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Journal articles on the topic 'Extended state observers'

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Published: 2 June 2025

Last updated: 19 July 2025

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Ali, Jarinah Mohd, and M. A. Hussain. "Artificial Intelligence Based State Observer in Polymerization Process." ASEAN Journal of Chemical Engineering 13, no. 2 (2014): 50. http://dx.doi.org/10.22146/ajche.49731.

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Observers or state estimators are devices used to estimate immeasurable key parameters that are due to noise, disturbances and mismatch. It is important to identify those variables prior to construct a control system and avoid fault or process disruption. In certain chemical processes, such observer usage produced unsatisfactory results therefore hybrid approached is the appropriate solution. Hybrid observers are combination of two or more conventional observers mainly to enhance the estimator’s performance and overcoming their limitations. In advanced cases, Artificial Intelligence algorithm is applied. This paper develops two hybrid observers namely sliding mode and extended Luenberger observers with fuzzy logic for approximating the monomer concentration in a polymerization reactor. It was found that the sliding mode observer- fuzzy combination is better based on noise handling with less oscillation.

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Martínez-García, Edgar Alonso, Joaquín Rivero-Juárez, Luz Abril Torres-Méndez, and Jorge Enrique Rodas-Osollo. "Divergent trinocular vision observers design for extended Kalman filter robot state estimation." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 233, no. 5 (2018): 524–47. http://dx.doi.org/10.1177/0959651818800908.

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Here, we report the design of two deterministic observers that exploit the capabilities of a home-made divergent trinocular visual sensor to sense depth data. The three-dimensional key points that the observers can measure are triangulated for visual odometry and estimated by an extended Kalman filter. This work deals with a four-wheel-drive mobile robot with four passive suspensions. The direct and inverse kinematic solutions are deduced and used for the updating and prediction models of the extended Kalman filter as feedback for the robot’s position controller. The state-estimation visual odometry results were compared with the robot’s dead-reckoning kinematics, and both are combined as a recursive position controller. One observer model design is based on the analytical geometric multi-view approach. The other observer model has fundamentals on multi-view lateral optical flow, which was reformulated as nonspatial–temporal and is modeled by an exponential function. This work presents the analytical deductions of the models and formulations. Experimental validation deals with five main aspects: multi-view correction, a geometric observer for range measurement, an optical flow observer for range measurement, dead-reckoning and visual odometry. Furthermore, comparison of positioning includes a four-wheel odometer, deterministic visual observers and the observer–extended Kalman filter, compared with a vision-based global reference localization system.

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Humaidi, Amjad J. "Experimental Design and Verification of Extended State Observers for Magnetic Levitation System Based on PSO." Open Electrical & Electronic Engineering Journal 12, no. 1 (2018): 110–20. http://dx.doi.org/10.2174/1874129001812010110.

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Introduction: This work presents analysis, design and implementation of two schemes of Extended State Observer (ESO) to estimate the position, velocity and unmeasurable states for magnetic levitation systems, Linear ESO (LESO) and Nonlinear ESO (NESO). The multiplicity of design parameters for both LESO and NESO made it difficult to find appropriate setting of these parameters such that to reach satisfactory performance of observation process. Methods: Particle Swarm Optimization (PSO) technique is used to improve performance of observation process by finding optimal tuned parameters of observer design parameter subjected to specified performance index. Theoretical results of both observers are firstly implemented in the environment of MATLAB/SIMULINK. Then, experimental state estimation of observers is set up based on feedback instrument (33-942S) to verify the simulated results. Results and Conclusion: Root Mean Square (RMS) of estimation error has been used as an indicator to assess the performance of observers. The simulated and practical results showed that LESO could give better estimation performance than NESO.

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Gu, Nan, Dan Wang, Zhouhua Peng, Jun Wang, and Qing-Long Han. "Disturbance observers and extended state observers for marine vehicles: A survey." Control Engineering Practice 123 (June 2022): 105158. http://dx.doi.org/10.1016/j.conengprac.2022.105158.

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Liu, Jiahao, Zhiqiang Zeng, Shangyao Shi, and Pengyun Chen. "Internal Model Principle-Based Extended State Observer for the Uncertain Systems with Nonconstant Disturbances." Actuators 13, no. 1 (2024): 29. http://dx.doi.org/10.3390/act13010029.

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Existing traditional expansion state observers exhibit good tracking performance for constant and low-frequency disturbances. However, their ability to track non-constant disturbances such as ramp and high-frequency harmonics is inadequate. This paper proposes an extended state observer design method based on the internal model principle. This method achieves precise tracking of non-constant disturbances in the system, effectively addressing the issue of disturbance estimation errors in conventional expansion state observers. When applied to control systems, this approach significantly mitigates or suppresses system vibrations caused by non-constant disturbances, thereby enhancing control accuracy. Furthermore, it demonstrates the stability of the controlled system and the active disturbance rejection controller parameters over a wide range of variations. Simulation results indicate that the ADRC controller based on the proposed observer in this paper offers notable advantages, including high tracking accuracy, strong disturbance rejection capability, and good stability, leading to commendable control performance.

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Zárate-Castrejón, José Luis, Pablo A. López-Pérez, Milagros López-López, et al. "Estimation of Sporulated Cell Concentration of Bacillus thuringiensis in a Batch Biochemical Reactor via Simple State Observers." Mathematics 12, no. 24 (2024): 3996. https://doi.org/10.3390/math12243996.

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This paper presents a contrast of two different observation strategies viz a nonlinear observer and a classical extended Luenberger observer applied to a bioreactor system for Bacillus thuringiensis production. The performance of the two observers was evaluated under different conditions, both with and without state perturbations. Firstly, equal initial conditions were considered without the presence of white noise in the measurement of dissolved oxygen concentration in the culture medium. The performance was then analyzed by perturbing the maximum cell growth rate with equal and different initial conditions, and, finally, the performance of the observer with the presence of white noise was evaluated. The proposed observer performed better than the extended Luenberger observer against initial conditions different from the model. The results of this study are of great interest, as they provide insight into the estimation of the state of the dynamics for the B. thuringiensis bioreactor in a batch mode. In addition, these results provide valuable information for future research in the design of observers for B. thuringiensis bioprocessing.

