Repetitive process based design and experimental verification of a dynamic iterative learning control law

This paper gives new results on iterative learning control (ILC) design and experimental verification using the stability theory of linear repetitive processes. Using this theory a control law can be designed in one step to force error convergence and produce acceptable transient dynamics. Previous research developed algorithms for the design of a static control law with supporting experimental verification. Should a static law not give the required levels of performance one option is to allow the control law to have internal dynamics. This paper develops a procedure for the design of such a control law with supporting experimental verification on a gantry robot, including a comparative performance against a static law applied to the same robot. The resulting ILC design is an efficient combination of linear matrix inequalities and optimization algorithms.     

基于LMI的多模型鲁棒预测控制

用线性矩阵不等式 (LMI)方法研究多模型鲁棒预测控制, 提出了状态反馈的综合方法, 并分析了闭环系统的可行性, 同时证明闭环系统渐近稳定. 在此基础上, 研究了带终端零状态的有限优化时域预测控制和无穷优化时域预测控制的性能, 证明了两者在性能上的一致性.     

Robust design of feedback feed-forward iterative learning control based on 2D system theory for linear uncertain systems

For a class of linear discrete-time uncertain systems, a feedback feed-forward iterative learning control (ILC) scheme is proposed, which is comprised of an iterative learning controller and two current iteration feedback controllers. The iterative learning controller is used to improve the performance along the iteration direction and the feedback controllers are used to improve the performance along the time direction. First of all, the uncertain feedback feed-forward ILC system is presented by an uncertain two-dimensional Roesser model system. Then, two robust control schemes are proposed. One can ensure that the feedback feed-forward ILC system is bounded-input bounded-output stable along time direction, and the other can ensure that the feedback feed-forward ILC system is asymptotically stable along time direction. Both schemes can guarantee the system is robust monotonically convergent along the iteration direction. Third, the robust convergent sufficient conditions are given, which contains a linear matrix inequality (LMI). Moreover, the LMI can be used to determine the gain matrix of the feedback feed-forward iterative learning controller. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed schemes.     

基于LMI的随动系统满意PID调节器设计

PID控制器在实际工程中应用广泛,而且工程上对随动系统的性能要求往往是多方面的．该文应用满意控制思想,研究了期望指标：扇形区域极点,稳态输出方差和动态误差系数约束下随动系统的PID控制设计问题．首先将PID控制参数设计转化为局部状态反馈问题,导出了3项指标约束的双线性矩阵不等式(BMI)描述．然后给出改进的迭代线性矩阵不等式(LMI)算法求解BMI可行解,得到使闭环系统满足3项期望指标的PID参数．最后给出了应用该方法数值算例．     

基于LMI和IMC的动态反馈抗饱和补偿设计

提出了一种基于线性矩阵不等式(LMI)和内模控制(IMC)的动态反馈抗饱和补偿器的设计方法,为此首先简要地介绍了基于统一框架的抗饱和补偿器设计方法,然后针对原框架计算量庞大的问题,利用模型精确的IMC结构中对象和控制器同时稳定就能保证系统闭环稳定的特性对框架进行改造,并进一步选取了具有(?)2范数形式的性能优化指标,通过整定控制器的方法来优化闭环系统的工作性能,给出了LMI形式的结果．最后给出了运用此方法设计补偿器的一个仿真实例．     

基于LMI的滑模控制在航空发动机中的应用

针对航空发动机运行过程中存在不确定性和稳定性问题,运用状态空间模型理论与线性矩阵不等式LMI相结合的方法设计了控制器,改善了航空发动机的控制性能。以某型涡扇发动机为控制对象,基于LMI对普通终端滑模变结构控制进行了优化设计,在滑模超平面设计中引入了动态补偿器,采用改进的幂次趋近律,对该动态系统进行了性能仿真验证。结果表明,本文提出的方法较之普通终端滑模变结构控制对系统性能有较大改善,不仅使系统主供油量变化率、尾喷口面积变化率等的控制更为平稳,且保证了系统鲁棒性和稳定性。     

