Reduced-order Extended State Observer Research Articles

Disturbance Rejection Control of Grid-Forming Inverter for Line Impedance Parameter Perturbation in Weak Power Grid

When a grid-forming (GFM) inverter is connected to a low- or medium-voltage weak power grid, the line impedance with resistive and inductive characteristics will cause power coupling. Typical GFM decoupling control strategies are designed under nominal line impedance parameters. However, there are deviations between the nominal line impedance and actual parameters, resulting in poor decoupling effects. Aiming at this problem, this paper proposes a power decoupling strategy based on a reduced-order extended state observer (RESO). Firstly, the power dynamic model of the GFM is established based on the dynamic phasor method. Then, the model deviation and power coupling due to line impedance parameter perturbation are estimated as internal disturbances of the system, and the disturbances are compensated on the basis of typical power control strategy and virtual impedance decoupling. Good decoupling performance is obtained under different impedance parameters, improving the control strategy’s robustness. Finally, the effectiveness of the proposed method is verified by the results of RT Box hardware-in-the-loop experiments.

Robust tracking control of flexible manipulators using hybrid backstepping/nonlinear reduced-order active disturbance rejection control

This study presents a novel hybrid control strategy for single-link flexible-joint robot manipulators, addressing inherent uncertainties and nonlinear dynamics. By integrating nonlinear reduced-order active disturbance rejection control (NRADRC) with backstepping control, the proposed method effectively estimates and mitigates nonlinear dynamics and external disturbances. Utilizing a nonlinear reduced-order extended state observer (NRESO) enhances resilience to internal and external uncertainties. The global stability of the proposed controller is rigorously established using the Lyapunov approach. Numerical comparisons with state-of-the-art nonlinear control methods demonstrate the superior efficiency and robustness of the proposed approach, especially under varying payloads and disturbances, advancing robotic control solutions.

Improved current control for PMSM via an active disturbance rejection controller

This article proposes an active disturbance rejection controller (ADRC) for regulating the dq axis currents of permanent magnet synchronous motors (PMSM). First, we establish actual PMSM model by considering ineluctable disturbances due to the variation of parameters, abrupt change of load, etc. Initially, we design dq axis current ADRCs incorporating an extended state observer (ESO). Compared to the commonly used proportional integral (PI) controller, the ADRC exhibits superior anti-interference capabilities in load and speed regulation. Secondly, we conduct a comprehensive analysis of ADRC’s key features, including ESO stability, dq-axis current tracking, and its anti-interference effectiveness in PMSM applications. Additionally, we offer methods for selecting parameters for both ADRC and ESO. Concurrently, we also examine the ADRC algorithm that utilizes a reduced-order extended state observer (RESO). The control performance of ADRC using RESO will be better than ESO. Finally, to verify the effectiveness of this method, we construct an experimental platform using the TMS320F28035. The results confirm the proposed method’s effectiveness.

Robust dynamic surface control of series elastic actuators based on reduced-order extended state observer

The compliance of series elastic actuators (SEAs) is significant for ensuring safe human–machine interaction. However, in practical applications, the SEA is inevitably encountered with unknown disturbances, such as parameter uncertainties, unmodeled dynamics, and environmental interferences. In this paper, a robust dynamic surface control scheme is presented to address the high-precision trajectory tracking problem of the SEA. Firstly, a reduced-order extended state observer (RESO) with only link-side position measurements is designed to estimate the unknown lumped disturbance and unmeasurable system states. Based on the estimated values from the RESO, a robust dynamic surface controller is proposed for the trajectory tracking of the SEA. Additionally, the finite-time filter is introduced to overcome the “explosion of complexity” in the backstepping controller, and the filtering error in the dynamic surface controller is reduced compared with the conventional first- and second-order filters. The stability of the closed-loop system is guaranteed by the Lyapunov theory. Finally, the effectiveness and superiority of the proposed control algorithm are verified through simulations and experiments.

Improved Stanley guidance law–based adaptive path-following control of underactuated ship with state-constrained and time-varying drift angle

To improve the following performance in large curve path and time-varying drift angle, a reduced-order extended state observer is added to the Improved Stanley Guidance Law (EISGL). Combining with the dynamic surface control (DSC), an adaptive auxiliary system is simultaneously built to compensate for the effect of the state constraints on the system. A barrier Lyapunov function combined with a prescribed performance function is designed to constrain the heading angle error of path following. Adaptive laws are also designed to approximate errors, estimating perturbation in poor sea condition. Lyapunov stability analysis shows that all signals are semi-global coherent and eventually bounded. In conclusion, the numerical comparison simulation experiments verify that the scheme has a strong anti-jamming capability and achieves good path following in large curve path.

