Extended Disturbance Observer Research Articles

Disturbance observer‐based model predictive control of a coaxial octorotor with variable centre of gravity

AbstractThis paper presents a model predictive control (MPC) approach based on the extended disturbance observer (EDOB) for trajectory tracking of a coaxial octorotor unmanned aerial vehicle (UAV). First, the system dynamic model is derived using Newton–Euler relations in the presence of time‐varying centre of gravity (COG); then, a two‐loop cascade structure is presented to perform the trajectory tracking task. Both loops are controlled using MPC with feedforward compensation based on the EDOB to improve disturbance rejection abilities. When the mass changes, the moment of inertia and COG are affected. The EDOB simultaneously estimates the effects of time‐varying mass, external disturbances, and parametric uncertainties in six degrees of freedom. After obtaining virtual control inputs using designed controllers, constrained control allocation is used to obtain rotors speed in a valid range. The proposed control scheme is evaluated using simulation. The simulation results show the ability of the developed control strategy in accurate trajectory tracking and stable flight in different conditions and being robust to uncertainty and disturbance.

Precise Landing on Moving Platform for Quadrotor UAV via Extended Disturbance Observer

Precise Landing on Moving Platform for Quadrotor UAV via Extended Disturbance Observer

High-Precision Control of Aviation Photoelectric-Stabilized Platform Using Extended State Observer-Based Kalman Filter.

The accuracy of the line-of-sight of aviation photoelectric optoelectronic stabilization platforms is limited by two factors: external disturbance and sensor noise. An extended state observer (ESO) can effectively improve their anti-interference ability. However, due to the serious problem of gyroscope noise, further improvement of an ESO's disturbance suppression effect is limited. This article proposes a control structure that combines a Kalman filter (KF) and ESO, effectively improving upon the interference suppression ability of a traditional ESO under the influence of noise. Firstly, an ESO was used to observe the lumped disturbance of the system, and then, the observed disturbance was compensated for in the control loop. Secondly, based on the compensation servo control system, the state equation of the system was reconstructed using a Kalman filter. Finally, the reconstructed filtered state variables were iterated onto the universal state observer, achieving the observation of disturbances while filtering out sensor noise. Under the conditions of a laboratory flight simulation turntable, the line-of-sight stability accuracy level was improved under disturbance excitation. It can be seen that the combination of a Kalman filter and extended disturbance observer proposed in this project improves the ESO's anti-interference ability under the influence of noise.

Spiking-Free Disturbance Observer-Based Sliding-Mode Control for Mismatched Uncertain System

Abstract For the mismatched uncertain system, a novel spiking-free disturbance observer (DO)-based sliding-mode control (SMC) scheme is developed. First, a DO is proposed to estimate the mismatched uncertainty. A new sliding-mode surface is developed by using the system states, the estimation of mismatched uncertainty, and a spike suppression term. Then, an SMC method is proposed by using the developed sliding-mode surface. Compared with existing SMC schemes, the proposed spiking-free DO-based SMC has two advantages: (1) the mismatched uncertainty can be effectively suppressed; (2) the harmful spike problem of extended disturbance observer (EDO)-based and extended state observer (ESO)-based SMC schemes when the observer gain is high can be avoided. Finally, the simulation is presented to show the effectiveness of the proposed scheme by comparing the proposed and existing SMC schemes.

Finite-Time Model-Free Adaptive Control for Discrete-Time Nonlinear Systems

This paper addresses the fast trajectory tracking problem for discrete-time nonlinear systems, and whereby a finite-time model-free adaptive control (FMFAC) approach is innovatively devised. Here, the nonlinear systems’ dynamics are completely unknown and the widespread disturbances are considered. The nonparametric dynamic linearization technique and the adaptive extended disturbance observer are firstly deployed to achieve real-time linearization of the discrete-time nonlinear system, and an efficient finite-time performance index function is thereafter devised, and thereby contributing to a novel FMFAC control scheme. Theoretical analysis indicates the finite-time model-free tracking control within a stable region can be guaranteed, and the boundedness of the control input signal can be ensured rigorously, even though under the effect of various disturbances. The key points of the proposed FMFAC approach are model-free and possessing the fast regulation ability, and the corresponding effectiveness and superiority are validated via simulation studies.

