On Performance Analysis of General Observers for Uncertain Systems

2017 ◽  
Author(s):  
Wenyan Bai ◽  
Chen Sen ◽  
Yi Huang ◽  
Wenchao Xue ◽  
Ping Liu
Keyword(s):  
Disturbance Observer ◽  
Uncertain Systems ◽  
Estimation Error ◽  
High Gain ◽  
State Observer ◽  
Extended State Observer ◽  
Exact Form ◽  
Extended State ◽  
Real State ◽  
General Observer

This paper aims to rigorously study the observer for general uncertain systems. The proposed observer is shown to be the general form of extended state observer (ESO), disturbance observer (DO), generalized extended state observer (GESO) and extended high gain observer (EHGO). The properties of this general observer is discussed by analyzing the estimation error. The paper illustrates that the output of the proposed general observers may not performs as the estimation the real state and uncertainty. We prove that this observer gives the estimations for the group of states and uncertainties whose exact form is given in the paper. Finally, numerical simulations for a typical example validate the theoretical analysis.

scholarly journals Robust Nonlinear Position Control with Extended State Observer for Single-Rod Electro-Hydrostatic Actuator

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2397
Author(s):  
Young Seop Son ◽  
Wonhee Kim
Keyword(s):  
Position Control ◽  
Estimation Error ◽  
External Disturbance ◽  
Input Function ◽  
High Gain ◽  
State Observer ◽  
Extended State Observer ◽  
Position Tracking ◽  
Extended State ◽  
Position Controller

In the existing literature, studies on position controller design using only position feedback, considering the disturbances for single-rod electro-hydrostatic actuators (EHAs), have not been reported. Herein, we propose a robust nonlinear position control with an extended state observer (ESO) for single-rod EHAs. A new EHA model that consists of position, velocity, and acceleration with an internal state variable is developed. Instead of the separated port pressure dynamics, the acceleration dynamics were defined. The external disturbance, model, and input function uncertainties were lumped into a disturbance. An ESO is developed to estimate the disturbance, as well as the position, velocity, and acceleration. In practice, it is difficult to accurately estimate the disturbance because it includes the external disturbance, system dynamics, and input function uncertainty. The poor estimation performance may degrade the position tracking performance, but a high gain cannot be used to suppress the estimation error because of the measurement noise amplification. To resolve this problem, a robust nonlinear position controller is developed via a backstepping procedure. In the controller, a nonlinear gain is implemented to sufficiently suppress position tracking without the use of a high gain. The stability of the closed-loop system is mathematically proven using the input-to-state stability. The proposed method is simple and suitable for real-time control.

Sampled-data extended state observer-based backstepping control of two-link flexible manipulator

2019 ◽  
Vol 41 (13) ◽  
pp. 3581-3599 ◽  
Author(s):  
Umesh Kumar Sahu ◽  
Bidyadhar Subudhi ◽  
Dipti Patra
Keyword(s):  
Control Strategies ◽  
Estimation Error ◽  
Experimental Studies ◽  
State Observer ◽  
Lyapunov Theory ◽  
Extended State Observer ◽  
Flexible Manipulator ◽  
Sampled Data ◽  
Extended State ◽  
Model Uncertainties

Currently, space robots such as planetary robots and flexible-link manipulators (FLMs) are finding specific applications to reduce the cost of launching. However, the structural flexible nature of their arms and joints leads to errors in tip positioning owing to tip deflection. The internal model uncertainties and disturbance are the key challenges in the development of control strategies for tip-tracking of FLMs. To deal with these challenges, we design a tip-tracking controller for a two-link flexible manipulator (TLFM) by developing a sampled-data extended state observer (SD-ESO). It is designed to reconstruct uncertain parameters for accurate tip-tracking control of a TLFM. Finally, a backstepping (BS) controller is designed to attenuate the estimation error and other bounded disturbances. Convergence and stability of the proposed control system are investigated by using Lyapunov theory. The benefits (control performance and robustness) of the proposed SD-ESO-based BS controller are compared with other similar approaches by pursuing both simulation and experimental studies. It is observed from the results obtained that SD-ESO-based BS Controller effectively compensates the deviation in tip-tracking performance of TLFM due to non-minimum phase behavior and model uncertainties with an improved transient response.

