Stabilization and Tracking Control of X‐Z Inverted Pendulum Using Flatness Based Active Disturbance Rejection Control

A flatness based robust active disturbance rejection control technique scheme with tracking differentiator is proposed for the problem of stabilization and tracking control of the X‐Z inverted pendulum known as a special underactuated, non‐feedback linearizable mechanical system. The differential parameterization on the basis of linearizing the system around an arbitrary equilibrium decouples the underactuated system into two lower order systems, resulting in two lower‐order extended state observers. Using a tracking differentiator to arrange the transient process utilizes the problem of stabilization and tracking control and gives a relatively small initial estimation error, which enlarges the range of the controller parameters. The convincing analysis of the proposed modified linear extended state observer is presented to show its high effectiveness on estimating the states and the extended states known as the total disturbances consisting of the unknown external disturbances and the nonlinearities neglected by the linearization. Simulation results on the stabilization and tracking control of the X‐Z inverted pendulum, including a comparative simulation with an all‐state‐feedback sliding mode controller are presented to show the advantages of the combination of flatness and active disturbance rejection control techniques.     

有源电力滤波器的自抗扰控制研究

针对采用PI控制器控制有源电力滤波器时存在谐波或基波电流指令而无法实现无静差调节,且数字化后会进一步增大稳态误差,使有源电力滤波器的补偿性能降低的问题,提出一种有源电力滤波器的自抗扰控制策略。该策略利用自抗扰控制器的非线性跟踪-微分器和扩张状态观测器分别处理参考输入和输出,并选择适当的状态误差,实现了对滤波的自动、精确补偿。仿真和实验结果表明,有源电力滤波器采用自抗扰控制策略后具有很强的鲁棒性、稳定性和适应性,控制性能有较大改善。     

Active disturbance rejection control for power plant with a single loop

The cascade proportional‐integral‐derivative (PID) control method is widely used in power plant control field. In this paper, an active disturbance rejection control (ADRC) for a power plant with a single loop is introduced for eliminating the shortcomings of the cascade PID control method. The proposed controller based on the ADRC method consists of a tracking differentiator (TD), an extended state observer (ESO) and a nonlinear combination of errors. In this approach, the processes with higher orders, uncertainties and unmodeled dynamics are viewed as lower‐ordered systems with general disturbances, and the general disturbances are estimated by ESO, and then actively compensated. Besides, only one measured output is needed in the proposed method instead of two or three in the cascade PID control method. Some simulation studies compared with the regular cascade PID control method show the proposed method has better performance beyond the regular cascade PID control method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A high-performance flight control approach for quadrotors using a modified active disturbance rejection technique

In practice, the parameters of the flight controller of the quadrotors are commonly tuned experimentally with respect to a certain type of reference, such as the step reference and the unit-ramp reference. In this way, the performance of the flight controller might be affected by the variations of the references in real-time flights. Besides, real-time dynamic effects such as measure noises, external disturbances and input delays, which are usually neglected in the reported works, could easily deteriorate the performances of the flight controllers. This work is thereby motivated to develop a high-performance flight control approach utilizing a modified disturbance rejection technique for the quadrotors suffering from input delays and external disturbances. This control approach is developed in a cascaded structure and the attitude angles are chosen as the pseudo control inputs of the translational flight of the quadrotors. To facilitate the development, the dynamic model of the quadrotors is firstly formulated by including the effects of input delays, and the dynamics of the pseudo control variables are identified through real-time experiments. Based on the identified model, the flight control approach is proposed with a modified active disturbance rejection technique, which consists of a time optimal tracking differentiator, an extended state observer/predictor, and a nonlinear proportional–derivative controller. The tracking differentiator is designed to generate smooth transient profiles for the references, and the extended state observer/predictor is implemented for lumped disturbance estimation and state estimation considering the input delays. With the aid of the tracking differentiator and the extended state observer/predictor, the nonlinear proportional–derivative controller can thereby establish a fast tracking control and effectively reject the estimated disturbances. To verify the feasibilities of this development, comparative tests are carried out in both simulations and experiments. The results show that in the presence of small lumped disturbances, such as the measurement zero-drift, the steady-state errors of the proposed control approach for the ramp responses are less than 2 cm, and in the tests of sinusoidal trajectory tracking, the cross-tracking errors are less than 0.04 m. When with large disturbance airflow that is equivalent to strong breeze, the steady-state error achieved by the proposed flight controller is also less than 10 cm. All of these facts demonstrate the effectiveness of this development.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