Prescribed-time output stabilization for mismatched uncertain systems using state-feedback control based on extended disturbance observer

This paper presents a prescribed-time output stabilization method for mismatched uncertain systems using state-feedback control and extended disturbance compensation. The settling-time interval is divided into a disturbance-estimation interval plus an output-stabilization interval, where a prescribed-time extended disturbance observer with finite time-varying gains (PTFG-EDO) and a modified time–space deformation approach (TSDA) control are applied in these intervals, respectively. Due to the prescribed-time convergence of the PTFG-EDO and the modified TSDA control, the settling time of the closed-loop system can be predetermined irrespective of the initial conditions, design parameters, and admissible disturbances. The chattering problem of the original TSDA control is greatly alleviated, and the disturbances, especially the mismatched disturbance which cannot be handled in the original TSDA control, are significantly suppressed. The effectiveness of the proposed PTFG-EDO-based control is demonstrated via numerical simulations.

Sliding mode tracking control for unmanned helicopter using extended disturbance observer

Sliding mode tracking control for unmanned helicopter using extended disturbance observer

Car‐following strategy of intelligent connected vehicle using extended disturbance observer adjusted by reinforcement learning

AbstractDisturbance observer‐based control method has achieved good results in the car‐following scenario of intelligent and connected vehicle (ICV). However, the gain of conventional extended disturbance observer (EDO)‐based control method is usually set manually rather than adjusted adaptively according to real time traffic conditions, thus declining the car‐following performance. To solve this problem, a car‐following strategy of ICV using EDO adjusted by reinforcement learning is proposed. Different from the conventional method, the gain of proposed strategy can be adjusted by reinforcement learning to improve its estimation accuracy. Since the “equivalent disturbance” can be compensated by EDO to a great extent, the disturbance rejection ability of the car‐following method will be improved significantly. Both Lyapunov approach and numerical simulations are carried out to verify the effectiveness of the proposed method.

Coordinated Symmetrical Altitude Position and Attitude Control for Stratospheric Airship Subject to Strong Aerodynamic Uncertainties

The stratospheric airship has important value in both commercial and military use. The altitude position control is very crucial for the airship to conduct specific missions, which is also a challenge because of both the severe relative aerodynamic mismatches and the large lag due to the quite low speed of the airship within 15 m/s. In this paper, a coordinated altitude and attitude control method was proposed to realize satisfactory altitude position control while maintaining the attitude stability by properly employing the two actuators, the propeller thrust and the elevator, in a consistent manner. In this process, the references for the vertical speed and the pitch were specified in a straightforward way of proportionating them by considering their physical characteristics and the inherent symmetrical relationship between them, which can be obtained through the kinematics. An extended disturbance observer was used to eliminate the severe aerodynamic uncertainties to symmetrically distribute the two actuator outputs by dynamically decoupling the vertical speed and the pitch angular rate loops into the two independent integrators. As a result, the explicit proportional controllers were sufficient to realize efficient command tracking. Rigorous theoretical investigation was provided to symmetrically prove the quantitative bounded property of the estimation and tracking errors. The simulation results demonstrated the effectiveness of the proposed approach, which can realize a 500-m altitude difference tracking within 200 s with less than 0.5 deg/s pitch angular rate.

Robust Model Predictive Control Based on Active Disturbance Rejection Control for a Robotic Autonomous Underwater Vehicle

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.

State-Following-Kernel-Based Online Reinforcement Learning Guidance Law Against Maneuvering Target

In this article, a state-following-kernel-based reinforcement learning method with an extended disturbance observer is proposed, whose application to a missile-target interception system is considered. First, the missile-target engagement is formulated as a vertical planar pursuit–evasion problem. The target maneuver is then estimated by an extended disturbance observer in real time, which leads to an infinite-horizon optimal regulation problem. Next, utilizing the local state approximation ability of state-following kernels, the critic neural network (NN) and actor NN for synchronous iteration are constructed to calculate the approximate optimal guidance policy. The states and NN weights are proven to be uniformly ultimately bounded using the Lyapunov method. Finally, numerical simulations against different types of nonstationary targets are effectively tested, and the results highlight the role of state-following kernels in the value function and policy approximation.

