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Numerical solution of nonlinear periodic optimal control problems using a Fourier integral pseudospectral method 用傅立叶积分伪谱法数值求解非线性周期优化控制问题
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-04 DOI: 10.1016/j.jprocont.2024.103326
Kareem T. Elgindy
Many real-world systems exhibit cyclical behavior and nonlinear dynamics. Optimal control theory provides a framework for determining the best periodic control strategies for such systems. These strategies achieve the desired goals while minimizing the costs, energy use, or other relevant metrics. This study addresses this challenge by introducing the Fourier integral pseudospectral (FIPS) method. This method is applicable to a general class of nonlinear periodic process control problems with equality and/or inequality constraints, assuming sufficiently smooth solutions. The FIPS method performs collocation of the problem’s integral form at an equidistant set of nodes. Furthermore, it utilizes highly accurate Fourier integration matrices (FIMs) to approximate all necessary integrals. This approach transforms the original problem into a nonlinear programming problem (NLP) with algebraic constraints. We employed a direct numerical optimization method to solve this NLP effectively. This study establishes rigorous convergence properties and derives error estimates for the Fourier series, interpolants, and quadratures employed within the context of process control applications, focusing on smooth and continuous periodic functions. Finally, the accuracy and efficiency of the FIPS method are demonstrated through two illustrative nonlinear process-control problems.
现实世界中的许多系统都表现出周期性行为和非线性动态。最优控制理论为确定此类系统的最佳周期控制策略提供了一个框架。这些策略既能实现预期目标,又能最大限度地降低成本、能源消耗或其他相关指标。本研究通过引入傅立叶积分伪谱(FIPS)方法来应对这一挑战。该方法适用于具有相等和/或不等式约束条件的一般非线性周期过程控制问题,并假定有足够平滑的解。FIPS 方法在一组等距节点处对问题的积分形式进行配位。此外,它还利用高精度的傅立叶积分矩阵(FIM)来逼近所有必要的积分。这种方法将原始问题转化为具有代数约束条件的非线性编程问题(NLP)。我们采用了一种直接数值优化方法来有效求解该 NLP。本研究建立了严格的收敛特性,并推导出在过程控制应用中使用的傅里叶级数、内插值和二次函数的误差估计,重点关注平滑和连续的周期函数。最后,通过两个示例性非线性过程控制问题证明了 FIPS 方法的准确性和高效性。
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引用次数: 0
FPGA-embedded optimization algorithm to maximize the acetate productivity in a dark fermentation process 在黑暗发酵过程中最大限度提高醋酸生产率的 FPGA 嵌入式优化算法
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.jprocont.2024.103323
José de Jesús Colín-Robles , Ixbalank Torres-Zúñiga , Mario A. Ibarra-Manzano , J. Gabriel Aviña-Cervantes , Víctor Alcaraz-González
This paper presents an optimization strategy to online maximize the acetate productivity rate in a dark fermentation (DF) process. The Golden Section Search algorithm is used to compute the maximum acetate productivity rate as a function of the inlet chemical oxygen demand (COD) and the dilution rate, selected as a manipulated variable. Such maximum productivity is considered as a reference by a Super-Twisting controller to regulate the real acetate productivity rate of the DF process. Due to the lack of sensors to measure the COD online, the optimization strategy includes an unknown input observation strategy integrated by a Luenberger observer interconnected to a Super-Twisting observer to estimate the inlet COD concentration. The optimization algorithm is embedded in an FPGA (Field Programmable Gate Array) device to minimize hardware resources and power consumption. The feasibility of the online optimization strategy embedded in an FPGA, using a digital architecture designed with a fixed-point format representation, is demonstrated by numerical simulations. Results show that the optimization strategy requires 53% of the logic elements and 100% of 8-bit multipliers of an FPGA Cyclone II and the power consumption estimated is only 190mW.