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Parada, Ricardo P., A. Tadeo Espinoza, Alejandro E. Dzul, and Francisco G. Salas. "Performance analysis of nonlinear observers applied to the fixed-wing unmanned aerial vehicles flight under decoupled-reduced model." International Journal of Micro Air Vehicles 9, no. 2 (2017): 111–23. http://dx.doi.org/10.1177/1756829317702673.

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In this paper, we present the design and implementation of two nonlinear observers: nonlinear extended state observer and sliding mode observer for estimating the pitch, yaw and roll angles and angular rates of a fixed-wing unmanned aerial vehicles system under a decoupled-reduced model in real flight experiments. A backstepping control law is designed for control in a decentralized way for altitude, yaw and roll of the airplane. This scheme allows us to test experimentally the feasibility of using the online estimated data from the observers in flight control, which is useful for increasing the robustness of the control and the safety of flight. Furthermore, a comparative analysis of the performance of both nonlinear observers is conducted.

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Siket, Máté, György Eigner, Dániel András Drexler, Imre Rudas, and Levente Kovács. "State and Parameter Estimation of a Mathematical Carcinoma Model under Chemotherapeutic Treatment." Applied Sciences 10, no. 24 (2020): 9046. http://dx.doi.org/10.3390/app10249046.

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One challenging aspect of therapy optimization and application of control algorithms in the field of tumor growth modeling is the limited number of measurable physiological signals—state variables—and the knowledge of model parameters. A possible solution to provide such information is the application of observer or state estimator. One of the most widely applied estimators for nonlinear problems is the extended Kalman filter (EKF). In this study, a moving horizon estimation (MHE)-based observer is developed and compared to an optimized EKF. The observers utilize a third-order tumor growth model. The performance of the observers is tested on measurements gathered from a laboratory mice trial using chemotherapeutic drug. The proposed MHE is designed to be suitable for closed-loop applications and yields simultaneous state and parameter estimation.

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Proietti, Massimiliano, Alexander Pickston, Francesco Graffitti, et al. "Experimental test of local observer independence." Science Advances 5, no. 9 (2019): eaaw9832. http://dx.doi.org/10.1126/sciadv.aaw9832.

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The scientific method relies on facts, established through repeated measurements and agreed upon universally, independently of who observed them. In quantum mechanics the objectivity of observations is not so clear, most markedly exposed in Wigner’s eponymous thought experiment where two observers can experience seemingly different realities. The question whether the observers’ narratives can be reconciled has only recently been made accessible to empirical investigation, through recent no-go theorems that construct an extended Wigner’s friend scenario with four observers. In a state-of-the-art six-photon experiment, we realize this extended Wigner’s friend scenario, experimentally violating the associated Bell-type inequality by five standard deviations. If one holds fast to the assumptions of locality and free choice, this result implies that quantum theory should be interpreted in an observer-dependent way.

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Asiri, Sharefa, Chadia Zayane-Aissa, and Taous-Meriem Laleg-Kirati. "An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/796539.

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Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.

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TEPPA-GARRAN, P., and G. GARCIA. "REDUCED ORDER EXTENDED STATE OBSERVER WITHOUT OUTPUT DERIVATIVE IN ADRC." Latin American Applied Research - An international journal 45, no. 4 (2015): 239–44. http://dx.doi.org/10.52292/j.laar.2015.404.

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As an observer based method; the ESO in ADRC introduces more phase lag when the observer order becomes higher. The key detriment of phase lag is the reduction of loop stability. A way to decrease the phase lag is to employ a RESO. Nevertheless, the underlying disadvantage of this approach is that RESO computation depends on output derivative. To overcome this problem, the derivative of the output is usually approximated from the difference of two neighbouring output sample values. However, this approach is not convenient for two raisons. First, the use of simple differences to derive the output is another source of phase lag. Second, observers are particularly sensitive to noise and derivative gains amplify noise increasing the sensitivity of the RESO. In this work, it is employed a method to obtain a RESO that does not depend on the output derivative. It is also developed the reduced order version of the GESO.

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Azar, Ahmad Taher, Farah Ayad Abdul-Majeed, Hasan Sh Majdi, et al. "Parameterization of a Novel Nonlinear Estimator for Uncertain SISO Systems with Noise Scenario." Mathematics 10, no. 13 (2022): 2261. http://dx.doi.org/10.3390/math10132261.

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Dynamic observers are commonly used in feedback loops to estimate the system’s states from available control inputs and measured outputs. The presence of measurement noise degrades the performance of the observer and consequently degrades the performance of the controlled system. This paper presents a novel nonlinear higher-order extended state observer (NHOESO) for efficient state and disturbance estimation in presence of measurement noise for nonlinear single-input–single-output systems. The proposed nonlinear function allows a fast reconstruction of the system’s states and is robust against uncertainties and measurement noise. An analytical parameterization technique is proposed to parameterize the coefficients of the proposed nonlinear higher-order extended state observer in the case of measurement noise in the output signal. Several scenarios are simulated to demonstrate the effectiveness of the proposed observer.

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Kang, Song, Yongfeng Rong, and Wusheng Chou. "Antidisturbance Control for AUV Trajectory Tracking Based on Fuzzy Adaptive Extended State Observer." Sensors 20, no. 24 (2020): 7084. http://dx.doi.org/10.3390/s20247084.

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In this paper, an output-feedback fuzzy adaptive dynamic surface controller (FADSC) based on fuzzy adaptive extended state observer (FAESO) is proposed for autonomous underwater vehicle (AUV) systems in the presence of external disturbances, parameter uncertainties, measurement noises and actuator faults. The fuzzy logic system is incorporated into both the observers and controllers to improve the adaptability of the entire system. The dynamics of the AUV system is established first, considering the external disturbances and parameter uncertainties. Based on the dynamic models, the ESO, combined with a fuzzy logic system tuning the observer bandwidth, is developed to not only adaptively estimate both system states and the lumped disturbances for the controller, but also reduce the impact of measurement noises. Then, the DSC, together with fuzzy logic system tuning the time constant of the low-pass filter, is designed using estimations from the FAESO for the AUV system. The asymptotic stability of the entire system is analyzed through Lyapunov’s direct method in the time domain. Comparative simulations are implemented to verify the effectiveness and advantages of the proposed method compared with other observers and controllers considering external disturbances, parameter uncertainties and measurement noises and even the actuator faults that are not considered in the design process. The results show that the proposed method outperforms others in terms of tracking accuracy, robustness and energy consumption.

