Active disturbance rejection control approach to output‐feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty

In this paper, we apply the active disturbance rejection control approach to output‐feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time‐varying gain are used in ESO design separately. The mean square practical stability for the closed‐loop system with constant gain ESO and the mean square asymptotic stability with time‐varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output‐feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust nonlinear control of atomic force microscope via immersion and invariance

This paper reports an immersion and invariance (I&I)–based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed‐loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov‐based analysis of the closed‐loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method.     

基于系统辨识的航空发动机稳态燃油自抗扰控制

自抗扰控制技术应用于航空发动机稳态燃油控制存在两个难点：发动机中的高频不确定动态导致扩张状态观测器(Extended State Observer,ESO)增益过高和名义控制系数整定困难。针对此现状,提出一种基于系统辨识的航空发动机稳态燃油自抗扰控制器。首先,使用经典Gram-Schmidt(Classical Gram-Schmidt,CGS)算法对控制系数和发动机未知动态进行辨识,将辨识信息加入ESO中设计改进ESO (Improved ESO,IESO),从而使总扰动中包含较少的高频动态,降低观测器增益。其次,基于IESO设计航空发动机稳态燃油自抗扰控制器,并根据辨识结果快速整定名义控制系数。最后,分析IESO观测误差的收敛性和闭环系统的稳定性。仿真结果表明,所提方法可以快速整定名义控制系数,有效降低观测器增益,进而提高系统的鲁棒性。     

自抗扰控制对具边界扰动和区间内反阻尼的波动方程的镇定

本文讨论边界具有外部扰动和区域内具有反阻尼的一维波动方程的的镇定问题. 主要的方法是后退反演变换和自抗扰控制方法. 即通过扩张状态观测器将扰动在线估计并在反馈控制中实时消除. 本文在扩张状态观测器中使用了两种增益调整策略——常数高增益与时变增益. 为避免常数高增益带来的峰值问题, 在控制环节中使用了饱和方法. 时变的增益可以在很大程度上减少扩张状态观测器中由于常数高增益引起的峰值问题同时可以达到完全消除干扰的镇定效果.     

An adaptive disturbance rejection control scheme for multivariable nonlinear systems

An adaptive disturbance rejection control scheme is developed for uncertain multi-input multi-output nonlinear systems in the presence of unmatched input disturbances. The nominal output rejection scheme is first developed, for which the relative degree characterisation of the control and disturbance system models from multivariable nonlinear systems is specified as a key design condition for this disturbance output rejection design. The adaptive disturbance rejection control design is then completed by deriving an error model in terms of parameter errors and tracking error, and constructing adaptive parameter-updated laws and adaptive parameter projection algorithms. All closed-loop signals are guaranteed to be bounded and the plant output tracks a given reference output asymptotically despite the uncertainties of system and disturbance parameters. The developed adaptive disturbance rejection scheme is applied to turbulence compensation for aircraft fight control. Simulation results from a benchmark aircraft model verify the desired system performance.     

Active disturbance rejection and Lyapunov redesign approaches for robust boundary control of plate vibration

In this paper, two approaches, namely active disturbance rejection control (ADRC) and Lyapunov redesign, are utilised to stabilise the vibration of a boundary-controlled flexible rectangular plate in the presence of exogenous disturbances. Based on ADRC, an estimation/cancellation strategy is applied where disturbance is estimated online by an extended state observer (ESO) and cancelled by injecting the output of ESO into the feedback loop. By the Lyapunov redesign, on the other hand, the control law intended for a nominal system is redesigned by adding a (discontinuous) control component that makes the system robust to large uncertainties. Both control algorithms are designed directly based on partial differential equation model of the plate so that spillover instabilities that are a result of model truncation are avoided. The established control schemes are able to stabilise the plate vibration by actuating and sensing only along the plate boundary while accounting for the dynamical effects of Gaussian curvature integral, in-plane membrane force and actuator mass. The stability of each control approach is proven using Lyapunov analysis. The efficacy of each proposed control is illustrated by simulation results.     

Active disturbance rejection control approach to stabilization of lower triangular systems with uncertainty

In this paper, we apply the active disturbance rejection control (ADRC) to stabilization for lower triangular nonlinear systems with large uncertainties. We first design an extended state observer (ESO) to estimate the state and the uncertainty, in real time, simultaneously. The constant gain and the time‐varying gain are used in ESO design separately. The uncertainty is then compensated in the feedback loop. The practical stability for the closed‐loop system with constant gain ESO and the asymptotic stability with time‐varying gain ESO are proven. The constant gain ESO can deal with larger class of nonlinear systems but causes the peaking value near the initial stage that can be reduced significantly by time‐varying gain ESO. The nature of estimation/cancelation makes the ADRC very different from high‐gain control where the high gain is used in both observer and feedback. Copyright © 2015 John Wiley & Sons, Ltd.     

