Active Disturbance Rejection Control for humanoid stable walking

The flatness-based active disturbance rejection control (ADRC) approach via online algebraic parameter identification is proposed to deal with the double tank problem. The control task is to maintain the lower tank level at a desired value by manipulating the inlet regulating valve. Firstly, the double tank problem is formulated based on the designed double tank platform, where the process input and output data are available in real-time in Matlab software installed in the upper monitor and the ABB AC800M in the lower computer. Then, the algebraic parameter identification algorithm is proposed to identify the unknown parameters of a typical second-order process, which was a flatness system with the lower tank level as the flat output. All the unmodelled dynamics, as well as the external disturbances are regarded as the total disturbance. Based on the identified model parameters of the process, an extended state observer is constructed to estimate the the flat output and its time derivative, as well as the total disturbance in real-time. A linear feedback control law is then designed to steer the lower tank level following the desired trajectory of the flat output, and thus the flatness-based ADRC approach is designed. The effectiveness of the proposed approach is validated by the simulation results based on the practical process input and output data in the platform.

A generalized active disturbance rejection control (ADRC) approach is proposed for general linear systems. The method follows the idea of the conventional ADRC by using extended state observer (ESO) to estimate the generalized disturbance and using it in the feedback control to attenuate it quickly. It is observed that the idea is appropriate under a matching condition assumption. The generalized ADRC method makes it possible to incorporate any known information of the plant in the control instead of just using the order and the gain information, thus better performance can be achieved, especially for nonminimum-phase processes and unstable processes. Moreover, the generalized ADRC structure is transferred to the well-known two-degree-of-freedom internal-model-control (IMC) structure, thus the stability analysis and parameter tuning can be done in the IMC framework.

In a surface vehicle ride, the passenger’s comfort is desirable, ensuring safety under various tight constraints. To consider this requirement, this article has proposed a lateral control for autonomous vehicle considering the lateral offset error constraints. A reduced-order dynamics of the vehicle has been considered for improving and easy implementation of backstepping. A nonlinear control has been developed by utilizing the Time-varying Asymmetric Barrier Lyapunov Function via the Active Disturbance Rejection Control (ADRC) approach. The Extended State Observer, a component of applied ADRC, estimates all unknown system states as well as the unknown disturbance. The desired trajectories (smooth and non-smooth) based on the yaw rate profile have been synthesized to test the performance of the vehicle. Simulation results are presented to show the effectiveness of the proposed closed-loop control strategy. The vehicle performance has been compared using the proposed method, the conventional Quadratic Lyapunov Function and Symmetric Barrier Lyapunov Function based control. The proposed control provides a smoother control signal, small tracking error and robustness in presence of hard road constraints for smooth/non-smooth vehicle motion.

There exists a steady-state error in the closed-loop system output with some conventional linear active rejection control approaches when the pitch channel control variable of the near space vehicle is the angle of attack. In this study, a cascaded linear active disturbance rejection control approach based on the cascaded control idea is proposed. Both the inner-loop controller and the outer-loop controller are designed by the linear active disturbance rejection control method. The inner-loop is built by angular rate feedback to improve dynamic performance of the closed-loop system, and the outer-loop is built by angle of attack feedback to remove the undesired steady-state error. The approach is employed to a hypersonic near space vehicle autopilot. The numerical simulations show that the proposed approach preserves the performances on time domain and frequency domain as good as those of the conventional active disturbance rejection control approaches, and it has the better performances on disturbance rejection and angle of attack command tracking accuracy than those of some previous active disturbance rejection control approaches.