Improved LMI conditions for gain scheduling and related control problems

The gain scheduling problem considered in this paper concerns a linear system whose state-space equations depend rationally on real, time-varying parameters, which are measured in real time. A stabilizing, parameter-dependent controller is sought, such that a given ℒ︁₂-gain bound for the closed-loop system is ensured. Sufficient linear matrix inequality (LMI) conditions are known, that guarantee the existence of such ‘gain-scheduled’ controllers. This paper improves these results in two directions. First, we show how to exploit the realness of the parameters using a ‘skew-symmetric scaling’ technique. Moreover, we show how to apply this technique in a time-varying and/or nonlinear setting. We first devise a general result pertaining to control synthesis of interconnection of dissipative operators, and apply it to the gain-scheduling problem. Owing to its generality, this result can be applied to other problems such as anti-windup control, nonlinear control and model reduction. © 1998 John Wiley & Sons, Ltd.     

基于LM I 的一类非线性时滞关联大系统的分散模糊控制

针对一类采用Takagi—Sugeno模糊模型描述的非线性时滞关联大系统，研究其分散模糊状态反馈控制器设计问题；利用Lyapunov稳定性分析理论和线性矩阵不等式等工具，得到了闭环系统的可镇定条件和相应的分散模糊状态反馈控制器；在此基础上，通过求解具有线性矩阵不等式组约束的凸优化问题，给出了具有较小反馈增益的分散模糊控制器设计方法。     

Integrated design of fault reconstruction and fault-tolerant control against actuator faults using learning observers

This paper addresses the problem of integrated fault reconstruction and fault-tolerant control in linear systems subject to actuator faults via learning observers (LOs). A reconfigurable fault-tolerant controller is designed based on the constructed LO to compensate for the influence of actuator faults by stabilising the closed-loop system. An integrated design of the proposed LO and the fault-tolerant controller is explored such that their performance can be simultaneously considered and their coupling problem can be effectively solved. In addition, such an integrated design is formulated in terms of linear matrix inequalities (LMIs) that can be conveniently solved in a unified framework using LMI optimisation technique. At last, simulation studies on a micro-satellite attitude control system are provided to verify the effectiveness of the proposed approach.     

基于LMI不确定离散随机系统输出反馈保性能控制

针对一类范数有界不确定离散随机系统,研究了具有输出反馈控制器的保性能控制,由此得到闭环系统的二次型性能指标上界的一般形式;然后应用LMI凸优化技术,推导出使闭环系统渐近稳定的最优保性能控制器的设计方法;最后通过仿真算例验证了所提出算法的可行性和有效性.     

LMI-based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.     

Iterative learning control design based on composite energy function with input saturation

In this work, an iterative learning control scheme is designed for a class of nonlinear uncertain systems with input saturation. The analysis of convergence in the iteration domain is based on composite energy function, which consists of both input and state information along the time and iteration axes. Through rigorous analysis, the learning convergence in the iteration domain can be guaranteed under the input saturation, provided the desired trajectory is realizable within the saturation bound.     

基于LMI的分散式深空飞行器编队控制

针对深空探测任务中飞行器编队的控制问题,提出了一种基于线性矩阵不等式(LMI)的分散式控制方案.该方案考虑了深守编队与传统的近地编队之间的差异,把该方案转化为一类LMI问题;对比传统的基于"黎卡提方程一线性二次调节器"(Riccati-LQR)的编队方法,本方法更精确地实现了控制目标,并减轻了通讯压力,降低了燃耗.对该方案的仿真实例,展示出在燃耗最小及编队质心位置不变的条件下,队形机动的实现过程;并对结果作出了分析.     

