Nonlinear Extended State Observer Research Articles

Research on improved active disturbance rejection control strategy for hydraulic-driven Stewart stabilization platform

Purpose In response to the severe lag in tracking the response of the Stewart stability platform after adding overload, as well as the impact of nonlinear factors such as load and friction on stability accuracy, a new error attenuation function and a parallel stable platform active disturbance rejection control (ADRC) strategy combining cascade extended state observer (ESO) are proposed. Design/methodology/approach First, through kinematic modeling of the Stewart platform, the relationship between the desired pose and the control quantities of the six hydraulic cylinders is obtained. Then, a linear nonlinear disturbance observer was established to observe noise and load, to enhance the system’s anti-interference ability. Finally, verification was conducted through simulation. Findings Finally, stability analysis was conducted on the cascaded observer. Experiments were carried out on a parallel stable platform with six degrees of freedom involving rotation and translation. In comparison to traditional PID and ADRC control methods, the proposed control strategy not only endows the stable platform with strong antiload disturbance capability but also exhibits faster response speed and higher stability accuracy. Originality/value A new error attenuation function is designed to address the lack of smoothness at d in the error attenuation function of the ADRC controller, reducing the system ripple caused by it. Finally, a combination of linear and nonlinear ESOs is introduced to enhance the system's response speed and its ability to observe noise and load disturbances. Stability analysis of the cascade observer is carried out, and experiments are conducted on a six-degree-of-freedom parallel stable platform with both rotational and translational motion.

Trajectory tracking control of four-rotor UAV based on nonlinear extended state observer and model predictive control in wind disturbance environment

In this paper, a novel hybrid controller utilizing a nonlinear extended state observer (NLESO) is introduced. According to the Newton-Euler equation, the four-rotor UAV is modeled and divided into the position subsystem and attitude subsystem. The position subsystem is controlled using the Model Predictive Control (MPC) algorithm. At the same time, the attitude controller utilizes the Sliding Mode Control (SMC) algorithm, which provides an enhanced level of responsiveness, resulting in reduced response times. The Nonlinear Extended State Observer (NLESO) is used in each controller in order to counteract the effects of disturbances. The findings obtained from the simulation experiments demonstrate that the controller design exhibits favorable tracking performance and robust resistance against external disturbances.

Double-loop control in air–ground cooperation for a switched-trajectory quadrotor under gust winds

In this paper, a double-loop tracking control strategy with finite-time convergence is investigated for a switched-trajectory quadrotor subjected to gust winds in air–ground cooperation. To handle the complexity of switched-trajectory tracking, an adaptive tracking differentiator is presented in an outer loop to arrange transition processes. Fast integral terminal sliding mode control is also used in the outer loop to improve convergence speed and tracking accuracy. The gust winds are estimated and compensated by a nonlinear extended state observer and a nonlinear controller with finite-time convergence in an inner loop, respectively. Convergency analyses are presented with the double-loop tracking control strategy for the switched-trajectory quadrotor. Comparison experiments with existing studies show superior performances of the proposed control method for the quadrotor in air–ground cooperation under gust winds.

Anti-disturbance control design of Exoskeleton Knee robotic system for rehabilitative care

In this study, Active Disturbance Rejection Control (ADRC) has been designed for motion control of knee-joint based on exoskeleton medical robot. The extended state observer (ESO) is the main part of ADRC structure, which is responsible for estimating both actual states and system uncertainties. The proposed control scheme has adopted two versions of observers as disturbance estimators: linear extended state observer (LESO) and nonlinear extended state observer (NESO). The efficacy of proposed ADRC is strongly related to the performance of used ESO. As such, a comparison study has been conducted to evaluate the performance of two ADRCs in terms of disturbance-rejection capability and robustness to variation in system parameters under two version of ESO (LSO and NLESO). In order to enhance the dynamic performance of ADRC, Particle Swarm Optimization (PSO) algorithm has been used to optimally tune the design parameters of control scheme. To show the effectiveness of proposed LESO-based ADRC and NLESO-based ADRC, numerical simulation have been conducted. The proposed controllers have tested for an uncertain exoskeleton-knee system, where a 20% change in parameters was permitted over their nominal values. The results indicate that the ADRC algorithm based on LESO outperforms the one based on NESO in terms of disturbances rejection ability and robustness to parameters’ variations.

