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.     

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.     

Extended state observer for MIMO nonlinear systems with stochastic uncertainties

ABSTRACT

In this paper, both linear extended state observer (ESO) and nonlinear ESO with homogeneous weighted functions are proposed for a class of multi-input multi-output (MIMO) nonlinear systems composed of coupled subsystems with large stochastic uncertainties. The stochastic uncertainties in each subsystem including internal coupled unmodelled dynamics and external stochastic disturbance without known statistical characteristics are lumped together as the stochastic total disturbance (extended state) of each subsystem. The linear ESO and nonlinear ESO are designed separately for real-time estimation of not only the unmeasured state but also the stochastic total disturbance of each subsystem. The practical mean square convergence of these two classes of ESOs are developed. Some numerical simulations are presented to demonstrate the effectiveness of the ESOs with the advantages of smaller peaking values and more accurate estimation by the nonlinear ESO.     

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。     

Extended state observer for uncertain lower triangular nonlinear systems subject to stochastic disturbance

The extended state observer (ESO) is the most important part of an emerging control technology known as active disturbance rejection control to this day, aiming at estimating “total disturbance” from observable measured output. In this paper, we construct a nonlinear ESO for a class of uncertain lower triangular nonlinear systems with stochastic disturbance and show its convergence, where the total disturbance includes internal uncertain nonlinear part and external stochastic disturbance. The numerical experiments are carried out to illustrate effectiveness of the proposed approach.     

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.     

Global adaptive control for a class of uncertain stochastic nonlinear systems with unknown output gain

This paper addresses the global adaptive control problem for a class of uncertain stochastic nonlinear systems in the output-feedback form. Due to the unknown output gain, we construct a full-order homogeneous observer instead of using the system output. Then, by adding a power integrator technique, an output-feedback controller is designed, as well as an adaptive law to deal with the unknown nonlinear growth rates. Based on the generalized stochastic Lyapunov stability theorem, it can be proved that all the signals of the closed-loop system are bounded in probability, and the system states converge to the origin almost surely.     

Linear extended state observer based sliding mode disturbance decoupling control for nonlinear multivariable systems with uncertainty

In this paper, the sliding mode dynamic disturbance decoupling tracking control method based on the linear extended state observer (LESO) is proposed for a class of square multivariable nonlinear uncertain system. The model plant contains the known linear dynamics, the unknown nonlinear dynamics and the internal and external disturbances, and the various input-output pairs are interacted. The system states are not available for measurement. An improved LESO is developed. The leading feature which is different from the typical ESO lies in that its extended state does not contain the known linear dynamics. The improved LESO can guarantee the error variables to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. So this ball radius can be arbitrarily as small as desired by tuning design parameters. And we give a simple method by which the gain parameters of LESO can be computed easily. This estimation to the total disturbance of the original system is introduced into the sliding mode control design to complete disturbance rejection and decoupling. Rigorous stability analysis shows that the system output can track the desired signal closely. Finally, a class of mass–spring–damper system is taken to make the numerical simulation analysis to illustrate the effectiveness of the proposed control method.     

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.     

Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems

In this paper, the problem of decentralized adaptive output-feedback stabilization is investigated for large-scale stochastic nonlinear systems with three types of uncertainties, including parametric uncertainties, nonlinear uncertain interactions and stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystems are stochastic input-to-state stable, an adaptive output-feedback controller is constructively designed by the backstepping method. It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability. In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin. The contributions of the work are characterized by the following novel features: (1) even for centralized single-input single-output systems, this paper presents a first result in stochastic, nonlinear, adaptive, output-feedback asymptotic stabilization; (2) the methodology previously developed for deterministic large-scale systems is generalized to stochastic ones. At the same time, novel small-gain conditions for small signals are identified in the setting of stochastic systems design; (3) both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states; (4) parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields, which may appear nonlinearly; (5) the concept of stochastic input-to-state stability and the method of changing supply functions are adapted, for the first time, to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control.     

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.     

