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 自动化学报  2018, Vol. 44 Issue (5): 935-942 PDF

Multi-rate Distributed Predictive Control and Its Application to Looper Control System of Hot Strip Rolling
ZHANG Xiao-Dong, GAO Shao-Shu, LIU Xin-Ping
College of Computer and Communication Engineering, China University of Petroleum, Qingdao 266580
Manuscript received : April 26, 2016, accepted: April 10, 2017.
Foundation Item: Supported by Natural Science Foundation of Shandong Provincial (ZR2014FP013), Qingdao Research Foundation for Basic Research China (14-2-4-115jch), The Economy & Technology Development of Zone of Qingdao Development of Science and Technology Plan Major Projects (2013-1-37)
Corresponding author. GAO Shao-Shu  Lecturer at the College of Computer and Communication Engineering, China University of Petroleum, Qingdao, Shandong. She received her Ph. D. degree in optical engineering from the Beijing Institute of Technology in 2013. Her research interest covers image processing and color night. Corresponding author of this paper
Recommended by Associate Editor YANG Chun-Hua
Abstract: Distributed model predictive control strategy is more suitable for dealing with multi-agent cooperative control systems. However the coupling effects among multiple agents are still a difficult point. In the paper, a multi-rate distributed model predictive control strategy is proposed for series structural systems, in which all the controllers of agents can be updated asynchronously and the coupling effects are fully taken into account to improve stability. Furthermore, a sufficient condition for the stability is generated. Finally, the control strategy is applied into a looper control system of hot strip rolling and simulation results show its feasibility and effectiveness.
Key words: Distributed model predictive control     multi-rate     looper system     multi-agent

1 多速率分布式预测控制策略

 图 2 活套系统示意图 Figure 2 Configuration of looper systems

 $$$\begin{split} &\left[\!\! \begin{array}{l} {\Delta {{\dot \theta }_i}(t, s)} \\ {\Delta {{\dot \omega }_i}(t, s)} \\ {\Delta {{\dot i}_i}(t, s)} \\ \end{array} \right] =\\ &\qquad\left[ \begin{array}{ccc} 0 & {\dfrac{1}{{{G_{i\_R}}}}} & 0 \\ { - \dfrac{1}{{{G_{i\_R}}}}\dfrac{{\partial {M_{i\_T}}}} {{\partial {\theta _i}}}\dfrac{1}{{{J_i}}}\dfrac{{180}}{\pi }} & 0 & {\dfrac{{{C_{i\_m}}}}{{{J_i}}}\dfrac{{180}}{\pi }} \\ 0 & 0 & { - \dfrac{1}{{{T_i}}}} \\ \end{array} \right]\times \\ &\qquad\left[ \begin{array}{l} \Delta\theta\\ \Delta\omega\\ \Delta i\\ \end{array} \right]+ \left[ \begin{array}{ccc} 0\\ 0\\ \dfrac{1}{T_{i\_i}} \end{array} \right]\times {\pmb u}_i+ \left[ \begin{array}{ccc} 0\\ 1\\ 0 \end{array} \right]\times\\ &\qquad\left(- \dfrac{1}{G_{i\_R}} \dfrac{\partial M_{i\_T}}{\partial\tau_i} \frac{1}{J_i}\dfrac{180}{\pi} \Delta\tau_i \right) \end{split}$$$ (19)

