Adaptive Extended State Observer Research Articles

Geometric prescribed‐time control of quadrotors with adaptive extended state observers

AbstractThis article studies an adaptive extended state observer (AESO) based prescribed‐time geometric attitude stabilization problem of quadrotors with endogenous uncertainties, exogenous disturbances, and actuator saturation, which can be estimated and compensated by AESOs. The employment of the geometric representation method for system attitude can effectively avoid ambiguity or singularity problems that may arise with other representations. The temporal and scale transformations are employed to solve the global boundedness problem on infinite time instead of the prescribed‐time convergence problem on finite time. By integrating the proposed controller with the backstepping technique, the system of quadrotors can be prescribed‐time stable. Further, a prescribed‐time geometric attitude control technique is devised such that the control signal is bounded and the state signals converge to a small domain near the equilibrium point in the prescribed time. The prescribed time is determined by the user and is independent of the initial conditions. The comparative simulations with different initial information are performed to demonstrate the effectiveness of the proposed design technique.

Adaptive Extended State Observer for the Dual Active Bridge Converters.

The DC-DC dual active bridge (DAB) converter has become one of the essential units for bidirectional energy distribution and connecting various renewable energy sources. When it comes to regulating the converter's output voltage, integrating an extended state observer (ESO) offers the advantage of eliminating the need for a current sensor, thereby reducing system costs. The ESO with a high observer bandwidth tends to acquire a faster system convergence and greater tracking accuracy. However, its disturbance suppression performance will become poor compared to the ESO with a low observer bandwidth. Based on this, the adaptive ESO (AESO) is proposed in this study to make a compromise between tracking performance and disturbance suppression. When the system is subjected to a high voltage error, the observer bandwidth will increase to improve the tracking performance and decrease to enhance the disturbance suppression. In order to demonstrate that the proposed method is effective, it is compared to the ESO with a fixed observer bandwidth and the improved model-based phase-shift control (MPSC). These comparisons are made through simulation and experimental results in various operation scenarios.

A Novel Current Measurement Offset Error Compensation Method Based on the Adaptive Extended State Observer for IPMSM Drives

Offset error from the measured phase current mostly causes a performance afflicted for interior permanent-magnet synchronous motor (IPMSM) drives, and innovative solutions are eagerly sought. Considering this, this paper proposes an adaptive extended state observer (AESO) to compensate the current measurement offset error (CMOE) without additional hardware. In the proposed scheme, the AESO is designed in a stationary coordinate system to estimate CMOE in DC form. Notably, the proposed AESO possesses a second-order low-pass filtering characteristics. With this, the proposed method shows a high robustness against the disturbances from the AC components caused by motor parameter changes, etc. Furthermore, the adaptive gains enable the proposed scheme to maintain a satisfactory performance under the motor frequency changes. The feasibility of the proposed scheme is thoroughly verified by extensive experimental tests based on the test bench of a 3-kW IPMSM drives.

Model-driven full system dynamics estimation of PMSM-driven chain shell magazine

Based on the system dynamic model, a full system dynamics estimation method is proposed for a chain shell magazine driven by a permanent magnet synchronous motor (PMSM). An adaptive extended state observer (AESO) is proposed to estimate the unmeasured states and disturbance, in which the model parameters are adjusted in real time. Theoretical analysis shows that the estimation errors of the disturbances and unmeasured states converge exponentially to zero, and the parameter estimation error can be obtained from the extended state. Then, based on the extended state of the AESO, a novel parameter estimation law is designed. Due to the convergence of AESO, the novel parameter estimation law is insensitive to controllers and excitation signal. Under persistent excitation (PE) condition, the estimated parameters will converge to a compact set around the actual parameter value. Without PE signal, the estimated parameters will converge to zero for the extended state. Simulation and experimental results show that the proposed method can accurately estimate the unmeasured states and disturbance of the chain shell magazine, and the estimated parameters will converge to the actual value without strictly continuous PE signals.