scholarly journals Robust tracking control for two classes of variable stiffness actuators based on linear extended state observer with estimation error compensation

2020 ◽  
Vol 17 (2) ◽  
pp. 172988142091177
Author(s):  
Jishu Guo ◽  
Junmei Guo ◽  
Zhongjun Xiao
Keyword(s):  
Linear System ◽  
Tracking Control ◽  
Estimation Error ◽  
Input Saturation ◽  
Variable Stiffness ◽  
State Observer ◽  
Extended State Observer ◽  
Extended State ◽  
Linear Extended State Observer ◽  
Variable Stiffness Actuators

In this article, a novel robust tracking control scheme based on linear extended state observer with estimation error compensation is proposed for the tracking control of the antagonistic variable stiffness actuator based on equivalent nonlinear torsion spring and the serial variable stiffness actuator based on lever mechanism. For the dynamic models of these two classes of variable stiffness actuators, considering the parametric uncertainties, the unknown friction torques acting on the driving units, the unknown external disturbances acting on the output links and the input saturation constraints, an integral chain pseudo-linear system with input saturation constraints and matched lumped disturbances is established by coordinate transformation. Subsequently, the matched lumped disturbances in the pseudo-linear system are extended to the new system states, and we obtain an extended integral chain pseudo-linear system. Then, we design the linear extended state observer to estimate the unknown states of the extended pseudo-linear system. Considering the input saturation constraints in the extended pseudo-linear system and the estimation errors of the linear extended state observer with fixed preset observation gains, the adaptive input saturation compensation laws and the novel estimation error compensators are designed. Finally, a robust tracking controller based on linear extended state observer, sliding mode control, adaptive input saturation compensation laws, and estimating error compensators is designed to achieve simultaneous position and stiffness tracking control of these two classes of variable stiffness actuators. Under the action of the designed controller, the semi-global uniformly ultimately bounded stability of the closed-loop system is proved by the stability analysis of the candidate Lyapunov function. The simulation results show the effectiveness, robustness, and adaptability of the designed controller in the tracking control of these two classes of variable stiffness actuators. Furthermore, the simulation comparisons show the effectiveness of the proposed estimation error compensation measures in reducing the tracking errors and improving the disturbance rejection performance of the controller.

scholarly journals On-Line Compensation for the Disturbance Rejection Rate of a Platform Seeker Based on a High-Gain Extended State Observer

2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Li Wei ◽  
Liu Shixiang ◽  
Zhang Wenjie ◽  
Xia Qunli
Keyword(s):  
Disturbance Rejection ◽  
Rejection Rate ◽  
High Gain ◽  
State Observer ◽  
Extended State Observer ◽  
Signal Extraction ◽  
Stable Region ◽  
Compensation Scheme ◽  
Extended State ◽  
On Line

This paper focuses on the on-line compensation of the disturbance rejection rate (DRR) for a platform seeker. The mathematical model of the typical platform seeker based on the inertial space is established, and the line-of-sight (LOS) rate from different signal extraction points is strictly derived. Considering the spring torque disturbance and damping torque disturbance caused by the missile attitude motion, the seeker DRR transfer functions are deduced and the amplitude and phase characteristics at different frequencies are also analyzed. In order to close the engineering practice, the DRR parasitic loop (DRRPL) model of the seeker is rationally simplified and the stable region of the parasitic loop from different extraction points is also obtained. However, to increase the stability and guidance accuracy of the missile terminal flight, the compensation scheme based on the high-gain extended state observer (ESO) is used to estimate the disturbance torques and eliminate the seeker DRR effect. Numerical simulations are conducted to verify the effectiveness of the proposed scheme. The simulation results show that the seeker DRR effect mainly exists in the middle and low frequencies and the stable region of the parasitic loop at different signal extraction points is different. The proposed compensation scheme can effectively eliminate the parasitic loop effect of the seeker and increase the flight stability of the missile. It can reduce the terminal miss distance of the missile and improve the strike accuracy.