 \begin{align} &\left[ \begin{array}{*{20}{ccccccccccccc}} {\Delta {{\dot \tau }_i}(t, s)} \\ {\Delta {{\dot V}_i}(t, s)} \\ \end{array}\right] = \notag\\ & \qquad\left[{\begin{array}{*{20}{cccccccccccccc}} {\dfrac{{{E_i}}}{{{l_i}}}\left( - \dfrac{{\partial {\beta _{i + 1}}}} {{\partial {\tau _i}}}{V_{i + 1}} - \dfrac{{\partial {f_i}}}{{\partial {\tau _i}}}{V_i}\right)} & \\ 0 & \\ \end{array}} \right.\notag\\ &\qquad\qquad \qquad\qquad \qquad\left.{\begin{array}{*{20}{cccccccccccccc}} & { - \dfrac{{{E_i}}}{{{l_i}}}(1 + {f_i})} \\ & { - \dfrac{1}{{{T_{i\_V}}}}} \\ \end{array}} \right]\times \notag\\ &\qquad \left[\begin{array}{*{20}{ccccccccc}} {\Delta {\tau _i}(t, s)} \\ {\Delta {V_i}} \\ \end{array}\right] + \left[\begin{array}{*{20}{cccccc}} 0 & {\dfrac{{{E_i}}}{{{l_i}}}(1 - {\beta _{i + 1}})} \\ 0 & 0 \\ \end{array}\right]\times\notag\\ &\qquad\left[\begin{array}{*{20}{cccc}} {\Delta {\tau _{i + 1}}(t, s)} \\ {\Delta {V_{i + 1}}} \\ \end{array}\right] + \left[\begin{array}{*{20}{cccccc}} 0 \\ {\dfrac{1}{{{T_{i\_V}}}}} \\ \end{array} \right]{{\pmb u}_i} +\notag\\ &\qquad\left[\begin{array}{*{20}{ccccccccccccc}} 1 \\ 0 \\ \end{array}\right] \dfrac{1}{{{G_{i\_R}}}} \dfrac{{{E_i}}}{{{l_i}}} \dfrac{{{\rm d}{l_i}}}{{{\rm d}{\theta _i}}}\Delta {\omega _i} \end{align} (20)

1) 在初始条件的作用下, 基于串联结构的活套系统, 下游机架轧制速度变化对上游机架张力系统的影响是逐步增强的.与多速率同步更新控制策略相比较(基于优化性能指标(11)求解控制律), 仿真结果如图 3 (a)(b)所示.采用异步更新控制方式能够预知关联子系统的扰动进行补偿, 控制律变化幅度相对较小, 从而提高活套张力系统的稳定性.而采用同步更新的控制方式, 第$i+1$机架控制律$\Delta {\pmb u}_{i+1}(k)$会直接作用在第$i$机架$\Delta {\pmb u}_i(k)$上, 使得第$i$机架当前的控制律变为$\Delta \bar{u}_i(k)=\Delta {\pmb u}_{i}(k)+(1-\beta_{i+1})\Delta {\pmb u}_{i+1}(k)$从而影响系统的稳定性和控制性能.

 图 3 控制器同步更新与异步更新比较 Figure 3 The comparison between simultaneous control and asynchronous control

2) 对比同步更新控制器方式(单机架活套系统的控制律更新周期与输出周期都为$T/M$), 基于式(1)、(2)和优化性能指标(11) (式(11)中令$M=1$), 求解控制律.仿真结果如图仿真结果如图 4 (a)~(c)所示.从仿真结果可以看出, 多速率异步更新控制方式与快采样同步更新控制方式的具有相近的控制性能, 但能够减小计算量, 减轻计算负担.

 图 4 快采样更新与异步更新比较 Figure 4 The comparison between fast-sample control and asynchronous control

 图 5 扰动情况下快采样更新与异步更新比较 Figure 5 The comparison between fast-sample control and asynchronous control with disturbance

3) 对比同步更新控制器方式(单机架活套系统的控制律更新周期与输出周期都为$T$), 基于式(1)、(2)和优化性能指标(11) (式(11)中令$M=1$), 与多速率异步控制方式相比较, 仿真结果如图 6 (a)~(d)所示.从仿真结果可以看出采用多速率异步更新方式能够明显地改善系统的控制性能.

 图 6 慢采样更新与异步更新比较 Figure 6 The comparison between slow-sample control and asynchronous control with disturbance
5 结论

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