A composite fractional order active disturbance rejection control method for a class of uncertain systems with multiple disturbances

The existing active disturbance rejection control (ADRC) method may not provide sufficient disturbance rejection to multiple mismatched disturbances for the fractional order systems. In this paper, a composite disturbance rejection approach is developed for a class of fractional order uncertain systems, by synthesizing the fractional order ADRC (FOADRC) approach and a disturbance observer (DO)-based compensation scheme. Taking advantage of more disturbance information and a filter structure, an improved DO is developed to achieve precise estimation of disturbances in the presence of sensor noises. In addition, a state transformation is developed to convert the system into a simple integral chain model with only matched disturbances. Then a composite control law is designed to compensate the disturbances and provide satisfying dynamic performance. The efficiency of the proposed method is demonstrated by a numerical simulation and an actual servo control simulation, as well as the comparison with two kinds of the existing ADRC methods and the commonly used integral sliding mode control (I-SMC) method.     

Generalized extended state observer–based repetitive control for systems with mismatched disturbances

A generalized extended state observer (GESO) is devised to improve the disturbances rejection performance in a repetitive‐control system (RCS) for a class of single‐input, single‐output nonlinear plants with nonintegral chain form and mismatched disturbances. By appropriately choosing a disturbance compensation gain and incorporating the disturbance estimate into a repetitive control law, a GESO‐based RCS is established. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of the disturbance compensation into the control input enables attenuating the lumped disturbance from the system output. Stability criteria and design algorithms have been developed for the system. A case study on the speed control of a rotational control system exhibits that the GESO‐based RCS delivers not only a promising disturbance rejection performance but also a superior property of tracking performance.     

基于线性自抗扰的开关磁阻电机调速控制研究

开关磁阻电机调速系统是复杂的非线性时变系统,负载扰动大,变量之间耦合严重,针对上述系统的性能特点提出采用线性自抗扰控制策略对系统进行控制的方法。首先为克服负载扰动变化,电机磁链呈非线性以及电流、位置等参数耦合的内外部干扰问题,设计扩张状态观测器对系统内扰和外扰进行准确估计并实时补偿。然后设计PD（比例-微分）控制器抑制系统给定与扩张状态观测器反馈的观测对象状态变量之间的跟踪误差。最后在仿真平台上对设计的控制系统进行试验并与传统PID控制方案进行对比,结果显示,对于给定的阶跃信号线性自抗扰控制器只需0.09s即可达到稳态且无超调,而PID控制器需要3s才能实现稳定跟踪。因此相比于传统PID控制,线性自抗扰控制器拥有更优的动静态性能,并且系统在外部负载扰动和内部模型参数变化的情况下也有良好的控制效果,表现出了很好的鲁棒特性。     

含有摩擦补偿的全方位移动机器人自抗扰控制

本文针对全方位移动机器人轨迹追踪中的摩擦补偿问题,提出了一种改进的非线性自抗扰控制器.首先建立了含有经典静态摩擦模型的全方位移动机器人动力学模型.其次,基于该模型设计非线性控制器和线性扩张状态观测器并给出了系统的稳定性分析.通过将模型已知项加入线性扩张状态观测器中得到摩擦力的估计值,并将估计值用于非线性控制器中摩擦补偿部分.为减小摩擦力对机器人低速运动轨迹追踪控制的影响,非线性控制器采用变增益控制器进行轨迹追踪控制.最后通过仿真结果验证本文提出控制器的有效性.     

航天器姿态自抗扰控制

为抑制航天器自身结构参数变化和内外扰动对姿态控制精度和姿态稳定度的影响, 设计了航天器姿态自抗扰控制器. 自抗扰控制器(ADRC)由跟踪微分器(TD)、扩张状态观测器(ESO)和姿态反馈控制器(AFC)3部分组成.跟踪微分器负责安排姿态指令过渡过程, 并提取其微分信号. 扩张状态观测器(ESO)充分利用姿态敏感器与速率陀螺的量测信息, 可对航天器姿态及内部和外部干扰进行观测. 姿态反馈控制器则在补偿ESO估计的干扰的同时,实现航天器的姿态控制. 与已有研究相比, 扩张状态观测器采用复合量测信息对状态估计进行校正, 性能较好. 而自抗扰控制器只采用一个环路即可实现姿态控制及干扰补偿, 结构简单. 对某航天器姿态控制系统的仿真结果表明,以上自抗扰控制器是可行的.     