Formation control for multi‐agent systems through an iterative learning design approach

This paper deals with formation control problems for multi‐agent systems by using iterative learning control (ILC) design approaches. Distributed formation ILC algorithms are presented to enable all agents in directed graphs to achieve the desired relative formations perfectly over a finite‐time interval. It is shown that not only asymptotic stability but also monotonic convergence of multi‐agent formation ILC can be accomplished, and the convergence conditions in terms of linear matrix inequalities can be simultaneously established. The derived results are also applicable to multi‐agent systems that are subject to stochastic disturbances and model uncertainties. Furthermore, the feasibility of convergence conditions and the effect of communication delays are discussed for the proposed multi‐agent formation ILC algorithms. Simulation results are given for uncertain multi‐agent systems to verify the theoretical study. Copyright © 2012 John Wiley & Sons, Ltd.     

Predictor‐based repetitive learning control for a class of remote control nonlinear systems

In this paper, a repetitive learning control (RLC) approach is proposed for a class of remote control nonlinear systems satisfying the global Lipschitz condition. The proposed approach is to deal with the remote tracking control problem when the environment is periodic or repeatable over infinite time domain. Since there exist time delays in the two transmission channels: from the controller to the actuator and from the sensor to the controller, tracking a desired trajectory through a remote controller is not an easy task. In order to solve the problem caused by time delays, a predictor is designed on the controller side to predict the future state of the nonlinear system based on the delayed measurements from the sensor. The convergence of the estimation error of the predictor is ensured. The gain design of the predictor applies linear matrix inequality (LMI) techniques developed by Lyapunov Kravoskii method for time delay systems. The RLC law is constructed based on the feedback error from the predicted state. The overall tracking error tends to zero asymptotically over iterations. The proof of the stability is based on a constructed Lyapunov function related to the Lyapunov Kravoskii functional used for the proof of the predictor's convergence. By well incorporating the predictor and the RLC controller, the system state tracks the desired trajectory independent of the influence of time delays. A numerical simulation example is shown to verify the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimentally verified generalized KYP Lemma based iterative learning control design

This paper considers iterative learning control law design for plants modeled by discrete linear dynamics using repetitive process stability theory. The resulting one step linear matrix inequality based design produces a stabilizing feedback controller in the time domain and a feedforward controller that guarantees convergence in the trial-to-trial domain. Additionally, application of the generalized Kalman–Yakubovich–Popov (KYP) lemma allows a direct treatment of differing finite frequency range performance specifications. The results are also extended to plants with relative degree greater than unity. To support the algorithm development, the results from an experimental implementation are given, where the performance requirements include specifications over various finite frequency ranges.     

动态区间系统的最优保性能控制--LMI方法

针对动态区间系统和一个给定的二次型性能指标,研究了其保性能控制问题,基于线性矩阵不等式(LMI)提出了最优保性能控制器设计方法,并将相关结果推广到参数不确定系统.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于设计动态区间系统与秩-1型参数不确定系统的最优保性能控制器,非常有效.     

Robust finite frequency range iterative learning control design and experimental verification

Iterative learning control is an application for two-dimensional control systems analysis where it is possible to simultaneously address error convergence and transient response specifications but there is a requirement to enforce frequency attenuation of the error between the output and reference over the complete spectrum. In common with other control algorithm design methods, this can be a very difficult specification to meet but often the control of physical/industrial systems is only required over a finite frequency range. This paper uses the generalized Kalman–Yakubovich–Popov lemma to develop a two-dimensional systems based iterative learning control law design algorithm where frequency attenuation is only imposed over a finite frequency range to be determined from knowledge of the application and its operation. An extension to robust control law design in the presence of norm-bounded uncertainty is also given and its applicability relative to alternative settings for design discussed. The resulting designs are experimentally tested on a gantry robot used for the same purpose with other iterative learning control algorithms.     

Iterative learning control design for Smith predictor

The Smith predictor has been used to improve the closed-loop performance for systems with time delays. This paper proposes a frequency-domain method to design an iterative learning control to further improve the performance of Smith predictor controller. For a time-invariant plant with multiplicative perturbations and a Smith predictor controller, we derive a sufficient and necessary condition (which has the same form as that of a general robust performance design problem) for the iterative process to converge for all admissible plant uncertainties. In addition, the iterative learning controller under plant uncertainty is designed. An illustrative example demonstrating the main result is presented.     

Set-point-related indirect iterative learning control for multi-input multi-output systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.