Energy-saving robust control of active suspension system based on bioinspired reference model

This paper proposes an energy-saving robust tracking control method for active suspension systems with a bio-inspired reference model and nonlinear extended state observer (NLESO). According to the principle of cheetah running biology, a bionic structure with nonlinear quasi-zero stiffness is designed, which also has ideal Sky-hook damping and vibration-absorbing mass. An NLESO is designed to estimate the total uncertain disturbance and the state of sprung mass in the suspension system, and then an energy-saving robust tracking controller is proposed. The controller consumes less control energy while isolating the vibration of the sprung mass, thus improving the riding comfort of vehicles and saving energy. The simulation results show that, compared with the reference control method, the vertical acceleration of the sprung mass is reduced by 80.68% and 92.42% respectively in the class C road and bump road conditions and the control energy is decreased by 31.71% and 30.50%, respectively. The control effect of the proposed controller for the active suspension system is verified.

Enhanced adaptive nonlinear extended state observer for pure feedback systems with matched and mismatched disturbances

Enhanced adaptive nonlinear extended state observer for pure feedback systems with matched and mismatched disturbances

Enhanced Active Disturbance Rejection Control With Measurement Noise Suppression for PMSM Drives via Augmented Nonlinear Extended State Observer

Enhanced Active Disturbance Rejection Control With Measurement Noise Suppression for PMSM Drives via Augmented Nonlinear Extended State Observer

Extended state observer design for uncertainty estimation in electronic throttle valve system

AbstractThe Electronic Throttle Valve (ETV) is the core part of automotive engines which are recently used in control-by-wire cars. The estimation of its states and uncertainty is instructive for control applications. This study presents the design of Extended State Observer (ESO) for estimating the states and uncertainties of Electronic Throttle Valve (ETV). Two versions of ESOs have been proposed for estimation: Linear ESO (LESO) and Nonlinear ESO (NESO). The model of ETV is firstly developed and extended in state variable form such that the extended state stands for the uncertainty in system parameters. The design of both structures of ESOs are developed and a comparison study has been conducted to show the effectiveness of the proposed observers. Numerical simulation has been conducted to assess the performance of observers in estimating the states and uncertainties of ETV. The simulated results showed that both full order and reduced order models of ETV have the same transient characteristics. Moreover, the effectiveness of two versions of observers has been examined based on Root Mean Square of Error (RMSE) indicator. The results showed that the NESO has less estimation errors for both states and uncertainties than LESO.

The Non-Singular Terminal Sliding Mode Control of Underactuated Unmanned Surface Vessels Using Biologically Inspired Neural Network

Underactuated Unmanned Surface Vessels (USVs) are widely used in civil and military fields due to their small size and high flexibility, and trajectory tracking control is a critical research area for underactuated USVs. This paper proposes a trajectory tracking control strategy using the Biologically Inspired Neural Network (BINN) for USVs to improve tracking speed and accuracy. A virtual control law is designed to obtain the required virtual velocity for trajectory tracking control, in which the velocity error is calibrated to ensure that the position error converges to zero. To observe and compensate for unknown and complex environmental disturbances such as wind, waves, and currents, a nonlinear extended state observer (NESO) is designed. Then, a controller based on Non-singular Terminal Sliding Mode (NTSM) is designed to resolve the problems of singular value and controller chattering and to improve the controller response speed. A BINN is introduced to simplify the process of differentiation, reduce the input values of the initial state, and solve the problem of thruster input saturation. Finally, the Lyapunov stability theory is utilized to analyze the stability of the proposed algorithm. The simulation results show that the proposed algorithm has a higher trajectory tracking accuracy and speed than traditional methods.

