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.     

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.     

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.     

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.     

Output tracking control of switched nonlinear systems with multiple time-varying delays

In this paper, the output tracking control problem for a class of switched nonlinear systems with multiple time-varying delays is studied based on equivalent-input-disturbance (EID) approach. More precisely, with the use of suitable Lyapunov-Krasovskii functional together with average dwell-time technique, an output feedback tracking controller is designed which makes that the states of resulting system can asymptotically track the desired trajectory. Further, the EID estimator is implemented to reject both matched and unmatched disturbances effectively without requiring any prior knowledge of the disturbances. Simulation results are presented to illustrate the effectiveness and potential of the developed EID-based output tracking control design technique. The results reveal the fact that the tracking controller based on EID provides a better tracking performance than the feedback controller based on sliding mode technique.     

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.     

Ecological interface design: progress and challenges

Ecological interface design (EID) is a theoretical framework for designing human-computer interfaces for complex sociotechnical systems. Its primary aim is to support knowledge workers in adapting to change and novelty. This literature review shows that in situations requiring problem solving, EID improves performance when compared with current design approaches in industry. EID has been applied to industry-scale problems in a broad variety of application domains (e.g., process control, aviation, computer network management, software engineering, medicine, command and control, and information retrieval) and has consistently led to the identification of new information requirements. An experimental evaluation of EID using a full-fidelity simulator with professional workers has yet to be conducted, although some are planned. Several significant challenges remain as obstacles to the confident use of EID in industry. Promising paths for addressing these outstanding issues are identified. Actual or potential applications of this research include improving the safety and productivity of complex sociotechnical systems.     

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.     

Robust observer-based optimal linear quadratic tracker for five-degree-of-freedom sampled-data active magnetic bearing system

This paper presents three observer/Kalman filter identification (OKID) approaches and develops a robust observer-based optimal linear quadratic digital tracker (LQDT) for the five-degree-of-freedom (five-DOF) sampled-data active magnetic bearing (AMB) system with various disturbances. The more detailed objectives are: (i) to construct both an equivalent linear time-invariant discrete-time model and its state estimator via the proposed OKID approaches for the AMB system, which might be an unknown nonlinear time-varying unstable system with both a specified rotation speed and a sampling rate; (ii) to provide an adaptive disturbance estimation scheme, which establishes an equivalent input disturbance (EID) estimator for the AMB system with unexpected disturbances; and (iii) to develop a robust observer-based optimal LQDT for the sampled-data AMB system with both a pre-specified time-varying speed and unexpected disturbances. The developed LQDT is able to recover the displacement of the rotor to the pre-specified trajectory position whenever it deviates from such trajectory.     

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...     

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.     

Decentralized control and state estimation of linear time-periodic systems

The main contributions of this article are the design of a decentralized controller and state estimator for linear time-periodic systems with fixed network topologies. The proposed method to tackle both problems consists of reformulating the linear periodic dynamics as a linear time-invariant system by applying a time-lifting technique and designing a discrete-time decentralized controller and state estimator for the time-lifted formulation. The problem of designing the decentralized estimator is formulated as a discrete-time Kalman filter subject to sparsity constraints on the gains. Two different algorithms for the computation of steady-state observer gains are tested and compared. The control problem is posed as a state feedback gain optimization problem over an infinite-horizon quadratic cost, subject to a sparsity constraint on the gains. An equivalent formulation that consists in the optimization of the steady-state solution of a matrix difference equation is presented and an algorithm for the computation of the decentralized gain is detailed. Simulation results for the practical cases of the quadruple-tank process and an extended 40-tank process are presented that illustrate the performance of the proposed solutions, complemented with numerical simulations using the Monte Carlo method.     

