Estimation of decenteralized unknown dynamics for a 2DOF manipulator using a time varying extended state observer

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.

In order to achieve dynamical pattern recognition of univariate time series from the perspective of structural stability, this paper proposes a method based on Extended State Observer (ESO) and deterministic learning for addressing the issue of recognizing the structural stability of the topological structure of dynamical patterns in univariate time series. The ESO is capable of reconstructing the system states and their unknown dynamics during the observation phase, while the deterministic learning effectively resolves the challenges associated with obtaining and modeling the derivative information of the dynamics. During the learning phase, the ESO is employed to recover state trajectories from sampled output signals. These trajectories utilize the regressed trajectories as inputs, satisfying the partially persistent excitation (PE) condition, thereby accurately approximating the unknown dynamics through the estimated regressed trajectories. Subsequently, we establish a novel recognition error system that approximates the first-order derivatives of the system dynamics using a finite difference method, thus avoiding the need for re-modeling the test patterns and enabling the identification of dynamic behaviors from the topological structural perspective. Finally, we theoretically demonstrate that the residuals of the recognition error system reflect the structural stability differences in system dynamics between the training and test patterns, and simulation further substantiate the effectiveness and accuracy of the proposed method.

Disturbances and uncertainties are the main concerns in control systems. To obtain this information in real time, the extended state observer is proposed as the core of the active disturbance rejection control. However, the estimation errors of extended state observer cannot converge to zero in the presents of unknown but bounded disturbances, which will bring unexpected tracking errors to the closed-loop system. By taking advantage of the linear extended state observer and the super-twisting algorithm, the super-twisting extended state observer is proposed to deal with the non-diminishing second-order derivable disturbances in this paper. The asymptotic convergence of the super-twisting extended state observer and the controller are proved by the Lyapunov method. Moreover, the effectiveness and robustness of the super-twisting extended state observer are verified by simulation analysis. Simulation results show that the proposed super-twisting extended state observer maintains the minimized estimation error with less settling time compared the with linear extended state observer. The tracking performance of the controller with the proposed observer is greatly improved.

In this article, a new approach to design a finite‐time extended state observer (FT‐ESO) for a class of uncertain nonlinear systems is proposed based on a novel coordinate transformation. First, a time‐varying extended state observer (ESO) is designed to make the estimation error uniformly bounded. In this regard, the dynamic of the estimation error is transformed into a linear system with a generalized disturbance term as its input. Then, the time‐varying gains of the ESO are designed to stabilize the system and consequently, to converge the estimation error to the neighborhood of zero and to remain uniformly bounded as t → t0 + T. In this article, without any knowledge about the disturbance, and uncertainties, a fault‐tolerant FT‐ESO is designed. Simulation results demonstrate the effectiveness of the proposed finite‐time ESO for serial robotic manipulators with any number of links, in the presence of disturbances and an unknown fault.

To regulate uncertainties in system dynamics and external disturbances, a robust controller is proposed for a plant with time-varying uncertainty. The design is based on the concept of extended state observer (ESO) with repetitive controller (RC). In real time estimation and mitigation of the total effect of various uncertainties, ESO based RC is particularly effective against a wide range of parameter variations, model uncertainties, and large disturbances. With only two tuning parameters, the controller provides a simple and user friendly solution to complex engineering problems in practice. The comparison results verified the effectiveness of the ESO based RC over state observer (SO) based RC.

This paper considers the path following problem of underactuated marine surface vessel in the presence of model uncertainty and external disturbances. A robust control strategy is proposed by employing the dynamic surface control and extended state observer. The key features of the presented control strategy include that, first, the extended state observer is proposed to estimate the model uncertainty and external disturbances of the underactuated marine surface vessel; second, in order to avoid the calculation of derivatives of virtual control signals, the dynamic surface control is used to design the robust control laws based on the output of the extended state observer. All regular paths are feasible by introducing the Serret-Frenet Line-of-Sight guidance. Uniformly ultimately bounded can be obtained based on the proposed control strategy by using Lyapunov theory. Simulation results demonstrate the effectiveness of the proposed control strategy.

In this paper, the problem of attitude tracking control for a class of vertical take-off landing (VTOL) aircraft in the presence of uncertain disturbances is addressed. The active disturbance rejection control (ADRC) method is utilized to address uncertain disturbances, while the radial basis function (RBF) neural network is considered for handling unknown nonlinear dynamics. By incorporating a modified tracking differentiator, a nonlinear state error feedback controller, and an extended state observer, the disturbance observation problem in the aircraft system is solved. These disturbances, seen as a combined disturbance in the aircraft system, are counteracted through the extended state observer. Furthermore, the unknown nonlinear dynamics within the aircraft system are approximated using the RBF neural network. Subsequently, the paper suggests adaptive ADRC strategies based on neural network and formulates adaptive control laws to estimate unknown parameters. The Lyapunov stability theory proves the effectiveness of the proposed control strategies. The simulation results show that the attitude tracking control problem of VTOL aircraft can be achieved under the proposed control strategies and adaptive control laws.

