自抗扰控制器的阶次与参数的选取

本文就选择不同阶次的自抗扰控制器时,对系统的控制参数选取进行了研究.结果表明:线性时不变系统的线性自抗扰控制,可等效为一个复合控制系统,其等效反馈补偿器为一超前校正单元串联一积分器;其等效前置滤波器为一滞后校正单元串联一微分器.观测器带宽和控制器带宽的比值,决定着反馈补偿器的最大相位超前角,而频带则决定着最大相位超前角的发生位置.同时,随着自抗扰控制器阶次的增加,补偿器的最大超前校正角也增加.通过对开环系统的频域分析,本文给出了利用该补偿器的频域特性进行自抗扰控制器参数设计的一般步骤,可大幅度减少工程师的反复试验过程,方便工程师应用.     

Energy transfer properties of non-linear systems in the frequency domain

In this paper, an analysis of the energy transfer properties of non-linear systems in the frequency domain is studied based on a new concept known as non-linear output frequency response functions (NOFRFs). The new concept allows the analysis to be implemented in a manner similar to the analysis of linear systems in the frequency domain, and provides great insight into the mechanisms which dominate the non-linear behaviour. The new analysis is also helpful for the design of non-linear systems in the frequency domain.     

An Active Disturbance Rejection Based Approach to Vibration Suppression in Two‐Inertia Systems

This study concerns the resonance problems found in motion control, typically described in a two‐inertia system model as compliance between the motor and the load. We reformulate the problem in the framework of active disturbance rejection control (ADRC), where the resonance is assumed to be unknown and treated as disturbance, estimated and mitigated. This allows the closed‐loop bandwidth to go well beyond the resonant frequency, which is quite difficult using existing methods. In addition, such level of performance is achieved with minimum complexity in the controller design and tuning: no parameter estimation or adaptive algorithm is needed, and the controller is tuned by adjusting one parameter, namely, the bandwidth of the control loop. It is also shown that the proposed solution applies to both the velocity and position control problems, and the fact that ADRC offers an effective and practical motion control solution, in the presence of unknown resonant frequency within the bandwidth of the control system. Finally, frequency response analysis is performed where stability margin is obtained before the simulation results are verified in the hardware experiments.     

Transfer function analysis and implementation of active disturbance rejection control

To support the adoption of active disturbance rejection control (ADRC) in industrial practice, this article aims at improving both understanding and implementation of ADRC using traditional means, in particular via transfer functions and a frequencydomain view. First, to enable an immediate comparability with existing classical control solutions, a realizable transfer function implementation of continous-time linear ADRC is introduced. Second, a frequency-domain analysis of ADRC components, performance, parameter sensitivity, and tuning method is performed. Finally, an exact implementation of discrete-time ADRC using transfer functions is introduced for the first time, with special emphasis on practical aspects such as computational efficiency, low parameter footprint, and windup protection.     

On tuning of ADRC with competing design indices: a quantitative study

Controller optimization has mostly been done by minimizing a certain single cost function. In practice, however, engineers must contend with multiple and conflicting considerations, denoted as design indices (DIs) in this paper. Failure to account for such complexity and nuances is detrimental to the applications of any advanced control methods. This paper addresses this challenge heads on, in the context of active disturbance rejection controller (ADRC) and with four competing DIs: stability margins, tracking, disturbance rejection, and noise suppression. To this end, the lower bound for the bandwidth of the extended state observer is first established for guaranteed closed-loop stability. Then, one by one, the mathematical formula is meticulously derived, connecting each DI to the set of controller parameters. To our best knowledge, this has not been done in the context of ADRC. Such formulas allow engineers to see quantitatively how the change of each tuning parameter would impact all of the DIs, thus making the guesswork obsolete. An example is given to show how such analytical methods can help engineers quickly determine controller parameters in a practical scenario.     

Two-dimensional frequency analysis for unconstrained model predictive control of cross-directional processes

This paper presents consistent criteria for evaluating the selection of tuning parameters for an industrial model predictive control of large-scale cross-directional (CD) processes using a two-dimensional (temporal and spatial) frequency analysis technique. The concept of rectangular circulant matrices (RCMs) and their properties are presented. It is shown that large-scale CD processes can be approximated as RCMs and then diagonalized by complex Fourier matrices, allowing analysis in terms of a family of SISO transfer functions across the spatial frequencies. Familiar concepts from control engineering such as bandwidth and stability margin are extended into the two-dimensional frequency domain, providing intuitive measures of closed-loop performance and robustness.     