Finite-time attitude tracking control of stratospheric airship in the presence of multiple disturbances

Abstract This paper proposes a composite non-singular fast terminal sliding mode attitude control scheme based on a reduced-order extended state observer for the stratospheric airship’s attitude system affected by multiple disturbances. First, the feedback linearisation method is applied to address the nonlinearity of the attitude motion model and achieve decoupling of the model in three channels. Second, the overall disturbances, encompassing airship parameter perturbations and external disturbances, are treated as an aggregate. A reduced-order extended state observer is designed for each channel to formulate a composite non-singular fast terminal sliding mode surface. In the control design phase, the hyperbolic sine function is adopted as replacement for the sign function to ensure the continuity of the control signal. The estimated disturbances are incorporated in the control law design to directly offset the effects of multiple disturbances on the attitude motion of the airship. Third, based on Lyapunov theory, it has been proven that the control law can drive the attitude tracking error to converge to zero within a finite time. Simulation results demonstrate that the proposed control scheme exhibits favorable disturbance rejection capability, as well as higher tracking accuracy and faster response speed.

Integrated guidance and control design by active disturbance rejection method for high-velocity target interceptor with DCS thruster

The present paper proposes a novel integrated guidance and control (IGC) method for engaging with high-speed targets such as ballistic projectiles. considering an extreme short period of terminal engagement due to high relative velocity between target and interceptor, it is particularly important for IGC law to show desirable performance in the presence of various uncertainties (e.g. variation in aerodynamic coefficients) and disturbances (e.g. target maneuver and drag). This article extends the ICG law for mismatched and feedback form equations based on the Active Disturbance Rejection Control (ADRC) method using the back-stepping technique and the Reduced-order Extended State Observer (RESO). The primary consideration is the application of thrusters on the center of mass as the Divert Control System (DCS), along with the daisy-chain technique for control allocation between the fins and thruster commands. Contrary to previous research, the filter and angle measurement error are modeled for the seeker as a crucial parameter to highlight the significance of the thruster. The simulation results indicate the efficiency of the developed method for near-miss or hit-to-kill engagement with tactical ballistic targets. It is shown that the thruster plays a significant role in high-altitude engagements, specifically in the presence of non-ideal seeker. Finally, using the Monte Carlo simulation, it is proved that adding inner loops to the developed technique will not remove the IGC’s advantage over the conventional approach and Non-singular Terminal Sliding Mode (NTSM) guidance law.

Reduced-Order Observer-Based Position Control of a Magnetic-Geared Servo Drive

Magnetic gears (MGs) emerged as an interesting alternative to conventional mechanical gears, owing mainly to their high torque densities and contactless operation. This paper presents a novel observer-based position control system for a magnetic-geared servo drive. The presented control system is based on two well established control strategies—field-oriented control (FOC) and state feedback control. The former is used to achieve effective torque control of a permanent magnet synchronous motor (PMSM) which is considered as an actuator that drives the high-speed rotor, whereas the latter is used to control the position of the low-speed rotor. A reduced-order extended state observer is used to estimate the position and speed of the low-speed rotor, thereby reducing the number of sensors required for the implementation of the controller. The whole control system is implemented on a microcontroller and tested on an existing prototype with a gear ratio of 18:1. The experimental results show that the presented control system guarantees precise positioning within a short amount of time and excellent disturbance rejection.

A Trajectory Tracking and Local Path Planning Control Strategy for Unmanned Underwater Vehicles

The control strategy of an underdriven unmanned underwater vehicle (UUV) equipped with front sonar and actuator faults in a continuous task environment is investigated. Considering trajectory tracking and local path planning in complex-obstacle environments, we propose a task transition strategy under the event-triggered mechanism and design the corresponding state space and action space for the trajectory tracking task under the deep reinforcement learning framework. Meanwhile, a feed-forward compensation mechanism is designed to counteract the effects of external disturbances and actuator faults in combination with a reduced-order extended state observer. For the path planning task under the rapidly exploring random tree (RRT) framework, a reward component and angular factors are introduced to optimize the growth and exploration points of the extended tree under the consideration of the shortest distance, optimal energy consumption, and steering angle constraints. The effectiveness of the proposed method was verified through continuous task simulations of trajectory tracking and local path planning.

