Application research on data-based third-order linear extended state observer filter for hot strip width

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.

Disturbances and uncertainties are the main concerns in control systems. To obtain this information in real time, the extended state observer is proposed as the core of the active disturbance rejection control. However, the estimation errors of extended state observer cannot converge to zero in the presents of unknown but bounded disturbances, which will bring unexpected tracking errors to the closed-loop system. By taking advantage of the linear extended state observer and the super-twisting algorithm, the super-twisting extended state observer is proposed to deal with the non-diminishing second-order derivable disturbances in this paper. The asymptotic convergence of the super-twisting extended state observer and the controller are proved by the Lyapunov method. Moreover, the effectiveness and robustness of the super-twisting extended state observer are verified by simulation analysis. Simulation results show that the proposed super-twisting extended state observer maintains the minimized estimation error with less settling time compared the with linear extended state observer. The tracking performance of the controller with the proposed observer is greatly improved.

Integrated flight-propulsion control (IFPC) in cruise mode is under study for ramjet powered supersonic vehicle. The longitudinal flight control and propulsion control model are built with system disturbance and measurement noise. We propose a decoupling active disturbance rejection control (ADRC) scheme for IFPC design. For velocity control loop, a second-order linear extended state observer (ESO) is used. The altitude control loop includes inner pitch angle control and outer altitude control. Two third-order linear ESOs are applied in the altitude control loop. These ESOs estimate the disturbances on altitude and pitch angle, and their parameters are determined by their bandwidth. Two tracking-differentiators (TD) ensure the transient process of velocity and altitude. The linear combinations of state error feedback are applied. The control design eliminates coupling effects between altitude and velocity and attenuates measurement noise.

In this paper, time-scale separation, feedback linearization (FL), and extended state observer (ESO) based new design for an acceleration tracking pitch autopilot of a tail controlled, skid-to-turn tactical missile is presented. The pitch plane dynamics has been split into pitch rate dynamics as fast, and the acceleration dynamics as a slow subsystem by exploiting the naturally existing time-scale separation between them. FL-based controllers are then designed for the subsystems separately. To achieve robustness in the presence of uncertainties and disturbances, an ESO is designed for each of the subsystem separately. The ESOs estimate the effect of uncertainties in the respective subsystem and the estimate is used to robustify the feedback linearizing controller designed for the respective nominal subsystem. The design neither requires accurate plant model nor any information about the uncertainty. Closed-loop stability for the overall system is established. The effectiveness of the design in meeting specified tracking performance in the presence of significant uncertainties, unmodeled dynamics, measurement noise, control input, and rate saturation, and in varying missile velocity and altitude scenario is illustrated by simulation. Furthermore, to analyze the performance for different initial conditions and parameter perturbations, Monte Carlo simulation study is carried out and the results are presented. Finally, performance comparison of the proposed design with some existing controllers is presented to showcase the efficacy of the proposed design.

Observing the state of totally unknown nonlinear systems is a problem that is addressed in the ADRC framework which relies on Extended State Observers (ESO). A weak point of available ESO designs is that they do not take into account explicitly the statistical knowledge on the measurement noise when this one is available. This paper introduces a generic approach that replaces the ESO observer by a Linear Kalman filter, taking into account the variance of any Gaussian measurement noise. This approach can be applied on a specific class of unknown nonlinear SISO systems. Despite the fact that a linear Kalman filtering is a model-based estimation, the proposed approach makes possible the observation of nonlinear and time-varying systems when no information exists on their structure, time-varying parameters and potential disturbances. The process noise associated to this linear observation approach is also provided.

A nonlinear Third-Order Extended State Observer (TESO) is proposed for the estimation of the rotor position and speed for sensorless Interior Permanent Magnet (IPM) synchronous motor drives. An optimized parameter tuning method is deployed to reconcile the needs of expanding the disturbance observation bandwidth and suppressing the measurement noise effectively. Both the steady state and transient performance of the TESO are verified through the experimental tests. In comparison with the performance of a conventional Linear Extended State Observer (LESO), the proposed observer is proved to have better noise suppression ability and disturbance observation performance in wide operating range.

Considering the strong nonlinearity, fast time-varying and strong coupling dynamic characteristics of the high-speed vehicles (HSV), combining with the fact that the extended state observer (ESO) can effectively observe the total disturbance of the system and the predictive sliding mode controller (PSMC) has strong robustness and the ability to reduce chattering, a predictive sliding mode control method with extended state observer is proposed in this paper. Firstly, the HSV model is simplified for the attack angle control; Secondly, the tracking sliding mode surface is predicted and the sliding mode control law is derived by using the optimized performance index, which will avoid the switching function and reduce chattering effectively; Thirdly, a linear extended state observer (LESO) is designed to observe the parameters perturbation and the total disturbances of the system, the estimated value is compensated into the PSMC. Fourthly, the numerical simulation shows that the PSMC with LESO can track the step instruction of angle of attack stably even if there are parameters deviations and external composite disturbances. In addition, the control amount does not exceed the rudder deflection angle of the actuator, and the chatter phenomenon is effectively alleviated.

