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摘要: 历经20多年的发展, 迭代学习模型预测控制在理论和应用方面都取得了长足的进步. 但由于批次工业过程复杂多样、结构各异、精细化程度较高, 现有的迭代学习模型预测控制理论仍面临着巨大挑战. 本文简要回顾了迭代学习模型预测控制理论的产生及发展, 阐述了二维预测模型、控制律迭代优化及二维稳定性等基本理论问题; 分析了现有方法在理论及应用方面的局限性, 说明了迭代学习模型预测控制在迭代建模、高效优化、变工况适应等方面面临的难点问题, 提出了可行的解决方案. 简要综述了近年来迭代学习模型预测控制理论和应用层面的发展动态, 指出了研究复杂非线性系统、快速系统、变工况系统对进一步完善其理论体系和拓宽其应用前景的意义, 展望了成品质量控制和动态经济控制等重要的未来研究方向.Abstract: After more than 20 years of development, iterative learning model predictive control (ILMPC) has made great progress in the aspects of theory and application. Since batch processes are featured by strong complexity, diversity, structural variety and high degree of refinement, the existing theories are still faced with great challenges. This paper reviews the generation and development of ILMPC, and expounds the basic theory of two-dimensional predictive model, iterative optimization of control law and two-dimensional stability; The limitations of existing methods are analysed from the perspectives of theory and application, and the issues on iterative modelling, efficient optimization and variable operation conditions are discussed in detail with available solutions provided. The new trends in the theory and application of ILMPC are comprehensively reviewed. The studies on complex nonlinear system, fast system and off-design system are clarified to make great significance for further perfecting ILMPC theory and broadening its application. The important future research directions consisting of end product quality control and dynamic economic control are outlined.
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电网频率是电力系统运行中最重要的关键参数之一, 系统频率的异常波动不仅影响电网的电能质量, 制约电力设备的正常使用, 严重的频率失衡甚至将导致并网设备脱网及系统崩溃, 对电力系统的稳定运行带来严重危害[1-2]. 因此, 系统频率的稳定控制是电力系统稳定不可或缺的重要组成. 电力系统频率的异常波动是由并网机组发电功率和用电负荷功率不平衡引起的, 因而, 电力系统能够根据系统频率的变化主动快速进行发用电控制以维持频率稳定就显得尤为重要[3]. 电力系统的一次调频就是当系统频率发生异常波动时, 自动迅速地作出响应, 改变并网机组的实时出力, 将系统频率稳定在一个合理安全的水平线上. 这对提高电能质量及电网频率控制水平, 迅速平息电网频率波动起到了重要作用[4-5].
电力系统是一个非线性时变强耦合的复杂系统, 其一次调频特性与每台并网运行的发电机调速器特性息息相关, 是每台并网运行机组调速器特性在当前电网工况下的综合特性[6]. 对于单台发电机组而言, 其一次调频特性与调速器自身的特性显著相关[7]. 而当机组并入电力系统时, 电力系统的一次调频特性不仅与机组自身的调速器特性有关, 也和所有并列运行的其他发电机组特性相关, 甚至还与机组所处的实时工况和机组间的相互作用有关[8]. 另一方面, 电网中各机组的发电类型、容量、设备结构(例如, 凝汽式机组的负荷响应速度明显高于背压式机组), 以及机组运行工况(例如, 滑压或定压、不同季节乃至一天内不同时间段的负荷率高低)等各类因素共同作用影响着电网的一次调频性能[9]. 所以, 在不同的电网运行工况下, 非常有必要对电网的一次调频性能进行在线估计, 使电网面对不断变化的负荷调节需求均能够具备足够的一次调频性能.
目前, 国内外对一次调频能力的研究偏向单台机组侧较多, 对电网一次调频性能的研究和计算比较分散, 整体性考虑电网一次调性能各个因素的综合性研究较少, 也未见实际的工程化应用. 此外, 由于很难、甚至无法对电网一次调频特性进行精确建模, 以至于无法有效估计电网真实的一次调频性能.
本文基于平行控制理论框架下由人工社会 (Artificial societies, A)、计算实验(Computational experiments, C)和平行执行 (Parallel execution, P) 构成的ACP理论体系, 构建了多源数据的电网一次调频性能平行计算平台. 本文提出的计算方法能够有效兼顾机组类型的静态特性和运行工况的动态特性, 并以平行执行方式完成人工估算系统与实际电力系统的滚动优化, 实现了电网一次调频性能的在线全面估计, 从而有效弥补其无法进行精确建模的不足, 有助于提高电网主动应对负荷突变的能力, 也是对电网一次调频性能管控的一种全新的可行性方式.
1. 平台整体框架设计
所谓平行系统, 是指由某一个自然的现实系统和对应的一个或多个虚拟或理想的人工系统所组成的共同系统[10]. 平行系统主要包括实际系统和人工系统, 其基本框架如图1所示[10].
设计平行系统的最主要目的是通过人工系统与实际系统的相互连接, 对二者之间的行为进行比对和分析, 完成对各自未来状况的“借鉴”和“预估”, 相应地调节各自的管理与控制方式, 达到实施有效解决方案以及学习和培训的目的[10-11].
人工系统试图尽可能地模拟实际系统, 对其行为进行预估, 从而为寻找对实际系统有效的解决方案或对当前方案进行改进提供依据[12]. 进一步, 通过观察实际系统与人工系统评估的状态之间的不同, 生成误差反馈信号, 对人工系统的评估方式或参数进行修正, 并重复进行新一轮的优化和评估[12].
目前, 平行系统理论已经在自动化码头[13]、智能交通[14]等领域中开展了应用研究, 但尚未用于现代电力系统. 现代电力系统是一个巨大的参数海量、广域分布、模型复杂的非线性复杂系统. 现阶段, 绝大多数电力仿真系统是基于物理模型进行的, 并没有深入地考虑人的行为、自然因素以及社会环境的影响, 这些因素限制了对复杂现代电力系统运行影响的评估, 尤其是无法定性、定量地对电力系统应对突发事件的能力问题进行分析评估[15].
为了克服采用传统仿真方法导致的上述局限, 本文将平行系统理论应用到电力系统的实际工程中, 改变传统的被动、离线的电力系统仿真方法, 建立人工电力平行计算平台, 进而实现管理与控制、实验与评估、学习与优化及故障诊断等功能. 以现代电网的海量数据为驱动, 电力平行计算平台为载体, 该平台可对正在运行的电力系统进行滚动式在线改进与不间断优化, 实现电网一次调频性能估算达到最优解, 为电力系统和复杂电网的能力优化与管理开辟一条新的途径[16].
基于上述平行系统理念, 本文设计了电网调频能力计算平台, 其整体框架如图2所示, 主要包括实际系统和人工平行系统两部分. 实际电力系统的频率控制本质上是一个以电力调控中心为中枢, 实现电源与负荷的电力供需平衡的闭环控制系统. 电力调控中心不仅需要满足区域内机组发电及负荷消纳的控制要求, 也肩负着电力系统实际运行产生的海量数据信息采集的重担. 人工平行系统中, 基于D5000电网调度系统的一次调频在线测试系统不仅能够在正常运行工况下测试控制区内的机组调频性能, 保证机组一次调频性能的测试结果更具真实性, 同时将历次测试数据存储、分析及评价, 实现机组一次调频的静态参数、动态性能的数据积累和量化管理. 将电力调控中心的海量数据和一次调频测试系统的特性数据应用于电网一次调频能力在线估计模型中, 通过实际电力系统和人工平行系统的彼此作用、相互修正, 既可以实现对实际电力系统的管理与控制,也能够完成对电网能力、行为与决策的评估与实验.
图 2 基于平行系统的计算平台整体框架Fig. 2 Overall framework of computing platform based on parallel systems2. 发电机组一次调频数据采集体系
当前, 电力系统已经发展成一个具有多源信息融合的综合性电力控制系统. 根据现有的SCADA(Supervisory control and data acquisition)、WAMS(Wide area measurement system)、OMS (Operations management system)等系统, 建立机组一次调频数据采集体系, 如图3所示. SCADA的一次调频在线测试系统能够在一次调频在线测试期间自动记录测试机组的有功PMU (Phasor measurement unit)数据, 整编录入历史库存储[17]. WAMS的机组性能考核系统能够不间断采集机组实际运行的一次调频动作、响应等广域量测数据, 实现机组转速不等率、积分电量、响应时间等一次调频性能指标的在线计算[18]. 基于OMS的网源协调信息管理系统, 通过设置统一的一次调频试验台账, 维护和存储机组的历次原始试验数据和参数, 统一存储于数据库中.