This paper presents the modeling and analysis of disturbances caused by model changes, unknown dynamics, and external forces during task execution of a wheeled Inverted PENdulum Type Assistant Robot. Compensating these disturbances and their effects results in the ability of the system to perform different tasks without changes in the control structure. This results in a unified controller for multiple tasks making the control system simple without sacrificing robustness. Estimation of these disturbances is performed using the extended state observer (ESO), which is a practical observer since it requires very little system information. To ensure proper application of the ESO, the analysis of the equilibrium states under disturbances was performed. The disturbance modeling and the effectiveness of the control are verified by results from disturbance and task tests. Finally, the bounded input bounded output behavior of the system with consideration to the disturbances is presented.

Robust internal model control based on a novel generalized extended state observer and its application on a two-inertia system

Unknown System Dynamics Estimator for Nonlinear Uncertain Systems

This article investigates the high-performance position control of servo systems based on high-order fully actuated (HOFA) approach with dynamical compensator and extended state observer (ESO). In the proposed control approach, the dynamics of servo systems is formulated via an HOFA model, in which the electrical subsystem is approximated to an inertia system by using the first-order Taylor expansion and the truncated method. Based on the HOFA model, a composite control law is synthesized to achieve the desired tracking error dynamics, and dynamical compensator is applied to offer additional design degrees of freedom for the control performance improvement. To cope with uncertainties and disturbances, a linear ESO is designed for online state estimation and disturbance compensation. The proposed approach can explicitly solve the control gains in an extremely straightforward and simple way. This brings a great convenience for the control system design, analysis and implementation. Experimental results on a servo motor system validate the superior performance of the proposed controller over some of the-state-of-art methods.

In this paper, an approximation-free funnel feedback controller is proposed for a class of nonlinear servomechanisms to achieve prescribed tracking error performance. An improved funnel function is proposed to guarantee the transient and asymptotic behavior of the tracking error within a given funnel boundary. The proposed funnel function removes the imposed assumption used in conventional funnel controls (e.g., systems with relative degree one or two) and avoids the potential singularity problem in prescribed performance controls. Moreover, an extended state observer (ESO) is used to address the effect of unknown dynamics in the control system (e.g., friction and disturbances), where the ESO parameters can be easily designed based on the control system bandwidth. The stability of the proposed control system with ESO and funnel function is analyzed via the Lyapunov theory. Comparative simulations and experimental results are conducted based on a practical turntable servomechanisms to validate the efficacy of the proposed method.

The active disturbance rejection control is used to design the control scheme for the vertical inverted pendulum system. Based on the original active disturbance rejection control algorithm, a linear/nonlinear switched extended state observer is proposed for such an unstable system with single input and double output, strong nonlinear and strong coupling. Firstly, the reason of the limited ability of nonlinear extended state observer to estimate large perturbations is analyzed, then a linear extended state observer is proposed to make up for the defects of NLESO, and the feasibility of the proposed linear/nonlinear auto disturbance rejection switching control is verified by numerical simulation.

A nonlinear Third-Order Extended State Observer (TESO) is proposed for the estimation of the rotor position and speed for sensorless Interior Permanent Magnet (IPM) synchronous motor drives. An optimized parameter tuning method is deployed to reconcile the needs of expanding the disturbance observation bandwidth and suppressing the measurement noise effectively. Both the steady state and transient performance of the TESO are verified through the experimental tests. In comparison with the performance of a conventional Linear Extended State Observer (LESO), the proposed observer is proved to have better noise suppression ability and disturbance observation performance in wide operating range.

Hovering over an asteroid is challenging due to both the large gravitational uncertainty and the strong external disturbance. When a spacecraft is not equipped with velocity sensors to simplify the navigation system and reduce the mass and costs, or the velocity sensors malfunction, the situation may be worse. In this paper, an extended state observer (ESO) is devised to estimate the velocity and the lumped disturbance simultaneously. The estimate errors are proved to be uniformly ultimately bounded with the assumption that the change rate of the lumped disturbance is bounded. To cope with control input saturation, a backstepping controller in conjunction with an auxiliary system is proposed for the hovering. Combining the controller with the ESO, we develop a disturbance rejection control scheme without velocity feedback. The stability of the whole closed-loop system is analyzed via the Lyapunov theory, showing that the control scheme can drive a spacecraft to the neighborhood of the desired hovering state. The numerical simulations of both body-fixed hovering and inertial hovering are conducted to demonstrate the effectiveness of the proposed scheme.