Fractional active disturbance rejection control

A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ω_o and controller bandwidth ω_c on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme.     

Control of unstable processes with time delays via ADRC

Active disturbance rejection control (ADRC) treats the external disturbance and internal uncertainties as a general disturbance, and uses an extended state observer (ESO) to estimate it in real-time and feeds it back in the control loop, thus can achieve good disturbance rejection performance. However, ADRC is not quite suitable for unstable delayed processes due to its inherent structure. In this paper, a two-degree-of-freedom (2DOF) control structure is proposed for unstable time- delayed systems. Set-point tracking and disturbance rejection are separated in this structure and ADRC is solely responsible for disturbance rejection. A method to tune the ADRC parameters using all the information of the system is proposed, and robustness and performance of the proposed method are analyzed. Simulation examples show that 2DOF-ADRC can achieve good tracking and disturbance rejection performance.     

音圈致动快速反射镜的降阶自抗扰控制

为改善航空光电载荷用音圈致动快速反射镜的控制性能,提出一种降阶自抗扰控制方法。首先,对快速反射镜(Fast Steering Mirror,FSM)模型进行了分析并获取了模型参数。根据自抗扰控制理论,设计了FSM的三阶通用自抗扰控制器。将电涡流传感器的测量结果视为已知,提出降阶扩张状态观测器及其对应的自抗扰控制器设计方法。根据控制器带宽设计思想,推导了对于FSM这类二阶欠阻尼对象的控制律,并给出了加入扰动补偿量的控制律的具体实现形式。实验结果表明,降阶自抗扰控制能明显改善FSM的位置阶跃响应动态性能,能实现无超调与振荡的阶跃响应,稳态时间由11.7 ms提升至9.2 ms,同时能够降低FSM对位置斜坡输入跟踪的稳态误差,并改善其速度响应动态过程,像移补偿稳速时间由10.2 ms提升至7.8 ms,提升约24%。降阶自抗扰控制具有实现简单、运算量小的特点,能够明显提升FSM的动态性能。     

Robust disturbance rejection control of a biped robotic system using high-order extended state observer

This study addressed the problem of robust control of a biped robot based on disturbance estimation. Active disturbance rejection control was the paradigm used for controlling the biped robot by direct active estimation. A robust controller was developed to implement disturbance cancelation based on a linear extended state observer of high gain class. A robust high-gain scheme was proposed for developing a state estimator of the biped robot despite poor knowledge of the plant and the presence of uncertainties. The estimated states provided by the state estimator were used to implement a feedback controller that was effective in actively rejecting the perturbations as well as forcing the trajectory tracking error to within a small vicinity of the origin. The theoretical convergence of the tracking error was proven using the Lyapunov theory. The controller was implemented by numerical simulations that showed the convergence of the tracking error. A comparison with a high-order sliding-mode-observer-based controller confirmed the superior performance of the controller using the robust observer introduced in this study. Finally, the proposed controller was implemented on an actual biped robot using an embedded hardware-in-the-loop strategy.     

基于ESO的PMSM系统自抗扰FCS-MPC策略

为了提高三相永磁同步电机(PMSM)系统的控制性能,以反双曲正弦函数为基础,通过改进的扩张状态观测器(ESO)获取转速和反电动势项高精度估值,以自抗扰控制作为转速控制调节器,提出了基于ESO的自抗扰有限控制集模型预测控制(FCS-MPC)策略,以减小电磁转矩脉动,降低算法的复杂性和计算量.与基于PI的 FCS-MPC策略相比,新的控制策略能够保证 PMSM系统稳定运行,具有良好的转速跟踪性、抗干扰性和鲁棒性.     