In this study, a type of direct-drive gearshift system integrated into a motor-transmission coupled drive system is introduced. It used two electromagnetic linear actuators (ELAs) to perform gearshift events. The adoption of ELAs simplifies the architecture of the gearshift system and has the potential to further optimize gearshift performance. However, a number of nonlinearities in the gearshift system should be investigated in order to enhance the performance of the direct-drive gearshift system. An active disturbance rejection control (ADRC) method was selected as the principal shifting control method due to the simple methodology and strong reliability. The nonlinear characteristics of the electromagnetic force produced by the ELA were subsequently reduced using the inverse system method (ISM) technique. The ADRC approach also incorporated an acceleration feedforward module to enhance the precision of displacement control. The extended state observer (ESO) module used a nonlinear function in place of the original function to improve the ability to reject disturbances. Comparative simulations and experiments were carried out between the ADRC method and improved ADRC (IADRC) method. The outcomes demonstrate the effectiveness of the designed control method. The shift force fluctuates less, and the shift jerk decreases noticeably during the synchronization procedure. In conclusion, combined with the optimized IADRC method, the direct-drive gearshift system equipped with ELAs shows remarkable gearshift performance, and it has the potential to be widely used in motor−transmission coupled drive systems for EVs.

In this paper, we consider boundary stabilization for a multi-dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables. The active disturbance rejection control (ADRC) approach is adopted in investigation. An extended state observer is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multi-dimensional system by infinitely many test functions. The disturbance is canceled in the feedback loop together with a collocated stabilizing controller. All subsystems in the closed-loop are shown to be asymptotically stable. In particular, the time varying high gain is first time applied to a system described by the partial differential equation for complete disturbance rejection purpose and the peaking value reduction caused by the constant high gain in literature. The overall picture of the ADRC in dealing with the disturbance for multi-dimensional partial differential equation is presented through this system. The numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction.

In this paper, the problem of maximizing energy yield from the available wind is addressed by using a robust Proportional-Derivative (PD) controller in combination with a Linear Active Disturbance Rejection Control (LADRC) approach. Firstly, the theory of the Wind Turbine (WT) pitch control algorithms is analysed and then based on the analysis, 1.5 MW WT model with a Servo System (SS) and Doubly Fed Induction Generator (DFIG) is developed. The blade pitch angle (R) is controlled to ensure that the variable speed WT system operate safely and the optimum power is achieved. Developed LADRC algorithm reveal dynamic performance of the blade pitch angle, rotor speed and rated power characteristics. Within the wind turbine standard operating regimes, controllers have shown promising results. Proposed LADRC technique validates superior performance. Finally, MATLAB/SIMULINK tool box establishes the corresponding model to simulation test in order to verify the effectiveness and correctness of the analysed algorithms. Simulation result demonstrates that the developed pitch servo control system has good dynamic, steady state performance and robustness.

The partial synchronization of two Hindmarsh-Rose (HR) neurons without coupling via active disturbance rejection control is investigated in this paper. As the external direct current changes, the single HR neuron exhibits various dynamical behaviors, such as resting potential state, bursting, chaos, spiking and so on. When each neuron is in chaotic state, the synchronization will occur only if the coupling between them exists and the coupling strength satisfies some condition. For non-coupled HR neurons, we adopt the active disturbance rejection control approach to achieve the partial synchronization. The simulation results demonstrate the effectiveness of the proposed method.

This paper addresses the synchronized control problem of relative position and attitude for unmanned aerial vehicles(UAVs) to achieve the task of formation keeping and transformation. First, using second-order autopilot model and aerodynamic coupling model, a three-dimensional(3-D) nonlinear kinematic and dynamic model of tight formation is established. Second, based on the leader-follower structure, a double-layer active disturbance rejection control scheme of tight formation is proposed, of which the superstructure is to control the whole formation guiding, while the substructure is to adjust the geometry of tight formation. A detailed design of active disturbance rejection controllers applicable to velocity, heading and altitude three channels is included. Finally, simulation results are presented to illustrate the validity and effectiveness of the proposed controllers, which have the following properties: (1) effectively accounting for formation keeping and transformation with smaller overshoot and quicker response can be obtained. (2) good adaptive ability is verified through the comparison with PID flight controller.