Adaptive Active Disturbance Rejection Control for Vehicle Steer-by-Wire under Communication Time Delays

In this paper, an adaptive active disturbance rejection control is newly designed for precise angular steering position tracking of the uncertain and nonlinear SBW system with time delay communications. The proposed adaptive active disturbance rejection control comprises the following two elements: (1) An adaptive extended state observer and (2) an adaptive state error feedback controller. The adaptive extended state observer with adaptive gains is employed for estimating the unmeasured velocity, acceleration, and compound disturbance which consists of system parameter uncertainties, nonlinearities, exterior disturbances, and time delay in which the observer gains are dynamically adjusted based on the estimation error to enhance estimation performances. Based on the accurate estimations of the adaptive extended state observer, the proposed adaptive full state error feedback controller is equipped with variable gains driven by the tracking error to develop control precision. The integration of the advantages of the adaptive extended state observer and the adaptive full state error feedback controller can improve the dynamic transient and static steady-state effectiveness, respectively. To assess the superior performance of the proposed adaptive active disturbance rejection control, a comparative analysis is conducted between the proposed control scheme and the classical active disturbance rejection control in two different cases. It is worth noting that the active disturbance rejection control serves as a benchmark for evaluating the performance of the proposed control approach. The results from the comparison studies executing two simulated cases validate the superiority of the suggested control, in which estimation, tracking response rate, and steering angle precision are greatly improved by the scheme proposed in this article.

Geometric Attitude Fault-Tolerant Control of Quadrotor Unmanned Aerial Vehicles with Adaptive Extended State Observers

This paper is concerned with the attitude tracking problem of quadrotor unmanned aerial vehicles (UAVs) with respect to endogenous uncertainties, exogenous disturbances and actuator failures. Two different control methods are proposed to solve this problem. First, an adaptive extended state observer (AESO)-based control framework is devised to tackle the difficulties caused by model uncertainties and external disturbances. A fault-tolerant control method is proposed to cope with the occurrence of actuator failure, which is modeled as a constant loss of effectiveness. Another method employs AESOs to compensate for lumped disturbances, which include endogenous uncertainties, exogenous disturbances and actuator failures. Then, the error can exponentially converge to a bounded set. Finally, simulations are performed to ensure the feasibility of the designed technique.

Sensorless Control of Variable Flux Memory Machines Based on Improved Extended EMF Model and Adaptive Extended State Observer

Sensorless Control of Variable Flux Memory Machines Based on Improved Extended EMF Model and Adaptive Extended State Observer

Finite-Time Tracking Control of a Flexible Link Manipulator Based on an Extended State Observer

In this paper, the finite-time trajectory tracking control problem of a flexible link manipulator (FLM) system with unknown parameters is investigated in joint space. An adaptive nonsingular terminal sliding mode (ANTSM) controller based on an extended state observer (ESO) is proposed to ensure that the tracking error converges to a small neighborhood of zero. Firstly, an adaptive ESO is introduced, which is used to estimate unknown system parameters, including the unknown rigid-flexible coupling coefficient and the unknown control gain. Then, an ESO based on the parameters estimated above is proposed to estimate the unmodeled dynamics and external disturbances of the system in real-time. Finally, an ANTSM controller based on ESO is studied to achieve finite-time trajectory tracking control and vibration suppression without any prior knowledge of system uncertainties and external disturbances. The finite-time convergence ability of the closed-loop system is proved by Lyapunov theory. Experimental results on the Quanser Flexible Link System verify the effectiveness of the proposed controller.

Backstepping integral sliding mode control for pneumatic manipulators via adaptive extended state observers

In this paper, a nonlinear control strategy is proposed for a pneumatic manipulator based on an adaptive extended state observer and a backstepping integral sliding mode controller. A single degree of freedom dynamic model is established for the pneumatic manipulator using an Euler–Lagrange dynamic equation. The adaptive extended state observer is designed by an adaptive law to estimate uncertainties and disturbances. The backstepping integral sliding mode controller is proposed using an integral sliding mode surface based on backstepping technique. Comparative experiments verify effectiveness of the proposed nonlinear control strategy for the pneumatic manipulator.