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PEREIRA-PINTO, FRANCISCO HEITOR I., ARMANDO M. FERREIRA, and MARCELO A. SAVI. "STATE SPACE RECONSTRUCTION USING EXTENDED STATE OBSERVERS TO CONTROL CHAOS IN A NONLINEAR PENDULUM." International Journal of Bifurcation and Chaos 15, no. 12 (2005): 4051–63. http://dx.doi.org/10.1142/s0218127405014490.

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Chaos control may be understood as the use of tiny perturbations for the stabilization of unstable periodic orbits embedded in a chaotic attractor. Since chaos may occur in many natural processes, the idea that chaotic behavior may be controlled by small perturbations of some physical parameter allows this kind of behavior to be desirable in different applications. In general, it is not necessary to have a mathematical model to achieve the control goal since all control parameters may be resolved from time series analysis. Therefore, state space reconstruction is an important task related to chaos control. This contribution analyzes chaos control performed using a semi-continuous method based on OGY approach and proposes the use of extended state observers in order to perform state space reconstruction. The use of extended state observers allows a direct application of the control method. Comparing with the delay coordinates method, extended state observers avoids the calculation of parametric changes related to delayed Poincaré sections that influence the system dynamics. The proposed procedure is applied in the control of chaos in a nonlinear pendulum, showing that it may be used to control chaos in mechanical systems.

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Wu, Nianzhe, Jianning Li, and Ju Xiong. "An Integrated Design of Course-Keeping Control and Extended State Observers for Nonlinear USVs with Disturbances." Journal of Marine Science and Engineering 13, no. 5 (2025): 967. https://doi.org/10.3390/jmse13050967.

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The integrated design problem of non-fragile controllers and extended state observers (ESOs) for nonlinear unmanned surface vehicles (USVs) under mismatched disturbances is addressed in this paper. First, an integrated model combining the USV system and the rudder system is developed, which includes a second-order underdamped system and a Norrbin nonlinear model incorporating uncertainties. Due to the coupling issues in the design of controllers and observers caused by parameter perturbations or other unmodeled dynamics, an integrated design method, which enables the simultaneous computation of controller gains, observer gains, and disturbance compensation gains, is proposed, effectively addressing these issues. Ultimately, the performance of the designed strategy is verified through a simulation, with the data used in the simulation derived from the real Qingshan USV.

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Trinh, Hoai An, Hoai Vu Anh Truong, and Kyoung Kwan Ahn. "Fault Estimation and Fault-Tolerant Control for the Pump-Controlled Electrohydraulic System." Actuators 9, no. 4 (2020): 132. http://dx.doi.org/10.3390/act9040132.

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This paper proposes a fault estimation and fault-tolerant control strategy with two observers for a pump-controlled electro-hydraulic system (PCEHS) under the presence of internal leakage faults and an external loading force. The mathematical model of the PCEHS is dedicatedly derived in the state-space form for developing control methodology. Two different observers are developed in which an extended state observer is applied to estimate the internal leakage flow rate, and a disturbance observer is used to deal with the external loading force. Then, the proposed control is designed based on the backstepping sliding mode technique in which estimated information from the observers is taken into consideration to guarantee the working performance of the system. With the proposed methodology, the robustness and stability of the controlled system are theoretically analyzed and proven by the Lyapunov theorem. Comparative simulation results are given to demonstrate the effectiveness of the proposed methodology through different testing conditions.

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Chen, Hua, Huilin Li, YiWen Yang, and Lulu Chu. "Fixed-time output tracking control for extended nonholonomic chained-form systems with state observers." Measurement and Control 53, no. 3-4 (2020): 400–408. http://dx.doi.org/10.1177/0020294019877519.

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This paper deals with the fixed-time tracking control problem of extended nonholonomic chained-form systems with state observers. According to the structure characteristic of such chained-form systems, two subsystems are considered to design controllers, respectively. First of all, using the fixed-time control theory, a controller is proposed to make the first tracking error subsystem converge to zero in bounded time independent initial state. Second, a state observer is proposed to estimate the unmeasurable states of the second subsystem. And the precise state estimation can be presented from the observer within finite time; moreover, the upper bound of time is a constant independent on the initial estimation error. Third, a fixed-time controller is designed to drive all states of the second chained-form subsystem to zero within pre-calculated time. Finally, the effectiveness of the proposed control scheme is validated by simulation results.

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Huba, Mikuláš, Mária Hypiusová, Peter Ťapák, and Damir Vrancic. "Active Disturbance Rejection Control for DC Motor Laboratory Plant Learning Object." Information 11, no. 3 (2020): 151. http://dx.doi.org/10.3390/info11030151.

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The paper deals with learning objects for introductory modeling of simple dynamical systems and design of controllers with disturbance observer-based integral action. They can be used to illustrate the design process of state controllers, state and disturbance observers, as well as to get in touch with a popular approach called active disturbance rejection control (ADRC). In both cases, external disturbances along with errors resulting from model inaccuracies are reconstructed using the extended state observer (ESO). In addition to simulation and design of regulators and observers in Matlab/Simulink, the learning objects focus on the development of relevant terminology and competencies in the field of simulation, modeling and experimentation in traditional laboratories, with the support of LMS Moodle and remote control. The main innovativeness of the paper is to clarify the relationship of ADRC to the traditional state space controllers design and modeling by using two types of linear models approximating controlled nonlinear systems.

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Zhao, Jiaqi, Dongzhu Feng, Jiashan Cui, and Xin Wang. "Finite-Time Extended State Observer-Based Fixed-Time Attitude Control for Hypersonic Vehicles." Mathematics 10, no. 17 (2022): 3162. http://dx.doi.org/10.3390/math10173162.