Real-time validation of optimal energy management in DC microgrids by using modified rejection controller based improved sparrow search algorithm

For optimal energy management in the DC microgrid, there are two major challenges, such as minimization of operational cost and balancing the power flow. Most of the benchmark techniques are used to develop energy management systems (EMS) by demonstrating either cost optimization or availability of power optimization. Unlike, a new optimal energy management (OEM) approach is introduced in this paper by considering both the operational cost and power flow during the grid-connected scenario in the DC ring microgrid (DCRM). To attain the OEM in the DCRM, a multi-objective optimization model is developed by utilizing major constraints, such as minimization of operational cost and power availability through a modified active disturbance rejection controller (M-ADRC) based improved sparrow search algorithm (ISSA). The improved nature of SSA is obtained by hybridizing the sine-cosine and Tent chaotic functions with SSA, i.e., SC-CSSA to avoid premature convergence in SSA. On the other hand, the disturbance rejection controller is modified by replacing the extended state observer (ESO) with a communication delay in non-linear ESO to enhance the robustness of the proposed DCRM. The main role of this controller is to regulate the fluctuations by maintaining stability in the voltage profile during various operating conditions. Further, the proposed M-ADRC based SC-CSSA algorithm results are validated over benchmark techniques to evidence the superiority of the proposed algorithm. To ensure realistic performance and robustness, the algorithm is validated in a real-time environment through hardware-in-the-loop (HIL) operation with the dSPACE DS1104 embedded processor. This testing approach guarantees simplicity, practicality, and effectiveness.

Robust Amplitude Control Set Model Predictive Control with Low-Cost Error for SPMSM Based on Nonlinear Extended State Observer

Robust Amplitude Control Set Model Predictive Control with Low-Cost Error for SPMSM Based on Nonlinear Extended State Observer

Current decoupling control of permanent magnet synchronous motor based on improved nonlinear extended state observer

Precise current decoupling is required to achieve good control performance in the vector control of permanent magnet synchronous motor (PMSM), but traditional decoupling methods are unable to solve the problem of poor current decoupling effectiveness when the system inductance parameters are mismatched. Therefore, a decoupling control method of PMSM based on improved nonlinear extended state observer (INESO) is proposed in this paper. Firstly, a smooth, differentiable nonlinear function is used to replace the traditional fal function, which overcomes the problem of discontinuous gain changes. Secondly, a time-varying gain is designed to address the problem of reduced observer performance due to differential peak values in traditional NESO. Finally, the stability of INESO and the current loop closed-loop system is proven, followed by simulation and experimental verification. The simulation and experimental results show the proposed method effectively observes and compensates for system uncertainties, including parameter perturbations, external disturbances, and unmodeled dynamics. This method achieves complete decoupling of d and q-axes currents, while suppressing interference and enhancing the control performance of PMSM. The proposed INESO decoupling method reduces the d-axis current fluctuation about 96% and 90% when the load changes abruptly under motor inductance parameter mismatch, and can reduce q-axis current fluctuation about 88% and 78% when the d-axis current steps, respectively, compared with the conventional Current Feedback Decoupling Control (CFDC) and CDDC decoupling methods.

On error-driven nonlinear ESO based control design with application to air–fuel ratio control of engines

In this paper, the tracking control problem of the uncertain control system is studied in the frame of uncertainties estimation and compensation. To eliminate the influence of external disturbances and internal uncertainties on the control system, the error-driven nonlinear extended state observer (EDN-ESO), whose gain is set as an increasing function with respect to the absolute value of estimation error of the system output, is proposed to improve the estimation performance for the “total disturbance”. Next, both the estimation error of proposed ESO and the tracking error of system output are proven to be bounded by selecting the lower bound and variation range of ESO’s bandwidth. Moreover, the convergence of the estimation error as well as the tracking error to zero is proven under certain conditions. Finally, the proposed design method is applied to the air–fuel ratio control system of gasoline engines, and the experimental results show that the proposed EDN-ESO can effectively adjust the observer gain, so as to enhance the tracking performance.