图 3 发电机组一次调频数据采集体系Fig. 3 Primary frequency control data acquisition system of generator sets2.1 机组一次调频在线测试系统
如图4所示, 在D5000系统中部署试验触发、结果展示、参数维护及统计分析功能. 试验触发功能可实现选定机组进行试验, 试验开始时将测试机组投入一次调频扰动测试模式, 调控中心向电厂侧下发调频测试开始信号和频率偏差信号, 机组根据接收的信号进行一次调频动作响应, 具体控制信息流程见图5所示.
图 4 机组一次调频在线测试与评价功能结构图Fig. 4 Functional structure diagram of unit primary frequency control online test and evaluation在一次调频在线测试期间, 系统自动记录测试机组的有功PMU数据, 整编录入D5000历史库, 永久保存, 供后期调频指标分析与数据展示使用[17]. 在结果展示功能中, 将频率扰动信号及电厂侧PMU装置上传的有功出力信号进行展示, 并根据有功出力曲线自动计算一次调频动作性能指标. 在浙江某厂#2机组进行一次调频在线测试系统联调试验时, 调控中心主站侧的操作及结果展示如图6所示, 发电厂机组一次调频动作响应曲线如图7所示.
图 6 机组一次调频在线测试主站侧界面图Fig. 6 Interface diagram of main station side of unit primary frequency control online test
图 7 浙江某厂#2机组一次调频在线测试动作曲线(75%负荷点 + 11 r/min转速偏差)Fig. 7 Action curves of primary frequency control online test of unit 2 of a power plant in Zhejiang (+11 r/min speed deviation at 75% load point)通过PMU实时采集高频度的功率、相位、相角等机组数据, 并利用PMU的GPS对时优势, 计算机组在一次调频在线测试中不同时刻、不同工况下的性能指标, 反向推算出机组实际的调频特性参数, 以此形成海量的机组一次调频特征数据, 实现机组一次调频静态参数、动态性能等特征数据的分析及管理[19].
2.2 网源协调信息管理系统
基于OMS的网源协调信息管理系统(如图8所示)能够实现设备台账、电气参数、涉网试验报告等技术资料的及时更新及有效管理, 打通厂网之间的涉网信息共享交互渠道, 更加科学、系统、高效地开展网源协调管理工作. 以各机组台账信息为基础, 实现对网内各并网机组数据信息的实时统计汇总; 以并网机组各类信息关键字为基础, 实现对特定类型、特定机组相关信息的快速查询和准确统计, 该系统所部署的功能模块如图9所示. 同时, 建立网源协调数据中心, 这是网源协调信息管理平台的核心内容, 可实现参数模型库、文档资料库、督办信息库及信息变更库的数据获取与整合、数据质量校核、合格率督办和数据查询等服务.
图 8 基于OMS的网源协调信息管理系统主界面Fig. 8 Main interface of grid power coordination information management system based on OMS
图 9 网源协调信息管理系统的功能模块Fig. 9 Functional modules of grid power coordination information management system在网源协调信息管理系统中, 通过设置统一的一次调频试验台账模板, 采集机组的历次试验数据, 以维护和存储机组的原始试验数据. 图10为浙江某百万千瓦机组A修后一次调频试验的数据台账.
图 10 浙江某厂#1机组A修后一次调频试验台账Fig. 10 Ledger of primary frequency control test after class a maintenance of unit 1 of a power plant in Zhejiang根据设置统一的数据台账, 可以追溯机组每一次试验工况, 分析不同工况下机组一次调频试验时的真实性能.
2.3 发电机组一次调频性能考核系统
发电机组一次调频性能考核系统是基于WAMS部署于D5000上的一次调频数据量化及评价系统[18]. 该系统通过PMU将现场采集的机组出力数据送至电网调控中心EMS (Energy management system)系统中, 并由EMS采集电网中的频率值及时间, 打包形成一个数据包存储于该系统, 以便进行量化处理.
机组一次调频贡献电量是机组一次调频多项指标的综合, 它反映机组对电网频率的实际贡献大小. 这一参数的引入使量化机组一次调频功能的动作力度和快速性成为可能.
在系统设计中, 机组对象被抽象封装成一个类, 每个机组都是该类的实例化. 类中数据为机组的实时信息, 包括机组基本参数(代号、装机容量、积分间隔、频率超前时间等)和积分电量以及其他计算辅助变量; 类中对数据的操作包含积分电量的计算和对数据库的读写操作等. 其中最为核心的函数为贡献电量积分函数, 用来计算和累积贡献电量, 以反映机组在实际运行时的一次调频动作性能.
一次调频性能考核系统通过采集各机组一次调频投退信号、有功功率和频率信息等广域量测信息, 实现机组转速不等率、积分电量、响应时间等一次调频性能指标的在线计算, 使系统能够考核机组是否贡献了满足要求的一次调频服务.
该系统依托于调度D5000系统, 能够不间断实时获取所有并网机组的一次调频动作性能. 据系统统计, 每个月一台机组的一次调频动作次数可达到近5000次(如表1所示), 大量原始数据的累积奠定了电网一次调频性能计算的数据基础.
表 1 机组一次调频月动作统计Table 1 Monthly action statistics of unit primary frequency control月份 强蛟厂 #3 机组 镇燃厂 #11 机组 动作总次数 正确动作数 动作总次数 正确动作数 8 2 491 2 389 408 381 9 4 085 3 948 1 464 1 369 10 4 965 4 760 2 956 2 822 3. 电网一次调频能力数据建模
目前, 国内外各类指标都是针对机组调频能力, 比如控制性能标准(Control performance standard, CPS)、投运率、贡献电量、调频效果等[20]. 现有的评价指标本质为事后评价, 不能预测电网总的调频裕度. 本文构建的数据平行驱动体系(如图11所示), 依靠电网运行的大数据, 通过不断演算、迭代优化, 形成调频能力的概率区间来衡量电网调频性能, 解决了电网一次调频能力的在线估计问题, 从而使电网的运行状态具有更高的可控性及透明度, 提高大电网应对负荷突变的能力.
图 11 电网一次调频能力估算技术路线图Fig. 11 Technical roadmap of grid primary frequency control capacity estimation3.1 同步电网一次调频能力建模
定义 1. PFCA (Primary frequency control ability)表示仅在一次调频作用情况下(即没有二次调频作用时), 某时间段内负荷变化与电网频率变化的比值[8], 可表示为
$$ {R_{{\rm{PFCA}}}} = \frac{{\left| {\text{电网负荷的变化}} \right|}}{{\left| {\text{电网频率的变化}} \right|}} $$ (1) 同步发电机并列运行的电网调频能力模型如图12所示. 在图12中,
${R_i}$ 为二次调频的给定值;${\delta _i}$ 为电网中第i台机组的不等率;${\alpha _i}$ 为电网中第i台机组装机容量/电力系统装机容量;${G_i}(s)$ 为第i台汽轮机的传递函数;${P_{NL}}(s)$ 为负载的标幺值;${\varphi _s}(s)$ 为电网转速变化的标幺值.${T_{\alpha \Sigma }} = \sum\nolimits_{i = 1}^M {{\alpha _i}} {T_{\alpha i}}$ 为电网的惯性时间常数;${T_{\alpha i}}$ 为第i台汽轮机的转子时间常数;$\beta _{\Sigma }$ 为电网负载频率特性系数.