Extended disturbance observer for nonlinear system with time‐varying disturbance gain

SummaryIn control engineering, the disturbance is a major problem that deteriorates system robustness. To address this problem, a disturbance observer (DOB) has been proposed and developed. In particular, a general method of estimating high‐order disturbance, expressed as a time series expansion, was studied (H‐DOB). However, systems to which H‐DOB are applicable are limited to those in which disturbance gain is constant. This constraint degrades the generality of H‐DOB because applicable systems are limited. Therefore, by expanding to a system with a time‐varying disturbance gain, we propose a more general H‐DOB. The DOB proposed in this paper redesigns the dynamics of the observer based on the structure of the H‐DOB. The proposed DOB is applicable even if the system is highly nonlinear. This paper verifies the convergence of the proposed DOB through proof. Using this proof, the same characteristic error dynamics can be obtained, so the same design method can be applied. The simulation for the verification of the proposed method performs disturbance estimation of the extension system. This simulation proves that, compared to H‐DOB, the proposed DOB has good disturbance estimation performance.

Advanced neural control technique for autonomous underwater vehicles using modified integral barrier Lyapunov function

This paper presents a novel approach for depth precision control of under-actuated autonomous underwater vehicles (AUV) subject to model uncertainties, ocean currents, and input constraints. Specifically, a transformation is made to convert the input constraint problem into a state constraint problem. Subsequently, an observer-based guidance law is developed to deal with the drift affected by unknown ocean currents by using an extended disturbance observer (EDO). An adaptive neural controller is then designed using the DSC technique and an advanced modified integral barrier Lyapunov function (mIBLF) to guarantee that all states are confined within the given constraint. Besides, a novel nonlinear disturbance observer is introduced to cope with external disturbances and neural network approximation errors. It is proved that all closed-loop signals are uniformly ultimately bounded by Lyapunov stability theory. Finally, comparative simulations are carried out to verify the effectiveness and outstanding characteristics of the proposed method.

A New Sliding Mode Control Algorithm of IGC System for Intercepting Great Maneuvering Target Based on EDO.

To intercept the great maneuvering target, combining with the sliding mode and the extended disturbance observer, a new control algorithm for integrated guidance and control (IGC) system is proposed in this paper. Firstly, the paper formulates the Missile–Target problem. Then the paper establishes an uncertain IGC dynamic model where the nonlinearities, the perturbations and the maneuvering of the target are regarded as disturbance. Secondly, a second-order disturbance observer is designed to estimate the disturbance and their derivatives.. After this, combining with the second-order disturbance observer, a modified sliding surface and the corresponding reaching law are designed to obtain the rudder deflection command directly. Thus, the real sense of IGC system is achieved. Next, the paper uses the Lyapunov stability theory to prove the stability of the system. Finally, the paper provides different simulation cases, which have different maneuver modes of the target, to demonstrate the superiority of the proposed method in reducing the response time, increasing the rudder response, and having a high interception probability.

Optimal Design and Command Filtered Backstepping Control of Exoskeleton With Series Elastic Actuator

Abstract The lower limb exoskeleton can improve mobility and safety during rehabilitation for human. However, most current exoskeleton systems are not capable of providing variable joint stiffness in response to changing external demands. In this paper, a knee exoskeleton based on the series elastic actuator (SEA) is designed for safe human-computer interaction. The structural dimensions of the exoskeleton actuation mechanism were optimized based on gait biomechanics to ensure stability and compactness. While maintaining the mechanism range of motion (ROM), this optimization ensures that less peak force is required during the gait cycle. However, the insertion of series elastic actuators inevitably brings new challenges for high precision control of the exoskeleton, such as the problems of modeling errors, compliance, friction, and external disturbances in the exoskeleton joint. To achieve high precision control of the exoskeleton, an extended disturbance observer (EDO) based command filtered backstepping control (CFBC) of the knee exoskeleton is developed. The effective observation of friction, external disturbances, and modeling errors in the system is obtained by the EDO. Compared with conventional backstepping control, the CFBC can not only solve the “explosion of complexity” problem through a command filter but also reduce filter errors by an error compensation mechanism. Based on the Lyapunov stability, all signals in the closed-loop system are semiglobal uniformly ultimately bounded. Finally, comparison simulation results demonstrate the effectiveness of the proposed control approach.

Inertia Optimization Control and Transient Stability Analysis of Wind Power Grid-Connected System

The virtual inertia control effectively makes up for the insufficient inertia caused by the high penetration wind power grid connection. However, it has an impact on the mechanical part of the wind turbine and greatly increases the difficulty of the dynamic stability analysis of the system, resulting in limited engineering practicability. Therefore, the state equation of the wind power grid-connected system is established in this paper, and the influence of virtual inertia control on wind turbine shafting oscillation is analyzed based on the small-signal theory. Secondly, the nonlinear extended disturbance observer is designed as the compensation signal of inertia control to improve its dynamic stability supportability. Based on the integral manifold method, the shafting model of the wind turbine is reduced, and the transient energy function of shafting is established, which provided the basis for the design of the shafting stability controller. Finally, a grid-connected wind power system with high permeability is installed, and the results demonstrate that under the proposed control strategy, the swing stability of power angle is significantly improved, and the wind turbine shafting oscillation is suppressed.