Diving control of Autonomous Underwater Vehicle based on improved active disturbance rejection control approach

This work aims to develop a robust model predictive control (MPC) based on the active disturbance rejection control (ADRC) approach by using a discrete extended disturbance observer (ESO). The proposed technique uses the ADRC approach to lump disturbances and uncertainties into a total disturbance, which is estimated with a discrete ESO and rejected through feedback control. Thus, the effects of the disturbances are attenuated, and a model predictive control is designed based on a canonical model free of uncertainties and disturbances. The proposed control technique is tested through simulation into a robotic autonomous underwater vehicle (AUV). The AUV’s dynamic model is used to compare the performance of a classical MPC and the combined MPC-ADRC. The evaluation results show evidence of the superiority of the MPC-ADRC over the classical MPC under tests of reference tracking, external disturbances rejection, and model uncertainties attenuation.

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.

In this study, pitch angle control is employed to maintain the output power and the rotor speed of the wind turbine, whenever the wind speed is higher than the base wind speed. Blade pitch is a key part of a wind turbine and it is a complex nonlinear system interrupted by many uncertainties. The proposed controller linear active disturbance rejection control is utilized to control the output power and rotor speed of the wind turbine. LADRC is based on the extended state observer and a proportional derivative control law. The distinguished feature of the LADRC is, that it can estimate the internal and external disturbances and to compensate for it in real time. The other advantage of the LADRC controller is that only two parameters need to be tuned: observer bandwidth and controller bandwidth. The purpose of the proposed pitch angle Control is to regulate the pitch angle of the wind turbine with respect to wind speed to improve the efficiency of the wind turbine and overcome the safety issues. To validate the effectiveness and superiority of the proposed controller, the results are compared with the conventional PD and Fuzzy logic controller. The simulation results show that the LADRC controller is better in performance as compared to the conventional PD and FLPI controller.

In this paper, an algorithm is developed to reject time and spatially varying boundary disturbances from a multidimensional Kirchhoff plate via boundary control. The disturbance and control input are assumed to be matched. The active disturbance rejection control approach is adopted for developing the algorithm. A state feedback scheme is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multidimensional system using infinitely many time-dependent test functions. The proposed control law cancels the disturbance using its estimated value. All subsystems in the closed loop are shown to be asymptotically stable. Simulation results are presented to validate the theoretical conclusions and to exhibit the reduction in the peaking phenomenon due to the use of time varying gains instead of constant high gains.

Hybrid underwater gliders (HUGs) combine buoyancy-driven gliding with propeller-assisted propulsion, offering extended endurance and enhanced mobility for complex underwater missions. However, precise depth control remains challenging due to system uncertainties, environmental disturbances, and inadequate adaptability of conventional control methods. This study proposes a novel optimized line-of-sight active disturbance rejection control (OLOS-ADRC) strategy for HUG depth tracking in the vertical plane. First, an Optimized Line-of-Sight (OLOS) guidance dynamically adjusts the look-ahead distance based on real-time cross-track error and velocity, mitigating error accumulation during path following. Second, a Tangent Sigmoid-based Tracking Differentiator (TSTD) enhances the disturbance estimation capability of the Extended State Observer (ESO) within the Active Disturbance Rejection Control (ADRC) framework, improving robustness against unmodeled dynamics and ocean currents. As a critical step before costly sea trials, this study establishes a high-fidelity simulation environment to validate the proposed method. The comparative experiments under gliding and hybrid propulsion modes demonstrated that OLOS-ADRC has significant advantages: the root mean square error (RMSE) for depth tracking was reduced by 83% compared to traditional ADRC, the root mean square error for pitch angle was decreased by 32%, and the stabilization time was shortened by 14%. This method effectively handles ocean current interference through real-time disturbance compensation, providing a reliable solution for high-precision HUG motion control. The simulation results provide a convincing foundation for future field validation in oceanic environments. Despite these improvements, the study is limited to vertical plane control and simulations; future work will involve full ocean trials and 3D path tracking.