Active disturbance rejection control to MIMO nonlinear systems with stochastic uncertainties: approximate decoupling and output-feedback stabilisation

ABSTRACT

In this paper, we apply the active disturbance rejection control, an emerging control technology, to output-feedback stabilisation for a class of uncertain multi-input multi-output nonlinear systems with vast stochastic uncertainties. Two types of extended state observers (ESO) are designed to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without requiring the statistical characteristics, uncertain nonlinear interactions between subsystems, and uncertainties caused by the deviation of control parameters from their nominal values. The estimations decouple approximately the system after cancelling stochastic total disturbance in the feedback loop. As a result, we are able to design an ESO-based stabilising output-feedback and prove the practical mean square stability for the closed-loop system with constant gain ESO and the asymptotic mean square stability with time-varying gain ESO, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.     

Dual closed‐loop tracking control for wheeled mobile robots via active disturbance rejection control and model predictive control

A dual closed‐loop tracking control is proposed for a wheeled mobile robot based on active disturbance rejection control (ADRC) and model predictive control (MPC). In the inner loop system, the ADRC scheme with an extended state observer (ESO) is proposed to estimate and compensate external disturbances. In the outer loop system, the MPC strategy is developed to generate a desired velocity for the inner loop dynamic system subject to a diamond‐shaped input constraint. Both effectiveness and stability analysis are given for the ESO and the dual closed‐loop system, respectively. Simulation results demonstrate the performances of the proposed control scheme.     

A novel redesign framework to extend the application scope of a class of disturbance‐rejection algorithms

In this paper, a novel redesign method is developed for a class of disturbance‐rejection algorithms so that they can be applied to pure‐feedback nonaffine‐in‐control nonlinear systems with matched and mismatched disturbances. First, a series of augmented dynamical equations, which evolve faster than the original system, are constructed to establish a boundary‐layer subsystem to derive the virtual and actual inputs for the nominal system. Then, the composite interconnected system is studied in the standard singular perturbed form. In the slow timescale, the reduced slow subsystem (RSS) is transformed into the chain of integrators form in the error coordinate, for which the existing antidisturbance methods can be employed. The tracking performance of the closed‐loop system is approximated by RSS under singular perturbation theory. The proposed redesign method is adopted to three existing disturbance‐rejection algorithms for a pure‐feedback nonaffine‐in‐control numerical example in the presence of matched and mismatched disturbances. The effectiveness is demonstrated by simulation experimental results.     

On Finite‐Time Stabilization of Active Disturbance Rejection Control for Uncertain Nonlinear Systems

This paper designs the active disturbance rejection control (ADRC) to achieve finite‐time stabilization for a class of uncertain nonlinear systems. The proposed control incorporates both an extended state observer (ESO) as well as an adaptive sliding mode controller. The ESO is utilized to estimate the full system states and the total uncertainties, and the adaptive strategy is incorporated to deal with the estimation errors. It is proved that, with the application of the proposed control law, semi‐global finite‐time stabilization can be achieved. Effectiveness of the proposed method is illustrated with a numerical example.     

Extended filtering high‐gain output feedback controller for a class of uncertain nonlinear systems subject to external disturbances

In this article, an extended filtering high‐gain output feedback controller is developed for a class of uncertain nonlinear systems subject to external disturbances. The nonlinearities under consideration satisfy a semiglobal Lipschitz condition. The proposed control architecture integrates the extended state observer (ESO), high gain, and low‐pass filter together. None of them is used alone. The ESO can not only estimate the unknown internal state, but also deliver a good property of disturbance rejection simultaneously due to the presence of high gain. Since the high gain deteriorates the robustness of the system, a low‐pass filtering mechanism is added in the control law to filter away aggressive signals and recover the robustness. The filtering control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed stability. The matched uncertainties are canceled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. Numerical examples are provided to illustrate the effectiveness of the novel design via comparisons with the model reference adaptive control method and L₁ adaptive controller.     

线性自抗扰控制器的稳定性研究

研究了线性扩张状态观测器(Extended state observer, ESO)的估计能力,并且分析了在线性自抗扰控制(Linear active disturbance rejection control, LADRC)下闭环系统的稳定性. 对于系统模型未知的情形, 给出了线性扩张观测器估计误差有界的证明, 并通过分析得出了如下结论: 在扩张状态观测器跟踪误差趋于零的前提下, 在线性自抗扰控制下的闭环系统可以实现对设定信号的精确跟踪以及输入-输出有界(Bounded input and bounded output, BIBO)稳定.     

On convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems

In this paper, the practical mean-square convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems modelled by the Itô-type stochastic differential equations with vast stochastic uncertainties is developed. We first design an extended state observer (ESO) to estimate both the unmeasured states and the stochastic total disturbance which includes unknown internal system dynamics, external stochastic disturbance without known statistical characteristics, unknown stochastic inverse dynamics, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then cancelled (compensated) in the feedback loop. An ESO-based output-feedback control is finally designed analogously as for the system without uncertainties. The practical mean-square reference tracking and practical mean-square stability of the resulting closed-loop system are achieved. The numerical experiments are carried out to illustrate the effectiveness of the proposed approach.     

Boundary stabilization of a cascade of ODE‐wave systems subject to boundary control matched disturbance

In this paper, we are concerned with a cascade of ODE‐wave systems with the control actuator‐matched disturbance at the boundary of the wave equation. We use the sliding mode control (SMC) technique and the active disturbance rejection control method to overcome the disturbance, respectively. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of solution for the closed‐loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed‐loop system. Considering that the SMC usually requires the large control gain and may exhibit chattering behavior, we then develop an active disturbance rejection control to attenuate the disturbance. The disturbance is canceled in the feedback loop. The closed‐loop systems with constant high gain and time‐varying high gain are shown respectively to be practically stable and asymptotically stable. Then we continue to consider output feedback stabilization for this coupled ODE‐wave system, and we design a variable structure unknown input‐type state observer that is shown to be exponentially convergent. The disturbance is estimated through the extended state observer and then canceled in the feedback loop by its approximated value. These enable us to design an observer‐based output feedback stabilizing control to this uncertain coupled system. Copyright © 2016 John Wiley & Sons, Ltd.     

Output feedback stabilization for a Kirchhoff‐type nonlinear beam with general corrupted boundary observation

This paper is concerned with the boundary output feedback stabilization for a Kirchhoff‐type nonlinear beam equation with boundary observation subject to a general disturbance. The active disturbance rejection control approach is adopted to design the controller and the disturbance estimator. By this approach, the disturbance is estimated by a relatively independent estimator and then canceled in the feedback loop. The existence and uniqueness of the classical solution to the closed‐loop system are proved. The asymptotical convergence of the closed‐loop system is obtained. Copyright © 2017 John Wiley & Sons, Ltd.     

Altitude control for flexible wing unmanned aerial vehicle based on active disturbance rejection control and feedforward compensation

For achieving the accurate trajectory tracking of the flexible wing unmanned aerial vehicle in the complicated missions, especially the vertical component, a feedforward compensation unit–based active disturbance rejection control (ADRC) is proposed. In ADRC, the internal dynamics and complicated influence of the total disturbance will be estimated and dynamically compensated by extended state observer (ESO). It puts a very high request on the observation ability of ESO with the unpredictable external disturbance, complex internal coupling influence, and the strong nonlinear characteristic of the proposed system. For this reason, by deeply analyzing the model of this system, the varying attitude influence on the altitude control will be deduced. Then, this influence will be compensated previously by a feedforward compensation unit. Through the previous compensation of the calculable part of the internal dynamics and total disturbance, the burden of ESO can be reduced largely. In this way, it improves the control effect of the ADRC with better observation precision of ESO. After that, based on the hardware‐in‐the‐loop simulation, the effectiveness of the proposed method is verified completely with the complicated flight missions. The robustness of the control effect and observation ability of ESO are also verified by the Monte Carlo simulation. At last, the results of actual flight experiment prove the advancement and practicability of the proposed ADRC method.     

Output Regulation and Active Disturbance Rejection Control: Unified Formulation and Comparison

Output regulation theory aims to design a controller for achieving reference tracking and disturbance rejection while maintaining system stability. Different from the stabilization problem about an equilibrium point, the output regulation problem is capable of characterizing more complicated steady‐state trajectories induced by reference and/or disturbance. Many efforts have been made to reveal how a steady‐state trajectory can be characterized, estimated, and hence compensated by a controller such that output regulation can be asymptotically achieved. When the steady‐state trajectory is approximately treated as a constant “quantity”, the standard output regulation implies an approximate version within which output regulation is practically achieved. It is revealed in this paper that such an approximate version of output regulation includes the later developed active disturbance rejection control (ADRC) method as a special case.     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

Stabilization of Uncertain Multi‐Order Fractional Systems Based on the Extended State Observer

The extended state observer (ESO) based controller has been used successfully with integer‐order systems involving large uncertainties. In this paper, the robust control of uncertain multi‐order fractional‐order (FO) systems based on ESO is investigated. First, we transform the multi‐order FO system into an equivalent system in the form of a same‐order state‐space equation. Then, the ESO for the new system is established for estimating both the state and the total disturbance. Sufficient conditions for bounded‐input and bounded‐output stability are derived, and the asymptotic stability of the closed loop system is analyzed, based on whether the states are available or not. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the proposed methodology.