本文介绍了一种在线最大化暗发酵(DF)工艺中醋酸盐生产率的优化策略。采用黄金分割搜索算法计算最大醋酸盐生产率,并将其作为入口化学需氧量(COD)和稀释率的函数。超级扭曲控制器将此最大生产率作为参考,以调节 DF 工艺的实际醋酸盐生产率。由于缺乏在线测量化学需氧量的传感器,优化策略包括一个未知输入观测策略,该策略由一个与超级扭转观测器相互连接的卢恩伯格观测器整合而成,用于估计入口处的化学需氧量浓度。优化算法嵌入到 FPGA(现场可编程门阵列)设备中,以最大限度地减少硬件资源和功耗。数值模拟证明了嵌入 FPGA 的在线优化策略的可行性,该策略采用定点格式表示的数字架构设计。结果表明,该优化策略只需要 FPGA Cyclone II 53% 的逻辑元件和 100% 的 8 位乘法器,功耗估计仅为 190mW。
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引用次数: 0
Data Science and Model Predictive Control: 数据科学与模型预测控制
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-11-01 DOI: 10.1016/j.jprocont.2024.103327
Marcelo M. Morato , Monica S. Felix
Model Predictive Control (MPC) is an established control framework, based on the solution of an optimisation problem to determine the (optimal) control action at each discrete-time sample. Accordingly, major theoretical advances have been provided in the literature, such as closed-loop stability and recursive feasibility certificates, for the most diverse kinds of processes descriptions. Nevertheless, identifying good, trustworthy models for complex systems is a task heavily affected by uncertainties. As of this, developing MPC algorithms directly from data has recently received a considerable amount of attention over the last couple of years. In this work, we review the available data-based MPC formulations, which range from reinforcement learning schemes, adaptive controllers, and novel solutions based on behavioural theory and trajectory representations. In particular, we examine the recent research body on this topic, highlighting the main features and capabilities of available algorithms, while also discussing the fundamental connections among approaches and, comparatively, their advantages and limitations.
模型预测控制(MPC)是一种成熟的控制框架,它基于优化问题的解决方案,以确定每个离散时间样本的(最优)控制行动。因此,文献中已经取得了重大的理论进展,例如针对最多样化的过程描述提供了闭环稳定性和递归可行性证明。然而,为复杂系统确定良好、可信的模型是一项受不确定性严重影响的任务。因此,最近几年,直接从数据中开发 MPC 算法受到了广泛关注。在这项工作中,我们回顾了现有的基于数据的 MPC 方案,其中包括强化学习方案、自适应控制器以及基于行为理论和轨迹表示的新型解决方案。特别是,我们考察了最近关于这一主题的研究成果,强调了现有算法的主要特点和能力,同时还讨论了各种方法之间的基本联系,以及它们的优势和局限性。
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引用次数: 0
Adaptive error feedback regulation for a 1-D anti-stable wave equation subject to harmonic disturbances 受谐波干扰的一维反稳定波方程的自适应误差反馈调节
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-10-28 DOI: 10.1016/j.jprocont.2024.103324
Shuangxi Huang , Qing-Qing Hu
In this paper, we study the error feedback regulation problem for a 1-D anti-stable wave equation with harmonic disturbances in all channels via utilizing the adaptive control method. The output to be regulated is non-collocated with the control and the reference signal is also a harmonic type. We first transform all the disturbances into one channel by an invertible transformation. Then we propose an adaptive observer through applying the only measurable tracking error. Next, we construct an observer-based error feedback controller, it is shown that the tracking error decays asymptotically to zero and all internal signals are bounded. Finally, the numerical simulations show that all the states are uniformly bounded, the unknown amplitudes of the harmonic disturbances and reference signal can be estimated and the tracking error decays to zero asymptotically.
本文利用自适应控制方法,研究了全通道谐波干扰的一维反稳定波方程的误差反馈调节问题。需要调节的输出与控制无关,参考信号也是谐波类型。我们首先通过可逆变换将所有干扰转换为一个通道。然后,通过应用唯一可测量的跟踪误差,我们提出了一种自适应观测器。接下来,我们构建了一个基于观测器的误差反馈控制器,结果表明跟踪误差渐近衰减为零,并且所有内部信号都是有界的。最后,数值模拟表明,所有状态都是均匀有界的,谐波干扰和参考信号的未知振幅可以估计,跟踪误差渐近衰减为零。
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引用次数: 0
Enhanced predictive PDF control of stochastic distribution systems with neural network compensation and its application 采用神经网络补偿的随机配电系统的增强型预测性 PDF 控制及其应用
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-10-24 DOI: 10.1016/j.jprocont.2024.103328
Ping Zhou, Xiaoyang Sun, Lixiang Zhang, Mingjie Li
Compared to the conventional control algorithms that use mean and variance as indicators, predictive probability density function (PDF) control can effectively handle the output PDF control problem of non-Gaussian stochastic distribution systems. However, the existing predictive PDF control method does not consider the construction error between output PDF and weight, thus the control performance is still unsatisfactory. Therefore, this paper proposes a new Enhanced Predictive PDF control method (En-PDF) to improve the output PDF control performance of stochastic distribution systems. The proposed method mainly consists of two parts: the predictive PDF control part and the neural network compensation control part aiming to reduce the bias of output PDF. First, the Radical Basis Functions (RBFs) are used to approximate the PDF of the stochastic systems output, and then a prediction model representing the relationship between input and weight is established using the subspace identification algorithm to design the predictive PDF control for the stochastic systems. Next, the Kullback-Leibler (KL) divergence is used to measure the similarity between the output PDF and the set PDF, combined with the weight error and compensation to design a new performance index. Based on this, the parameters of the neural network are adjusted using the gradient descent algorithm to obtain the optimal compensation, and the stability and tracking performance of the proposed algorithm are analyzed using inductive reasoning method. Finally, the predictive PDF control input with the compensation work together on the controlled plant to achieve high-performance control of the output PDF of non-Gaussian stochastic distribution systems. Both simulation experiments and physical control experiments validate the effectiveness and superiority of the proposed method.
