High-Precision Control of Aviation Photoelectric-Stabilized Platform Using Extended State Observer-Based Kalman Filter.

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.

The active disturbance rejection control (ADRC) extended to the fractional-order control system, fractional-order proportional–integral (PI) and proportional–integral–derivative (PID) controllers are the most commonly used controller. This paper presents a simple fractional-order control system combined with ADRC control system. By treating the fractional-order as a common disturbance and actively rejecting it, an ADRC can achieve the desired response. External disturbance, sensor noise, and parameter disturbance is also estimated using extended state observer. Simulation on ADRC fractional order model stability analyzes. The results showed that, ADRC fractional order control system object has good control performance.

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.

To regulate uncertainties in system dynamics and external disturbances, a robust controller is proposed for a plant with time-varying uncertainty. The design is based on the concept of extended state observer (ESO) with repetitive controller (RC). In real time estimation and mitigation of the total effect of various uncertainties, ESO based RC is particularly effective against a wide range of parameter variations, model uncertainties, and large disturbances. With only two tuning parameters, the controller provides a simple and user friendly solution to complex engineering problems in practice. The comparison results verified the effectiveness of the ESO based RC over state observer (SO) based RC.

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 paper proposes an extended state observer (ESO) based second-order sliding-mode (SOSM) control for three-phase two-level grid-connected power converters. The proposed control technique forces the input currents to track the desired values, which can indirectly regulate the output voltage while achieving a user-defined power factor. The presented approach has two control loops. A current control loop based on an SOSM and a dc-link voltage regulation loop which consists of an ESO plus SOSM. In this work, the load connected to the dc-link capacitor is considered as an external disturbance. An ESO is used to asymptotically reject this external disturbance. Therefore, its design is considered in the control law derivation to achieve a high performance. Theoretical analysis is given to show the closed-loop behavior of the proposed controller and experimental results are presented to validate the control algorithm under a real power converter prototype.

This paper investigates a velocity tracking control approach for air‐breathing supersonic vehicles with uncertainties and external disturbances. Considering angle of attack is difficult to be precisely measured in practice, extended state observer technique is introduced into the state reconstruction design. In order to avoid possible oscillations in the design of the traditional extended state observer (TESO), a modified extended state observer (MESO) is developed, where a new smooth function is proposed to replace nonsmooth function of TESO. On the basis of it, an active disturbance rejection controller (ADRC) is designed for velocity control systems. Simultaneously, the closed‐loop stability is rigorously proved by using Lyapunov theory. Finally, numeric simulations are conducted to validate the effectiveness of the proposed method.

In this paper, an adaptive iterative learning control algorithm is designed based on extended state observer. Traditional robotic path tracking control has low control precision and poor control performance. A basic structure of the double joint manipulator is used for study. The system model is established, and a manipulator trajectory tracking control scheme is proposed. The specific algorithm principle and implementation method are given. The proposed algorithm consists of variable gain PD control, adaptive control, and extended state observer. The PD control can change the control gain adaptively because of the adaptive feedback loop to ensure the system stability. The extended state observer regards both the internal interference and the external random disturbance of the system. The state is used to compensate for the uncertainty of both. Experiment results show that the proposed algorithm improves the range and performance of the trajectory tracking error while improving the system convergence, and improves the control performance of the system.

Unmanned air vehicles (UAVs) have received tremendous importance because of their civil, military, industrial, agricultural and security etc. applications. As compared to terrestrial robots, UAVs have to face stronger aerodynamic as well as gravitational forces which effect the dynamics of these flying structures. The control and estimation of unavailable plant states in UAVs is a challenging task due to their nonlinear dynamics in the presence of external uncertainties like air load and noise effects. Practically, external aerodynamic disturbances and sensor noise can alter the desired performance of the aerial robots leading to instability and loss of control of UAVs. Information of all plant states is important for better control and navigation of UAVs. In this paper it is assumed that all plant states are not available, therefore, nonlinear observer design techniques are used to estimate unavailable states of quadrotor plant with least error. The designed nonlinear observer's results are compared in simulations in the presence of external disturbance and sensor noise. Sliding mode observers implemented in this paper exhibit the property of finite time convergence of error dynamics both with and without disturbances and noise.

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.

This paper discusses the problem of friction disturbance compensation of tank gun servo system. For the friction uncertainties and non-model dynamics in tank azimuth gun control system, the azimuth Gun Control system model and friction model are established firstly, then considering them as a composite disturbance, and then, extended states observer (ESO), a new observer is proposed to observe and compensate this composite disturbance, and using the compensation loop of active disturbance rejection control (ADRC) as the inner loop of traditional PID controller. Finally, the simulation results show that the anti-interference ability could be improved by the designing of ADRC with traditional PID control, which has the feature of "passive anti-interference" and "active anti-interference". The stable precision of visible axis and low speed feature could be well improved.

In this paper, a feedback linearization (FL)-based control law made implementable using an extended state observer (ESO) is proposed for the trajectory tracking control of a flexible-joint robotic system. The FL-based controller cannot be implemented unless the full transformed state vector is available. The design also requires exact knowledge of the system model making the controller performance sensitive to uncertainties. To address these issues, an ESO is designed, which estimates the state vector, as well as the uncertainties in an integrated manner. The FL controller uses the states estimated by ESO, and the effect of uncertainties is compensated by augmenting the FL controller with the ESO-estimated uncertainties. The closed-loop stability of the system under the proposed observer-controller structure is established. The effectiveness of the ESO in the estimation of the states and uncertainties and the effectiveness of the FL + ESO controller in tracking are demonstrated through simulations. Lastly, the efficacy of the proposed approach is validated through experimentation on Quanser's flexible-joint module.

In this technical note, the active disturbance rejection control (ADRC) is generalized to uncertain nonaffine-in-control nonlinear systems. The proposed controller incorporates both an extended state observer (ESO) as well as a dynamic inversion. The ESO is designed to estimate system state and total uncertainty, which includes the uncertain internal dynamics and the external disturbance, and is nonaffine-in-control. Based on the output of the ESO, the dynamic inversion is used to deal with the nonaffine-in-control problem. The proposed control has a multi-time-scale structure, in which the ESO is the fastest time scale; the dynamic inversion is the second; and the considered nonlinear system is the slowest. The practical convergence of the resulting closed-loop system is obtained. An example is presented to illustrate the efficiency of the proposed method.

As a classical disturbance observation method, the extended state observer (ESO) is commonly used in controllers for disturbance estimation and feedback control. However, the ESO relies mainly on input–output signals and does not fully utilize information from system derivatives and the system’s dynamic structure. This underuse limits its effectiveness for vertical take-off and landing (VTOL) uncrewed aerial vehicles (UAVs). This limitation is especially problematic in small tailless VTOL UAVs (ST-VTOL UAVs). While these UAVs can switch modes and operate in confined spaces, they are highly susceptible to disturbances such as wind. To address this issue, this paper applies a novel disturbance rejection controller to an ST-VTOL UAV. Specifically, the controller replaces the traditional linear ESO with an enhanced state compensation function observer (SCFO) and integrates it with an equivalent sliding mode controller (ESMC). Simulation results demonstrate that the SCFO achieves substantially higher disturbance-estimation accuracy than both the classical ESO and its fal–function–enhanced variant. Flight experiments on the ST-VTOL UAV confirm that the proposed method reduces tracking error compared with a conventional PID controller and maintains stable hovering under external disturbances.