On the rejection of internal and external disturbances in a wind energy conversion system with direct-driven PMSG

This paper deals with the critical issue in a wind energy conversion system (WECS) based on a direct-driven permanent magnet synchronous generator (PMSG): the rejection of lumped disturbance, including the system uncertainties in the internal dynamics and unknown external forces. To simultaneously track the motor speed in real time and capture the maximum power, a maximum power point tracking strategy is proposed based on active disturbance rejection control (ADRC) theory. In real application, system inertia, drive torque and some other parameters change in a wide range with the variations of disturbances and wind speeds, which substantially degrade the performance of WECS. The ADRC design must incorporate the available model information into an extended state observer (ESO) to compensate the lumped disturbance efficiently. Based on this principle, a model-compensation ADRC is proposed in this paper. Simulation study is conducted to evaluate the performance of the proposed control strategy. It is shown that the effect of lumped disturbance is compensated in a more effective way compared with the traditional ADRC approach.     

Modified reduced order observer based linear active disturbance rejection control for TITO systems

This paper proposes an observer based control approach for two input and two output (TITO) plant affected by the lumped disturbance which includes the undesirable effect of cross couplings, parametric uncertainties, and external disturbances. A modified reduced order extended state observer (ESO) based active disturbance rejection control (ADRC) is designed to estimate the lumped disturbance actively as an extended state and compensate its effect by adding it to the control. The decoupled mechanism has been used to determine the controller parameters, while the proposed control technique is applied to the TITO coupled plant without using decoupler to show its efficacy. Simulation results show that the proposed design is efficiently able to nullify the interactions within the loops in the multivariable process with better transient performance as compared to the existing proportional-integral-derivative (PID) control methods. An experimental application of two tanks multivariable level control system is investigated to present the validity of proposed scheme.     

Fixed-time output feedback trajectory tracking control of marine surface vessels subject to unknown external disturbances and uncertainties

This paper proposes a novel fixed-time output feedback control scheme for trajectory tracking of marine surface vessels (MSVs) subject to unknown external disturbances and uncertainties. A fixed-time extended state observer (FESO) is proposed to estimate unknown lumped disturbances and unmeasured velocities, and the observation errors will converge to zero in fixed time. Based on the estimated values, a novel fixed-time trajectory tracking controller is designed for an MSV to track a time-varying reference trajectory by the extension of an adding a power integrator (API), and the tracking errors can converge to zero in fixed time as well. Additionally, the convergence time of the controller and the FESO is independent of initial state values. Finally, simulation results and comparisons illustrate the superiority of the proposed control scheme.     

自抗扰控制器的发展及其应用

本文介绍了自抗扰控制器(ADRC)的发展过程-从非线性PID到扩张状态观测器的产生,再到自抗扰控制器的形成。同时,全面阐述了自抗扰控制器(ADRC)的基本结构,参数整定原理并以具体实例验证了ADRC良好的控制性能．     

基于自抗扰控制器的磁浮平台水平推力控制

介绍一种新型的磁浮平台,针对该磁浮平台水平运动这一多变量、非线性、强耦合的系统,提出一种改进的自抗扰控制器,克服常规自抗扰控制器非线性状态误差反馈控制律中非线性函数的不平滑性,并探索出一套行之有效的控制器参数整定规则,同时利用扩张状态观测器观测出内部扰动和外部扰动,并对它们进行补偿。仿真对比分析和试验结果表明,这种改进的自抗扰控制器具有很好的动态、静态特性及鲁棒性。     

Tuning of linear active disturbance rejection controller with robustness specification

Active disturbance rejection control (ADRC) treats all the model uncertainties and all the external disturbances as a generalized disturbance. It uses an extended state observer (ESO) to estimate the generalized disturbance in real time, and compensate it using a state-feedback control law, thus can achieve good disturbance rejection performance. For linear ADRC (LADRC), the parameters can be tuned via the bandwidths of the ESO and the feedback control, thus an LADRC can be regarded as a fixed-structured controller with several parameters to tune, just like a PID controller. To help tuning the parameters of LADRC, a tuning rule is proposed in this paper, with the aim to minimize the load disturbance attenuation performance in the integral of time square error sense, under the constraint of a specified robustness measure for the first-order processes with deadtime. The tuning rule is tested for a variety of benchmark systems and the gravity drained tanks case, and the performances are compared with the well-known PID tuning methods.     

