引用本文:方 勇,王 泉,杜军朝,闫昱晓,袁志毅.复印机碳粉供应系统鲁棒模型预测控制[J].控制理论与应用,2026,43(2):436~442.[点击复制]
FANG Yong,WANG Quan,DU Jun-zhao,YAN Yu-xiao,YUAN Zhi-yi.Robust model predictive control of copier toner supply system[J].Control Theory & Applications,2026,43(2):436~442.[点击复制]
复印机碳粉供应系统鲁棒模型预测控制
Robust model predictive control of copier toner supply system
摘要点击 133  全文点击 19  投稿时间：2023-12-28  修订日期：2025-05-22
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DOI编号  10.7641/CTA.2024.30832
  2026,43(2):436-442
中文关键词  模型预测控制  复印机  系统辨识  碳粉供应  鲸鱼优化算法
英文关键词  model predictive control  copier  system identification  toner supply  whale optimization algorithm
基金项目  国家自然科学基金项目(61972302), 陕西省重点技术研发计划基金项目(2021ZDLGY07–01), 河北省三三三人才工程资助项目(C20231172)资助.
作者单位E-mail
方 勇 西安电子科技大学计算机科学与技术学院 fangyong368@163.com 
王 泉* 西安电子科技大学计算机科学与技术学院 qwang@xidian.edu.cn 
杜军朝 西安电子科技大学计算机科学与技术学院  
闫昱晓 中船汉光科技股份有限公司  
袁志毅 中船汉光科技股份有限公司  
中文摘要
      维持碳粉浓度稳定以确保印刷质量是复印机工程应用中的关键难题. 为解决复印机碳粉供应控制系统存 在的长时滞与不确定性问题, 本文设计了一种基于鲁棒模型预测控制策略. 首先, 采用系统辨识法获得碳粉供应系 统物理特性的数学模型; 其次, 针对复印机碳粉供应系统构建鲁棒模型预测控制器, 并引入改进的鲸鱼优化算法对 控制器参数进行优化; 最后, 基于控制器代价函数求解最优碳粉补充量, 对系统持续实施在线滚动优化控制. 试验结 果显示, 相较于应用广泛的PI控制器, 基于鲁棒模型预测的碳粉供应控制器在执行固定、递增和随机图像覆盖率任 务时, 碳粉浓度变化均方根误差分别降低了8.0%, 4.8% 和25.0%, 标准差分别降低了1.4%, 5.4%和14.4%, 表明该方 法可有效降低印刷过程中碳粉浓度变化离散程度, 具有更优越的动态性能控制效果.
英文摘要
      Maintaining the stability of toner concentration to ensure printing quality is a key problem in the engineering application of copiers. In order to solve the problem of long time delay and uncertainty in the toner supply control system of copier, a predictive control strategy based on robust model is designed. Firstly, the mathematical model of the physical characteristics of the toner supply system is obtained by using the system identification method; Then, a robust model predictive controller is designed for the toner supply system of the copier, and an improved whale optimization algorithm (WOA) is introduced to optimize the controller parameters; Finally, the optimal toner supplement is calculated based on the cost function of the controller, and the on-line rolling optimization control of the system is implemented continuously. The experimental results show that compared with the widely used PI controller, the robust model prediction-based toner supply controller has decreased the root-mean-square error of toner concentration change by 8.0%, 4.8% and 25.0%, and the standard deviation by 1.4%, 5.4% and 14.4% in the tasks of fixed, incremental and stochastic image coverage, which indicates that this method can effectively reduce the dispersion of toner concentration in the printing process, and has a better dynamic performance control effect.