Enhanced reduced-order extended state observers-based position tracking error constraint control of a pump-controlled hydraulic system via multiparameter singular perturbation theory

In this paper, the position tracking error constraint control is investigated for a pump-controlled hydraulic system (PHS) subject to an unmeasurable velocity signal and disturbances. A barrier Lyapunov function (BLF)-based backstepping controller is designed, and a set of enhanced reduced-order extended state observers (RESOs) is proposed to estimate the velocity and disturbances. Dynamic surface control (DSC) is used to avoid a repeated calculation of the derivatives of virtual control inputs. Multiparameter singular perturbation theory is utilized to clarify the working mechanism of the enhanced RESOs and the closed-loop system stability properties. Theoretical analysis results reveal that the closed-loop system is uniformly ultimately bounded and the position tracking error is always constrained within a prescribed bound by a proper selection of the perturbation parameters. Moreover, the final position tracking error can be arbitrarily small by further tuning these parameters. In addition, the enhanced RESOs are proven capable of improving the convergence performance of the closed-loop system. Experiments are conducted on an actual PHS to validate the superiority of the proposed control strategy.

An Adaptive Line-of-Sight (ALOS) Guidance Law for Path Following of Aircraft and Marine Craft

This brief presents a novel nonlinear adaptive line-of-sight (ALOS) guidance law for path following, compensating for drift forces due to wind, waves, and ocean currents. The ALOS guidance law is proven to have uniform semiglobal exponential stability (USGES) properties during straight-line path following at constant speed. The ALOS guidance law performs similar to the classical integral line-of-sight (ILOS) and adaptive ILOS guidance laws when the sideslip angle is nearly constant. The ALOS guidance law, however, has better tracking capabilities when compensating for rapidly varying sideslip caused by a time-varying disturbance. This is because the integral state of the ALOS guidance law is additive to the unknown sideslip angle (disturbance matching). In contrast, the ILOS guidance laws must compensate sideslip through a saturating arctangent function. The study also includes an input-to-state stable (ISS) reduced-order extended state observer for estimation of the line-of-sight (LOS) crab angle, known as the ELOS guidance law. The performance of the ALOS, ILOS, and ELOS guidance laws is compared by simulating rapid changes in the sideslip angle to stress the critical assumptions of the algorithms. Finally, a case study of the Remus 100 autonomous underwater vehicle (AUV) exposed to stochastic ocean currents is used to compare the performance of the ILOS, ALOS, and ELOS algorithms during normal operation.

Three-dimensional approximate cooperative integrated guidance and control with fixed-impact time and azimuth constraints

A novel three-dimensional (3D) approximate cooperative integrated guidance and control (ACIGC) scheme based on backstepping control (BC), sliding mode control (SMC), dynamic surface control (DSC), and a 3D reduced-order extended state observer (ESO) for multiple hypersonic skid-to-turn (STT) missiles simultaneously attacking ground-maneuver targets is proposed in this study, which considers a fixed-impact azimuth and time constraints. First, we established a novel integrated guidance and control (IGC) model that includes the missile-target relative distance and azimuth based on the missile-target engagement dynamics, attitude dynamics, and first-order delay dynamics of the rudder. It is a 3D fifth-order strict-feedback time-varying nonlinear model with mismatched uncertainties. Second, a 3D ACIGC scheme was designed, where a cooperative strategy was designed by transforming a fixed-impact time constraint into a nominal range-to-go constraint. The IGC model consists of seeker, guidance, angle-of-attack, attitude, and rudder subsystems based on the BC, and the SMC designs each subsystem. The DSC obtains the derivatives of virtual control commands, which solves the “differential explosion” caused by the BC. The unknown target acceleration, unmodeled parts of the system states, perturbations caused by time-varying parameters, and external disturbances are regarded as lumped disturbances, which are estimated and compensated for by the 3D reduced-order ESO to improve the robustness. Subsequently, the closed-loop system was proven to be stable, and the system states were ultimately uniformly bounded using Lyapunov theory. Finally, the simulation results of three missiles attacking a simultaneously ground-maneuvering target and Monte Carlo simulations demonstrated the effectiveness and robustness of the proposed ACIGC scheme.