内模控制框架下时延系统扩张状态观测器参数整定

作为一种有效的控制设计方法, 自抗扰控制研究获得了广泛关注, 然而针对自抗扰控制器的参数整定方法则相对较少. 本文针对一阶惯性加延迟系统, 将线性自抗扰控制转化为内模控制结构, 导出了其中控制器、滤波器、乘性不确定性、互补灵敏度函数的对应表达式, 随后, 利用频域鲁棒稳定性判据, 分析了自抗扰控制器核心—–扩张状态观测器的参数对闭环系统稳定性的影响. 基于该分析, 总结出一阶惯性加延迟系统扩张状态观测器的两条参数整定准则. 数值仿真结果验证了该整定准则的有效性.     

线性扩张状态观测器及其高阶形式的性能分析

扩张状态观测器(ESO)作为自抗扰控制(ADRC)的核心组件,其自身及高阶扩展形式的性能分析与评估至关重要.借助Lyapunov逆定理证明了任意扩张阶数下线性扩张状态观测器(LESO)重构状态误差的收敛性,并得出了观测误差上界与扩张阶数的定量关系式;在分别考虑扩张阶数、观测器带宽以及剪切频率的情况下,探讨了高阶及传统LESO的动态响应、干扰抑制能力与观测器参数间的关系;最后,结合改进的ADRC控制器,在估计能力、峰值现象的抑制、滤噪性能等方面对高阶及传统LESO进行了性能评估与仿真验证.所得出的结论可为ADRC应用中ESO的选取提供有效的理论依据.     

Frequency domain stability criteria for stochastic systems

The stability of a class of dynamical systems containing random parameters is investigated. An input-output stability concept is formulated for stochastic systems. The specific class of systems considered consists of those feedback systems whose open loop consists of the cascade of a white noise multiplicative gain and a linear deterministic dynamical system. Necessary and sufficient frequency domain conditions for stability are derived and it is shown that the uncertainty has a destabilizing effect. The resulting stability conditions depend on the open-loop stability, the rms value of the stochastic gain element, and the effective bandwidth of the linear element.     

Superheated steam temperature control based on modified active disturbance rejection control

Control of superheated steam temperature (SST) is becoming more and more challenging because of unknown disturbances caused by the frequent and extensive load changes and strict control requirements for the efficiency and safety. This is becoming even severe while the intermittent renewables penetration is growing. To this end, the working principle of SST is depicted and the models of SST are identified from the open-loop step response data. Considering the sluggish responses to the disturbances caused by high order dynamics, a modified active disturbance rejection control (ADRC) is proposed to enhance the control performance. Stability analysis of modified ADRC is derived theoretically to perfect the theory of modified ADRC. Then a practical tuning procedure is summarized for modified ADRC that can be readily understood by field engineers even though it involves trial and error tests. A simulation example shows that modified ADRC can improve the performance of tracking and disturbance rejection simultaneously while maintain a good robustness. A modified ADRC based cascade control strategy is proposed for the SST control system and the control performance is initially confirmed by a simulation based on the identified models. A field application in a 300 MW circulating fluidized bed (CFB) power plant demonstrates the advantages of the proposed strategy, which shows the temperature deviation can be significantly reduced in both the small-scale load varying condition and the large-scale load varying condition. The successful application of the proposed SST control system indicates a promising future of modified ADRC in power industry with the increasing demand on integrating more renewables into the power grid.     

Inter-sample output predictor based sampled-data ADRC supporting high precision control of VCM servo systems

Ultra high precision servo control systems usually require fast sampling rate to achieve desired digital control performance, where output sampling restrictions (such as sensor bandwidth) pose major challenges for such applications. In this paper, we propose a novel sampled-data multi-rate active disturbance rejection control (ADRC) architecture under sampling rate restrictions, where a digital extended state observer (ESO) with inter-sample output prediction structure is employed to construct inter-sample dynamics between two consecutive sampling instants, such that high frequency disturbances can be better rejected. The convergence of the estimation and the stability of the closed-loop system are analyzed based on Lyapunov function method and separation principle. The proposed control architecture is implemented on a voice coil motor (VCM) actuated micro–nano servo gantry, demonstrating significant performance improvement over existing single-rate or multi-rate ADRC methods.     

THE PERFORMANCE OF DISCRETE LINEAR TIME VARYING CONTROL OF LINEAR PERIODIC PLANTS

This paper analyzes the performance of discrete linear time varying (LTV) control of discrete linear periodically time varying (LPTV) plants for l₂ disturbance rejection. It extends the results of [11–13] for linear periodic controllers to general LTV control of LPTV plants. It is shown that LPTV control provides strictly better control performance than linear strictly time varying control for LPTV plants. The analysis is carried out in frequency domain. This approach provides not only new results on disturbance rejection of LTV control but also some new insight into properties of general LTV systems.     

基于频率跟踪方式的智能滤波信号处理系统研究

频域模式化分析或时域波形理论等方法在实现与应用上存在一定局限性.介绍了一种较新颖的自适应滤波系统的实现方法,它是利用FFT谱分析抽取的信号主频来实现滤波中心频率实时跟踪及带宽分段变化.实验测试结果表明：该系统具有在较强背景噪声下,跟踪提取有用信号并精确计算信号频率的功能,可为涡街流量计信号处理等工程实际中信号的进一步应用提供研究基础.     