Output feedback control for the driving cylinder of hydraulic support with error constraint

The position control of the driving cylinder of hydraulic support affects the straightness of the underground coal mining face, so this paper focuses on improving tracking performance of the driving cylinder system. Since only position signal of the system is measurable, a Levant differentiator is designed to estimate the velocity and acceleration of the driving cylinder system, which can reduce the effect of the measurement noise. Besides, the parameter changes, modelling errors and external disturbances are treated as a lumped disturbance, an extended disturbance observer is constructed to estimate the lumped disturbance and compensate for the proposed controller. Moreover, barrier Lyapunov function is introduced to limit the tracking error into a small set around zero, and then the stability of the close-loop system is proved. Both the performance of differentiator and disturbance observer is verified in simulation experiments in MATLAB/Simulink. Finally, an experiment rig for the driving cylinder system of hydraulic support is established and comparative experiments are carried out. The experiment results show that the proposed extended disturbance observer-based output feedback controller with error constraint has a satisfied effectiveness in improving tracking performance.

SMC-Based Integrated Guidance and Control for Beam Riding Missiles With Limited LBPU

This article proposes a novel integrated guidance and control (IGC) law for laser beam riding missiles subjected to power limited laser beam projector unit (LBPU) to ensure the line deviation constraint and fast convergence in a fixed time. By analyzing the LBPU constraints, the improved IGC model is constructed with the help of fixed-time prescribed performance function. Consequently, the LBPU constraints, fast convergence requirement and mismatched uncertainties are involved in this IGC model. The control law is presented by combining sliding mode control and extended disturbance observer. The stability of closed-loop system and the LBPU constraint satisfaction are guaranteed. The effectiveness and robustness of proposed control are illustrated by numerical simulations and Monte Carlo tests.

Extended disturbance observer based robust sliding mode control for active suspension system

In this paper, the approach of reduced-order extended state observer (RO-ESO) proposed by Zuo and Nayfeh (J Sound Vib 265(2):459–465, 2003) for estimation of un-modeled dynamics and disturbances in the antilock braking system is extended to the half car active suspension system (HCASs). Reduced-order ESO is used to estimate the lumped parametric uncertainties, un-modeled dynamics, and external disturbances affecting the performance of HCASs. Here, the estimation accuracy is further improved by the modification of RO-ESO. Modified and extended disturbance observer (E-DO) is proposed to estimate these lumped disturbances and their derivatives, thus reducing disturbance estimation error. A sliding mode control (SMC) based controller is designed to stabilize the vehicle body’s heave and pitch motion using an active suspension system, resulting in ride comfort improvement with guaranteed suspension space constraint and road holding. The proposed E-DO-based SMC (E-DO-SMC) controller’s effectiveness and robustness is analyzed by MATLAB simulations conducted on two different road excitations. The results obtained are compared with RO-ESO based SMC (RO-ESO-SMC) and passive suspension system.

Control of a class of fractional-order systems with mismatched disturbances via fractional-order sliding mode controller

This paper presents a new fractional-order sliding mode controller (FOSMC) for disturbance rejection and stabilization of a class of fractional-order systems with mismatched disturbances. To design this control strategy, firstly, a fractional-order extended disturbance observer (FOEDO) is proposed to estimate the matched and mismatched disturbances and their derivatives. Then, according to the design procedure of the sliding mode controller and based on the designed FOEDO, a proper sliding mode surface is proposed. Subsequently, the proposed FOSMC is designed to guarantee that the system states reach the sliding surface and stay on it forever. The stability of the controlled fractional-order systems is proved via fractional-order Lyapunov stability theory. The numerical examples are used to illustrate the effectiveness of the proposed fractional-order controller. The simulation results of the proposed FOSMC are compared with the results of some other researchers’ works to show the superiority of the proposed control method. The new approach displays some attractive features such as fast response, the chattering reduction, robust stability, less disturbance estimation error, the mismatched disturbance, noise rejection, and better control performance.