与以均值和方差为指标的传统控制算法相比,预测概率密度函数(PDF)控制能有效处理非高斯随机分布系统的输出 PDF 控制问题。然而,现有的预测式 PDF 控制方法并未考虑输出 PDF 与权重之间的构造误差,因此控制性能仍不尽如人意。因此,本文提出了一种新的增强预测式 PDF 控制方法(En-PDF),以改善随机分布系统的输出 PDF 控制性能。本文提出的方法主要由两部分组成:预测 PDF 控制部分和旨在减少输出 PDF 偏差的神经网络补偿控制部分。首先,利用激基函数(RBF)逼近随机系统输出的 PDF,然后利用子空间识别算法建立代表输入和权重之间关系的预测模型,设计随机系统的预测 PDF 控制。接着,利用库尔巴克-莱布勒(KL)发散来衡量输出 PDF 与设定 PDF 之间的相似度,并结合权重误差和补偿来设计新的性能指标。在此基础上,利用梯度下降算法调整神经网络参数,以获得最佳补偿,并利用归纳推理方法分析了所提算法的稳定性和跟踪性能。最后,预测性 PDF 控制输入与补偿共同作用于被控植物,实现了对非高斯随机分布系统输出 PDF 的高性能控制。仿真实验和物理控制实验都验证了所提方法的有效性和优越性。
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引用次数: 0
Fixed-time active fault-tolerant control for a class of nonlinear systems with intermittent faults and input saturation 一类具有间歇性故障和输入饱和的非线性系统的固定时间主动容错控制
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-10-24 DOI: 10.1016/j.jprocont.2024.103319
Xuanrui Cheng, Ming Gao, Li Sheng, Yongli Wei
In this paper, the problem of fixed-time active fault-tolerant control is studied for systems with sector-bounded nonlinearities, intermittent faults, and input saturation. Since intermittent faults appear and disappear randomly, a fixed-time scheme is considered in the active fault-tolerant control algorithm, composed of detection, isolation, estimation, and the control unit. Utilizing homogeneity-based observers, the fixed-time state estimation is available in the presence of unknown but bounded disturbances, and a fault diagnosis unit is proposed. An input saturation compensator is introduced to analyze the effect of input saturation, and its auxiliary variables are used in the reconfigurable control law. The fault-tolerant controller, which is constructed via the information provided by the fault diagnosis unit and saturation compensator, has two switching modes. As a consequence, intermittent faults are compensated via the designed active fault-tolerant control method and the system reaches practical stability with the entire convergence time bounded in a fixed time. Finally, the example of a heat control system is exploited to demonstrate the effectiveness of the developed active fault-tolerant control scheme.