scholarly journals Finite-Time Anti-Disturbance Inverse Optimal Attitude Tracking Control of Flexible Spacecraft

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Chutiphon Pukdeboon ◽  
Anuchit Jitpattanakul
Keyword(s):  
Optimal Control ◽  
Lyapunov Function ◽  
Finite Time ◽  
Estimation Error ◽  
State Observer ◽  
Flexible Spacecraft ◽  
Extended State Observer ◽  
Inverse Optimal Control ◽  
Extended State ◽  
Attitude Tracking

We propose a new robust optimal control strategy for flexible spacecraft attitude tracking maneuvers in the presence of external disturbances. An inverse optimal control law is designed based on a Sontag-type formula and a control Lyapunov function. An adapted extended state observer is used to compensate for the total disturbances. The proposed controller can be expressed as the sum of an inverse optimal control and an adapted extended state observer. It is shown that the developed controller can minimize a cost functional and ensure the finite-time stability of a closed-loop system without solving the associated Hamilton-Jacobi-Bellman equation directly. For an adapted extended state observer, the finite-time convergence of estimation error dynamics is proven using a strict Lyapunov function. An example of multiaxial attitude tracking maneuvers is presented and simulation results are included to show the performance of the developed controller.

scholarly journals An Adaptive Nonlinear Extended State Observer for the Sensorless Speed Control of a PMSM

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Minggang Gan ◽  
Chenyi Wang
Keyword(s):  
Electromotive Force ◽  
Estimation Error ◽  
Permanent Magnet Synchronous Motor ◽  
Speed Control ◽  
State Observer ◽  
Lyapunov Theory ◽  
Extended State Observer ◽  
Rotor Speed ◽  
Extended State ◽  
Nonlinear Extended State Observer

This paper presents a sensorless speed control strategy for a permanent-magnet synchronous motor (PMSM) based on an adaptive nonlinear extended state observer (ANLESO). In this paper, an extended state observer (ESO), which takes back-EMF (back electromotive force) as an extended state, is used to estimate the rotor position and the rotor speed because of its simpler structure and higher accuracy. Both linear ESO (LESO) and nonlinear ESO (NLESO) are considered to estimate the back-EMF of PMSM, and NLESO is finally implemented due to its obvious advantage in convergence. The convergence characteristics of the estimation error of the observer are analyzed by the Lyapunov theory. In order to take both stability and steady-state error into consideration, an adaptive NLESO is proposed, which adaptively adjusts the parameters of NLESO to a compromised value. The performance of the proposed method was demonstrated by simulations and experiments.

scholarly journals Attitude-constrained reorientation control for spacecraft based on extended state observer

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879452 ◽  
Author(s):  
Yu Cheng ◽  
Dong Ye ◽  
Zhaowei Sun
Keyword(s):  
Actuator Saturation ◽  
Estimation Error ◽  
External Disturbance ◽  
Parametric Uncertainty ◽  
State Observer ◽  
Extended State Observer ◽  
Extended State ◽  
Finite Time Stability ◽  
Backstepping Controller ◽  
The Difference

This article investigates the spacecraft attitude reorientation control problem in the presence of attitude constraint, actuator saturation, parametric uncertainty, and external disturbance. First, a nonlinear tracking law based on a strictly convex potential function is proposed to generate the virtual control angular velocity which has only one global minimum. Then, utilizing the auxiliary system governed by the difference between the upper bound of actuator torque and the untreated command torque, a novel backstepping controller is presented, which is able to satisfy the constraint of actuator saturation and guarantee the stability of control system. In addition, an extended state observer with the uniformly ultimately bounded estimation error and finite-time stability is put forward to realize the real-time compensation of the compound disturbance consisting of parametric uncertainty and external disturbance. Therefore, it enhances the robustness and improves the accuracy of the extended state observer–based backstepping controller. Finally, simulation results validate the effectiveness and reliability of the proposed schemes.

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