Active Disturbance Rejection Control for Uncertain Nonlinear Systems With Sporadic Measurements

This paper deals with the problem of active disturbance rejection control (ADRC) design for a class of uncertain nonlinear systems with sporadic measurements. A novel extended state observer (ESO) is designed in a cascade form consisting of a continuous time estimator, a continuous observation error predictor, and a reset compensator. The proposed ESO estimates not only the system state but also the total uncertainty, which may include the effects of the external perturbation, the parametric uncertainty, and the unknown nonlinear dynamics. Such a reset compensator, whose state is reset to zero whenever a new measurement arrives, is used to calibrate the predictor. Due to the cascade structure, the resulting error dynamics system is presented in a non-hybrid form, and accordingly, analyzed in a general sampled-data system framework. Based on the output of the ESO, a continuous ADRC law is then developed. The convergence of the resulting closed-loop system is proved under given conditions. Two numerical simulations demonstrate the effectiveness of the proposed control method.      

An integrated approach to hypersonic entry attitude control

This paper presents an integrated approach based on dynamic inversion(DI)and active disturbance rejection control(ADRC)to the entry attitude control of a generic hypersonic vehicle(GHV).DI is frstly used to cancel the nonlinearities of the GHV entry model to construct a basic attitude controller.To enhance the control performance and system robustness to inevitable disturbances,ADRC techniques,including the arranged transient process(ATP),nonlinear feedback(NF),and most importantly the extended state observer(ESO),are integrated with the basic DI controller.As one primary task,the stability and estimation error of the second-order nonlinear ESO are analyzed from a brand new perspective:the nonlinear ESO is treated as a specifc form of forced Li′enard system.Abundant qualitative properties of the Li′enard system are utilized to yield comprehensive theorems on nonlinear ESO solution behaviors,such as the boundedness,convergence,and existence of periodic solutions.Phase portraits of ESO estimation error dynamics are given to validate our analysis.At last,three groups of simulations,including comparative simulations with modeling errors,Monte Carlo runs with parametric uncertainties,and a six degrees-of-freedom reference entry trajectory tracking are executed,which demonstrate the superiority of the proposed integrated controller over the basic DI controller.     

状态约束下连铸结晶器振动位移系统的抗干扰控制

针对伺服电机驱动的连铸结晶器振动位移系统中存在的机械加工精度误差、摩擦非线性等不确定性和负载转矩扰动等问题,考虑伺服电机单方向变速转动产生的状态约束,提出了一种基于切换函数的抗干扰控制方案。首先,针对系统中状态约束且不可测及前向通道含有非线性周期函数（近似正弦函数,逆解非唯一）传递关系的问题,通过建立偏心轴转角误差与结晶器振动位移之间的函数关系,解决系统自身的状态约束问题。其次,针对系统存在的不确定性和负载转矩扰动问题,设计切换函数重构系统中存在的整体不确定性,通过扩张状态观测器对整体不确定性进行估计,将估计值与滑模控制方法相结合设计输出反馈控制器,实现结晶器振动位移的跟踪控制。最后,通过Lyapunov理论证明了控制系统的稳定性,通过仿真验证了本文所提方法的有效性。     

载人潜水器的干扰特性分析与自适应滑模控制

针对在实际运行中会受到未知外部环境干扰和模型不确定性等因素影响的蛟龙号载人潜水器系统,本文设计了一种基于干扰特性指标的新型自适应滑模控制方法,实现对有益干扰的利用和有害干扰的补偿.首先,文章给出载人潜水器系统的运动学和动力学模型;然后,本文设计非线性干扰观测器估计系统所受的集总扰动,并提出一种扇形区域干扰特性指标,用于判断干扰对系统的影响;其次,文章设计一种基于干扰特性指标的自适应滑模控制方法,并且根据李雅普诺夫理论进行严格的稳定性分析;最后,通过数值仿真,验证所设计的滑模控制方法的优越性.其优越性主要体现在:不仅能够有效缓解抖振现象,并且避免控制增益高估的问题.     

