Performance comparison of SO and ESO based RC

This paper considers the path following problem of underactuated marine surface vessel in the presence of model uncertainty and external disturbances. A robust control strategy is proposed by employing the dynamic surface control and extended state observer. The key features of the presented control strategy include that, first, the extended state observer is proposed to estimate the model uncertainty and external disturbances of the underactuated marine surface vessel; second, in order to avoid the calculation of derivatives of virtual control signals, the dynamic surface control is used to design the robust control laws based on the output of the extended state observer. All regular paths are feasible by introducing the Serret-Frenet Line-of-Sight guidance. Uniformly ultimately bounded can be obtained based on the proposed control strategy by using Lyapunov theory. Simulation results demonstrate the effectiveness of the proposed control strategy.

The pitching axis is the main axis of a satellite camera and is used to control the pitch posture of satellite cameras. A control strategy based on extended state observer (ESO) is designed to obtain a fast response speed and highly accurate pitching axis control system and eliminate disturbances during the adjustment of pitch posture. First, a sufficient condition of stabilization for ESO is obtained by analyzing the steady-state error of the system under step input. Parameter tuning and disturbance compensation are performed by ESO. Second, the ESO of speed loop is designed by the speed equation of the pitching axis of satellite cameras. The ESO parameters are obtained by pole assignment. By ESO, the original state variable observes the motor angular speed and the extended state variable observes the load torque. Therefore, the external load disturbances of the control system are estimated in real time. Finally, simulation experiments are performed for the system on the cases of nonload starting, adding external disturbances on the system suddenly, and the load of system changing suddenly. Simulation results show that the control strategy based on ESO has better stability, adaptability, and robustness than the PI control strategy.

This paper presents an extended state observer (ESO) based repetitive control (RC) to compensate periodic signals, aperiodic disturbances, and uncertainties of the plant with relative degree equal to or greater than zero. Since linear ESO has only two tuning parameters, the proposed controller provides a simple and user friendly solution to complex engineering problems in practice. Moreover, due to the model free approach of a ESO-based control, it can be applied to a wide variety of plants. The design procedures are proposed to ensure a stable system. Various types of disturbances are used in simulations and experiments which show that the ESO-based RC cannot only reject periodic and aperiodic disturbances but also handle the plant parameter uncertainty. The comparison studies demonstrate that the ESO-based RC has superb performance.

The achievable performance of the piezo-actuated nano-positioning stages is severely limited by the intrinsic nonlinearities of the actuators, the lightly damped resonant mode of the flexure-hinge mechanism, and the external disturbances. To overcome all these limitations, this paper presents a novel robust dual-loop control scheme with a Kalman filter-based extended state observer and H∞ control for nano-positioning stages to implement high-bandwidth tracking operations. In this scheme, the extended state observer (ESO) is first developed and assisted by the identified system model to estimate both the system states and total disturbances, where the estimated disturbance is compensated by the direct feedback. In particular, to further improve the estimation performance, the Kalman filter is thus incorporated into the ESO to optimize the observer gain. Then, the state-feedback-based inner-loop controller is designed via the pole-placement method to damp the resonant mode of nano-positioning stages. Finally, a H∞ robust controller is adopted in the outer-loop to eliminate the influence resulting from the external disturbances, nonlinearities, and unmodeled dynamics on tracking operations. To validate the effectiveness of the proposed approach, comparative experiments are conducted on a piezo-actuated nano-positioning stage. Experimental results demonstrate that the proposed control scheme improves the control bandwidth of the system from 3.6 kHz (the stand-alone H∞ controller) to 5.52 kHz, which is 93.5% of the first resonant frequency of the original system. Moreover, it shows excellent robustness against the variation of system dynamics due to the change in the mounted mass and the external disturbances.

