Robust disturbance rejection for repetitive control systems with time‐varying nonlinearities

This paper presents a disturbance‐rejection method for a modified repetitive control system with a nonlinearity. Taking advantage of stable inversion, an improved equivalent‐input‐disturbance (EID) estimator that is more relaxed for system design is developed to estimate and cancel out the influence of the disturbance and nonlinearity in the low‐frequency domain. The high‐frequency influence is filtered owning to the low‐pass nature of the linear part of the closed‐loop system. To avoid the restrictive commutative condition and choose a Lyapunov function of a more general form, a new design algorithm, which takes into account the relation between the feedback control gains and the observer and improved EID estimator gains, is developed for the nonlinear system. Furthermore, comparisons with the generalized extended‐state observer (GESO) and conventional EID methods are conducted. A clear relation between the developed estimator and the GESO is also clarified. Finally, simulations show the effectiveness and the advantage of the developed 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.     

Robust disturbance rejection in modified repetitive control system

This study concerns disturbance rejection for a modified repetitive control system (MRCS) that contains a strictly proper plant with time-varying uncertainties. Since an MRCS is affected by both periodic and aperiodic disturbances, and since the disturbances are often unknown, an equivalent-input-disturbance (EID)-based estimator was added to an MRCS to yield an EID-based MRCS that compensates for all types of disturbances. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of an EID estimate into the control input enables rejection of unknown periodic and aperiodic disturbances. A robust stability condition for the MRCS was established in the form of a linear matrix inequality, and the condition was used to design the parameters of the controller. This design method handles uncertainties and enables the preferential adjustment of the tracking and control performance of the MRCS. Simulation results demonstrate the validity of the method.     

基于等价输入干扰滑模观测器的磁悬浮球系统模型预测控制

本文针对系统不确定性和外部干扰引起的磁悬浮球系统控制性能下降的问题,提出了一种基于等价输入干扰滑模观测器的模型预测控制(MPC+EIDSMO)方法.首先将原系统转化为EID系统,采用等价输入干扰滑模观测器对EID系统状态变量及等价输入干扰进行估计;然后基于状态估计值设计模型预测控制器,并将等价输入干扰估计值以前馈的方式...     

Active Disturbance Rejection in Affine Nonlinear Systems Based on Equivalent‐Input‐Disturbance Approach

This paper presents a disturbance rejection method for an affine nonlinear system. The control system is constructed based on the equivalent‐input‐disturbance (EID) approach. An affine nonlinear state observer is used to reconstruct the state of the affine nonlinear system and to estimate an EID. The well‐known differential mean value theorem enables us to describe the closed‐loop system in the state space as a linear‐parameter‐varying system. This makes it easy to derive sufficient conditions of global uniform ultimate boundedness in term of linear matrix inequalities (LMIs) by using a Lyapunov function and convexity theory. Controllers are designed based on the LMIs. A numerical example is used to illustrate the design of the control system. And a comparison between the EID‐based control and the sliding‐mode control demonstrates the effectiveness and advantages of the EID‐based control method.     

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.     

Application of the observer/Kalman filter identification method to unknown time-delay disturbed systems and the associated optimal digital tracker design

ABSTRACT

Many practical systems are described as unknown multi-input-multi-output (MIMO) time-delay systems with unknown disturbances. The properties and performance of multi-time-delay MIMO systems are quite different compared to delay-free systems, in particular if the time-delay is long. In addition, for practical implementation digital controllers are often required instead of analog controllers. This paper presents: (i) an overview of the mathematical modelling based on the observer/Kalman filter identification (OKID) method, with some insight on known/unknown MIMO systems; (ii) a study of the pole-zero maps of the identified delay-free system and the known/unknown time-delay system for various sampling periods; (iii) a development of the explicit pole-zero map of the sampled-data MIMO neutral system with multiple discrete and disturbed time delays; (iv) an utilisation of the OKID method for known/unknown time-delay sampled-data MIMO systems with unknown disturbances; (v) an extension of the existing equivalent-input-disturbance (EID) estimator, to determine a robust tracker for the unknown time-delay system with unknown disturbances; and (vi) an investigation on the unknown time-delay system with stable or unstable zeros to determine which traditional or customised tracker can be applied. In addition, simulation studies are performed on the relationship between pole-zero maps and delay times.     

Robust H∞ control of uncertain singular systems based on equivalent‐input‐disturbance approach

In this paper, a robust H_∞ control problem is considered for an uncertain singular system. An active disturbance rejection method called equivalent input disturbance (EID) is used to reduce the influence of exogenous disturbances and uncertainties on the system. At the first, there exists an EID, which can produces the same effect on the system as disturbances and uncertainties do in the control channel according to the EID concept. Then, an EID estimator is constructed to estimate the influence of EID on the system. Finally, based on Lyapunov stability theory, a static output feedback‐based robust H_∞ controller combined with EID estimate is designed, guaranteeing that closed‐loop system is admissible (regular, impulse‐free, and stable) with a prescribed H_∞ performance level. Compared with traditional H_∞ control method, H_∞ control based on EID method improve the control performance of the system. A numerical example demonstrates the validity of the method.     