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A finite-time extended, state-observer-based, fixed-time backstepping control algorithm was designed for hypersonic flight vehicles. To enhance the robustness of the controller, two novel finite-time extended state observers were introduced to compensate for the negative effects of lumped disturbances such as uncertainties and external disturbances. Two hyperbolic sine tracking differentiators were used to approximate the derivatives of the virtual control signals and guidance commands, thereby alleviating the computational burden associated with traditional backstepping control. Furthermore, a fixed-time backstepping attitude controller was used to guarantee that the tracking errors converged to a small neighbor of the origin in fixed time. According to the simulation results, the proposed controller outperformed a fixed-time sliding mode disturbance, observer-based, finite-time backstepping controller in terms of the tracking precision and convergence rate. Moreover, the proposed controller was noted to be robust in simulations involving lumped disturbances.

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Wang, Ruiying, and Jun Shen. "Disturbance Observer and Adaptive Control for Disturbance Rejection of Quadrotor: A Survey." Actuators 13, no. 6 (2024): 217. http://dx.doi.org/10.3390/act13060217.

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Quadrotors are widely applied in many fields, but they often face various external disturbances in actual operation. This makes it necessary to design a controller that can handle disturbances. Disturbance observer and adaptive control techniques are commonly used disturbance rejection techniques, the core idea of which is to estimate the disturbances in real time and incorporate the estimated values into the controller to suppress the disturbances. In this paper, various disturbance observers and adaptive control techniques, including nonlinear disturbance observers, extended state observers, neural networks, and fuzzy logic systems, are introduced, along with their variants or different structures. These techniques improve the adaptability and robustness of quadrotors to complex environments. Finally, future research directions for the disturbance rejection of quadrotors are also presented.

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Abed, K., and H. K. E. Zine. "Intelligent fuzzy back-stepping observer design based induction motor robust nonlinear sensorless control." Electrical Engineering & Electromechanics, no. 2 (February 24, 2024): 10–15. http://dx.doi.org/10.20998/2074-272x.2024.2.02.

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Introduction. The control algorithm of Induction Motor (IM) is massively dependent on its parameters; so, any variation in these parameters (especially in rotor resistance) gives unavoidably error propagates. To avoid this problem, researches give more than solution, they have proposed Variable Structure Control (VSC), adaptive observers such as Model Reference Adaptive System, Extended Luenberger Observer (ELO) and the Extended Kalman Filter (EKF), these solutions reduce the estimated errors in flux and speed. As novelty in this paper, the model speed observer uses the estimated currents and voltages as state variables; we develop this one by an error feedback corrector. The Indirect Rotor Field Oriented Control (IRFOC) uses the correct observed value of speed; in our research, we improve the observer’s labour by using back-stepping Sliding Mode (SM) control. Purpose. To generate the pulse-width modulation inverter pulses which reduce the error due of parameters variations in very fast way. Methods. We develop for reach this goal an exploration of two different linear observers used for a high performance VSC IM drive that is robust against speed and load torque variations. Firstly, we present a three levels inverter chosen to supply the IM; we present its modelling and method of control, ending by an experiment platform to show its output signal. A block diagram of IRFOC was presented; we analyse with mathematic equations the deferent stages of modelling, showed clearly the decoupling theory and the sensorless technique of control. The study described two kinds of observers, ELO and EKF, to estimate IM speed and torque. By the next of that, we optimize the step response using the fuzzy logic, which helps the system to generate the PI controller gains. Both of the two observers are forward by SM current controller, the convergence of SM-ELO and SM-EKF structures is guaranteed by minimizing the error between actual and observed currents to zero. Results. Several results are given to show the effectiveness of proposed schemes.

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Rauh, Andreas, Saif S. Butt, and Harald Aschemann. "Nonlinear state observers and extended Kalman filters for battery systems." International Journal of Applied Mathematics and Computer Science 23, no. 3 (2013): 539–56. http://dx.doi.org/10.2478/amcs-2013-0041.

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Abstract The focus of this paper is to develop reliable observer and filtering techniques for finite-dimensional battery models that adequately describe the charging and discharging behaviors. For this purpose, an experimentally validated battery model taken from the literature is extended by a mathematical description that represents parameter variations caused by aging. The corresponding disturbance models account for the fact that neither the state of charge, nor the above-mentioned parameter variations are directly accessible by measurements. Moreover, this work provides a comparison of the performance of different observer and filtering techniques as well as a development of estimation procedures that guarantee a reliable detection of large parameter variations. For that reason, different charging and discharging current profiles of batteries are investigated by numerical simulations. The estimation procedures considered in this paper are, firstly, a nonlinear Luenberger-type state observer with an offline calculated gain scheduling approach, secondly, a continuous-time extended Kalman filter and, thirdly, a hybrid extended Kalman filter, where the corresponding filter gains are computed online.

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Erazo, Christiav, Fabiola Angulo, and Gerard Olivar. "Stability analysis of the extended state observers by Popov criterion." Theoretical and Applied Mechanics Letters 2, no. 4 (2012): 043006. http://dx.doi.org/10.1063/2.1204306.

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Manin, Alexander A., Sergey V. Sokolov, Arthur I. Novikov, Marianna V. Polyakova, Dmitriy N. Demidov, and Tatyana P. Novikova. "Kalman Filter Adaptation to Disturbances of the Observer’s Parameters." Inventions 6, no. 4 (2021): 80. http://dx.doi.org/10.3390/inventions6040080.