Load Frequency Control (LFC) is critical for ensuring stable operation of power systems, especially under diverse operating conditions. Within the analyzed single-area power network, the area control error (ACE) has been effectively managed despite uncertainties in system dynamics and the presence of external disturbances. The most recent study on disturbance rejection mechanisms has revealed that Active Disturbance Rejection Control (ADRC) is an effective controller for controlling uncertainty in systems, whether the system is linear or nonlinear. The importance of the ADRC controller resides in its model-free nature, that requires little understanding of the system model. The extended state observer (ESO) facilitates continuous estimation and compensation for disturbances, whether originating within the system or from external environments. However, certain process disturbances, such as time-delay, makes ADRC controller design more difficult. A solution to this problem is to use a Disturbance Observer (DO) which improves system performance. This study presents a comparative analysis of six control strategies: General Active Disturbance Rejection Control (ADRC) Controller with neglected delay, Delayed Input ADRC Controller, Smith Predictor ADRC Controller (ADRC-SP), Disturbance Observer (DO), PID (Proportional plus Integral plus Derivative) Controller, and PI (Proportional plus Integral) Controller, for their effectiveness in LFC of a single-area power system. Controllers are evaluated based on key performance metrics such as settling time, rise time, overshoot, and Integral of Absolute Error (IAE) under three scenarios: step load change, variable wind speed penetration, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$12 ~\mathrm{m} / \mathrm{s}$</tex> constant wind speed penetration. The results highlight the superior performance of the Disturbance Observer in minimizing settling time, overshoot, and Integral Absolute Error (IAE), making it the most robust and efficient controller among the evaluated strategies.

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The accuracy of the line-of-sight of aviation photoelectric optoelectronic stabilization platforms is limited by two factors: external disturbance and sensor noise. An extended state observer (ESO) can effectively improve their anti-interference ability. However, due to the serious problem of gyroscope noise, further improvement of an ESO's disturbance suppression effect is limited. This article proposes a control structure that combines a Kalman filter (KF) and ESO, effectively improving upon the interference suppression ability of a traditional ESO under the influence of noise. Firstly, an ESO was used to observe the lumped disturbance of the system, and then, the observed disturbance was compensated for in the control loop. Secondly, based on the compensation servo control system, the state equation of the system was reconstructed using a Kalman filter. Finally, the reconstructed filtered state variables were iterated onto the universal state observer, achieving the observation of disturbances while filtering out sensor noise. Under the conditions of a laboratory flight simulation turntable, the line-of-sight stability accuracy level was improved under disturbance excitation. It can be seen that the combination of a Kalman filter and extended disturbance observer proposed in this project improves the ESO's anti-interference ability under the influence of noise.

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

This paper proposes a new type of extended state observer (ESO) for state observation of nonlinear system with measurement noise. ESO can observe the inner and outer disturbance of uncertain system and it is the foundation of active disturbance-rejection controller, while the measurement noise degrades the performance of the normal ESO. In this paper, fal function feedback structure is used to deal with measurement noise, then ESO is applied, thus their combination can eliminate the effect of measure noise on ESO. Comparing with the method of extending a rank state to ESO and the method of extending the filter equation to ESO, this new method does not need to extend the rank of ESO. So the tracking error increasing problem and the parameter tuning problem which are brought by the rank increase of ESO can be avoided. The simulation results shows that this method can satisfactorily track states for system with measurement noise.

Electro-hydraulic position servo system of valve-controlled symmetrical cylinder (EPSSVCS) is a very important and widely used electro-hydraulic servo system, the performance of which is often affected by friction nonlinearity and external random disturbances together with unmodeled dynamic factors such as parameter uncertainty in practical work. To improve the tracking performance of the system, a backstepping sliding mode control algorithm (BSMC) based on an extended state observer was presented in this paper. Firstly, a nonlinear mathematical model of the EPSSVCS was established which takes into account the composite disturbance induced by the systematic friction nonlinearity, external disturbances and unmodeled dynamic factors. Then, an extended state observer (ESO) was designed which can effectively estimate the velocity, acceleration, and composite disturbance of the valve-controlled cylinder online. Furthermore, a kind of BSMC was presented based on the online ESO estimates and the displacement feedback signals. The control law was given and the system stability was proved. The analysis results showed that the output signal of the system can effectively track the input signal under the influence of typical external disturbances and unmodeled dynamic factors, which illustrated the effectiveness of the established nonlinear mathematical model and the stability of the designed control system. Moreover, by taking the parameters of the electro-hydraulic servo system of a certain type of CNC machine tool as a real example, the proposed algorithm (BSMC) was compared with the conventional PID control algorithm, the backstepping sliding mode control algorithm (BSC), and the adaptive robust control algorithm (ARC), and the results verified the superiority of the BSMC. This work may provide a useful reference for the research in the field of related control systems.