A longitudinal study of the effects of ecological interface design on deep knowledge

Some researchers have argued that providing operators with externalized, graphic representations can lead to a trade-off whereby deep knowledge is sacrificed for cognitive economy and performance. This article provides an initial empirical investigation of this hypothesis by presenting a longitudinal study of the effect of ecological interface design (EID), a framework for designing interfaces for complex industrial systems, on subjects' deep knowledge. The experiment continuously observed the quasi-daily performance of the subjects' over a period of six months. The research was conducted in the context of DURESS II, a real-time, interactive thermal-hydraulic process control simulation that was designed to be representative of industrial systems. The performance of two interfaces was compared, an EID interface based on physical and functional (P+F) system representations and a more traditional interface based solely on a physical (P) representation. Subjects were required to perform several control tasks, including startup, tuning, shutdown and fault management. Occasionally, a set of knowledge elicitation tests was administered to assess the evolution of subjects' deep knowledge of DURESS II. The results suggest that EID can lead to a functionally organized knowledge base as well as superior performance, but only if subjects actively reflect on the feedback they get from the interface. In contrast, if subjects adopt a surface approach to learning, then EID can lead to a shallow knowledge base and poor performance, although no worse than that observed with a traditional interface.     

Feedback control of distributed parameter systems with spatially concentrated controls†

The problem of designing an optimal feedback controller is discussed for a distributed parameter system governed by a partial differential equation of parabolic type. A quadratic performance index is evaluated with spatially concentrated and time-discrete control, and controllability of this system is investigated. Also an estimator with multi-pointwise observation is constructed. Computational algorithms of these controller and estimator are derived, and to show their validities, a few numerical examples are given     

基于状态观测器的约束鲁棒模型预测控制

模型不确定情况下的鲁棒问题是模型预测控制的一个根本问题。本文采用线性矩阵不等式(LMI)，研究多模型不确定性描述情况下的鲁棒模型预测控制问题。在输入输出约束条件下，最小化最坏情况下的无穷时域目标函数，获得保证系统稳定的基于状态观测器的状态反馈增益并且给出观测器增益的设计方法。实例说明算法可行且保证闭环系统渐近稳定。     

分数阶多机器人的领航–跟随型环形编队控制

针对多机器人系统的环形编队控制复杂问题,提出一种基于分数阶多机器人的环形编队控制方法,应用领航–跟随编队方法来控制多机器人系统的环形编队和目标包围,通过设计状态估测器,实现对多机器人的状态估计.由领航者获取系统中目标状态的信息,跟随者监测到领航者的状态信息并完成包围环绕编队控制,使多机器人系统形成对动态目标的目标跟踪....     

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.     

Ecological interface design and sensor noise

This paper investigates the effects of the presence and magnitude of sensor noise on operators' performance and control stability when they use an Ecological Interface Design (EID) interface and a non-EID interface. Sensor noise was gradually increased in selected low-level physical sensors of DURESS III, a representative thermal-hydraulic process simulation. There are two important findings. First, participants in the EID condition achieved target goals significantly faster across all magnitudes of sensor noise. Second, participants in the EID condition exhibited more stable control; experiencing fewer and shorter oscillations around the target goals. This is the first study to empirically investigate the impact of the presence and magnitude of sensor noise on the robustness and effectiveness of an EID interface. These findings are important if EID is to be applied in industrial settings.     

Generalized-Extended-State-Observer and Equivalent-Input-Disturbance Methods for Active Disturbance Rejection: Deep Observation and Comparison

Active disturbance-rejection methods are effective in estimating and rejecting disturbances in both transient and steady-state responses. This paper presents a deep observation on and a comparison between two of those methods: the generalized extended-state observer (GESO) and the equivalent input disturbance (EID) from assumptions, system configurations, stability conditions, system design, disturbance-rejection performance, and extensibility. A time-domain index is introduced to assess the disturbance-rejection performance. A detailed observation of disturbance-suppression mechanisms reveals the superiority of the EID approach over the GESO method. A comparison between these two methods shows that assumptions on disturbances are more practical and the adjustment of disturbance-rejection performance is easier for the EID approach than for the GESO method.      

一类不规则损失输出数据系统的自校正PID控制算法

针对输出误差模型描述的不规则损失输出数据系统,提出一种自校正PID控制算法.首先结合辅助模型辨识思想和最小二乘原理设计参数估计器,在线估计系统参数,并设计一个损失输出估计器来估算采样间损失输出,使控制系统得到一个具有与期望输出相同采样周期的反馈信号;再根据系统参数的估计值实时调整自校正PID控制器参数,使系统实际输出跟...