大纯滞后纯积分对象的二阶自抗扰控制

具有纯滞后的一阶惯性关节是研究滞后问题的典型对象，采用修改后的二阶抗扰控制器ADRC（Auto-Disturbance-Rejection Controller)，研究了大纯滞后纯积分对象的控制，仿真表明，二阶ADRC能有效控制该类对象，并表现出较强的鲁棒性和抗扰性，而且在一定程度上不存在所谓的模糊型失配问题，此外，给出了滞后时间从0开始不断增加的控制器参数调整表和基于时间尺度的控制器参数调整依据，具有一定的工程实用价值。     

Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models

This paper introduces a new approach for nonlinear and non-stationary (time-varying) system identification based on time-varying nonlinear autoregressive moving average with exogenous variable (TV-NARMAX) models. The challenging model structure selection and parameter tracking problems are solved by combining a multiwavelet basis function expansion of the time-varying parameters with an orthogonal least squares algorithm. Numerical examples demonstrate that the proposed approach can track rapid time-varying effects in nonlinear systems more accurately than the standard recursive algorithms. Based on the identified time domain model, a new frequency domain analysis approach is introduced based on a time-varying generalised frequency response function (TV-GFRF) concept, which enables the analysis of nonlinear, non-stationary systems in the frequency domain. Features in the TV-GFRFs which depend on the TV-NARMAX model structure and time-varying parameters are investigated. It is shown that the high-dimensional frequency features can be visualised in a low-dimensional time–frequency space.     

Minimax frequency domain performance and robustness optimization of linear feedback systems

It is shown that feedback system design objectives, such as disturbance attenuation and rejection, power and bandwidth limitation, and robustness, may be expressed in terms of required bounds of the sensitivity function and its complement on the imaginary axis. This leads to a minimax frequency domain optimization problem, whose solution is reduced to the solution of a polynomial equation.     

HD motion‐picture evaluation method for overdrive technology in the frequency domain

Abstract— In this paper, the development of an advanced level‐adaptive overdrive (A‐LAO) method applicable to a full‐HD LC projector with 1.84 Mpixels, which reduced the gray‐level response time to less than 16 msec, is introduced. In addition, it is shown that a response of less than 8 msec can be achieved by combining the A‐LAO method with a frame interpolation method (120‐Hz refresh). A new motion‐picture evaluation method using frequency‐domain analysis, in other words, perceived bandwidth instead of the conventional time‐domain‐analysis response time evaluation, is reported.     

基于最小拍观测器的自抗扰控制器设计与性能分析

自抗扰控制器设计中,扩张状态观测器需要较高的观测带宽,才能更快的观测出状态变量.本文采用最小拍观测器,使得其具有最快的观测速度.以2阶系统为例,得到了离散系统下,基于最小拍观测器的自抗扰控制器的等价复合控制模型,其开环补偿器等价为超前校正器.仿真结果表明,基于最小拍观测器的自抗扰控制器可以最快的观测出系统状态变量,且控制器带宽的选取一般应小于采样周期的倒数.由于不再需要设计观测器带宽,从而简化了参数设计.     

基于时频分析方法LPFT的语音处理GUI系统

由于语音的非平稳性及时变性,时频分析方法是处理语音信号的重要工具.然而线性短时傅里叶变换的时频聚集性较差,而双线性维格纳变换在处理多分量信号时会受到交叉项的干扰.为了克服以上两种时频分析方法的缺点,利用短时傅里叶变换的扩展形式即局部多项式傅里叶变换LPFT来处理语音信号,建立了基于LPFT的语音处理GUI系统,实现了在时域、频域和时频域对语音的分析和对比.并给出语音处理的例子,验证了LPFT方法与其它方法相比所具有的优势.该系统简明直观,是语音处理的较好的平台.     

Intelligence evolution for service robot: An ADRC perspective

The strategy of active disturbance rejection control (ADRC) and its applications in intelligence evolution for service robot are summarized. It is also shown that the philosophy of ADRC is consistent with the essential characteristics of intelligence evolution. Most importantly, we concentrate on five core issues which will be encountered when applying ADRC to deal with intelligence evolution for service robot, that is, how to eliminate the impact of unknown composite disturbances, how to handle the nonholonomic constraints in uncalibrated visual servoing, how to realize eye hand torque coordination, how to deal with the disturbance in simultaneous localization and mapping (SLAM), and how to reject the imperfections induced by network in human robot interaction. The main purpose of this paper is to clarify the challenges encountered on intelligence evolution for service robot when one applies ADRC to, hoping that more and more researchers can give some suggestions or work together to deal with these problems, and flourishing results of ADRC from both theory and applications.