图 12 M台同步发电机并列运行的电网调频能力模型图Fig. 12 Model diagram of power grid frequency regulation capacity of M synchronous generators operating in parallel$${\varphi _s}(s) = - \frac{1}{{{T_{\alpha \Sigma }}s + {\beta _{\Sigma} } + G(s)}}{P_{NL}}(s)$$ (2) 其中,
$$G(s) = \sum\limits_{i = 1}^M {\frac{{{\alpha _i}}}{{{\delta _i}}}} {G_i}(s)$$ (3) 各变量前加
$\Delta $ 作为静态标记, 静态下电网周波变化可表示为$$\Delta \varphi = - \mathop {\lim }\limits_{s \to 0} s\dfrac{1}{{{T_{\alpha \Sigma }}s + {\beta _{\Sigma} } + G(s)}}\Delta {P_{NL}}\dfrac{1}{s}$$ (4) 由于汽轮机传递函数可以表示为
$${G_i}(s) = \frac{{\prod\limits_{i = 1}^m {({T_i}s + 1)} }}{{\prod\limits_{i = 1}^n {({T_i}s + 1)} }}$$ (5) 故
$$\Delta \varphi = -\frac{ \Delta {P_{NL}}}{\sum\limits_{i = 1}^M {\frac{{{\alpha _i}}}{{{\delta _i}}}} + {\beta _{\Sigma} }}$$ (6) 由此得到, 在静态情况下电网的一次调频能力可表示为
$${R_{{\rm{PFCA}}}}(static) = {R_G} + {R_L}\qquad\qquad\qquad\;\;$$ (7) $${R_{{\rm{PFCA}}}}(static) = \frac{{\left| {\Delta {P_{NL}}} \right|}}{{\left| {\Delta \varphi } \right|}} = \sum\limits_{i = 1}^M {\frac{{{\alpha _i}}}{{{\delta _i}}}} + {\beta _{\sum} }$$ (8) ${R_G} = \sum\nolimits_{i = 1}^M ({{{{\alpha _i}}}/{{{\delta _i}}}})$ 定义为电网的等值调差率, 等效为所有挂网同步发电机组一次调频出力总和的最大值.${R_L} = {\beta _{\sum} }$ 为电网负载频率特性系数, 等效为电网负荷对频率变化的贡献能力.对于某台额定功率
${P_{ei}}$ , 不等率${\delta _i}$ 的机组而言, 其在$\Delta f$ 频率扰动下的一次调频能力的实际贡献为$${k_i} = \frac{{\Delta P_{{\rm{real}}}^ * }}{{\Delta {f^ * }}} = \frac{{{\eta _i}}}{{{\delta _i}}}\qquad\qquad\qquad\qquad\qquad\;\;$$ (9) $${\eta _i} = \frac{{\Delta {P_{{\rm{real}}}}}}{{\Delta {P_{{\rm{ expect}}}}}} =\frac{ \Delta {P_{{\rm{real}}}}}{\frac{{\Delta f \times {P_{ei}}}}{{{f_e} \times {\delta _i}}}} = \frac{{\Delta P_{{\rm{real}}}^ * }}{{\Delta {f^ * }}} \times {\delta _i}$$ (10) 显然, 在
$\Delta f$ 频率扰动下的同步电网中所有挂网运行机组的一次调频实际出力总和为$$ {R_{{\rm{PFCA}}}}(real) = \sum\limits_{i = 1}^M {{\alpha _i}\frac{{{\eta _i}}}{{{\delta _i}}}} = \sum\limits_{i = 1}^M {{\alpha _i}{k_i}} \le {R_G} = \sum\limits_{i = 1}^M {\dfrac{{{\alpha _i}}}{{{\delta _i}}}} $$ (11) 3.2 机组一次调频能力数据模型
从式(11)中可以发现电网一次调频能力主要取决于各挂网运行机组的转速不等率.
机组在不同功频下的转速不等率不尽相同, 将每台机组的转速不等率设定为常数势必难以准确描述机组的一次调频能力. 调度D5000系统具有各类丰富的一次调频数据(如图13所示), 其中, 机组性能考核系统实时采集的机组一次调频动作数据量最大, 每月达几千次. 而网源协调信息管理系统中存储的一次调频参数及试验数据, 则表征机组一次调频性能的理论出力和实际能力上下限值. 一次调频在线测试系统可以探测机组在不同工况下的大频差真实能力, 完善整个机组的一次调频数据集. 本文将采用极大似然估计及数值拟合等算法对调度D5000系统中的多源一次调频数据进行有效整合, 以获取机组真实的一次调频性能功频特性图谱.
图 13 发电机组一次调频动作历史数据库Fig. 13 Historical database of primary frequency control actions of generator sets可以从D5000系统中获取不同时刻机组一次调频能力的数据, 从而构造出机组转速不等率的样本空间. 我们用随机变量
${\delta _i}$ 表示单台机组在第i个时间段内的转速不等率. 利用D5000系统中不同时间的转速不等率数据, 可以构造用于描述转速不等率的随机变量${\delta _1},\cdots,{\delta _n}$ . 由于机组的短期特性通常不会发生变化, 可以认为${\delta _1},\cdots,{\delta _n}$ 独立同分布. 按照中心极限定理, 随机变量${\delta _1},\cdots,{\delta _n}$ 独立同分布, 当n很大时,$({{\sum\nolimits_{i = 1}^n {{\delta _i}} - n\mu }})/({{\sqrt n \sigma }})$ 近似服从标准正态分布${\rm{N}}({\rm{0,1}})$ . 设$X = \sum\nolimits_{i = 1}^n {{\delta _i}}$ , 则X服从正态分布${\rm{N}}(n\mu ,n{\sigma ^2})$ .本文通过极大似然估计来估计
$\mu $ 和${\sigma ^2}$ , 似然函数可以表示为$$ \begin{split} L(n\mu ,n{\sigma ^2}) =\;& \prod\limits_{i = 1}^N {\frac{1}{{\sqrt {2{\text{π}} } \sigma }}{{\rm{e}}^{ - \frac{{{{({X_i} - \mu )}^2}}}{{2{\sigma ^2}}}}}}= \\ & {(2{\text{π}} {\sigma ^2})^{ - \frac{N}{2}}}{{\rm{e}}^{ - \frac{1}{{2{\sigma ^2}}}\sum\limits_{i = 1}^N {{{({X_i} - \mu )}^2}} }} \end{split} $$ (12) 那么, 似然函数的对数为
$$ \begin{split} &\lg L(n\mu ,n{\sigma ^2}) = - \frac{N}{2}\lg (2{\text{π}} {\sigma ^2}) - \frac{1}{{2{\sigma ^2}}}\sum\limits_{i = 1}^N {{{({X_i} - \mu )}^2}} = \\ &\qquad - \frac{N}{2}\lg (2{\text{π}} ) - \frac{N}{2}\lg ({\sigma ^2}) - \frac{1}{{2{\sigma ^2}}}\sum\limits_{i = 1}^N {{{({X_i} - \mu )}^2}} \end{split} $$ (13) 则似然方程组为
$$\left\{ {\begin{aligned} & {\frac{{\partial \lg L(n\mu ,n{\sigma ^2})}}{{\partial \mu }} = \frac{1}{{{\sigma ^2}}}\sum\limits_{i = 1}^N {({X_i} - \mu ) = 0} } \qquad\;\;\,(14{\rm{a}})\\ & {\frac{{\partial \lg L(n\mu ,n{\sigma ^2})}}{{\partial {\sigma ^2}}} = - \frac{N}{{2{\sigma ^2}}} + \frac{1}{{2{\sigma ^4}}}\sum\limits_{i = 1}^N {{{({X_i} - \mu )}^2} = 0} } \end{aligned}} \right.\tag{14b}$$ 求解(14a), 得
$$n\hat \mu = \overline X = \frac{1}{N}\sum\limits_{i = 1}^N {{X_i}} $$ (15) 代入(14b), 得
$$n{\hat \sigma ^2} = \frac{1}{N}\sum\limits_{i = 1}^N {({X_i} - \overline X } {)^2}$$ (16) 那么,
$\mu $ 和${\sigma ^2}$ 的最大似然估计为$$ \hat \mu = \frac{{\rm{1}}}{n}\overline X , \;{\hat \sigma ^2} = \frac{{\rm{1}}}{n}\frac{1}{N}\sum\limits_{i = 1}^N {({X_i} - \overline X } {)^2} $$ (17) 本文用大写字母表示所有涉及的样本, 因为最大似然估计
$\hat \mu $ 和${\hat \sigma ^2}$ 均为统计量, 脱离具体的试验或观测, 它们都是随机的. 依据3套系统得到3个维度的真实观测数据, 采用上述的估计算法, 即可得到机组功频坐标下的一次调频性能估计值, 记为$K$ , 显然$K = \hat \mu $ , 从而得到功频坐标下的机组一次调频性能网格如表2所示, 对浙江某660万千瓦级超临界机组进行原始数据采集和数值迭代模拟, 可得到该机组的一次调频性能三维分布, 如图14所示, 其中, 横轴$f$ 和$P$ 分别为电网频率和机组实际出力值, 纵轴$K$ 表示为机组一次调频性能值.表 2 发电机组一次调频性能网格表Table 2 Grid table of primary frequency control performance of generator sets频率
功率f1 f2 Λ fN−1 fN P1 K11 K12 K1Λ K1(N−1) K1N P2 K21 K22 K2Λ K2(N−1) K2N Λ KΛ1 KΛ2 KΛΛ KΛ(N−1) KΛN PN−1 K(N−1)1 K(N−1)1 K(N−1)Λ K(N−1)(N−1) K(N−1)N PN KN1 K(N−1)1 KNΛ KN(N−1) KNN 
图 14 发电机组一次调频性能功频图谱Fig. 14 Power frequency spectrum of primary frequency control performance of generator sets4. 电网一次调频性能数据分析及估计
4.1 浙江电网一次调频性能分析
2018年10月22日10 : 36时, 浙江省全社会口径用电负荷39753.02 MW, 受电17849.91 MW (占全省用电负荷的52.9%), 发电21903.11 MW (占全省用电负荷的47.1%). 其中, 浙江省调统调机组共并网45台(不含新能源), 其中纯凝汽燃煤机组39台, 背压供热燃煤机组2台, 燃气机组4台, 并网机组平均负荷率约为58.25%, 总发电负荷16221.59 MW, 占当时全省用电负荷的40.8%.