The suspension gap of the electromagnetic suspension maglev train is around 8 mm. In practice, it is found that the system gap fluctuations are amplified due to the inner coupling of the suspension module system in the maglev train. In addition, maglev trains are affected by load disturbances and parameter perturbations during operation. These uncertainties reduce the ride comfort. Therefore, it is necessary to propose a novel control strategy to suppress inner coupling while reducing the influence of uncertainties on the system. In this paper, a control strategy based on feedback linearization and extended state observer (ESO) is proposed to address this challenge. Firstly, the suspension module system model is established with parameter uncertainties and external disturbances. Additionally, the inner coupling of the suspension module is represented in this model. Subsequently, the feedback linearization method based on differential geometry theory is applied to reduce the effect of inner coupling. Meanwhile, the system uncertainties are transformed into equivalent disturbances by this method. Afterward, a linear ESO is designed to estimate the equivalent disturbances. Finally, a state feedback controller is used to achieve stable suspension and compensate for the disturbances. Simulation and experimental results show that the proposed decoupled control strategy significantly suppresses the influence of inner coupling and uncertainties on the system compared with the traditional PID control strategy.

This paper presents a parameters tuning method based on the genetic algorithm for an active disturbance rejection controller (ADRC) of a hydraulic spherical motion actuator. The dynamic model of the hydraulic spherical motion actuator derived by Lagrange approach is evidently a nonlinear coupling system with parameters time-varying and model uncertainties, which will inevitably influence the tracking performance. To improve the trajectory tracking performance, a robust ADRC based on genetic optimization, which consists of a nonlinear tracking differentiator, extended state observer, and nonlinear state error feedback, is proposed. Utilize the genetic algorithm to optimize the parameters of the ADRC automatically. In the process of ADRC parameter optimization, the evaluation function is established, in which the dynamic performance and the input constraints of the controller are comprehensively considered. Finally, the effectiveness of the proposed approach is validated via the simulation results.

The active disturbance rejection control is used to design the control scheme for the vertical inverted pendulum system. Based on the original active disturbance rejection control algorithm, a linear/nonlinear switched extended state observer is proposed for such an unstable system with single input and double output, strong nonlinear and strong coupling. Firstly, the reason of the limited ability of nonlinear extended state observer to estimate large perturbations is analyzed, then a linear extended state observer is proposed to make up for the defects of NLESO, and the feasibility of the proposed linear/nonlinear auto disturbance rejection switching control is verified by numerical simulation.

This paper presents a sliding mode synchronization controller (SMSC) based on extended state observer (ESO) for the dual-drive system in gantry-type machine tools (GTMT). This controller achieves not only excellent tracking accuracy but also high synchronization performance. Firstly, a sliding mode synchronization controller is designed for the dual-drive system based on a simplified mode. Then, in order to handle the difficulties associated with the parameter uncertainties, external disturbances and coupling effects of the dual-drive system, a linear extended state observer (LESO) is designed. In this active disturbance rejection control (ADRC) technology, the total disturbances are treated as an extended state of the system and compensated with the disturbance observed value. Moreover, Rigorous theoretical analysis is performed to show that the proposed control method is able to achieve asymptotical tracking and synchronization performance for the dual-drive system in GTMT. Finally, Simulation studies are carried out and the results show that the proposed control strategy performs an improved tracking and synchronization motion control in comparison to the independent axis P-PI control approach.

In order to solve the problem of poor re-producibility and large particles in pulse bias arc ion plating (AIP), this paper proposes an incremental fuzzy control scheme based on the extended state observer (ESO) for DC/DC converter. According to researches about equivalent load model of pulse bias AIP in the vacuum environment, the relationship between the influence factors on load and output performance is discussed. Then, based on the small signal model of DC/DC converter, a new 3-order mode-compensation ESO is built to decrease the observing error. In addition, the method of phase plane for designing fuzzy control rule is presented to optimize the rule, and the stability of designing fuzzy control system is analyzed by the Lyapunov theory. The simulation and experimental results have demonstrated that the tracking performance and robustness of pulse bias power supply with the proposed scheme are significantly improved.

Vibration is a common problem in rotating machine. Active Magnetic Bearing (AMB) produces controllable magnetic force to levitate rotor and the control algorithm contributes to reduce vibration. This paper proposes a vibration suppression strategy based on active disturbance rejection control (ADRC). ADRC applies extend state observer (ESO) to estimate generalized disturbance. However, in AMB system, disturbance is mainly caused by centrifugal force, whose frequency is rotating frequency. For sinusoidal disturbance, ESO cannot estimate it absolutely. To estimate sinusoidal disturbance in AMB system, generalized integrator ESO (GI-ESO) is applied in ADRC. The resonant frequency of GI is set as rotating frequency. Transfer function of error of GI-ESO is analyzed and notch feature at resonant frequency is displayed. The transfer function of third-order of ADRC applied GI-ESO is obtained. Stability of proposed vibration suppressing strategy is analyzed by root locus. Results of simulations show better effect for sinusoidal disturbance estimation of GI-ESO. After applying ADRC based on GI-ESO, vibration of displacement in AMB system is reduced effectively, which shows the effectiveness of proposed vibration suppressing strategy.

A new state observer for active disturbance rejection control with measurement noise and output delay using the PDE-backstepping predictor

This paper proposes an extended state observer based sliding mode controller for the speed control of permanent magnet DC motor. The state space model of the system is simplified using a linear state transformation and input transformation to design a linear extended state observer which estimates the system states and the disturbances. Then, a sliding surface is designed which includes the estimated disturbance in addition to the system states to make the sliding mode controller insensitive to the load variations. The proposed controller is validated through numerical simulations and the results shows that the extended state observer based sliding mode controller is capable of maintaining desired speed in the presence of changes in load torque. The comparison of the proposed controller with the integral Sliding mode controller shows a better transient response.