Optimal Output Feedback Controllers for Spacecraft Attitude Tracking

This paper investigates the problem of output feedback attitude tracking control of a rigid spacecraft in the presence of external disturbances. Two optimal control laws with a disturbance estimator are developed to deal with this problem. An adapted extended state observer is used to estimate the angular velocity tracking errors and to allow for compensation for the total disturbances. The proposed control can be expressed as the sum of a nonlinear optimal controller and an estimated disturbance. For the optimal controller, the state‐dependent Riccati equation and optimal Lyapunov techniques are employed to solve the infinite‐time nonlinear optimal control problem. The developed controllers can minimize a performance index and ensure the stability of the closed‐loop system and external disturbance attenuation. On the other hand, using the adapted extended state observer, the asymptotic convergence of estimation error dynamics is proven. An example of multiaxial attitude manoeuvres is given and simulation results are included to demonstrate and verify the usefulness of the proposed controllers.     

Differential flatness‐based ADRC scheme for underactuated fractional‐order systems

This article mainly studies the fractional‐order active disturbance rejection control (FOADRC) schemes for the underactuated commensurate fractional‐order systems (FOSs). The FOADRC framework for linear FOSs‐based fractional proportion integration differentiation is constructed by using the fractional‐order tracking differentiator and the fractional‐order extended state observer, and the necessary conditions for the system to have stable controllers are provided. The FOADRC scheme for underactuated FOSs based on differential flatness is proposed. For underactuated FOSs, a set of flat output expressions with a fixed format is given under the controllable condition of the system. Moreover, making the flat output as the equivalent of the system output is simple and easy to analyze and calculate. Subsequently, the FOADRC scheme is designed by using the flat output. Finally, the scheme proposed in this article is verified by a simulation example.     

Active DIsturbance Rejection Control of Surface Vessels Using Composite Error Updated Extended State Observer

In this paper, a composite‐errors‐based active disturbance rejection control law is proposed for surface vessels with exogeneous disturbances. The low‐frequency disturbances from wind, wave and ocean currents are estimated by a novel composite‐errors‐based extended state observer (ESO). Since the composite errors are composed of trajectory tracking errors and estimation errors, the disturbance rejection control is feedforward‐feedback composite control. The advantages of feedforward control and feedback control are exploited to reject system disturbances. Compared with conventional ESO‐based active disturbance rejection control, smaller estimation errors and smaller tracking errors can be achieved by the proposed disturbance compensation control. The effectiveness and superiority of the designed control law are illustrated by theoretical analysis and simulation results.     

An approach to improve active disturbance rejection control

ABSTRACT

In order to reduce the error and phase delay of the classical extended state observer (ESO) in estimating the system state and disturbance, in this paper, we combine ESO and tracking differentiator (TD) to construct a tracking differential extended state observer (TDESO). The observation error and observation speed of TDESO are also discussed. Then a nonlinear active disturbance rejection control system improved by TDESO for a linear plant is transformed into a Lurie system. Moreover, the circular criterion is used to analyse the absolute stability of the transformed Lurie system. Finally, TDESO is optimised and an improved linear state error feedback (PLSEF) is proposed to improve the rapidity of the system by using simulation and time domain analysis. And a second-order system is used to illustrate the performance of the proposed scheme. The simulation results show that our algorithm is effective.     

