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.     

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.     

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.     

Finite‐Time Fault‐Tolerant Control for a Class of Non‐Affine Nonlinear System Using Sliding Mode Disturbance Observer

This study investigates a finite‐time fault‐tolerant control scheme for a class of non‐affine nonlinear system with actuator faults and unknown disturbances. A global approximation method is applied to non‐affine nonlinear system to convert it into an affine‐like expression with accuracy. An adaptive terminal sliding mode disturbance observer is proposed to estimate unknown compound disturbances in finite time, including external disturbances and system uncertainties, which enhances system robustness. Controllers based on finite‐time Lyapunov theory are designed to force tracking errors to zero in finite time. Simulation results demonstrate the effectiveness of proposed 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 Repetitive Control and Disturbance Rejection Based on Two‐Dimensional Model and Equivalent‐Input‐Disturbance Approach

A new configuration of a modified repetitive‐control system has been devised for a class of strictly proper plants that suppresses exogenous disturbances and uncertainties in the dynamics of the plant. It extends the applicability of the control system. The system consists of four parts: a two‐dimensional augmented model of the plant, which takes into account the difference in characteristics between continuous control and discrete learning in repetitive control; an equivalent‐input‐disturbance estimator; a state observer; and a state‐feedback controller. A robust‐stability condition expressed in terms of a linear matrix equality is used to determine the gains of the observer and the controller. Finally, a comparison of our method with repetitive control based on linear active disturbance rejection control (LADRC) shows how effective our method is and that it is superior to LADRC‐based repetitive control.     

Low dimensional disturbance observer‐based control for nonlinear parabolic PDE systems with spatio‐temporal disturbances

In this paper, a design problem of low dimensional disturbance observer‐based control (DOBC) is considered for a class of nonlinear parabolic partial differential equation (PDE) systems with the spatio‐temporal disturbance modeled by an infinite dimensional exosystem of parabolic PDE. Motivated by the fact that the dominant structure of the parabolic PDE is usually characterized by a finite number of degrees of freedom, the modal decomposition method is initially applied to both the PDE system and the PDE exosystem to derive a low dimensional slow system and a low dimensional slow exosystem, which accurately capture the dominant dynamics of the PDE system and the PDE exosystem, respectively. Then, the definition of input‐to‐state stability for the PDE system with the spatio‐temporal disturbance is given to formulate the design objective. Subsequently, based on the derived slow system and slow exosystem, a low dimensional disturbance observer (DO) is constructed to estimate the state of the slow exosystem, and then a low dimensional DOBC is given to compensate the effect of the slow exosystem in order to reject approximately the spatio‐temporal disturbance. Then, a design method of low dimensional DOBC is developed in terms of linear matrix inequality to guarantee that not only the closed‐loop slow system is exponentially stable in the presence of the slow exosystem but also the closed‐loop PDE system is input‐to‐state stable in the presence of the spatio‐temporal disturbance. Finally, simulation results on the control of temperature profile for catalytic rod demonstrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Event‐Triggered Consensus of Nonlinear Multi‐Agent Systems with Unknown External Disturbance

This paper addresses the consensus problem of nonlinear multi‐agent systems with unknown external disturbance. First, a distributed observer is proposed to estimate the state and unknown disturbance of each agent simultaneously. Then, a novel event‐triggered control scheme based on the agent state estimation and disturbance estimation is proposed. Unlike the existing strategies, our event‐triggered conditions depend on agent state estimation and disturbance estimation, which are more effective and practical. Under this observer and control strategy, some sufficient conditions are derived to ensure the consensus of the multi‐agent system with unknown external disturbance. Moreover, the Zeno‐behavior of triggering time sequences is also excluded. Finally, a simulation example is given to verify the theoretical analysis.     

一类具有非线性扰动的多重时滞不确定系统鲁棒预测控制

针对一类具有非线性扰动且同时存在多重状态和输入时滞的不确定系统, 提出 一种鲁棒预测控制器设计方法. 基于预测控制滚动优化原理, 运用Lyapunov稳定性 理论和线性矩阵不等式 (Linear matrix inequalities, LMIs)方法, 首先近似求解无限时域二次性能指标优化问题, 然后优化非 线性扰动项所应满足的最大上界, 定量地研究鲁棒预测控制在范数有界意义下的扰动抑制 问题, 并给出了鲁棒预测控制器存在的充分条件. 最后通过仿真验证了所提方法的有效性.     

Torque tracking control of electric load simulator with active motion disturbance and nonlinearity based on T‐S fuzzy model

This paper develops a high performance nonlinear control method for an electric load simulator (ELS). The tracking performance of the ELS is mainly affected by the actuator's active motion disturbance and friction nonlinearity. First, a nonlinear model of ELS is developed, and then the Takagi‐Sugeno fuzzy model is used to represent the friction nonlinearity ofthe ELS. A state observer is constructed to estimate the speed of the load system. For converting the tracking control into a stabilization problem, a new control design called virtual desired state synthesis is proposed to define the internal desired states. External disturbances are attenuated based on an H_∞ criterion and the stability of the entire closed‐loop model is investigated using the well‐known quadratic Lyapunov function. Meanwhile, the feedback gains and the observer gains are obtained separately by solving a set of linear matrix inequalities (LMIs). Both a simulation and experiment were performed to validate the effectiveness of the developed algorithm.