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Currently, one of the most effective algorithms for state estimation of stochastic systems is a Kalman filter. This filter provides an optimal root-mean-square error in state vector estimation only when the parameters of the dynamic system and its observer are precisely known. In real conditions, the observer’s parameters are often inaccurately known; moreover, they change randomly over time. This in turn leads to the divergence of the Kalman estimation process. The problem is currently being solved in a variety of ways. They include the use of interval observers, the use of an extended Kalman filter, the introduction of an additional evaluating observer by nonlinear programming methods, robust scaling of the observer’s transmission coefficient, etc. At the same time, it should be borne in mind that, firstly, all of the above ways are focused on application in specific technical systems and complexes, and secondly, they fundamentally do not allow estimating errors in determining the parameters of the observer themselves in order to compensate them for further improving the accuracy and stability of the filtration process of the state vector. To solve this problem, this paper proposes the use of accurate observations that are irregularly received in a complex measuring system (for example, navigation) for adaptive evaluation of the observer’s true parameters of the stochastic system state vector. The development of the proposed algorithm is based on the analytical dependence of the Kalman estimate variation on the observer’s parameters disturbances obtained using the mathematical apparatus for the study of perturbed multidimensional dynamical systems. The developed algorithm for observer’s parameters adaptive estimation makes it possible to significantly increase the accuracy and stability of the stochastic estimation process as a whole in the time intervals between accurate observations, which is illustrated by the corresponding numerical example.

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Sandoval-Chileño, M. A., N. Lozada-Castillo, R. Cortez, A. Luviano-Juárez, and J. Vazquez-Arenas. "State of charge estimator based on tractable extended state observers for supercapacitor packs." Journal of Energy Storage 85 (April 2024): 111086. http://dx.doi.org/10.1016/j.est.2024.111086.

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Abed, K., and H. K. E. Zine. "Intelligent fuzzy back-stepping observer design based induction motor robust nonlinear sensorless control." Electrical Engineering and Electromechanics 2024, no. 2 (2024): 10–15. https://doi.org/10.20998/2074-272X.2024.2.02.

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Introduction. The control algorithm of Induction Motor (IM) is massively dependent on its parameters; so, any variation in these parameters (especially in rotor resistance) gives unavoidably error propagates. To avoid this problem, researches give more than solution, they have proposed Variable Structure Control (VSC), adaptive observers such as Model Reference Adaptive System, Extended Luenberger Observer (ELO) and the Extended Kalman Filter (EKF), these solutions reduce the estimated errors in flux and speed. As novelty in this paper, the model speed observer uses the estimated currents and voltages as state variables; we develop this one by an error feedback corrector. The Indirect Rotor Field Oriented Control (IRFOC) uses the correct observed value of speed; in our research, we improve the observer’s labour by using back-stepping Sliding Mode (SM) control. Purpose. To generate the pulse-width modulation inverter pulses which reduce the error due of parameters variations in very fast way. Methods. We develop for reach this goal an exploration of two different linear observers used for a high performance VSC IM drive that is robust against speed and load torque variations. Firstly, we present a three levels inverter chosen to supply the IM; we present its modelling and method of control, ending by an experiment platform to show its output signal. A block diagram of IRFOC was presented; we analyse with mathematic equations the deferent stages of modelling, showed clearly the decoupling theory and the sensorless technique of control. The study described two kinds of observers, ELO and EKF, to estimate IM speed and torque. By the next of that, we optimize the step response using the fuzzy logic, which helps the system to generate the PI controller gains. Both of the two observers are forward by SM current controller, the convergence of SM-ELO and SM-EKF structures is guaranteed by minimizing the error between actual and observed currents to zero. Results. Several results are given to show the effectiveness of proposed schemes.

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Shi, Di, Zhong Wu, and Wusheng Chou. "Anti-disturbance trajectory tracking of quadrotor vehicles via generalized extended state observer." Journal of Vibration and Control 26, no. 13-14 (2019): 1173–86. http://dx.doi.org/10.1177/1077546319892752.

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During the trajectory tracking process and low altitude flight of quadrotor, wind gust and ground effect will significantly affect the accuracy and stability of the controller. Therefore, it is vital for a quadrotor to have a robust controller against multiple disturbances. To mitigate this challenge, an active anti-disturbance control strategy based on generalized extended state observer is proposed in this article. Firstly, quadrotor dynamics is modeled as cascaded translational and rotational loops, and the characteristics of wind gust and ground effect are analyzed. Secondly, two generalized extended state observers are constructed for those loops respectively to estimate and attenuate the impact of wind gust and ground effect, and the position and attitude controller are designed based on backstepping method. Finally, real time experiments are carried out on hovering and circle trajectory tracking conditions. The results illustrate that the proposed controller has more advantages in high precision trajectory tracking and low altitude flight of quadrotor in existence of multiple disturbances.

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Pécute;Rez-Lozano, Rigoberto, and Rogelio Soto. "From Pole Placement Feedback to Estimator Design Using Analog Computers." International Journal of Electrical Engineering & Education 30, no. 4 (1993): 317–28. http://dx.doi.org/10.1177/002072099303000405.

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From pole placement feedback to estimator design using analog computers This paper describes analog-based control lab. simulations. Simulations deal with pole placement feedback and asymptotic observers. For asymptotic state observers, the transfer function approach is just outlined. All simulations are implemented using the state variable approach. Simulations are extended to analyze heuristic pole-placement selection and to evaluate reduced-order estimators.

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LUVIANO-JUÁREZ, ALBERTO, JOHN CORTÉS-ROMERO, and HEBERTT SIRA-RAMÍREZ. "SYNCHRONIZATION OF CHAOTIC OSCILLATORS BY MEANS OF GENERALIZED PROPORTIONAL INTEGRAL OBSERVERS." International Journal of Bifurcation and Chaos 20, no. 05 (2010): 1509–17. http://dx.doi.org/10.1142/s0218127410026654.

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The problem of synchronization of chaotic oscillators, using state observers, is handled through the use of a simplified perturbed linear integration model of the chaotic system output dynamics. The linear simplified model of the chaotic system does not entitle approximate linearizations, nor state coordinate transformations, but, simply, a pure linear integration model with additive unknown but bounded perturbation inputs lumping all the output dynamics nonlinearities. An extended linear state observer (here addressed as Generalized Proportional Integral (GPI) observer) is proposed for the accurate estimation of the phase variables and the perturbation input of the nonlinear output dynamics. The effectiveness of the approach is tested in the synchronization of two study cases: The Genesio–Tesi chaotic system and the Rossler oscillator. As an application of the estimation process, a coding–decoding process involving encrypted messages, in transmitted phase variables, is implemented using a Rossler chaotic system.