Design and Control of an Aerial Manipulator With Invariant Center of Gravity for Physical Interaction

Abstract The deployment of manipulators enhances the versatility and flexibility of unmanned aerial vehicles (UAVs) in aerial physical interaction tasks but also challenges their designs and controls due to variations in the center of gravity (CoG), moment of inertia, and reaction wrenches. This work presents a novel design of a two-degree-of-freedom dual-tool manipulator with invariant-center-of-gravity (ICoG) property. The ICoG conditions are strictly deduced, and a practical optimization-based parameter tuning method is proposed. A novel adaptive extended state observer (AESO)-based impedance control method is developed with actuator dynamics taken into account. The AESO can estimate and compensate for both the lumped disturbance, including the influences of moment-of-inertia variation and counter torque, and the unmeasurable states for the controller. In addition, a switching adaptive law is proposed to attenuate the peaking phenomenon under high observer gains. The impedance controller is designed using an auxiliary impedance tracking error to overcome the difficulty of the increased system order. The Lyapunov approach is used to evaluate the stability of the entire system. The proposed approach is implemented on a fully actuated hexarotor with a prototype of the ICoG manipulator. Comparative experiments are conducted to validate the effectiveness and advantages of the proposed design and control methods.

Adaptive Integral Extended State Observer-Based Improved Multistep FCS-MPCC for PMSM

In this article, an improved multi-step finite control set model predictive current control (FCS-MPCC) based on adaptive integral extended state observer (AIESO) is proposed for permanent magnet synchronous motor (PMSM). The improved multi-step FCS-MPCC based on sector is introduced in the current loop. The elements of the voltage vector set are reduced with different sector division method, so it could reduce the computational burden to some extent. Meanwhile, considering that the high gain extended state observer (ESO) will obtain faster convergence, better tracking accuracy in theory and the system disturbance rejection can be enhanced, but the noise suppression performance will become poor. Thus, the adaptive extended state observer (AESO) is proposed to balance the disturbance rejection and noise suppression. When system subject to disturbance, the adaptive gain will increase to enhance the system disturbance rejection and become small to improve the noise suppression in steady-state. However, disturbed by time-varying disturbance, the small gain in the steady state will lead to poor steady-state tracking accuracy. To improve the steady-state tracking accuracy, AIESO is proposed by adding the integral term into AESO. Finally, in order to avoid the sector misjudgment caused by parameter mismatch, the strategy based on extended state observer is used for disturbance compensation. However the selection of inductance is closed related to the estimated burden of the observer. Thus, the inductance parameter estimation method is proposed to update the initial inductance value to reduce the estimated burden, which can help to suppress the parameter mismatches with a smaller estimated burden of the observer. The simulation and experimental results verify the effectiveness of the proposed method.

Effective Position Error Compensation in Sensorless Control Based on Unified Model of SPMSM and IPMSM

Sliding mode observer (SMO) has attracted extensive attention in the field of medium- and high-speed sensorless control of permanent magnet synchronous (PMSM) because of its strong robustness and stability. However, the traditional methods are vulnerable to dc bias caused by measurement errors and parameter changes. Therefore, an improved SMO algorithm by disturbance observer compensation is proposed in this article. The algorithm unifies the mathematical models of surface PMSM and interior PMSM. Besides, a band-pass filter (BPF) is used to replace the traditional low-pass filter, so it can effectively suppress dc bias and high-frequency noise. In addition, at any BPF center frequency, the proposed disturbance observer with LPF characteristics can perfectly compensate the position error caused by the digital filter in real time. Moreover, through sensitivity analysis, the influence of model uncertainty on the observation position is studied, and an adaptive extended state observer is added to mitigate the influence of parameter mismatch on the performance, and hence improving the estimation accuracy. Finally, a triple redundant permanent magnet assisted synchronous reluctance motor is taken as an example to verify the feasibility and effectiveness of the proposed observer.