本文研究了具有扇区约束非线性、间歇性故障和输入饱和的系统的固定时间主动容错控制问题。由于间歇性故障的出现和消失是随机的,因此在由检测、隔离、估计和控制单元组成的主动容错控制算法中考虑了固定时间方案。利用基于同质性的观测器,可在存在未知但有界的干扰时进行固定时间状态估计,并提出了故障诊断单元。引入了输入饱和补偿器来分析输入饱和的影响,其辅助变量被用于可重构的控制法则中。通过故障诊断单元和饱和补偿器提供的信息构建的容错控制器有两种切换模式。因此,间歇性故障可通过所设计的主动容错控制方法得到补偿,系统达到实际稳定性,整个收敛时间被限定在一个固定的时间内。最后,以热控制系统为例,证明了所开发的主动容错控制方案的有效性。
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引用次数: 0
Pre-connected and trainable adjacency matrix-based GCN and neighbor feature approximation for industrial fault diagnosis 用于工业故障诊断的基于邻接矩阵和邻近特征近似的预连接和可训练邻接矩阵
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-10-24 DOI: 10.1016/j.jprocont.2024.103320
Hao-Yang Qing, Ning Zhang, Yan-Lin He, Qun-Xiong Zhu, Yuan Xu
Industrial fault diagnosis methods based on graph convolution network (GCN) becomes a hot topic for its great feature extraction ability to multivariate time-series data. However, GCNs ignore inter-sample temporality when constructing the adjacency matrix (AM), leading to low prediction accuracy. A novel fault diagnosis method based on pre-connected and trainable AM-based GCN and neighbor feature approximation (PTGCN-FA) is proposed at the node-level task. Firstly, PTGCN-FA introduces the temporal nearest neighbors into spatial nearest neighbors to pre-connect and construct the AM. Then, the AM is trained only where the samples are connected, which makes the best weights obtained and reduces the time complexity of the model. Finally, after the GCN layers, the trained AM is introduced into the approximation of features, which are neighbors in the original sample space. Two process industry cases are carried out, and the simulation results including diagnosis accuracy, confusion matrix, study to the ratio of labeled data and an ablation experiment verify PTGCN-FA has more efficient and accurate diagnostic performance than related methods. Additionally, the analysis of the temporal neighborhood weight parameter shows that the performance of fault diagnosis can be improved by considering both temporal and spatial information between samples.
基于图卷积网络(GCN)的工业故障诊断方法因其对多变量时间序列数据的强大特征提取能力而成为热门话题。然而,GCN 在构建邻接矩阵(AM)时忽略了样本间的时间性,导致预测准确率较低。在节点级任务中,提出了一种基于预连接和可训练 AM 的 GCN 和邻接特征逼近(PTGCN-FA)的新型故障诊断方法。首先,PTGCN-FA 将时间近邻引入空间近邻,以预连接并构建 AM。然后,只在样本连接的地方训练 AM,从而获得最佳权重并降低模型的时间复杂度。最后,在 GCN 层之后,将训练好的 AM 引入到特征逼近中,这些特征是原始样本空间中的邻居。仿真结果包括诊断准确率、混淆矩阵、标注数据比率研究和烧蚀实验,验证了 PTGCN-FA 比相关方法具有更高效、更准确的诊断性能。此外,对时间邻域权重参数的分析表明,通过同时考虑样本间的时间和空间信息,可以提高故障诊断的性能。
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引用次数: 0
Just-in-time framework for robust soft sensing based on robust variational autoencoder 基于稳健变异自动编码器的稳健软传感即时框架
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-10-22 DOI: 10.1016/j.jprocont.2024.103325
Fan Guo , Kun Liu , Biao Huang
Modeling with high-dimensional data subject to abnormal observations have always been a practical interest. In this paper, under the just-in-time learning (JITL) framework, a robust soft sensor modeling approach is developed based on robust Variational Autoencoder (VAE). Unlike the vanilla VAE that extracts features from the given dataset under the Gaussian prior assumption, robust VAE employs Student’s t-distribution as prior distribution to handle abnormal data. Under assumption of the Student’s t-prior, the proposed robust VAE model is capable of describing collected data contaminated with outliers. Once the robust VAE model is trained, each robust feature variable in the latent space can be determined. Subsequently, similarity measure is calculated using robust Kullback-Leibler divergence between two Student’s t-distributions, that is, the distribution of a new data sample and that of each historical data sample. After completing similarity measurement for a query sample, the weights for input-output historical data can be determined. Based on these weighted historical data samples, a robust probabilistic principal component regression (PPCR) is utilized to perform local modeling for prediction. Numerical simulations, including the Tennessee Eastman and Penicillin fermentation benchmark processes, are utilized to validate the proposed JITL-based robust soft sensor modeling method.