基于非线性参数的电液伺服系统滑模控制

针对在电液伺服系统跟踪控制中存在非线性不确定参数和外界扰动的问题,提出了一种基于积分微分器的滑模Lyapunov函数的控制方法。首先,在只有位移信号测量输出的情况下,采用高阶积分链式微分器对其速度和加速度信息进行预估。系统存在非线性不确定参数,利用微分器对状态和不确定项的实时估计,设计出积分滑模控制器,实现自适应规律以及对电液伺服系统中不确定扰动的抑制。搭建电液伺服系统AMESim模型并与Matlab构成联合仿真平台,对控制器进行仿真。仿真表明,该控制器具有良好的对非线性不确定参数变化的补偿能力和跟踪性能。     

Anti‐windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance

A novel anti‐windup design method is provided for a class of uncertain nonlinear systems subject to actuator saturation and external disturbance. The controller considered incorporates both an active disturbance rejection controller as well as an anti‐windup compensator. The dynamical uncertainties and external disturbance are treated as an extended state of the plant, and then estimate it using an extended state observer and compensate for it in the control action, in real time. The anti‐windup compensator produces a signal based on the difference between the controller output and the saturated actuator output, and then augment the signal to the control to deal with the windup phenomenon caused by actuator saturation. We first show that, with the application of the proposed controller, the considered nonlinear system is asymptotically stable in a region including the origin. Then, in the case that the controller in linear form, we establish a linear matrix inequality‐based framework to compute the extended state observer gain and the anti‐windup compensation gain that maximize the estimate of the domain of attraction of the resulting closed‐loop system. The effectiveness of the proposed method is illustrated by a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.     

离散型自抗扰控制器在四旋翼飞行姿态控制中的应用

本文首先介绍了自抗扰控制器的结构组成,包括跟踪微分器、扩张状态观测器以及非线性状态误差反馈律,及各部分的典型算法.针对四旋翼盘旋系统的姿态控制问题,设计了3种离散型自抗扰控制器,搭建了仿真结构图,并进行了参数整定,得到了优良的仿真结果.进而在实际装置上进行试验,调试出了令人满意的姿态实时控制结果.实时控制结果表明,文中所设计的自抗扰控制器可以满足控制精度及快速性的要求,并且具有抗干扰性能、稳定控制能力以及对非线性强耦合系统的解耦能力.最后,总结并分析了3种自抗扰控制器的优缺点及适用范围.     

基于扩张状态观测器的UCAV自适应滑模控制

针对固定翼UCAV（Unmanned Combat Aerial Vehicle）系统中存在的不确定性和外部扰动，设计了一种基于扩张状态观测器的自适应超扭曲滑模控制器用来抑制系统扰动，从而提高对于UCAV的控制性能。建立固定翼UCAV的六自由度非线性模型，针对姿态控制和速度控制分别设计扩张状态观测器对模型中难以精确测量的状态量和外部扰动进行估计，依据奇异摄动原理分别对姿态和速度设计自适应超扭曲滑模控制器，实现对UCAV的姿态和速度的跟踪控制。采用某型固定翼UCAV非线性模型对所设计的控制器进行仿真验证，并且与传统的自抗扰滑模控制方法进行了对比，仿真结果表明，基于扩张状态观测器的自适应超扭曲滑模控制器具有更小的超调量和稳态误差。     

Trigger‐based tracking control for a class of uncertain nonlinear systems via an event‐triggered extended state observer

An event‐triggered observer‐based output feedback control issue together with triggered input is investigated for a class of uncertain nonlinear systems subject to unknown external disturbances. Two separate event‐triggered conditions are located on the measurement channel and control channel, respectively. An event‐triggered extended state observer (ETESO) is employed to estimate unmeasurable states and compensate uncertainties and disturbances in real time while it is not required for real‐time output measurement. Then, combined with backstepping method and active disturbance rejection control, an output feedback control scheme is proposed, where an event‐triggered input is developed for reducing the communication rate between the controller and the actuator. The triggered instants are determined by a time‐varying event‐triggered condition. Two simulations, including a numerical example and an permanent‐magnet motor, are illustrated to verify the effectiveness of the proposed schemes.     

Straight‐Line Tracking Control of an Agricultural Vehicle with Finite‐Time Control Technique

For the agricultural vehicle straight‐line tracking system, three control algorithms based upon the finite‐time control technique have been proposed to force the vehicle to track a straight line. Without considering the lumped disturbance, a backstepping‐like finite‐time state‐feedback controller is first developed. On this basis, an adaptive state‐feedback controller in conjunction with integral sliding mode is further developed in the presence of the lumped disturbance. Finally, a sliding mode disturbance observer is given to estimate the lumped disturbance, and the composite control scheme is presented. Under the composite controller, the lumped disturbance can be compensated and thus the disturbance rejection property has been significantly improved. Simulation results verify the proposed control algorithms.