Nonlinear Extended State Observer Based Super-Twisting Terminal Sliding Mode Synchronous Control for Parallel Drive Systems

Addressing the issue to restrain the nonlinear coupling disturbance in the multimotor parallel drive system and acquiring perfect driving control performance, a novel super-twisting terminal sliding mode synchronous control (STSC) is proposed. In this control scheme, a lumped error (LE) with a synchronization coefficient is designed to transform coupled control into LE convergence. Then, a recursive terminal sliding mode function with two layers is introduced. Based on this sliding mode function, the STSC scheme is proposed, and it can guarantee the LE finite-time convergence and the continuous control action in nature. A nonlinear extended state observer (NESO) is introduced to enhance robustness. Moreover, the NESO not only provides an estimation of disturbance but also provides a smooth velocity signal. Therefore, differential operations and filtering operations are avoided. Finally, a compound control scheme is obtained. Compared with conventional super-twisting algorithm (STA), the robustness is enhanced by embedding NESO-based disturbance compensation, and the advantage of continuous control action is inherited. The major advantages of this scheme are characterized by output-based information only used, good model adaptability, and strong disturbance rejection ability. Experimental results show the effectiveness of the proposed control law.

One new composite control based smooth nonlinear fractional order sliding mode algorithm and disturbance compensation for PMSM with parameter uncertainties

To achieve high-quality control of PMSM with parameter uncertainties, a nonlinear smooth fractional order sliding mode composite control (NSFOSMCC) strategy is designed in this paper. This approach incorporates a novel nonlinear smooth fractional order sliding mode controller, a novel adaptive super-twisting (AST) algorithm, and a modified nonlinear extended state observer (ESO) to achieve enhanced motor performance. To effectively overcome the disadvantages of simplicity and toughness associated with the conventional fractional order sliding mode controller, a novel nonlinear smooth fractional order sliding mode controller is designed. A novel AST technique is introduced to effectively weaken chattering issues. The modified nonlinear ESO is used to estimate the uncertainty parameters of the PMSM. By combining the modified nonlinear ESO with the latest sliding mode controller, a new composite controller called NSFOSMCC strategy is developed for PMSM. The proposed NSFOSMCC strategy, utilizing a combination of “feedforward plus feedback,” is implemented for PMSM with parameter uncertainties. The reliability and stability of the controller are thoroughly established through the utilization of the Lyapunov stability theorem. Furthermore, comparative results show strong evidence supporting the effectiveness of the novel composite control strategy.

Output tracking for nonlinear stochastic systems driven by bounded and colored noises

In this paper, we consider practical tracking problem for a class of nonlinear stochastic systems driven by bounded and colored noises by means of active disturbance rejection control approach. The nonlinear extended state observer with homogeneous weighted functions is constructed to estimate in real time the unmeasurable state and the total stochastic disturbance that affects system performance. An observer-based output feedback is designed to guarantee the almost surely practical convergence of the tracking errors. The existence of the global weak solution of the closed-loop system is proved and the tracking convergence accuracy is shown to be higher than that of linear one under the same tuning parameters. Some numerical simulations are carried out to validate the effectiveness of the proposed controller.

Novel Composite Speed Control of Permanent Magnet Synchronous Motor Using Integral Sliding Mode Approach

Permanent magnet synchronous motors (PMSMs) are widely applied in industry, and proportional integral (PI) controllers are often used to control PMSMs. Aiming at the characteristics of the poor anti-disturbance ability and speed ripple of traditional PI controllers, a novel composite speed controller for PMSMs is proposed in this paper that uses a novel sliding mode control (SMC). To improve the chattering problem of traditional SMC, a high-order approaching law super-twisting algorithm (STA) is applied. Considering the internal and external disturbance of motor driver systems, such as motor parameter drifts and load torque changes, a disturbance estimator based on an extended state observer (ESO) is proposed, and it is used for the feed-forward compensation of the current. The composite super-twisting integral sliding mode controller (ST-ISMC) with a nonlinear ESO is tested by simulations and experiments, and the comparative results verify that the proposed controller has the higher control accuracy, smaller speed ripple and stronger robustness.