据此, 按照式(11)进行计算, 得到浙江2018年10月22日10 : 36时省调统调并网机组的实际调频能力为12.2327, 根据当时的用电负荷进行折算后约为6 762.23 MW/Hz, 略高于浙江电网ACE系统中自然频率特性系数5 979 MW/Hz[21]. 推此及彼, 采用本文的方法可以得到浙江统调机组每天任意时刻的实际调频能力值, 如图15所示.
图 15 2018年10月22日浙江统调机组实际调频能力时刻图Fig. 15 Time map of actual primary frequency control performance of Zhejiang dispatching unit on October 22, 2018显然, 由图15可以明显得知, 电网的实际调频性能与并网机组台数、并网机组类型、机组平均负荷率等因素息息相关, 是一项电网拓扑结构的综合表征.
4.2 大频差时浙江电网一次调频容量分析
电网频率是描述电力系统发电与用电平衡关系的一个重要变量. 电网中用电负荷的随机特性使电网频率也成为随机变量. 电力负荷的随机变化部分是相互独立、不相关的[22]. 由中心极限定理可知, 连续的独立随机变量叠加后是正态分布的, 因此, 电力系统中负荷的随机性分量也是正态分布的. 在通常情况下, 电网频率的概率分布也就可近似认为是正态分布[23], 因此, 假设发生直流闭锁时的浙江电网系统最低频率近似正态分布, 并结合近三年的历次直流闭锁数据分析, 可得表3数据.
表 3 大频差时浙江电网一次调频数据分析Table 3 Data analysis of primary frequency control data of Zhejiang power grid in large frequency difference situations指标 均值 标准差 95 % 置信区间 最低频率 (Hz) 49.877 0.1022 [49.841, 49.914] 实际出力 (标幺值) 11.9216 6.5165 [9.5856, 14.2575] 出力限值 (%Pe) 3.94 0.90 [3.61, 4.27] 装机容量 (MW) 36 633.71 5 509.92 [34 658.58, 8 608.85] 装机总数 (台数) 68 12 [63, 72] 根据表3, 可知电网频率的最大变化差值为
$$ \Delta f=50-49.841=0.159\;{\rm{Hz}} $$ 最大概率功率缺额为
$$ {P_{{\rm{Loss}}}} = {\beta _{{\rm{ACE}}}} \times \frac{{\Delta f}}{{{f_N}}}=5\;979 \times 0.159=950.66 \;{\rm{MW}} $$ 按浙江历次直流闭锁数据, 可知在不少于63台同步发电机组, 总装机不低于34 658.58 MW的条件下, 浙江统调机组一次调频能力为9.5856 (95%以上), 折算后为6 644.46 MW/Hz, 在最大概率频差0.159 Hz下, 浙江电网可提供一次调频最大能力至少约为1 056.47 MW (3.1% MCR (Maximum continuous rating)), 能够满足功率缺额950.66 MW的要求, 也就是说, 浙江统调机组一次调频能力可以保证电网在直流闭锁等大频差工况下系统频率不低于49.841 Hz.
5. 结束语
机组的转速不等率与电网频率往往呈非线性关系, 采用固定的转速不等率来计算机组的一次调频能力误差较大. 本文基于数据平行驱动体系, 依靠电网运行的大数据, 建立了更为准确的电网一次调频模型, 对提升电网频率控制水平具有非常重要的意义.
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图 8 传统分层控制结构与ILEMPC结构对比
Fig. 8 Comparison of hierarchical control structure and ILEMPC structure
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[1] Tomazi K G, Linninger A A, Daniel J R. Batch processing industries. Batch Processes. Boca Raton, FL: CRC Press, 2006. 7−39 [2] Myerson A S. Handbook of Industrial Crystallization. London, UK: Butterworths-Heinemann, 2001. [3] Tchobanoglous G, Burton F L, Stensel H D. Wastewater Engineering: Treatment and Reuse (4th edition). New York: McGraw-Hill, 2003. [4] Liu T, Gao F R. Industrial Process Identification and Control Design. London: Springer-Verlag, 2012. [5] McCormick K. Manufacturing in Global Pharmaceutical Industry. London: Urch, 2003. [6] Schmidt E, Winkelbauer J, Puchas G, Henrich D, Krenkel W. Robot-based fiber spray process for small batch production. Annals of Scientific Society for Assembly, Handling and Industrial Robotics. Berlin, Heidelberg: Springer Vieweg, 2020. 295−305 [7] Mazurek J, Ashford N A. Making Microchips: Policy, Globalization, and Economic Restructuring in the Semiconductor Industry. Cambridge, MA: MIT Press, 1998. [8] 卢静宜, 曹志兴, 高福荣. 批次过程控制: 回顾与展望. 自动化学报, 2017, 43(6): 933-943Lu Jing-Yi, Cao Zhi-Xing, Gao Fu-Rong. Batch process control--overview and outlook. Acta Automatica Sinica, 2017, 43(6): 933-943 [9] Yang Y, Gao F R. Injection velocity control using a self-tuning adaptive controller. International Polymer Processing, 1999, 14(2): 196-204 doi: 10.3139/217.1537 [10] Yang Y, Gao F R. Adaptive control of the filling velocity of thermoplastics injection molding. Control Engineering Practice, 2000, 8(11): 1285-1296 doi: 10.1016/S0967-0661(00)00060-5 [11] Nagy Z, Agachi S. Model predictive control of a PVC batch reactor. Computer & Chemical Engineering, 1997, 21(6): 571-591 [12] Nagy Z K, Braatz R D. Robust nonlinear model predictive control of batch processes. AIChE Journal, 2003, 49(7): 1776-1786 doi: 10.1002/aic.690490715 [13] Stenz R, Kuhn U. Automation of a batch distillation column using fuzzy and conventional control. IEEE Transactions on Control Systems Technology, 1995, 3(2): 171-176 doi: 10.1109/87.388125 [14] Frey C W, Kuntze H B. A neuro-fuzzy supervisory control system for industrial batch processes. IEEE Transactions on Fuzzy Systems, 2001, 9(4): 570-577 doi: 10.1109/91.940969 [15] Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robots by learning. Journal of Robotic Systems, 1984, 1(2): 123-140 doi: 10.1002/rob.4620010203 [16] Lee K S, Bang S H, Yi S, Son J S, Yoon S C. Iterative learning control of heat-up phase for a batch polymerization reactor. Journal of Process Control, 1996, 6(4): 255-262 doi: 10.1016/0959-1524(96)00048-0 [17] Lee J H, Lee K S. Iterative learning control applied to batch processes: An overview. Control Engineering Practice, 2007, 15(10): 1306-1318 doi: 10.1016/j.conengprac.2006.11.013 [18] Liu T, Gao F R. Robust two-dimensional iterative learning control for batch processes with state delay and time-varying uncertainties. Chemical Engineering Science, 2010, 65(23): 6134-6144 doi: 10.1016/j.ces.2010.08.031 [19] Gao F R, Yang Y, Shao C. Robust iterative learning control with applications to injection molding process. Chemical Engineering Science, 2001, 56(24): 7025-7034 doi: 10.1016/S0009-2509(01)00339-6 [20] Shi J, Gao F R, Wu T J. Robust iterative learning control design for batch processes with uncertain perturbations and initialization. AIChE Journal, 2006, 52(6): 2171-2187 doi: 10.1002/aic.10835 [21] Hao S L, Liu T, Paszke W, Galkowski K. Robust iterative learning control for batch processes with input delay subject to time-varying uncertainties. IET Control Theory & Applications, 2016, 10(15): 1904-1915 [22] Chi R H, Hou Z S, Xu J X. Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition. Automatica, 2008, 44(8): 2207-2213 doi: 10.1016/j.automatica.2007.12.004 [23] Tayebi A. Adaptive iterative learning control for robot manipulators. Automatica, 2004, 40(7): 1195-1203 doi: 10.1016/j.automatica.2004.01.026 [24] Li X D, Xiao T F, Zheng H X. Adaptive discrete-time iterative learning control for non-linear multiple input multiple output systems with iteration-varying initial error and reference trajectory. IET Control Theory & Applications, 2011, 5(9): 1131-1139 [25] Chi R H, Hou Z S, Jin S T. A data-driven adaptive ILC for a class of nonlinear discrete-time systems with random initial states and iteration-varying target trajectory. Journal of the Franklin Institute, 2015, 352(6): 2407-2424 doi: 10.1016/j.jfranklin.2015.03.014 [26] Márquez-Vera M A, Ramos-Velasco L E, Suárez-Cansino J, Márquez-Vera C A. Fuzzy iterative learning control applied in a biological reactor using a reduced number of measures. Applied Mathematics and Computation, 2014, 246: 608-618 doi: 10.1016/j.amc.2014.08.072 [27] Jia L, Shi J P, Chiu M S. Integrated neuro-fuzzy model and dynamic R-parameter based quadratic criterion-iterative learning control for batch process. Neurocomputing, 2012, 98: 24-33 doi: 10.1016/j.neucom.2011.05.046 [28] Wang Y C, Chien C J, Teng C C. Direct adaptive iterative learning control of nonlinear systems using an output-recurrent fuzzy neural network. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2004, 34(3): 1348-1359 doi: 10.1109/TSMCB.2004.824525 [29] Xiong Z H, Zhang J. A batch-to-batch iterative optimal control strategy based on recurrent neural network models. Journal of Process Control, 2005, 15(1): 11-21 doi: 10.1016/j.jprocont.2004.04.005 [30] Li D W, He S Y, Xi Y G, Liu T, Gao F R, Wang Y Q, et al. Synthesis of ILC-MPC controller with data-driven approach for constrained batch processes. IEEE Transactions on Industrial Electronics, 2020, 67(4): 3116-3125 doi: 10.1109/TIE.2019.2910034 [31] Chi R H, Hou Z S, Jin S T, Huang B. An improved data-driven point-to-point ILC using additional on-line control inputs with experimental verification. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 49(4): 687-696 doi: 10.1109/TSMC.2017.2693397 [32] Wang Y Q, Liu T, Zhao Z. Advanced PI control with simple learning set-point design: Application on batch processes and robust stability analysis. Chemical Engineering Science, 2012, 71: 153-165 doi: 10.1016/j.ces.2011.12.028 [33] Liu T, Wang X Z, Chen J H. Robust PID based indirect-type iterative learning control for batch processes with time-varying uncertainties. Journal of Process Control, 2014, 24(12): 95-106 doi: 10.1016/j.jprocont.2014.07.002 [34] Shen C, Shi Y, Buckham B. Trajectory tracking control of an autonomous underwater vehicle using Lyapunov-based model predictive control. IEEE Transactions on Industrial Electronics, 2018, 65(7): 5796-5805 doi: 10.1109/TIE.2017.2779442 [35] Yue M, An C, Li Z J. Constrained adaptive robust trajectory tracking for WIP vehicles using model predictive control and extended state observer. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 48(5): 733-742 doi: 10.1109/TSMC.2016.2621181 [36] Bone G M. A novel iterative learning control formulation of generalized predictive control. Automatica, 1995, 31(10): 1483-1487 doi: 10.1016/0005-1098(95)00051-W [37] Lee K S, Chin I S, Lee H J, Lee J H. Model predictive control technique combined with iterative learning for batch processes. AIChE Journal, 1999, 45(10): 2175-2187 doi: 10.1002/aic.690451016 [38] Lee K S, Lee J H. Convergence of constrained model-based predictive control for batch processes. IEEE Transactions on Automatic Control, 2000, 45(10): 1928-1932 doi: 10.1109/TAC.2000.881002 [39] Chin I, Qin S J, Lee K S, Cho M. A two-stage iterative learning control technique combined with real-time feedback for independent disturbance rejection. Automatica, 2004, 40(11): 1913-1922 doi: 10.1016/j.automatica.2004.05.011 [40] Xiong Z H, Zhang J, Wang X, Xu Y M. Tracking control for batch processes through integrating batch-to-batch iterative learning control and within-batch on-line control. Industrial & Engineering Chemistry Research, 2005, 44(11): 3983-3992 [41] Wang L M, Zhang R D, Gao F R. Iterative learning predictive control for batch processes. Iterative Learning Stabilization and Fault-Tolerant Control for Batch Processes. Singapore: Springer, 2020. 189−214 [42] Mo S Y, Wang L M, Yao Y, Gao F R. Two-time dimensional dynamic matrix control for batch processes with convergence analysis against the 2D interval uncertainty. Journal of Process Control, 2012, 22(5): 899-914 doi: 10.1016/j.jprocont.2012.03.002 [43] Shi J, Gao F R, Wu T J. Single-cycle and multi-cycle generalized 2D model predictive iterative learning control (2D-GPILC) schemes for batch processes. Journal of Process Control, 2007, 17(9): 715-727 doi: 10.1016/j.jprocont.2007.02.002 [44] Shi J, Zhou H, Cao Z K, Jiang Q Y. A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm. Journal of Process Control, 2014, 24(10): 1527-1537 doi: 10.1016/j.jprocont.2014.07.004 [45] Shi J, Yang B, Cao Z K, Zhou H, Yang Y. Two-dimensional generalized predictive control (2D-GPC) scheme for the batch processes with two-dimensional (2D) dynamics. Multidimensional Systems and Signal Processing, 2015, 26(4): 941-966 doi: 10.1007/s11045-015-0336-5 [46] Liu X J, Kong X B. Nonlinear fuzzy model predictive iterative learning control for drum-type boiler-turbine system. Journal of Process Control, 2013, 23(8): 1023-1040 doi: 10.1016/j.jprocont.2013.06.004 [47] Wang Y Q, Zhou D H, Gao F R. Iterative learning model predictive control for multi-phase batch processes. Journal of Process Control, 2008, 18(6): 543-557 doi: 10.1016/j.jprocont.2007.10.014 [48] Oh S K, Lee J M. Iterative learning model predictive control for constrained multivariable control of batch processes. Computers & Chemical Engineering, 2016, 93: 284-292 [49] Oh S K, Lee J M. Iterative learning control integrated with model predictive control for real-time disturbance rejection of batch processes. Journal of Chemical Engineering of Japan, 2017, 50(6): 415-421 doi: 10.1252/jcej.16we333 [50] Zhang R D, Gao F R. Two-dimensional iterative learning model predictive control for batch processes: A new state space model compensation approach. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(2): 833-841 doi: 10.1109/TSMC.2018.2883754 [51] Oh S K, Park B J, Lee J M. Point-to-point iterative learning model predictive control. Automatica, 2018, 89: 135-143 doi: 10.1016/j.automatica.2017.11.010 [52] Li D W, Xi Y G, Lu J Y, Gao F R. Synthesis of real-time-feedback-based 2D iterative learning control-model predictive control for constrained batch processes with unknown input nonlinearity. Industrial & Engineering Chemistry Research, 2016, 55(51): 13074-13084 [53] Zhang R D, Xue A K, Wang J Z, Wang S Q, Ren Z Y. Neural network based iterative learning predictive control design for mechatronic systems with isolated nonlinearity. Journal of Process Control, 2009, 19(1): 68-74 doi: 10.1016/j.jprocont.2008.01.008 [54] Lu J Y, Cao Z X, Gao F R. Multipoint iterative learning model predictive control. IEEE Transactions on Industrial Electronics, 2019, 66(8): 6230-6240 doi: 10.1109/TIE.2018.2873133 [55] Jia L, Han C, Chiu M S. Dynamic R-parameter based integrated model predictive iterative learning control for batch processes. Journal of Process Control, 2017, 49: 26-35 doi: 10.1016/j.jprocont.2016.11.003 [56] Ma L L, Liu X J, Kong X B, Lee K Y. Iterative learning model predictive control based on iterative data-driven modeling. IEEE Transactions on Neural Networks and Learning Systems, 2021, 32(8): 3377-3390 doi: 10.1109/TNNLS.2020.3016295 [57] Guo H Q, Liu C Z, Yong J W, Cheng X Q, Muhammad F. Model predictive iterative learning control for energy management of plug-In hybrid electric vehicle. IEEE Access, 2019, 7: 71323-71334 doi: 10.1109/ACCESS.2019.2919684 [58] Wu S, Jin Q B, Zhang R D, Zhang