MPPT Novel Controller Based on Passivity for the PV Solar Panel-Boost Power Converter Combination

This article deals with the MPPT controller based on passivity, which calculates through a dynamic average model between the PV solar panel and the boost power converter under uniform irradiance conditions. The MPPT algorithm is a linear controller based on the exact tracking error dynamics passive output feedback (ETEDPOF) controller design methodology. The algorithm includes suitable adaptive feedforward pre-compensation, which explicitly depends on the precisely estimated resistance of the boost converter. The MPP reaches by regulating the voltage and current of the boost converter to hold the PV maximum power in the system's input capacitor. The controller desired references such as the inductor current, the output voltage, and the average input control are in terms of the PV maximum power nominal values, which remain always fixed. A reduced-order extended state observer (RESO) develops to estimate the boost converter's output resistance, adapting to the controller's desired references. Simulation and experimental results demonstrate the effectiveness, stability, and robustness of the MPPT algorithm based on passivity as compared to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Incremental Conductance</i> (IC) algorithm, under sudden output resistor changes, high irradiance, and high temperature in the solar panels.

Robust adaptive event-triggered path following control for autonomous surface vehicles in shallow waters

This paper utilizes an adaptive event-triggered mechanism to investigate the path following control of autonomous surface vehicles (ASVs) in shallow waters. Given the challenges posed by the shallow water environment to ASV maneuverability and heading stability, the controller design must enhance the robustness and reduce model complexity. Firstly, a time-varying drift angle-based course guidance law was proposed using a position error dynamics model and a reduced-order extended state observer. Secondly, to simplify the controller's design steps, the ASV's surge and sway motion models are decoupled and transformed. Then, an event-triggered mechanism controller was designed to activate the ASV's rudder angle and shaft speed. In addition, a new robust term was introduced to further estimate the residuals of the RBF neural network, the external disturbances and the event-triggered residual term, thus eliminating the requirement for an upper bound on the unknown disturbances and residuals. The proposed control method based on the robust adaptive event-triggered mechanism can guarantee that all estimation and tracking errors are uniformly ultimately bounded. Simulation results demonstrate that the controller can ensure effective path following of vessels in shallow waters.

Sideslip angle estimation based active disturbance rejection 3D trajectory tracking control for powered parafoil system and hardware-in-the-loop simulation verification

The powered parafoil system is a cutting-edge flight vehicle that features a thrust mechanism with a propeller and an airdrop parafoil, providing outstanding benefits like extended flight endurance and elevated load-bearing capacity. However, the powered parafoil is a highly intricate and nonlinear system that relies on two actuators, steering gear, and thrust. Due to its underactuated and coupled characteristics, it presents significant challenges for three-dimensional (3D) trajectory tracking control. To address these issues, including the lack of convergence in lateral tracking error with existing trajectory tracking methods, this paper proposes a novel guidance system that provides both the guided yaw angle and forward velocity, where a reduced-order extended state observer (ESO) is utilized to estimate the sideslip angle. The input-to-state stable (ISS) theory proves the convergence of the guidance system. Furthermore, two linear active disturbance rejection controllers (LADRCs) are employed to decouple the horizontal and vertical control systems and facilitate tracking the horizontal trajectory and altitude. The proposed method is demonstrated through hardware-in-the-loop (HIL) trajectory tracking simulations on 3D straight lines and circular trajectories. Additionally, Monte Carlo simulations validate the robustness of the proposed control system.

Super-Twisting Sliding Mode Control for the Trajectory Tracking of Underactuated USVs with Disturbances

For an underactuated unmanned surface vehicle (USV), time-varying external disturbances affect the accuracy of trajectory tracking. To ensure trajectory tracking accuracy, in this paper the reduced-order extended state observer (ESO) and the super-twisting second-order sliding mode controller are adopted. The ESO is designed to address the unknown time-varying sideslip angle in the guidance law. Additionally, the super-twisting technology contributes to a reduced chattering effect of the sliding mode. The Lyapunov method is used to analyze the stability of the tracking system and prove that the proposed controllers can ensure the convergence of the tracking errors in finite time. The simulation experiments of the proposed super-twisting sliding mode control (STSMC) and adaptive sliding mode control (ASMC) methods are compared. The results show that the STSMC method enables the USV to complete the task of the reference trajectory tracking. The chattering of the STSMC is also significantly reduced compared to that of the ASMC.