利用受异常观测影响的高维数据建模一直是人们关注的实际问题。本文在及时学习(JITL)框架下,基于稳健变异自动编码器(VAE)开发了一种稳健软传感器建模方法。与在高斯先验假设下从给定数据集中提取特征的普通 VAE 不同,鲁棒 VAE 采用了 Student's t 分布作为先验分布来处理异常数据。在 Student's t 先验假设下,所提出的鲁棒 VAE 模型能够描述受到异常值污染的收集数据。一旦训练出稳健 VAE 模型,就能确定潜空间中的每个稳健特征变量。随后,利用两个学生 t 分布(即新数据样本的分布和每个历史数据样本的分布)之间的鲁棒 Kullback-Leibler 发散计算相似度。完成查询样本的相似性测量后,就可以确定输入输出历史数据的权重。在这些加权历史数据样本的基础上,利用稳健概率主成分回归(PPCR)进行局部建模预测。利用包括田纳西伊士曼和青霉素发酵基准过程在内的数值模拟来验证所提出的基于 JITL 的鲁棒软传感器建模方法。
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引用次数: 0
Experimental implementation of extremum-seeking control: Gas fuel efficiency at electrical generation under power requirements 极值搜索控制的实验实施:电力需求下的发电气体燃料效率
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-10-22 DOI: 10.1016/j.jprocont.2024.103322
Ricardo Femat , Jesús Torres-Mireles , Nimrod Vázquez-Nava
A current challenge stands for operating the emergency power system (EPS) that involves the challenge of supplying sufficient electrical energy at same time the fuel consumption is minimum. A complication arises as power requirements change during the EPS operation which can be seen as uncertain load disturbances. In such a context, the extremum-seeking (ES) is alternative towards the efficient energy conversion when control goal involves fuel optimization along the time operation. Here, the dynamical response of a gas fueled power plant is identified via Hammerstein model. The model is realized such that an ES control is designed for automatically reaching an extreme in face to distinct (unmeasured and uncertain) power requirements. The ES control is designed and experimentally tested at an electrical generator at distinct power requirements. The results show the minimum gas fuel consumption remains in face to distinct power requirements.
目前,应急电力系统(EPS)的运行面临着一个挑战,即在提供充足电能的同时,将燃料消耗降至最低。在 EPS 运行过程中,电力需求会发生变化,这可以被视为不确定的负载干扰,因此出现了一个复杂问题。在这种情况下,当控制目标涉及沿时间运行的燃料优化时,极值搜索(ES)是实现高效能源转换的替代方法。在此,通过 Hammerstein 模型确定了燃气燃料发电厂的动态响应。通过该模型,可以设计出一种 ES 控制,在面对不同(无法测量和不确定)的功率要求时自动达到极值。设计的 ES 控制装置已在一台发电机上按不同的功率要求进行了实验测试。结果表明,在不同的功率要求下,气体燃料消耗量仍然最小。
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引用次数: 0
Robust bilinear tracking control of a parabolic trough solar collector via saturation 通过饱和对抛物面槽式太阳能集热器进行鲁棒双线性跟踪控制
IF 3.3 2区 计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS Pub Date : 2024-10-19 DOI: 10.1016/j.jprocont.2024.103321
Sarah Mechhoud , Zehor Belkhatir
This paper investigates the problem of robust tracking control of heat transport in a Parabolic Trough Solar Collector (PTSC), where the output has to track a desired reference trajectory. In this work, the PTSC is modeled by state-space bilinear dynamics. The manipulated variable is the pump volumetric flow rate, and the source term, i.e., solar irradiance, is assumed to be unmeasured. In addition, the actuator’s physical constraints induce saturation bounds on the manipulated variable and need to be considered explicitly in the controller design. To deal with these challenges, we first propose a saturated state-feedback law that meets the control objectives. Then, we reconstruct the unknown time-varying source term using an adaptive estimator. Later, through Lyapunov stability analysis, we prove that the closed-loop system and the output tracking error are uniformly ultimately stable. Numerical simulations attest to the performance of the proposed control strategy.
本文研究了抛物槽式太阳能集热器(PTSC)中热量传输的鲁棒跟踪控制问题,其中输出必须跟踪所需的参考轨迹。在这项工作中,PTSC 采用状态空间双线性动力学建模。操纵变量是泵的容积流量,源项(即太阳辐照度)假定是不可测量的。此外,执行器的物理约束会对操纵变量产生饱和约束,需要在控制器设计中明确考虑。为了应对这些挑战,我们首先提出了一种满足控制目标的饱和状态反馈定律。然后,我们使用自适应估计器重建未知时变源项。之后,通过 Lyapunov 稳定性分析,我们证明了闭环系统和输出跟踪误差是均匀最终稳定的。数值模拟证明了所提控制策略的性能。
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引用次数: 0
期刊
Journal of Process Control
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