Design of equivalent-input-disturbance estimator using a generalized state observer

In this paper, we present a design method based on the concept of equivalent input disturbance (EID) to reject disturbances for a linear time-invariant system. A generalized state observer (GSO) is used to estimate an EID of the external disturbances, and the pole-assignment algorithm is employed to select the matrices of the GSO. Simulation and experimental results of a rotational speed control system demonstrate the validity of our method.     

基于NDOB的匹配/非匹配不确定性系统滑模控制

针对一类n阶匹配与非匹配不确定性和扰动共存的系统,提出了一种新颖的基于非线性干扰观测器的滑模控制方法。将非匹配扰动的估计值融入到滑模面,设计了集成扰动观测的滑模控制。与传统的滑模控制方法相比,该方法在匹配与非匹配不确定性和扰动出现时具有较好的抑制能力,并能有效地抑制切换增益所引起的抖振现象。利用李雅普诺夫理论和输入-输出稳定性概念严格证明了闭环系统的稳定性。最后通过两个仿真实例验证了所提控制方法的有效性。     

EID‐Estimation‐Based Periodic Disturbance Rejection for Sintering Ignition Process with Input Time Delay

Sintering plays a key role in generating blast furnace burden in metallurgical processes. The continuous production and stable quality of sintering significantly depends on the stable and precise control of sintering ignition, which, however, is achieved through an input time delay system, and suffers from different and unknown disturbances. To reject disturbances and enhance the control precision of ignition temperature, this paper introduces a modified equivalent input disturbance (EID)‐based disturbance compensation that is suitable for controlling sintering ignition. First, the periodic properties of disturbances induced by gas pressure fluctuations are obtained based on spectral density decomposition. Second, to obtain the dynamics of sintering ignition, an iterative subspace modeling method is developed, which estimates not only the model parameters but also the length of time delay. By considering the periodic property, a control structure of sintering ignition based on the modified EID‐based compensation is proposed, in which an additional time‐delay element is designed to make the phase difference between EID estimation and real disturbance close to zero. Finally, the validity of the proposed method is verified by a simulation.     

基于扰动补偿的多源受扰系统反步控制设计

针对一类多源受扰系统的跟踪控制问题, 提出基于降阶广义扩张状态观测器(ROGESO)的指令滤波反步控制设计方法. 首先, 将各通道中的总扰动分别作为扩展状态变量, 通过构造ROGESO对其进行同步实时估计. 在此基础上, 利用反步法递归设计虚拟控制律, 实现各级子系统的镇定, 并将各通道的扰动估计值反馈至对应子系统的虚拟控制律中进行反向补偿, 提高系统的扰动抑制性能, 保证系统输出对参考输入信号的高精度跟踪. 然后, 应用Lyapunov函数分析闭环系统的稳定性. 最后, 通过数值仿真验证所提方法的有效性.     

Novel disturbance-observer-based control for systems with high-order mismatched disturbances

A novel disturbance-observer-based control method is investigated to attenuate the high-order mismatched disturbances. First, a finite-time disturbance observer (FTDO) is proposed to estimate the disturbances as well as the derivatives. By incorporating the outputs of FTDO, the original system is then reconstructed, where the mismatched disturbances are transformed to the matched ones that are compensated by feed-forward algorithm. Moreover, a feedback control law is developed to achieve the stability and tracking performance requirements for the systems. Finally, the proposed composite control method is applied to an unmanned helicopter system. The simulation results demonstrate that the proposed control method exhibits excellent control performance in the presence of high-order matched and mismatched disturbances.     

基于自抗扰控制的机器人定位策略

机器人定位即需根据传感器测量对自身位置进行估计. 由于机器人系统模型的复杂非线性, 工况环境中的不确定干扰, 定位结果不可避免地会受到系统内外扰动的影响. 现有的定位算法往往仅能依赖模型或传感配置以及算法自身的鲁棒性被动抗扰, 这使得定位系统的抗扰能力有限、应用场景受限. 本文基于自抗扰控制思想提出一种 能够主动补偿系统内外扰动的机器人定位策略. 该策略将系统中所有能够影响最终定位结果的不确定因素统一视为总扰动, 并设计扩张状态观测器实现对总扰动的观测, 在此基础上构建控制器补偿总扰动影响, 以使定位结果更加准确. 与传统的定位抗扰策略相比, 本文所提出的抗扰定位策略并不依赖于模型或特定的传感配置, 能够处理任意有界的扰动类型, 理论上能够成为定位抗干扰的终极解决路径. 最后, 基于李雅普诺夫理论证明了系统的稳定性. 仿真和实车实验验证了本文提出的基于自抗扰控制的机器人定位策略能够有效地观测系统总扰动, 并补偿扰动影响, 提高定位结果的准确度.     

