A new type extended state observer for system with measurement noise

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.

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.

A practical data-based third-order linear extended state observer (ESO) filter is proposed based on state estimated by ESO. The filter is simple to use with only one parameter to tune. Then its transfer function, parameters tuning method and discrete simulation realization are given respectively. The proposed ESO filter is applied to the tracking of sine signal and square signal, the filter of signal with white Gaussian noise, and the filter of the width data for hot strip rolling mill in real time with measurement noise. Simulation results show the proposed ESO filter is practical without signal model, noise model and statistical characteristic of the measurement noise. Only according to present moment of the measurement data, it could meet the requirement with appropriate parameter.

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

This paper develops a nonsingular terminal sliding mode controller (NTSMC) based on extended state observer (ESO) for a buck converter subject to load disturbances and input voltage variations. First, a novel modeling method is developed to transform the matched and mismatched disturbances caused by load resistance and input voltage variations into a uniform matched total disturbance. Second, an ESO is established to estimate the differential of the output voltage and the total disturbance. Third, a NTSMC based on ESO is designed to achieve faster tracking speed and better tracking accuracy around the expected voltage. In addition, the theoretical stability of the proposed controller is analyzed by a Lyapunov stability criterion. Finally, both simulation and experimental results show that the proposed NTSMC-ESO controller with the novel modeling method can attenuate the input voltage variation effectively and has a better load disturbance rejection ability than the reduced-order ESO based sliding mode controller. Abbreviations: ADRC: active disturbance rejection control; ESO: extended state observer; NTSMC: nonsingular terminal sliding mode control; RESO: reduced-order extended state observer; SMC: sliding mode control;

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.

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.

PurposeThis paper aims to study a disturbance rejection controller to improve the anti-interference capability and the position tracking performance of airborne radar stabilized platform that ensures the stability and clarity of synthetic aperture radar imaging.Design/methodology/approachThis study proposes a disturbance rejection control scheme for an airborne radar stabilized platform based on the active disturbance rejection control (ADRC) inverse estimation algorithm. Exploiting the extended state observer (ESO) characteristic, an inversely ESO is developed to inverse estimate the unmodeled state and extended state of the platform system known as total disturbances, which greatly improves the estimation performance of the disturbance. Then, based on the inverse ESO result, feedback the difference between the output of the tracking differentiator and the inverse ESO result to the nonlinear state error feedback controller (NLSEF) to eliminate the effects of total disturbance and ensure the stability of the airborne radar stabilized platform.FindingsSimulation experiments are adopted to compare the performance of the ADRC inverse estimation algorithm with that of the proportional integral derivative controller which is one of the mostly applied control schemes in platform systems. In addition, classical ADRC is compared as well. The results have shown that the ADRC inverse estimation algorithm has a better disturbance rejection performance when disturbance acts in airborne radar stabilized platform, especially disturbed by continuous airflow under some harsh air conditions.Originality/valueThe originality of this paper is exploiting the ESO characteristic to develop an inverse ESO, which greatly improves the estimation performance of the disturbance. And the ADRC inverse estimation algorithm is applied to ameliorate the anti-interference ability of the airborne radar stabilization platform, especially the ability to suppress continuous interference under complex air conditions.

Electromechanical actuators (EMA) are becoming more and more widely used. As the core technology of EMA, servo control technology determines their performance. In this paper, an active disturbance rejection control (ADRC) method with an improved extended state observer (ESO) is proposed to design a cascade controller of EMA based on permanent magnet synchronous motor (PMSM). The mathematical model of PMSM in a two-phase rotating coordinate system is established, then it is decoupled by an id=0 current control method to realize the vector control of the motor. In a three closed-loop vector control system, a PID controller including current loop, speed loop and position loop is designed. To solve the problems caused by measurement noise, the filter link and system are modeled as a whole, and an improved ESO is constructed. On this basis, an ADRC controller of the speed loop and position loop of PMSM is designed and simulated based on Simulink. Based on the physical test platform, a load step test and load disturbance test of ADRC are completed. The results show that, in comparison to the PID method, the ADRC method shortens the response time by 25% on average, and reduces the overshoot by 60% on average. So, it can be concluded that ADRC has good static and dynamic performance, which has a good guiding role for engineering practice.

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.

In permanent magnetic synchronous motor (PMSM) speed regulation system, the tracking performance and disturbance rejection property of the system are coupled when using conventional active disturbance rejection control (ADRC) controller, which complicates the parameter setting of the controller. A decoupled ADRC controller with position feedback is proposed in this paper. Extended state observer (ESO) is modified to make disturbance rejection property of the system independent of the proportional coefficient, which affects both the tracking performance and the disturbance rejection property in the conventional ADRC control system. Using the modified ESO, the tracking performance and disturbance rejection property can be adjusted by the proportional coefficient and the bandwidth of ESO respectively, thus simplifies the parameter setting of the controller. Extensive experiments are performed on dSPACE DS1103 to verify the validity and practicality of the proposed algorithm.

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.

ABSTRACTIn order to reduce the error and phase delay of the classical extended state observer (ESO) in estimating the system state and disturbance, in this paper, we combine ESO and tracking differentiator (TD) to construct a tracking differential extended state observer (TDESO). The observation error and observation speed of TDESO are also discussed. Then a nonlinear active disturbance rejection control system improved by TDESO for a linear plant is transformed into a Lurie system. Moreover, the circular criterion is used to analyse the absolute stability of the transformed Lurie system. Finally, TDESO is optimised and an improved linear state error feedback (PLSEF) is proposed to improve the rapidity of the system by using simulation and time domain analysis. And a second-order system is used to illustrate the performance of the proposed scheme. The simulation results show that our algorithm is effective.

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.

Control design for pressurized water reactor (PWR) is difficult due to associated non-linearity, modelling uncertainties and time-varying system parameters. Extended state observer (ESO) based active disturbance rejection control (ADRC) presents a simple and robust solution which is almost model free and has few tuning parameters. However, conventional ESO suffers from noise over-amplification in the obtained estimates due to high-gain construction which in turn degrades the noise sensitivity of the closed-loop system and limits the achievable dynamic performance in practical scenarios. To overcome this problem, two recent techniques namely cascade ESO (CESO) and low-power higher-order ESO (LHESO) are implemented for control of PWR. Simulation analysis is conducted in MATLAB to illustrate the performance improvement obtained over conventional ESO based ADRC, particularly in case of time-varying disturbances. Extensive simulation analysis is also conducted to investigate robustness towards parametric uncertainties. The study also presents a comparison of conventional ESO, CESO and LHESO to highlight their advantages as well as limitations which in turn would help the users in selecting the appropriate scheme for their particular use-case.