RESO-based distributed bipartite tracking control for stochastic MASs with actuator nonlinearity

This paper focuses on addressing the bipartite tracking control issue for stochastic nonlinear multiagent systems (MASs) with unmeasured states, unknown external disturbances and actuator nonlinearity. During the design procedure, a category of distributed reduced-order extended state observers (RESOs) are constructed to compensate for the total disturbances and estimate unknown states. Moreover, in order to solve the adverse impacts caused by actuator nonlinearity (saturation and dead-zone), an auxiliary variable and the Nussbaum gain method are adopted. Compared with the existing results, the proposed scheme has a better approximation effect. Based on distributed RESOs, the command-filtered backstepping method, and stochastic Lyapunov stability theory, a bipartite tracking control protocol is designed such that all signals of the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) in probability. Finally, the effectiveness and superiority of the proposed method are verified via simulation examples and comparison results.

Enhanced Reduced-Order Extended State Observer for Motion Control of Differential Driven Mobile Robot.

Motion control is critical in mobile robot systems, which determines the reliability and accuracy of a robot. Due to model uncertainties and widespread external disturbances, a simple control strategy cannot match tracking accuracy with disturbance immunity, while a complex controller will consume excessive energy. For precise motion control with disturbance immunity and low energy consumption, a control method based on an enhanced reduced-order extended state observer (ERESOBC) is proposed to control the motor-wheels dynamic model of a differential driven mobile robot (DDMR). In this method, only unknown state error and negative disturbance are estimated by the enhanced reduced-order extended state observer (ERESO), which reduces the required energy of the observer. In addition, a simple state-feedback-feedforward controller is used to track the reference signal and compensate for negative disturbance. Through numerical simulation and application example, the tracking performance and disturbance rejection performance of DDMR are compared with the traditional control method based on enhanced extended state observer (EESOBC), and the results show the superiority of the ERESOBC method.

Structural Vibration Suppression Using a Reduced-Order Extended State Observer-Based Nonsingular Terminal Sliding Mode Controller with an Inertial Actuator

In this paper, we mainly aimed to design a reduced-order extended state observer-based active vibration controller for a structural vibration control system with total disturbances, i.e., model uncertainties, higher harmonics, and external excitations. A reduced-order extended state observer (RESO)-based nonsingular terminal sliding mode vibration control (RESO–NTSMVC) method is proposed for the vibration suppression of an all-clamped plate structure with an inertial actuator. First, a second-order state space model of the thin plate, with an inertial actuator, was established by solving the dynamic partial differential equation and analyzing the physical model. Second, the total disturbances, i.e., model uncertainties, higher harmonics, and external excitations, were estimated and compensated for by using a RESO via a feedforward part. Third, a NTSMVC based on an estimated value was designed to obtain a fast-tracking rate and effective vibration suppression performance. In addition, the stability of the closed-loop system was proven by using a Lyapunov stability criterion. Finally, a semi-physical experimental instrument was built based on the MATLAB/Simulink real-time environment and the NI-PCIE6343 acquisition card to verify strong anti-disturbance performance and effective vibration control performance of the designed method. The experimental comparison results showed that the vibration amplitudes of the proposed method could be reduced by 11.7 dB, when the traditional extended state observer-based nonsingular terminal sliding mode vibration control (ESO–NTSMVC) method achieved a control effect of only 6.5 dB. The comparative experimental results showed that the proposed method possessed better vibration suppression performance and anti-disturbance performance.

An Extended State Loop Filter With Position Error Observer for Sensorless IPMSM Drives

Sensorless drives of interior permanent magnet synchronous motors (IPMSMs) find a broad range of applications due to their inherent benefits. In practical electrified propulsions, the IPMSM drives are usually working in highly utilized conditions where the performance and stability could deteriorate. Without considerable compensation, this vulnerability causes the existing phase-locked loops (PLLs), estimators, or observers to lose the synchronization with the rotor position. To achieve better performance and reduce the estimation error, in a PLL-type framework for sensorless control, a position error observer (PEO) utilizing the current errors as correction terms plays the role of the phase detector. A reduced-order extended state observer (ESO) is presented to form the loop filter with a switched nonsmooth feedback structure. The outstanding property of the PEO and nonsmooth ESO is verified through experiments. The results demonstrate its strong adaptability for model uncertainties and disturbances along with the quick convergence speed and minimal oscillation.