J F, Gao F R. Improved design of constrained model predictive tracking control for batch processes against unknown uncertainties. ISA Transactions, 2017, 69: 273-280 doi: 10.1016/j.isatra.2017.04.006 [59] Lu J Y, Cao Z X, Gao F R. Ellipsoid invariant set-based robust model predictive control for repetitive processes with constraints. IET Control Theory & Applications, 2016, 10(9): 1018-1026 [60] Park B J, Oh S K, Lee J M. Stochastic iterative learning model predictive control based on stochastic approximation. IFAC-PapersOnLine, 2019, 52(1): 604-609 doi: 10.1016/j.ifacol.2019.06.129 [61] Long Y S, Xie L H. Iterative learning stochastic MPC with adaptive constraint tightening for building HVAC systems. IFAC-PapersOnLine, 2020, 53(2): 11577-11582 doi: 10.1016/j.ifacol.2020.12.636 [62] Lu J Y, Cao Z X, Wang Z, Gao F R. A two-stage design of two-dimensional model predictive iterative learning control for nonrepetitive disturbance attenuation. Industrial & Engineering Chemistry Research, 2015, 54(21): 5683-5689 [63] Lee J H, Lee K S, Kim W C. Model-based iterative learning control with a quadratic criterion for time-varying linear systems. Automatica, 2000, 36(5): 641-657 doi: 10.1016/S0005-1098(99)00194-6 [64] Ahn H S, Chen Y Q, Moore K L. Iterative learning control: Brief survey and categorization. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 2007, 37(6): 1099-1121 doi: 10.1109/TSMCC.2007.905759 [65] Michalska H, Mayne D Q. Robust receding horizon control of constrained nonlinear systems. IEEE Transactions on Automatic Control, 1993, 38(11): 1623-1633 doi: 10.1109/9.262032 [66] 陆宁云, 王福利, 高福荣, 王姝. 间歇过程的统计建模与在线监测. 自动化学报, 2006, 32(3): 400-410Lu Ning-Yun, Wang Fu-Li, Gao Fu-Rong, Wang Shu. Statistical modeling and online monitoring for batch processes. Acta Automatica Sinica, 2006, 32(3): 400-410 [67] 赵春晖, 王福利, 姚远, 高福荣. 基于时段的间歇过程统计建模、在线监测及质量预报. 自动化学报, 2010, 36(3): 366-374 doi: 10.3724/SP.J.1004.2010.00366Zhao Chun-Hui, Wang Fu-Li, Yao Yuan, Gao Fu-Rong. Phase-based statistical modeling, online monitoring and quality prediction for batch processes. Acta Automatica Sinica, 2010, 36(3): 366-374 doi: 10.3724/SP.J.1004.2010.00366 [68] Zhu J L, Wang Y Q, Zhou D H, Gao F R. Batch process modeling and monitoring with local outlier factor. IEEE Transactions on Control Systems Technology, 2019, 27(4): 1552-1565 doi: 10.1109/TCST.2018.2815545 [69] 孙明轩, 黄宝健. 迭代学习控制. 北京: 国防工业出版社, 1999.Sun Ming-Xuan, Huang Bao-Jian. Iterative Learning Control. Beijing: National Defense Industry Press, 1999. [70] 池荣虎, 侯忠生, 黄彪. 间歇过程最优迭代学习控制的发展: 从基于模型到数据驱动. 自动化学报, 2017, 43(6): 917-932Chi Rong-Hu, Hou Zhong-Sheng, Huang Biao. Optimal iterative learning control of batch processes: From model-based to data-driven. Acta Automatica Sinica, 2017, 43(6): 917-932 [71] 席裕庚. 预测控制. 北京: 国防工业出版社, 1993.Xi Yu-Geng. Predictive Control. Beijing: National Defense Industry Press, 1993. [72] 陈虹. 模型预测控制. 北京: 科学出版社, 2013.Chen Hong. Model Predictive Control. Beijing: Science Press, 2013. [73] Yu Q X, Hou Z S, Bu X H, Yu Q F. RBFNN-based data-driven predictive iterative learning control for nonaffine nonlinear systems. IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(4): 1170-1182 doi: 10.1109/TNNLS.2019.2919441 [74] Anand E, Panneerselvam R. A study of crossover operators for genetic algorithm and proposal of a new crossover operator to solve open shop scheduling problem. American Journal of Industrial & Business Management, 2016, 6(6): 774-789 [75] Kordestani J K, Rezvanian A, Meybodi M R. An efficient oscillating inertia weight of particle swarm optimisation for tracking optima in dynamic environments. Journal of Experimental & Theoretical Artificial Intelligence, 2016, 28(1-2): 137-149 [76] Pang C Y, Hu W, Li X, Hu B Q. Apply local clustering method to improve the running speed of ant colony optimization. arXiv preprint arXiv: 0907.1012v2, 2009. [77] Chuang L Y, Hsiao C J, Yang C H. Chaotic particle swarm optimization for data clustering. Expert Systems with Applications, 2011, 38(12): 14555-14563 doi: 10.1016/j.eswa.2011.05.027 [78] Hu X Q, Beratan D N, Yang W T. A gradient-directed Monte Carlo approach to molecular design. The Journal of Chemical Physics, 2008, 129(6): Article No. 064102 [79] Gorski J, Pfeuffer F, Klamroth K. Biconvex sets and optimization with biconvex functions: A survey and extensions. Mathematical Methods of Operations Research, 2007, 66(3): 373-407 doi: 10.1007/s00186-007-0161-1 [80] Xu J X, Yan R. On initial conditions in iterative learning control. IEEE Transactions on Automatic Control, 2005, 50(9): 1349-1354 doi: 10.1109/TAC.2005.854613 [81] Park K H. An average operator-based PD-type iterative learning control for variable initial state error. IEEE Transactions on Automatic Control, 2005, 50(6): 865-869 doi: 10.1109/TAC.2005.849249 [82] Sun M X, Wang D W. Initial condition issues on iterative learning control for non-linear systems with time delay. International Journal of Systems Science, 2001, 32(11): 1365-1375 doi: 10.1080/00207720110052021 [83] Fang Y, Chow T W S. 2-D analysis for iterative learning controller for discrete-time systems with variable initial conditions. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2003, 50(5): 722-727 doi: 10.1109/TCSI.2003.811029 [84] Meng D Y, Jia Y M, Du J P, Yuan S Y. Robust discrete-time iterative learning control for nonlinear systems with varying initial state shifts. IEEE Transactions on Automatic Control, 2009, 54(11): 2626-2631 doi: 10.1109/TAC.2009.2031564 [85] Chi R H, Hou Z S, Jin S T. Data-weighting based discrete-time adaptive iterative learning control for nonsector nonlinear systems with iteration-varying trajectory and random initial condition. Journal of Dynamic Systems, Measurement, and Control, 2012, 134(2): Article No. 021016 [86] Oh S K, Lee J M. Stochastic iterative learning control for discrete linear time-invariant system with batch-varying reference trajectories. Journal of Process Control, 2015, 36: 64-78 doi: 10.1016/j.jprocont.2015.09.008 [87] Xiao T F, Li X D, Ho J K L. An adaptive discrete-time ILC strategy using fuzzy systems for iteration-varying reference trajectory tracking. International Journal of Control, Automation & Systems, 2015, 13(1): 222-230 [88] Li X F, Xu J X, Huang D Q. An iterative learning control approach for linear systems with randomly varying trial lengths. IEEE Transactions on Automatic Control, 2014, 59(7): 1954-1960 doi: 10.1109/TAC.2013.2294827 [89] Li X F, Xu J X, Huang D Q. Iterative learning control for nonlinear dynamic systems with randomly varying trial lengths. International Journal of Adaptive Control & Signal Processing, 2015, 29(11): 1341-1353 [90] Shi J T, He X, Zhou D H. Iterative