Saturated adaptive feedback control of electrical‐optical gyro‐stabilized platform based on cascaded adaptive extended state observer with complex disturbances

AbstractIt is still an open and challenging issue to the typical position control problems of the three‐axis electrical‐optical gyro‐stabilized platform systems (TEOGSP), due to inherent characteristics, for example, measurement noise, input saturation, parametric uncertainties, largely unknown load disturbance. To solve this problem, a saturated adaptive robust feedback controller using an adaptive cascaded extended state observer (SAFCESO) is proposed for compromising between the measurement noise effect and the sensitivity to disturbances. Firstly, the matched and mismatched disturbances existing in the TEOGSP system are estimated and rejected by the cascaded adaptive extended state observers (CESO). Secondly, the parametric uncertainties are evaluated by the adaptive control, and the match disturbances are attenuated by the robust control. Moreover, the adaptive robust control law does not require the velocity measurement signal and internal dynamics information of the system, which is practical to implement. Hence, all various uncertainties could be mainly compensated. Then, the improved auxiliary systems governed by smooth switching functions are developed and incorporated into the control design to compensate for the effect of the input saturation. Finally, the command filters are introduced to limit the magnitude of the virtual control and to calculate the derivative of the virtual control, respectively. The extensive comparative experimental results in the TEOGSP systems showed that the proposed SAFCESO method had superiorities in terms of high‐precision tracking accuracy, robustness, and noise reduction.

Hybrid adaptive extended state observer for event‐triggered networked nonlinear systems subject to deception attacks and external disturbances

AbstractIn this article, the estimation problem is investigated for a class of continuous‐time networked nonlinear systems under both deception attacks and external disturbances. A novel adaptive extended state observer is adopted to estimate the states and disturbance under random deception attacks. The dynamic event‐triggered mechanism (ETM) is adopted so as to save the communication resource. Meanwhile, the inter‐sample output predictor is proposed to estimate the state between two consecutive triggering instants. The main purpose of the addressed problem is to design the adaptive gain parameters of the novel extended state observer such that the estimation error dynamics is mean‐square exponentially bounded stable. Sufficient conditions are first established to ensure the existence of the desired adaptive extended state observer. In addition, it is proven that the Zeno behavior can be avoided when the dynamic ETM is utilized. Finally, a simulation example is provided to verify the effectiveness of the proposed design method.

Tracking control for small autonomous underwater vehicles in the Trans-Atlantic Geotraverse hydrothermal field based on the modeling trajectory

• A multi-parameter high-order extended state observer is designed to estimate lumped uncertainties. • A fixed-time fault-tolerant adaptive trajectory tracking controller is presented. • The desired trajectory is constructed by interpolating the path. • The simulation topography is built according to the TAG active mound. This paper investigates the fixed-time trajectory tracking problem of small autonomous underwater vehicles (S-AUVs) in the Trans-Atlantic Geotraverse (TAG) active mound with ocean current, unknown disturbances, model uncertainties, actuator faults, and input saturations. First, the effect of the near-bottom environment of the mound on S-AUVs is analyzed in detail from three issues. Without the upper bound and gradient of lumped uncertainties, a high-order adaptive extended state observer (ESO) is designed. Then, a continuous fixed-time sliding mode manifold is applied to obtain fast convergence performance. In order to realize the fixed-time convergence of tracking errors, an adaptive fault-tolerant trajectory tracking control law with an auxiliary dynamic system (ADS) is proposed. In addition, the simulated topography of the TAG mound is constructed and the trajectory based on path points is modeled by cubic spline interpolation. The effectiveness and superiority of the proposed algorithm are validated by comprehensive simulations.

Distributed model-free formation control of networked fully-actuated autonomous surface vehicles.

This paper presents a distributed constant bearing guidance and model-free disturbance rejection control method for formation tracking of autonomous surface vehicles subject to fully unknown kinetic model. First, a distributed constant bearing guidance law is designed at the kinematic level to achieve a consensus task. Then, by using an adaptive extended state observer (AESO) to estimate the total uncertainties and unknown input coefficients, a simplified model-free kinetic controller is designed based on a dynamic surface control (DSC) design. It is proven that the closed-loop system is input-to-state stable The stability of the closed-loop system is established. A salient feature of the proposed method is that a cooperative behavior can be achieved without knowing any priori information. An application to formation control of autonomous surface vehicles is given to show the efficacy of the proposed integrated distributed constant bearing guidance and model-free disturbance rejection control.