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Abbas, Ahmed H. R., Akhmedov Abdulaziz, Ahmed Hussein Alawadi, P. B. Edwin Prabhakar, Santhosh Kumar C, and Lalitkumar Wadhwa. "Advancements in Sensorless Control Techniques for Electric Drives." E3S Web of Conferences 540 (2024): 02010. http://dx.doi.org/10.1051/e3sconf/202454002010.

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This study reviews the work around the burgeoning field of sensorless control techniques in electric drives, fuelled by advances in power electronics and digital signal processing. The review categorizes these techniques into two primary approaches: methods relying on motor terminal quantities and those utilizing state observers. Terminal-based methods offer simplicity by measuring motor voltages and currents, while state observer techniques like the Extended Kalman Filter and Sliding Mode Observer provide higher accuracy through the estimation of internal motor states. Despite challenges such as parameter estimation and potential system instability, the study concludes that the benefits of sensorless control, including cost reduction and enhanced reliability, make it an increasingly vital component in the future of electric drive systems.

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Mai, Ge, Hongliang Wang, Yilin Wang, Xinghua Wu, Peiyao Jiang, and Genyuan Feng. "Nonlinear Extended State Observer and Prescribed Performance Fault-Tolerant Control of Quadrotor Unmanned Aerial Vehicles Against Compound Faults." Aerospace 11, no. 11 (2024): 903. http://dx.doi.org/10.3390/aerospace11110903.

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Addressing trajectory and attitude control challenges in quadrotor UAVs amid compound faults and unknown external disturbances, this paper introduces a fault-tolerant control method predicated on nonlinear extended state observers. Initially, the UAV’s dynamic model is optimized and decoupled, forming a rapid non-singular terminal sliding mode surface that circumvents the singular phenomena typical in conventional terminal sliding mode controls. A nonlinear extended state observer is then deployed to estimate the unknown states triggered by compound faults and disturbances within the control system. Theoretical analysis shows that beyond accurately estimating faults and disturbances, the proposed controllers adaptively adjust the system’s dynamic and steady-state performances, ensuring rapid stabilization of all error responses. Numerical simulations indicate significant enhancements in control precision and robustness against compound faults and disturbances, with response times and energy consumption remaining within acceptable limits for practical applications.

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Rojas, Harvey David, Herbert Enrique Rojas, and John Cortés-Romero. "Fault diagnosis based on algebraic identification assisted by extended state observers." Nonlinear Dynamics 107, no. 1 (2021): 871–88. http://dx.doi.org/10.1007/s11071-021-07053-3.

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Rodríguez, Antonio J., Emilio Sanjurjo, Roland Pastorino, and Miguel Á. Naya. "Multibody-Based Input and State Observers Using Adaptive Extended Kalman Filter." Sensors 21, no. 15 (2021): 5241. http://dx.doi.org/10.3390/s21155241.

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The aim of this work is to explore the suitability of adaptive methods for state estimators based on multibody dynamics, which present severe non-linearities. The performance of a Kalman filter relies on the knowledge of the noise covariance matrices, which are difficult to obtain. This challenge can be overcome by the use of adaptive techniques. Based on an error-extended Kalman filter with force estimation (errorEKF-FE), the adaptive method known as maximum likelihood is adjusted to fulfill the multibody requirements. This new filter is called adaptive error-extended Kalman filter (AerrorEKF-FE). In order to present a general approach, the method is tested on two different mechanisms in a simulation environment. In addition, different sensor configurations are also studied. Results show that, in spite of the maneuver conditions and initial statistics, the AerrorEKF-FE provides estimations with accuracy and robustness. The AerrorEKF-FE proves that adaptive techniques can be applied to multibody-based state estimators, increasing, therefore, their fields of application.

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Pu, Zhiqiang, Ruyi Yuan, Jianqiang Yi, and Xiangmin Tan. "A Class of Adaptive Extended State Observers for Nonlinear Disturbed Systems." IEEE Transactions on Industrial Electronics 62, no. 9 (2015): 5858–69. http://dx.doi.org/10.1109/tie.2015.2448060.

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Liu, Bei, Yang Yi, Hong Shen, and Chengbo Niu. "Composite observer-based integral sliding mode dynamical tracking control for nonlinear systems subject to actuator faults and mismatched disturbances." Measurement and Control 53, no. 7-8 (2020): 1309–17. http://dx.doi.org/10.1177/0020294020923077.

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This brief proposes a novel composite observer-based integral sliding mode tracking control algorithm for a class of nonlinear systems affected by both actuator faults and mismatched disturbances. First, different types of observers, including the extended state observer, the fault diagnosis observer, and the disturbance observer, are integrated to estimate the unknown system state, actuator faults, and mismatched disturbances timely. Then, in accordance with the estimation information, the integral sliding surface and the integral sliding mode controller are proposed, which can tolerate the actuator faults and reject the mismatched disturbances. Meanwhile, the state trajectories can be driven into the specified sliding surface in a finite time. Furthermore, not only the stability, but the favorable dynamical tracking and the output constraints of closed-loop augmented systems can be guaranteed. Finally, the validities of the proposed algorithm are embodied by the simulation results of typical A4D systems.

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Németh, Balázs, Tamás Hegedűs, and Péter Gáspár. "Design Framework for Achieving Guarantees with Learning-Based Observers." Energies 14, no. 8 (2021): 2039. http://dx.doi.org/10.3390/en14082039.

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The paper proposes a novel framework for state observer design, in which learning-based observers are incorporated. The aim of the method is to provide a framework, which is able to guarantee the limitation of the observation error, even if the error of the learning-based observer under all scenarios cannot be verified. The framework is based on the robust H∞ design method, which is able to provide guarantees on the resulted observer. Moreover, the observer design process is extended with a controller design, which leads to a joint robust H∞ controller-observer design. In this paper the proposed method is applied on a vehicle control problem, such as lateral path following. In this problem the goal of the observer is to provide an accurate lateral velocity signal for the vehicle, which is used in the controlled system for the generation of front wheel steering angle. The effectiveness of the method is illustrated through simulation examples on high-fidelity vehicle dynamic simulator CarMaker.