This study addresses the limitations inherent in the traditional Extended State Observer (ESO) within the Active Disturbance Rejection Control (ADRC) framework, specifically targeting issues such as large observation errors, low accuracy, and significant overshoot in estimating the total angular velocity perturbation of torque motors. To overcome these challenges, a Fractional-Order Extended State Observer (FOESO) is proposed. This observer utilizes a novel nonlinear function with improved smoothness and continuity near the origin to enhance observation precision. Furthermore, Repetitive Control (RC), based on the internal model principle, is introduced to mitigate periodic errors and further refine accuracy. By integrating the high-precision estimation of the FOESO with the periodic disturbance rejection of the RC, a composite strategy termed Repetitive Control and Fractional-Order Active Disturbance Rejection Control (RC-FOADRC) is developed. This strategy upgrades the conventional ADRC architecture to achieve stable, high-precision system state observation with minimal error. Experimental analysis targeting the angular velocity of a torque motor validates the effectiveness and feasibility of the proposed RC-FOADRC strategy compared to traditional methods.

Robust tracking control for vehicle electronic throttle using adaptive dynamic sliding mode and extended state observer

This article investigates the spacecraft attitude reorientation control problem in the presence of attitude constraint, actuator saturation, parametric uncertainty, and external disturbance. First, a nonlinear tracking law based on a strictly convex potential function is proposed to generate the virtual control angular velocity which has only one global minimum. Then, utilizing the auxiliary system governed by the difference between the upper bound of actuator torque and the untreated command torque, a novel backstepping controller is presented, which is able to satisfy the constraint of actuator saturation and guarantee the stability of control system. In addition, an extended state observer with the uniformly ultimately bounded estimation error and finite-time stability is put forward to realize the real-time compensation of the compound disturbance consisting of parametric uncertainty and external disturbance. Therefore, it enhances the robustness and improves the accuracy of the extended state observer–based backstepping controller. Finally, simulation results validate the effectiveness and reliability of the proposed schemes.

A new design method of the repetitive control system for linear systems with time-varying norm-bounded uncertainties is presented, which can design a low-pass filter of the repetitive controller and a stabilizing controller simultaneously in the repetitive control system. Using a Lyapunov functional for the repetitive control system, sufficient conditions are derived in terms of a linear matrix inequality (LMI), which ensure robust stability of the repetitive control system and achieve the prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance. Based on derived conditions, the problem of designing a stabilizing controller and finding the cut-off frequency of a low-pass filter is reformulated as an optimization problem with an LMI constraint of the free parameter. Then, an iterative algorithm is presented to calculate the largest cut-off frequency of a low-pass filter and design the corresponding state-feedback controller simultaneously. A numerical example is presented to illustrate the validity of the proposed method.

An anti-windup compensate algorithm for active disturbance rejection mechanism is proposed in this paper. This paradigm extends the traditional anti-windup scheme to the Active Disturbance Rejection Control (ADRC) mechanism, to deal with the input saturation nonlinearity and meanwhile reject the disturbance automatically by using Extended State Observer (ESO) . The output of anti-windup compensator is treated as a part of unknown disturbances and is introduced into the ESO, which can online observe both internal and external disturbances (parameter uncertainties and model mismatches). The controller input is yielded by using a nonlinear feedback combination, and it is used to compensate the integrator windup caused by the saturation nonlinearity element. On the other hand, in order to determine the parameters of the ESO and the anti-windup compensator feedback gain, the ℒ 2 gain is adopted. The effectiveness and the robustness against model and parameter uncertainties of the proposed method is verified by an example of the seeker platform.