Fast fixed-time vertical plane motion control of autonomous underwater gliders in shallow water

In this paper, a fast fixed-time vertical plane motion controller is proposed for autonomous underwater gliders (AUGs) gliding in shallow water. The influence of speed-sensorless conditions, model uncertainties, unknown time-varying external disturbances, input saturations, and state delay are taken into account. To improve control performance, a fast fixed-time stable system is first presented. Based on the system, an adaptive extended state observer (ESO) is developed for estimating speed, model uncertainties, and external disturbances. A fast fixed-time controller is designed for improving the gliding efficiency and reducing the risk of hitting the ocean floor. Moreover, an input saturation auxiliary system and an advance compensation method are presented to cope with input saturations and state delay. According to Lyapunov theory, it is proved that the AUG states can converge into a small neighborhood within a fixed time. Finally, simulation results demonstrate the rapidity and effectiveness of the designed control method.

Fully distributed prescribed performance formation control for UAVs with unknown maneuver of leader

This paper focuses on the formation control for multiple quadrotor unmanned aerial vehicles (UAVs) in a leader-follower structure. Taking account of the unknown maneuver of the leader and external disturbances, a novel fully distributed prescribed performance formation controller is proposed. Firstly, to obtain a quick convergence rate of errors and desired control precision, a performance function is introduced into a time-varying barrier Lyapunov function (TV-BLF). Then, a distributed adaptive extended state observer (AESO) is constructed to estimate the maneuver of the leader and external disturbances simultaneously. A distributed formation controller is established further based on the TV-BLF and estimations of the AESO. It is proved rigorously that by using the proposed formation controller, the desired formation pattern can be formed while the prescribed performance is guaranteed. Moreover, no global topology information is required in the proposed AESO and controller, which means that the formation can be realized in a fully distributed way. Last, simulations are performed to validate the effectiveness and the superiority of the presented scheme.

A High-Performance Compound Control Method for a Three-Axis Inertially Stabilized Platform under Multiple Disturbances

Symmetry is presented in the frame structure, modeling, and disturbance analysis of the three-axis inertially stabilized platform (ISP), which affects the control performance of the ISP. To realize high-performance control for the ISP, a nonlinear dynamic model based on the geographic coordinates and a compound control method based on the adaptive extended state observer (ESO) and adaptive back-stepping integral sliding mode control (SMC) are proposed. The nonlinear dynamic model based on geographic coordinates could avoid the degradation of measurement and control performance due to complex coordinate transformations. An adaptive ESO (AESO) has been developed to estimate the unknown disturbances of ISP. With the information from the ISP system, the adaptive bandwidth of AESO can deal with the peaking phenomenon without introducing excessive noise. Furthermore, based on the integral sliding mode, the adaptation laws of parameter uncertainty and disturbance estimation compensation have been developed for the back-stepping integral SMC method, which can reduce the estimation burden and improve the disturbance estimation accuracy of AESO. The asymptotic stability of the compound control method has been proven by the Lyapunov stability theory. Through a series of simulations and experiments, the effectiveness of the compound method is validated.

An Adaptive Active Disturbance Rejection Control Strategy for Speed-Sensorless Induction Motor Drives

Speed-sensorless control of induction motor drives based on the extended state observer (ESO) attracts much popularity due to its key characteristics, e.g., satisfactory estimation performance, and high robustness against disturbances. However, the conventional ESO generally uses fixed high gains to achieve fast convergence. This may bring about the concern of noise sensitivity. Moreover, a proportional-integral (PI)-type speed controller is mostly adopted in speed-sensorless control of induction motor drives, which may cause unsatisfactory system dynamics. To address these, an adaptive active disturbance rejection control (ADRC) strategy is proposed for speed-sensorless induction motor drives in this article. In this scheme, a third-order adaptive ESO (AESO) is first used to estimate the speed, the phase, and the overall disturbance. Then, a speed controller based on the state error feedback control rate (SEFCR) is designed to improve system dynamics. In practice, disturbances like dc offsets may further challenge estimation performance, and hence, a closed-loop flux observer (CLFO) is employed to deal with this issue. Additionally, a parameter sensitivity analysis of the CLFO is also provided to evaluate the performance of the proposed scheme. Finally, extensive experimental tests have been carried out to validate the effectiveness of the proposed.