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Schimmack, Manuel, Květoslav Belda, and Paolo Mercorelli. "Sensor Fusion for Power Line Sensitive Monitoring and Load State Estimation." Sensors 23, no. 16 (2023): 7173. http://dx.doi.org/10.3390/s23167173.

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This paper deals with a specific approach to fault detection in transformer systems using the extended Kalman filter (EKF). Specific faults are investigated in power lines where a transformer is connected and only the primary electrical quantities, input voltage, and current are measured. Faults can occur in either the primary or secondary winding of the transformer. Two EKFs are proposed for fault detection. The first EKF estimates the voltage, current, and electrical load resistance of the secondary winding using measurements of the primary winding. The model of the transformer used is known as mutual inductance. For a short circuit in the secondary winding, the observer generates a signal indicating a fault. The second EKF is designed for harmonic detection and estimates the amplitude and frequency of the primary winding voltage. This contribution focuses on mathematical methods useful for galvanic decoupled soft sensing and fault detection. Moreover, the contribution emphasizes how EKF observers play a key role in the context of sensor fusion, which is characterized by merging multiple lines of information in an accurate conceptualization of data and their reconciliation with the measurements. Simulations demonstrate the efficiency of the fault detection using EKF observers.

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Sandoval-Chileño, Marco A., Luis A. Castañeda, Alberto Luviano-Juárez, Octavio Gutiérrez-Frías, and Jorge Vazquez-Arenas. "Robust State of Charge estimation for Li-ion batteries based on Extended State Observers." Journal of Energy Storage 31 (October 2020): 101718. http://dx.doi.org/10.1016/j.est.2020.101718.

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Jankowska, Kamila, Mateusz Dybkowski, Viktor Petro, and Karol Kyslan. "Classification of Speed Sensor Faults Based on Shallow Neural Networks." Applied Sciences 13, no. 12 (2023): 7263. http://dx.doi.org/10.3390/app13127263.

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This paper presents a novel speed sensor fault detection, classification, and compensation mechanism in a permanent magnet synchronous motor (PMSM) drive system. Application is based on state variable observers and shallow neural networks (NN). Classical fault detection mechanism based on state variable observers has been extended with neural networks. This enables improved detection efficiency and increases immunity to false alarms. In addition, the use of neural networks allowed for the classification of the failure type. Three types of failures are considered in the paper: signal loss, scaling error, and signal interference. The detection efficiency of the proposed solution is about 97%. On the other hand, the classification of the worst type of failure—signal loss—was achieved at the level of 100%. Other considered failure types are classified at the level of 80–90%. In addition, tests were carried out for two types of observers—model reference adaptive system and sliding mode observer—to compare the results. The work presents experimental results carried out for various operating conditions of the drive system. The failure classification times in the experimental tests were achieved at a level of less than 30 ms.

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Majid, H., and H. Abouaïssa. "Comparative Study of a Super-Twisting Sliding Mode Observer and an Extended Kalman Filter for a Freeway Traffic System." Cybernetics and Information Technologies 15, no. 2 (2015): 141–58. http://dx.doi.org/10.1515/cait-2015-0034.

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Abstract Traffic state estimation represents one of the important ingredients for traffic prediction and forecasting. The work presented in this paper deals with the estimation of traffic state variables (density and speed), using the so called Super- Twisting Sliding Mode Observer (STSM). Several numerical simulations, using simulated and real data, show the relevance of the proposed approach. In addition, a comparative study with the Extended Kalman Filter (EKF) is carried-out. The comparison indices concern convergence and stability, dynamic performance and robustness. The design of the two observers is achieved using a nonlinear second order traffic flow model in the same highway traffic and geometric conditions.

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Tatjewski, Piotr. "Disturbance modeling and state estimation for offset-free predictive control with state-space process models." International Journal of Applied Mathematics and Computer Science 24, no. 2 (2014): 313–23. http://dx.doi.org/10.2478/amcs-2014-0023.

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Abstract Disturbance modeling and design of state estimators for offset-free Model Predictive Control (MPC) with linear state-space process models is considered in the paper for deterministic constant-type external and internal disturbances (modeling errors). The application and importance of constant state disturbance prediction in the state-space MPC controller design is presented. In the case with a measured state, this leads to the control structure without disturbance state observers. In the case with an unmeasured state, a new, simpler MPC controller-observer structure is proposed, with observation of a pure process state only. The structure is not only simpler, but also with less restrictive applicability conditions than the conventional approach with extended process-and-disturbances state estimation. Theoretical analysis of the proposed structure is provided. The design approach is also applied to the case with an augmented state-space model in complete velocity form. The results are illustrated on a 2×2 example process problem.

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Zhao, Gaoyang, Weilin Zhu, Jinyuan Wang, Jianyong Yao, Hui Sun, and Ning Zhou. "Adaptive-Extended-State-Observer-Based Robust Control of Electrohydraulic Missile Launcher With Disturbances Rejection." Journal of Physics: Conference Series 2891, no. 10 (2024): 102003. https://doi.org/10.1088/1742-6596/2891/10/102003.

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Abstract In this paper, a disturbance-compensated robust controller was used for electrohydraulic missile launchers with the aim of improving the motion accuracy of the system. In the case of both matched and unmatched disturbances, adaptive extended state observers were employed in order to estimate unmodelled disturbances, external disturbances, and so forth. It was thus resolved to implement a feedforward compensation mechanism in order to counteract the effects of unknown disturbances, based on online estimates of the disturbances with the intention of enhancing the performance of the proposed controller. In addition, in order to address the problems of difficulty in obtaining the differential value of the virtual control law and “Curse of Dimensionality”, an improved first-order sliding-mode differentiator (IFOSMD) was employed. The theoretical analysis demonstrated the stability of the multi-observer and the closed-loop system under the proposed control scheme. The efficacy of the controller was demonstrated through the utilisation of numerical simulations.