Tuning of linear ADRC with known plant information

Linear active disturbance rejection control (ADRC) is known for its simplicity and its performance in disturbance attenuation. Currently, tuning of linear ADRC (LADRC) is via the bandwidth idea. In this paper, tuning of LADRC with known plant information is investigated. It is shown that there are limitations using only two bandwidths to tune the LADRC controllers. To take advantage of the known plant information, a generalized ADRC (GADRC) method is proposed. Then the intrinsic link between the conventional LADRC and GADRC is analyzed. It is shown that the available plant model information used in GADRC can be utilized in the designs of the observer gain and the controller gain of the conventional LADRC. Simulation results demonstrate that with known plant information incorporated, the performance of a conventional LADRC can indeed be improved, especially for unstable, time-delayed and non-minimum phase processes.     

自适应线性自抗扰控制器的设计

自抗扰控制器对于抑制不确定的扰动有良好的效果,但其控制器参数较多且整定困难。为了实现自适应的线性自抗扰控制器,对线性自抗扰控制器的参数整定策略展开了研究。首先,设计了基于观测误差的线性扩张观测器参数自适应整定算法。接着,设计了自抗扰控制器线性反馈环节的参数的自适应整定算法。最后,利用李雅普诺夫方法,证明上述自适应整定算法得到的参数可以保证扩张状态观测器的观测误差和被控系统最终输出误差都收敛至零。实验结果表明:精密气浮运动平台低速工况下,自适应线性自抗扰控制器的参数在0.8s内即可迅速完成整定计算;线性扩张观测器观测误差绝对值小于2nm;被控精密气浮运动平台的速度波动不大于5%。自适应线性自抗扰控制器实现了控制器参数在线整定,控制器的性能表现满足要求。     

Finite-time sliding mode controller for perturbed second-order systems

This paper presents a novel finite-time sliding mode controller applied to perturbed second order systems. The proposed scheme employs a disturbance observer that can identify growing in time disturbances. Then, the observer is combined with a sliding mode controller to achieve finite-time stabilization of the second-order system. The convergence of the observer as well as the finite-time stability of the closed-loop system is theoretically demonstrated. Besides, it is also shown that the finite-time convergence properties of a given controller can be enhanced when using a compensation term based on the disturbance observer. The proposed controller is compared with a twisting algorithm and a finite-time sliding mode controller with disturbance estimation. Also, a conventional proportional integral derivative (PID) controller is combined with the proposed disturbance observer in a trajectory tracking task. Numerical simulations indicate that the proposed controller attains finite-time stabilization of the second order system by requiring a less amount of power than that demanded by the other control schemes and without being affected by the peaking phenomenon. Besides, the performance of the PID technique is enhanced by applying the proposed control methodology.     

航空光电稳定平台的自抗扰控制系统

对航空光电稳定平台模型进行分析并利用电流环简化了平台模型。阐述了影响平台稳定性的扰动及抑制扰动的方法,提出一种基于预报修正的自抗扰控制系统。首先,提出了一种预报修正方法,采用"先预报,后修正"的方法来减小扰动观测值的滞后和超调;然后,设计了基于二阶扩张状态观测器的自抗扰控制系统,对扰动进行线性化动态补偿;最后,在振动平台上对系统进行了速度稳定实验、目标跟踪实验和鲁棒性分析。结果表明,与经典的平方滞后超前控制方法相比,本文设计的控制方法对扰动的隔离度至少提高了5.88dB。另外,设计的系统具有很强的鲁棒性,在系统参数改变±15%的范围内,仍得到很好的控制效果。由于所设计的控制系统具有很强的实用性和鲁棒性,在工程实际应用中提高了航空光电稳定平台的抗扰动性能。     