Compensation for state‐dependent nonlinearity in a modified repetitive control system

This paper presents an estimation and compensation of state‐dependent nonlinearity for a modified repetitive control system. It is based on the equivalent‐input‐disturbance (EID) approach. The nonlinearity is estimated by an EID estimator and compensated by incorporation of the estimate into the repetitive control input. A two‐dimensional model of the EID‐based modified repetitive control system is established that enables the preferential adjustment of control and learning actions by means of 2 tuning parameters. The singular‐value‐decomposition technique and Lyapunov stability theory are used to derive a linear‐matrix‐inequality–based asymptotic stability condition. Exploiting the stability condition and an overall performance evaluation index, a design algorithm is developed. Simulation results for the tracking control of a chuck‐workpiece system show that the method not only compensates state‐dependent nonlinearity but also improves the tracking performance for the periodic reference input, thereby demonstrating the validity of the method.     

热连轧板宽板厚的实用自抗扰解耦控制

针对热连轧板宽板厚多变量系统存在强耦合、大时滞和随机不确定等难题,提出了一种线性自抗扰动态解耦方案.考虑到系统的大时滞问题,在常规的降阶扩张状态观测器(ESO)之前,增加了一个纯时滞环节.为了把所设计的实用自抗扰控制(ADRC)与常规PID控制器进行公平比较,各控制器的最佳参数均采用变尺度混沌优化方法得到.仿真结果表明,优化后的ADRC不仅具有较好的解耦性能,而且对模型参数的不确定性和外扰具有较强的鲁棒性和参数适应性.     

多星发射上面级主动抗扰姿态控制技术研究

针对多星发射的运载火箭上面级在入轨段由于卫星分离产生的质量偏移,从而引起的三轴姿态严重耦合问题展开了研究,提出了基于广义扩张状态观测器的改进预测函数控制姿态控制方法.该控制方法将质心偏移造成上面级结构参数偏差和引入的干扰力矩以及其他未知系统参数偏差、外界扰动和未建模动态视为集总扰动,并将该非匹配干扰通过等效输入扰动技术转换为匹配干扰,由广义扩张状态观测器对变化后的系统状态和未知集总扰动同时观测.将集总扰动在反馈回路予以补偿保证了预测模型与上面级真实动力学模型有较高匹配度,进一步保证预测函数控制有较高的控制跟踪精度和较快的响应速度,并对外界扰动和参数偏差有较强的鲁棒性.文中算例仿真和性能对比验证了该方法的有效性及可行性.     

四旋翼飞行器的自抗扰飞行控制方法

针对四旋翼飞行器参数不确定性和外部干扰敏感的问题,本文提出一种基于自抗扰控制器的控制系统设计方法.在为期望姿态和高度安排过渡过程的基础上,设计了扩张状态观测器对内扰和外扰进行估计并实时补偿,能够很好地克服飞行器的强耦合性、模型不确定性以及风速变化等外部干扰问题.此外本文还设计了非线性状态误差反馈控制律来有效抑制跟踪误差.在仿真平台上对自抗扰控制系统进行稳定控制、姿态跟踪、高度控制、抗扰性及鲁棒性实验,并与串级PID控制系统进行定量对比分析.仿真结果表明,本文所设计的自抗扰控制器不仅能够很好地估计并补偿系统所受内外部干扰,而且对四旋翼飞行器参数的不确定性具有较强的鲁棒性,能够满足飞行器姿态调节快速和高稳定度的控制要求,性能指标明显优于串级PID控制器.     

A GESO based MPC approach to contour error control of networked motion control system

This paper presents a generalised extended state observer (GESO) based model predictive control (MPC) approach to contour error control for networked multi-axis motion system (NMAMS) with network-induced delays. First, the uncertainties induced by the network-induced delays are modelled as an additive bounded disturbance, and a novel model predictive controller based on the GESO is designed for the uniaxial trajectory tracking control system. The GESO is used to estimate the system state and the disturbance simultaneously, and the effects of the uncertainties induced by the delays are eliminated by the proposed GESO based controller. Then the contour error estimation method is adopted, and a PID controller is designed to compensate the contour error. Finally, experiments are carried out to demonstrate the effectiveness of the proposed method.     

Aperiodic disturbance rejection in a modified repetitive-control system

This paper presents a method of designing a modified output-feedback repetitive-control system (MOFRCS) that exploits the equivalent-input-disturbance (EID) approach to improve the aperiodic-disturbance rejection performance. The aperiodic disturbances are estimated by an EID estimator and suppressed by incorporation of the estimation into a repetitive control law. First, the configuration of the EID-based MOFRCS is described. Next, a sufficient stability condition is derived by employing the separation and small gain theorems. Then, the methods of designing an MOFRCS and an EID estimator are explained. Finally, some simulation results of a rotational control system are used to demonstrate the validity of the method.