, an input-to-state stability condition is presented for the position synchronization system. Finally, experiments on a four-motors position synchronization control platform are presented to demonstrate the effectiveness and superiority of the proposed method.

Generalized extended state observer–based repetitive control for systems with mismatched disturbances

SummaryA generalized extended state observer (GESO) is devised to improve the disturbances rejection performance in a repetitive‐control system (RCS) for a class of single‐input, single‐output nonlinear plants with nonintegral chain form and mismatched disturbances. By appropriately choosing a disturbance compensation gain and incorporating the disturbance estimate into a repetitive control law, a GESO‐based RCS is established. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of the disturbance compensation into the control input enables attenuating the lumped disturbance from the system output. Stability criteria and design algorithms have been developed for the system. A case study on the speed control of a rotational control system exhibits that the GESO‐based RCS delivers not only a promising disturbance rejection performance but also a superior property of tracking performance.

Robust disturbance rejection for repetitive control systems with time‐varying nonlinearities

SummaryThis paper presents a disturbance‐rejection method for a modified repetitive control system with a nonlinearity. Taking advantage of stable inversion, an improved equivalent‐input‐disturbance (EID) estimator that is more relaxed for system design is developed to estimate and cancel out the influence of the disturbance and nonlinearity in the low‐frequency domain. The high‐frequency influence is filtered owning to the low‐pass nature of the linear part of the closed‐loop system. To avoid the restrictive commutative condition and choose a Lyapunov function of a more general form, a new design algorithm, which takes into account the relation between the feedback control gains and the observer and improved EID estimator gains, is developed for the nonlinear system. Furthermore, comparisons with the generalized extended‐state observer (GESO) and conventional EID methods are conducted. A clear relation between the developed estimator and the GESO is also clarified. Finally, simulations show the effectiveness and the advantage of the developed method.