A novel practical control approach for rate independent hysteretic systems

A disturbance rejection based control approach, active disturbance rejection control (ADRC), is proposed for hysteretic systems with unknown characteristics. It is an appealing alternative to hysteresis compensation because it does not require a detailed model of hysteresis, by treating the nonlinear hysteresis as a common disturbance and actively rejecting it. The stability characteristic of the ADRC is analyzed. It is shown that, in the face of the inherent dynamic uncertainties, the estimation and closed-loop tracking errors of ADRC are bounded, with their bounds monotonously decreasing with the observer and controller bandwidths, respectively. Simulation results on a typical hysteretic system further demonstrate the effectiveness of the proposed approach.     

基于LADRC的电动舵机高动态控制方法

自抗扰控制(Active Disturbance Rejection Control,ADRC)继承了PID控制基于误差反馈的优点,在控制中不需要模型的先验知识,并结合了经典调节理论与现代控制理论各自的优点,因而在实际工程中得到了广泛应用。文中分析了电动舵机传统PID控制中存在的动态响应慢和抗扰能力弱的问题;建立了基于直接转矩控制的舵机系统数学模型;设计了线性扩张状态观测器,并给出了观测器参数的简便确定方法,通过观测器观测出的扰动将系统补偿为串联积分器的形式;采用不同的控制器对补偿后的系统进行稳定性分析,根据稳定性和实现难易程度,决定采用比例微分负反馈控制器。最后对设计的观测器和控制器进行了仿真,仿真结果表明,设计的观测器和控制器与传统PID控制相比在动态响应和抗扰能力上都具有巨大的优势。     

基于ADRC的液压支护机器人自适应控制

为促进深层围岩液压支架自动化控制的研究,提出了一种基于ADRC的自适应控制系统。首先,通过液压支架支护系统的拉格朗日动力学分析,建立了液压支架动力学模型。针对该模型的动力耦合和时变特性设计了ADRC控制器,并对跟踪微分器、扩张观测器和非线性误差反馈3部分进行了离散化、分离式的参数整定。最终以MATLAB / Simulink为平台,对液压支架模型和控制系统进行了联合仿真实现,并设计了ADRC与PID控制的对比实验。仿真实验结果表明,该ADRC控制器与PID控制器相比具有更好的控制效果和运动品质。     

A compound control strategy combining velocity compensation with ADRC of electro-hydraulic position servo control system

In order to enhance the anti-jamming ability of electro-hydraulic position servo control system at the same time improve the control precision of the system, a compound control strategy that combines velocity compensation with Active Disturbance Rejection Controller (ADRC) is proposed, and the working principle of the compound control strategy is given. ADRC controller is designed, and the extended state observer is used for observing internal parameters uncertainties and external disturbances, so that the disturbances of the system are suppressed effectively. Velocity compensation controller is designed and the compensation model is derived to further improve the positioning accuracy of the system and to achieve the velocity compensation without disturbance. The compound control strategy is verified by the simulation and experiment respectively, and the simulation and experimental results show that the electro-hydraulic position servo control system with ADRC controller can effectively inhibit the external disturbances, the precise positioning control is realized after introducing the velocity compensation controller, and verify that the compound control strategy is effective.     

Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems

The paper considers the tracking problem for a class of uncertain linear time invariant (LTI) systems with both uncertain parameters and external disturbances. The active disturbance rejection tracking controller is designed and the resulting closed-loop system׳s characteristics are comprehensively studied. In the time-domain, it is proven that the output of closed-loop system can approach its ideal trajectory in the transient process against different kinds of uncertainties by tuning the bandwidth of extended state observer (ESO). In the frequency-domain, different kinds of parameters׳ influences on the phase margin and the crossover frequency of the resulting control system are illuminated. Finally, the effectiveness and robustness of the controller are verified through the actuator position control system with uncertain parameters and load disturbances in the simulations.