Robust output regulation of a triaxial MEMS gyroscope via nonlinear active disturbance rejection

This paper presents a nonlinear disturbance rejection–based controller for the robust output regulation of a triaxial microelectromechanical system (MEMS) vibratory gyroscope. In a MEMS gyroscope, parameter variations, mechanical couplings, suspension system nonlinearities, thermal noise, and centripetal/Coriolis forces are the main uncertainty sources. In the dynamical equations of the gyroscope, these uncertainties appear as a matched total disturbance, which does not coincide with the required structure of a standard output regulation problem. More specifically, the total disturbance is not guaranteed to belong to the solution space of a fixed dynamical system. Therefore, we propose a control system that comprises a nominal output regulator equipped with a disturbance rejection loop. On the basis of a suitable reference dynamics of the gyroscope, the control system is developed as the stabilization of a zero‐error invariant manifold in the tracking error space. In the disturbance rejection loop, a nonlinear extended state observer (ESO) is designed to estimate the total disturbance. The convergence of the ESO is analyzed in a Lyapunov‐Lurie framework by linear matrix inequalities (LMIs). In the nominal output regulation loop, the stabilization problem of the desired manifold is tackled by introducing a suitable distance coordinate. Next, to achieve guaranteed attenuation of the ESO estimation errors, an energy‐to‐peak design is pursued. On the basis of the center manifold theory, the stability of the overall closed‐loop system is guaranteed. The efficacy of the proposed control method is assessed through software simulations.     

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.     

Output feedback regulation control for a class of cascade nonlinear systems by time‐varying Kalman observer

The global output feedback regulation problem is studied for a class of cascade nonlinear systems. The considered system represents more general classes of nonlinear uncertain systems, including the integral input‐to‐state stable (iISS) unmodeled dynamics, the unknown control direction, the parameter uncertainty, and the external disturbance additively in the input channel. Technically, we explore the changing supply rate technique for the iISS system to deal the iISS unmodeled dynamics and apply the Nussbaum‐type gain into the control design to overcome the unknown control direction. Additionally, a dynamic extended state observer in the form of a time‐varying Kalman observer is novelly constructed to overcome the unmeasured state components in the nonlinear uncertainties. It is shown that the global regulation problem is well addressed by the proposed method, and its efficacy is demonstrated by a fan speed control system.     

基于自抗扰技术的网络化无刷直流电机控制系统时延补偿

采用自抗扰控制技术解决网络化无刷直流电机转速控制系统的时延补偿问题. 首先, 建立含有时变网络诱导时延的无刷直流电机控制系统模型, 并将时变时延引起的不确定动态描述为系统模型的不确定性; 然后, 设计自抗扰控制器, 对时延引起的不确定动态进行动态线性化补偿, 从而消除时变时延对系统性能的影响; 最后, 通过仿真研究表明了所设计的自抗扰补偿方法的有效性和优越性.

     

Global output-feedback stabilization for a class of uncertain time-varying nonlinear systems

This paper investigates the global output-feedback stabilization for a class of uncertain time-varying nonlinear systems. The remarkable structure of the systems is the presence of uncertain control coefficients and unmeasured states dependent growth whose rate is inherently time-varying and of unknown polynomial-of-output, and consequently the systems have heavy nonlinearities, serious uncertainties/unknowns and serious time-variations. This forces us to explore a time-varying plus adaptive methodology to realize the task of output-feedback stabilization, rather than a purely adaptive one. Detailedly, based on a time-varying observer and transformation, an output-feedback controller is designed by skillfully combining adaptive technique, time-varying technique and well-known backstepping method. It is shown that, with the appropriate choice of the design parameters/functions, all the signals of the closed-loop system are bounded, and furthermore, the original system states globally converge to zero. It is worth mentioning that, the heavy nonlinearities are compensated by an updating law, while the serious unknowns and time-variations are compensated by a time-varying function. The designed controller is still valid when the system has an additive input disturbance which, essentially different from those studied previously, may not be periodic or bounded by any known constant.