Robust adaptive output feedback for the formation control of heterogeneous ships based on a nonlinear extended state observer

This study considers the formation control problem of heterogeneous ships with unknown time-varying disturbances, dynamic uncertainties, and unmeasurable speeds, a robust adaptive output feedback formation control scheme for the heterogeneous ships based on nonlinear extended state observer is developed. In order to solve the heterogeneous ships formation control problem with leader-following structure, transforming the formation control problem into a class of ship trajectory tracking problem by improving the design of the virtual ship. Firstly, a nonlinear extended state observer is designed for estimating ship speeds due to technical limitations and external disturbances. Then, combining the adaptive neural networks with disturbances adaptive law to deal with the unknown time-varying disturbances and dynamic uncertainties. Meanwhile, the second-order tracking differentiator is designed to calculate the derivative of the virtual control law, which has higher precision comparing to the first-order filter. Stability theory is proved that all the signal of closed-loop control system are uniformly ultimately bounded, and the tracking errors can converge into arbitrary small neighborhoods around zero. Finally, comparative simulations were performed to demonstrate the effectiveness of the proposed controller.

Fault compensations in resonant grounded power systems with residual current compensation inverters using an adaptive nonlinear extended state observer‐based model predictive controller

AbstractThis paper proposes a new adaptive nonlinear extended state observer‐based model predictive controller (ANLESO‐MPC) for residual current compensation (RCC) inverters to compensate fault characteristics in resonant grounded power systems (RGPSs). In the proposed scheme, the adaptation feature is used to adapt the adjustable inductor appearing in the dynamical model of RGPSs by satisfying the desired fault current compensation requirement which in turn will ensure the resonance condition. Since the adapted parameter is used in the control signal, the ANLESO‐MPC offers robustness against parameter sensitivity. The neutral voltage is considered as a disturbance and the change in this voltage as an extended state to estimate this disturbance while incorporating the adapted parameter so that the adaptive nonlinear extended state observer (ANLESO) provides robustness against disturbances. Finally, the model predictive controller (MPC) is designed for the RCC inverter utilizing estimated disturbances and adapted parameters to fully achieve the fault current compensation. The performance of the controller is evaluated using simulations in MATLAB/Simulink and OPAL‐RT real‐time platforms under varying fault impedances as the fault characteristics change with variations in the fault impedance. Results are also compared with a conventional MPC where the proposed ANLESO‐MPC seems more effective to compensate fault characteristics.

Zero-Voltage Ride-Through Scheme of PMSG Wind Power System Based on NLESO and GFTSMC

In this paper, a scheme for zero-voltage ride through of a permanent magnet synchronous generator wind power system is proposed. Maintaining the stability of DC-link voltage is the key to realizing zero-voltage ride through. A braking chopper is used to dissipate the active power to restrain the rise of DC-link voltage during a grid fault. However, the braking chopper-caused disturbance to the double closed-loop control of the grid side converter makes the control effect on DC-link voltage worse. Therefore, a robust current feedforward control, based on a nonlinear extended state observer and global fast terminal sliding mode control is proposed. A nonlinear extended state observer estimates the total disturbance in the system and compensates for the control law. Global fast terminal sliding mode control enables the system to reach the sliding mode surface in a finite time, and its control law is continuous without switching terms, thereby eliminating the chattering phenomenon. A nonlinear extended state observer and global fast terminal sliding mode control change the current feedforward control into a nonlinear robust current feedforward control. The control effect is improved, and the use of current transformers is reduced in practical applications, thereby reducing costs. The validity of this scheme has been verified by simulation.