learning control for nonlinear stochastic systems with variable pass length. Journal of the Franklin Institute, 2016, 353(15): 4016-4038 doi: 10.1016/j.jfranklin.2016.07.005 [91] Liu S D, Wang J R. Fractional order iterative learning control with randomly varying trial lengths. Journal of the Franklin Institute, 2017, 354(2): 967-992 doi: 10.1016/j.jfranklin.2016.11.004 [92] Shen D, Zhang W, Wang Y Q, Chien C J. On almost sure and mean square convergence of P-type ILC under randomly varying iteration lengths. Automatica, 2016, 63: 359-365 doi: 10.1016/j.automatica.2015.10.050 [93] Shen D, Zhang W, Xu J X. Iterative learning control for discrete nonlinear systems with randomly iteration varying lengths. Systems & Control Letters, 2016, 96: 81-87 [94] Wei Y S, Li X D. Robust higher-order ILC for non-linear discrete-time systems with varying trail lengths and random initial state shifts. IET Control Theory & Applications, 2017, 11(15): 2440-2447 [95] Meng D Y, Zhang J Y. Deterministic convergence for learning control systems over iteration-dependent tracking intervals. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(8): 3885-3892 doi: 10.1109/TNNLS.2017.2734843 [96] Zeng C, Shen D, Wang J R. Adaptive learning tracking for uncertain systems with partial structure information and varying trial lengths. Journal of the Franklin Institute, 2018, 355(15): 7027-7055 doi: 10.1016/j.jfranklin.2018.07.031 [97] Shen D, Xu J X. Adaptive learning control for nonlinear systems with randomly varying iteration lengths. IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(4): 1119-1132 doi: 10.1109/TNNLS.2018.2861216 [98] Yu Q X, Hou Z S. Adaptive fuzzy iterative learning control for high-speed trains with both randomly varying operation lengths and system constraints. IEEE Transactions on Fuzzy Systems, 2021, 29(8): 2408-2418 doi: 10.1109/TFUZZ.2020.2999958 [99] Jin X. Iterative learning control for MIMO nonlinear systems with iteration-varying trial lengths using modified composite energy function analysis. IEEE Transactions on Cybernetics, 2021, 51(12): 6080-6090 doi: 10.1109/TCYB.2020.2966625 [100] Yin C K, Xu J X, Hou Z S. A high-order internal model based iterative learning control scheme for nonlinear systems with time-iteration-varying parameters. IEEE Transactions on Automatic Control, 2010, 55(11): 2665-2670 doi: 10.1109/TAC.2010.2069372 [101] Yin C K, Xu J X, Hou Z S. An ILC scheme for a class of nonlinear continuous-time systems with time-iteration-varying parameters subject to second-order internal model. Asian Journal of Control, 2011, 13(1): 126-135 doi: 10.1002/asjc.320 [102] Yu M, Li C Y. Robust adaptive iterative learning control for discrete-time nonlinear systems with time-iteration-varying parameters. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, 47(7): 1737-1745 doi: 10.1109/TSMC.2017.2677959 [103] Yu M, Chai S. Adaptive iterative learning control for discrete-time nonlinear systems with multiple iteration-varying high-order internal models. International Journal of Robust and Nonlinear Control, 2021, 31(15): 7390-7408 doi: 10.1002/rnc.5690 [104] Meng D Y, Moore K L. Robust iterative learning control for nonrepetitive uncertain systems. IEEE Transactions on Automatic Control, 2017, 62(2): 907-913 doi: 10.1109/TAC.2016.2560961 [105] Meng D Y, Moore K L. Convergence of iterative learning control for SISO nonrepetitive systems subject to iteration-dependent uncertainties. Automatica, 2017, 79: 167-177 doi: 10.1016/j.automatica.2017.02.009 [106] Meng D Y. Convergence conditions for solving robust iterative learning control problems under nonrepetitive model uncertainties. IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(6): 1908-1919 doi: 10.1109/TNNLS.2018.2874977 [107] Altin B, Willems J, Oomen T, Barton K. Iterative learning control of iteration-varying systems via robust update laws with experimental implementation. Control Engineering Practice, 2017, 62: 36-45 doi: 10.1016/j.conengprac.2017.02.005 [108] Hao S L, Liu T, Rogers E. Extended state observer based indirect-type ILC for single-input single-output batch processes with time- and batch-varying uncertainties. Automatica, 2020, 112: Article No. 108673 doi: 10.1016/j.automatica.2019.108673 [109] Jin S T, Hou Z S, Chi R H. A novel data-driven terminal iterative learning control with iteration prediction algorithm for a class of discrete-time nonlinear systems. Journal of Applied Mathematics, 2014, 2014: Article No. 307809 [110] Yu Q X, Hou Z S. Data-driven predictive iterative learning control for a class of multiple-input and multiple-output nonlinear systems. Transactions of the Institute of Measurement and Control, 2016, 38(3): 266-281 doi: 10.1177/0142331215592692 [111] Bigras P, Lambert M, Perron C. Robust force controller for industrial robots: Optimal design and real-time implementation on a KUKA robot. IEEE Transactions on Control Systems Technology, 2012, 20(2): 473-479 doi: 10.1109/TCST.2011.2112661 [112] Hwang C L, Hung J Y. Stratified adaptive finite-time tracking control for nonlinear uncertain generalized vehicle systems and its application. IEEE Transactions on Control Systems Technology, 2019, 27(3): 1308-1316 doi: 10.1109/TCST.2018.2810851 [113] Sahu J N, Gangadharan P, Patwardhan A V, Meikap B C. Catalytic hydrolysis of urea with fly ash for generation of ammonia in a batch reactor for flue gas conditioning and NOx reduction. Industrial & Engineering Chemistry Research, 2009, 48(2): 727-734 [114] Zhou L M, Jia L, Wang Y L. Quadratic-criterion-based model predictive iterative learning control for batch processes using just-in-time-learning method. IEEE Access, 2019, 7: 113335-113344 doi: 10.1109/ACCESS.2019.2934474 [115] Liu X J, Ma L L, Kong X B, Lee K Y. An efficient iterative learning predictive functional control for nonlinear batch processes. IEEE Transactions on Cybernetics, DOI: 10.1109/TCYB.2020.3021978 [116] 马乐乐, 刘向杰. 非线性快速批次过程高效迭代学习预测函数控制. 自动化学报, 2022, 48(2): 515-530Ma Le-Le, Liu Xiang-Jie. A high efficiency iterative learning predictive functional control for nonlinear fast batch processes. Acta Automatica Sinica, 2022, 48(2): 515-530 [117] Rosolia U, Ames A D. Iterative model predictive control for piecewise systems. IEEE Control Systems Letters, 2022, 6: 842-847 doi: 10.1109/LCSYS.2021.3086561 [118] Liang C, Zou Y, Cai C X. Robust predictive iterative learning control for linear time-varying systems. Asian Journal of Control, 2022, 24(1): 333-343 doi: 10.1002/asjc.2477 [119] Qiu W W, Xiong Z H, Zhang J, Hong Y D, Li W Z. Integrated predictive iterative learning control based on updating reference trajectory for point-to-point tracking. Journal of Process Control, 2020, 85: 41-51 doi: 10.1016/j.jprocont.2019.11.003 [120] Liu X J, Ma L L, Kong X B, Lee K Y. Robust model predictive iterative learning control for iteration-varying-reference batch processes. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(7): 4238-4250 doi: 10.1109/TSMC.2019.2931314 [121] 马乐乐, 刘向杰. 变参考轨迹下的鲁棒迭代学习模型预测控制. 自动化学报, 2019, 45(10): 1933-1945Ma Le-Le, Liu Xiang-Jie. Robust model predictive iterative learning control with iteration-varying reference trajectory. Acta Automatica Sinica, 2019, 45(10): 1933-1945 [122] Lin N, Chi R H, Huang B. Auxiliary predictive compensation-based ILC for variable pass lengths. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(7): 4048-4056 doi: 10.1109/TSMC.2019.2930670 [123] Yang B, Xu Z H, Yang Y, Gao F R. Application of two-dimensional predictive functional control in injection molding. Industrial & Engineering Chemistry Research, 2015, 54(41): 10088-10102 [124] 李茜, 夏伯锴. 注塑机注射速度的模型预测迭代学习控制. 控制工程, 2009, 16(4): 429-431 doi: 10.3969/j.issn.1671-7848.2009.04.014Li Qian, Xia Bo-Kai. Model prediction iterative learning control of ram velocity for injection molding machines. Control Engineering of China, 2009, 16(4): 429-431 doi: 10.3969/j.issn.1671-7848.2009.04.014 [125] Balaji S, Fuxman A, Lakshminarayanan S, Forbes J F, Hayes R E. Repetitive model predictive control of a reverse flow reactor. Chemical Engineering Science, 2007, 62(8): 2154-2167 doi: 10.1016/j.ces.2006.12.082 [126] Marquez-Ruiz A, Loonen M, Saltik M B, Özkan L. Model learning predictive control for batch processes: A reactive batch distillation column case study. Industrial & Engineering Chemistry Research, 2019, 58(30): 13737-13749 [127] Bo C M, Yang L, Huang Q Q, Li J, Gao F R. 2D multi-model general predictive iterative learning control for semi-batch reactor with multiple reactions. Journal of Central South University, 2017, 24(11): 2613-2623 doi: 10.1007/s11771-017-3675-6 [128] Lautenschlager B, Lichtenberg G. Data-driven iterative learning for model predictive control of heating systems. IFAC-PapersOnLine, 2016, 49(13): 175-180 doi: 10.1016/j.ifacol.2016.07.947 [129] Wang Y Q, Dassau E, Doyle F J. Closed-loop control of artificial pancreatic β-cell in type 1 diabetes mellitus using model predictive iterative learning control. IEEE Transactions on Biomedical Engineering, 2010, 57(2): 211-219 doi: 10.1109/TBME.2009.2024409 [130] Wang Y Q, Zisser H, Dassau E, Jovanovič L, Doyle F J III. Model predictive control with learning-type set-point: Application to artificial pancreatic β-cell. AIChE Journal, 2010, 56(6): 1510-1518 doi: 10.1002/aic.12081 [131] 杨跃男, 王友清. 内模强化学习型模型预测控制及其在人工胰脏上的应用. 控制理论与应用, 2012, 29(8): 1057-1062Yang Yue-Nan, Wang You-Qing. Internal model control-enhanced learning-type model predictive control: Application to artificial pancreas. Control Theory & Applications, 2012, 29(8): 1057-1062 [132] Xie S W, Ren J. High-speed AFM imaging via iterative learning-based model predictive control. Mechatronics, 2019, 57: 86-94 doi: 10.1016/j.mechatronics.2018.11.008 [133] Chin I S, Lee K S, Lee J H. A technique for integrated quality control, profile control, and constraint handling for batch processes. Industrial & Engineering Chemistry Research, 2000, 39(3): 693-705 [134] Lee K S, Lee J H. A generic framework for integrated quality and profile control for industrial batch processes. IFAC Proceedings Volumes, 2001, 34(25): 53-63 doi: 10.1016/S1474-6670(17)33801-6 [135] Lee K S, Lee J H. Iterative learning control-based batch process control technique for integrated control of end product properties and transient profiles of process variables. Journal of Process Control, 2003, 13(7): 607-621 doi: 10.1016/S0959-1524(02)00096-3 [136] Dong C C, Chin I, Lee K S, Rho H, Rhee H, Lee J H. Integrated quality and tracking control of a batch PMMA reactor using a QBMPC technique. Computers & Chemical Engineering, 2000, 24(2-7): 953-958 [137] 柴天佑, 复杂工业过程运行优化与反馈控制. 自动化学报, 2013, 39(11): 1744-1757 doi: 10.3724/SP.J.1004.2013.01744Chai Tian-You. Operational optimization and feedback control for complex industrial processes. Acta Automatica Sinica, 2013, 39(11): 1744-1757 doi: 10.3724/SP.J.1004.2013.01744 [138] Chai T Y, Qin S J, Wang H. Optimal operational control for complex industrial processes. Annual Reviews in Control, 2014, 38(1): 81-92 doi: 10.1016/j.arcontrol.2014.03.005 [139] Scattolini R. Architectures for distributed and hierarchical Model Predictive Control--a review. Journal of Process Control, 2009, 19(5): 723-731 doi: 10.1016/j.jprocont.2009.02.003 [140] 邹涛, 潘昊, 丁宝苍, 于海斌. 双层结构预测控制研究进展. 控制理论与应用, 2014, 31(10): 1327-1337 doi: 10.7641/CTA.2014.31295Zou Tao, Pan Hao, Ding Bao-Cang, Yu Hai-Bin. Research development of two-layered predictive control. Control Theory & Applications, 2014, 31(10): 1327-1337 doi: 10.7641/CTA.2014.31295 [141] Rawlings J B, Amrit R. Optimizing process economic performance using model predictive control. Nonlinear Model Predictive Control. Berlin Heidelberg: Springer, 2009. 119−138 [142] Diehl M, Amrit R, Rawlings J B. A Lyapunov function for economic optimizing model predictive control. IEEE Transactions on Automatic Control, 2011, 56(3): 703-707 doi: 10.1109/TAC.2010.2101291 [143] Ellis M, Durand H, Christofides P D. A tutorial review of economic model predictive control methods. Journal of Process Control, 2014, 24(8): 1156-1178 doi: 10.1016/j.jprocont.2014.03.010 [144] Cai X, Sun P, Chen J H, Xie L. ILC strategy for progress improvement of economic performance in industrial model predictive control systems. Journal of Process Control, 2014, 24(12): 107-118 doi: 10.1016/j.jprocont.2014.09.010 [145] Lu P C, Chen J H, Xie L. Iterative learning control (ILC)-based economic optimization for batch processes using helpful disturbance information. Industrial & Engineering Chemistry Research, 2018, 57(10): 3717-3731 [146] Lu P C, Chen J H, Xie L. Disturbance-based alternate feedback control scheme to enhance economic performance of batch processes. Industrial & Engineering Chemistry Research, 2019, 58(10): 4143-4153 [147] Long Y S, Xie L H, Liu S. Nontracking type iterative learning control based on economic model predictive control. International Journal of Robust and Nonlinear Control, 2020, 30(18): 8564-8582 doi: 10.1002/rnc.5261 [148] Morrison J, Nagamune R, Grebenyuk V. An iterative learning approach to economic model predictive control for an integrated solar thermal system. IFAC-PapersOnLine, 2020, 53(2): 12777-12782 doi: 10.1016/j.ifacol.2020.12.1930 [149] Heidarinejad M, Liu J F, Christofides P D. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal, 2012, 58(3): 855-870 doi: 10.1002/aic.12672 -
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