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Ding, Weiwen. "A review of sensorless permanent magnet synchronous motors with adaptive observer." MATEC Web of Conferences 404 (2024): 02011. http://dx.doi.org/10.1051/matecconf/202440402011.

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With the widespread use of Permanent Magnet Synchronous Motor (PMSM) in industrial applications, sensorless PMSM has a major advantage over conventional PMSM. This work examines sensorless PMSM with adaptive observers, encompassing important methods such as the sliding mode observer (SMO), adaptive nonlinear extended state observer (ANLESO), Luenberger observer, and extended Kalman filter (EKF). These methods are investigated with the aim of achieving accurate observation and estimation of parameters such as rotor position in PMSM systems, and their effectiveness in solving the problems of insufficient torque and the high energy consumption is analyzed. The operational challenges of PMSM are briefly reviewed at the outset of this paper, and then the control strategies of the four previously stated methodologies are thoroughly described, with an emphasis on the benefits of these approaches in sensorless PMSM. The article concludes by summarising the research progress and future directions of these techniques, pointing out their potential to improve PMSM performance and stability.

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Czopek, Paweł, and Jakub Bernat. "Design and Analysis of the Model Based Control System for an MRE Axisymmetric Actuator." Electronics 12, no. 21 (2023): 4386. http://dx.doi.org/10.3390/electronics12214386.

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The magnetorheological elastomer membrane is an interesting kind of smart material that is gaining new innovative applications. This work is focused on the design of the control system for magnetorheological elastomer actuators. In general, the plant is characterized by fast oscillations and slow drift. Therefore, controllers utilize the described features to obtain the solution aimed at, which makes them unique. We analyze two approaches based on output feedback with state estimation. The control algorithms have different observers to estimate the state. The first is a Linear Extended State Observer, which is applied to reject the disturbances in a case with a simple model. The second is a Linear State Observer, which is used to estimate a state based on the plant model. Furthermore, in both cases, we have the same proportional-derivative controller after decoupling the dynamics. The main goal of the paper is to examine both controllers for the magnetorheological actuator. Therefore, the designed control systems are verified in a series of experiments.

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Liu, Anquan, Tao Li, Yu Gu, and Haohui Dai. "String Stability of Homogenous Vehicle Platoons Based on Cooperative Extended State Observers." IFAC-PapersOnLine 53, no. 2 (2020): 14432–37. http://dx.doi.org/10.1016/j.ifacol.2020.12.1442.

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Abdul-Adheem, Wameedh Riyadh, Ahmad Taher Azar, Ibraheem Kasim Ibraheem, and Amjad J. Humaidi. "Novel Active Disturbance Rejection Control Based on Nested Linear Extended State Observers." Applied Sciences 10, no. 12 (2020): 4069. http://dx.doi.org/10.3390/app10124069.

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In this paper, a Novel Active Disturbance Rejection Control (N-ADRC) strategy is proposed that replaces the Linear Extended State Observer (LESO) used in Conventional ADRC (C-ADRC) with a nested LESO. In the nested LESO, the inner-loop LESO actively estimates and eliminates the generalized disturbance. Increasing the bandwidth improves the estimation accuracy which may tolerate noise and conflict with H/W limitations and the sampling frequency of the system. Therefore, an alternative scenario is offered without increasing the bandwidth of the inner-loop LESO provided that the rate of change of the generalized disturbance estimation error is upper bounded. This was achieved by the placing of an outer-loop LESO in parallel with the inner one that estimates and eliminates the remaining generalized disturbance originating from the inner-loop LESO due to bandwidth limitations. The stability of LESO and nested LESO was investigated using Lyapunov stability analysis. Simulations on uncertain nonlinear single-input-single-output (SISO) system with time-varying exogenous disturbance revealed that the proposed nested LESO could successfully deal with a generalized disturbance in both noisy and noise-free environments, where the Integral Time Absolute Error (ITAE) of the tracking error for the nested LESO was reduced by 69.87% from that of the LESO.

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Huang, Yuan, Junzheng Wang, Dawei Shi, and Ling Shi. "Performance Assessment of Discrete-Time Extended State Observers: Theoretical and Experimental Results." IEEE Transactions on Circuits and Systems I: Regular Papers 65, no. 7 (2018): 2256–68. http://dx.doi.org/10.1109/tcsi.2017.2780161.

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Madoński, R., and P. Herman. "Survey on methods of increasing the efficiency of extended state disturbance observers." ISA Transactions 56 (May 2015): 18–27. http://dx.doi.org/10.1016/j.isatra.2014.11.008.

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Xiao, Zijian, Xiaohua Liu, Ze-Hao Wu, Pengyu Zeng, and Zhongwen Liang. "Homogeneous nonlinear event-triggered extended state observers for uncertain MIMO random systems." Communications in Nonlinear Science and Numerical Simulation 148 (September 2025): 108827. https://doi.org/10.1016/j.cnsns.2025.108827.

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Shao, Lihuan, Changfeng Zheng, Yan Zhang, Guanling Xie, Xiyu Hao, and Xiaolong Zheng. "Research on Permanent Magnet Synchronous Motor Sensorless Control System Based on Integral Backstepping Controller and Enhanced Linear Extended State Observer." Applied Sciences 13, no. 3 (2023): 1680. http://dx.doi.org/10.3390/app13031680.

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The traditional sensorless control system of permanent magnet synchronous motor (PMSM) has the problems of low estimation accuracy and poor anti-interference ability. Moreover, the position estimation performance is subjected to position harmonic ripples caused by inverter nonlinearities and flux spatial harmonics. To optimize the dynamic performance of the PMSM sensorless control system, this paper proposes a sensorless control scheme that combines integral backstepping control with enhanced linear extended state observer (ELESO). The ELESO consists of two linear extended state observers (LESOs), which estimate the internal and external disturbances of the system, to improve the estimation accuracy of rotor position. Then, the integral backstepping controller processes the estimated rotor position and speed information to obtain d and q-axis voltages. The sensorless control scheme is implemented in the Matlab/Simulink and verified by experiments. The simulation and experiment show that the scheme can effectively suppress load interference and improve control accuracy.

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