模式切换类经济预测控制切换时间在线估计

doi:10.11949/0438-1157.20191573

摘要/Abstract

摘要：

针对一类非线性仿射系统，提出一种在线估计切换时间的经济模型预测控制算法，并将其拓展到长周期控制过程中。有限时间内，将切换时间作为变量实时更新估计，确定最优的切换操作点，以保证每一时刻都可以在控制目标可达的前提下经济性能最优，避免了传统切换经济预测控制策略可能出现的控制目标不可达或经济性能较差的情况。进一步，将该策略作为单周期应用到长周期优化控制过程中，当系统受到扰动时，开始一个新的优化控制周期，实现优化模式与控制模式的灵活切换，同时可以及时应对扰动的出现。该策略保证系统的综合性能最优，仿真结果证明了方法的有效性。

关键词: 过程系统工程, 化工过程系统, 过程控制, 经济模型预测控制, 模型预测控制, 在线估计

Abstract:

For a kind of nonlinear affine systems, an economic model predictive control algorithm for online estimation of switching time is proposed and extended to the long period control process. In a limited time, the switching time is used as a variable to estimate in real time, and the optimal switching point is determined, so as to ensure that the economic performance is optimal at every moment under the premise that the control objective is reachable. The situations of unreachable control objective and poor economic performance caused by traditional switching economic model predictive control strategy are avoided. Furthermore, the strategy is applied as a single cycle to the long period optimization control process. Once the disturbance occurs, a new optimization control cycle is started. The flexible switching between the optimized mode and the control mode can be realized, and the disturbance can be dealt with in time. The simulation results show the effectiveness of the method.

Key words: process system engineering, chemical process system, process control, economic model predictive control, model predictive control, online estimation

中图分类号:

TP 273

冯思琦, 罗雄麟. 模式切换类经济预测控制切换时间在线估计[J]. 化工学报, 2020, 71(S2): 225-240.

Siqi FENG, Xionglin LUO. Online estimation of switching time for a class of optimization-control mode switch of economic model predictive control[J]. CIESC Journal, 2020, 71(S2): 225-240.

图/表 16

图1 切换EMPC简单示意图

Fig.1 Simple diagram of switching EMPC

图2 切换EMPC下系统状态空间演化图例[实线代表经济优化模式状态轨迹(模式1)；点虚线代表控制模式状态轨迹(模式2)]

Fig.2 An illustration of the state-space evolution of a system under switching EMPC

图3 切换时间估计策略示意图

Fig.3 Estimated switching time strategy

图4 应用数值解确定切换时间原理图

Fig.4 An illustration of applying a numerical solution to determine the switching time

图5 切换时间校正原因示意图

Fig.5 The reason for correcting the switching time

图6 长周期下OEST-EMPC控制策略示意图

Fig.6 An illustration of OEST-EMPC strategy under long period

图7 单周期下不同切换时间的状态轨迹对比

Fig.7 Comparison of state trajectories at different switching times under single cycle

表1 单周期下不同切换时间系统的控制性能与经济性能

Table 1 Control and economic performance of the system at different switching times under single cycle

项目

t_s在线

估计

控制性能(终端状态到控制目标区间边界的距离)

图8 单周期下系统各变量随时间变化的曲线

Fig.8 Time-varying curves of system variables under single cycle

图9 长周期OEST-EMPC与传统切换EMPC下系统的状态轨迹对比

Fig.9 Comparison of system state trajectories between OEST-EMPC and traditional switching EMPC under long period

表2 长周期下OEST-EMPC与传统切换EMPC综合性能对比

Table 2 Comprehensive performance comparison between OEST-EMPC and traditional switching EMPC under long period

项目	OEST-EMPC	传统切换EMPC(t_s=10 s)
控制性能(终端状态到控制目标区间边界的距离)	-0.16	-0.17
经济性能(平均经济性能指标)	6.12	9.17

图10 长周期OEST-EMPC算法下各变量随时间变化的曲线

Fig.10 Time-varying curves of system variables under OEST-EMPC algorithm in long period

图11 长周期下OEST-EMPC与传统切换EMPC下系统的状态轨迹对比

Fig.11 Comparison of system state trajectories between OEST-EMPC and traditional switching EMPC under long period

图12 长周期OEST-EMPC算法下各变量随时间变化的曲线

Fig.12 Time-varying curves of various variables under the long-period OEST-EMPC algorithm

图13 OEST-EMPC与传统切换EMPC下系统的经济性能指标

Fig.13 Comparison of economic performance indexes between OEST-EMPC and traditional switching EMPC

表3 长周期下OEST-EMPC与传统切换EMPC综合性能对比

Table 3 Comprehensive performance comparison between OEST-EMPC and traditional switching EMPC under long period

项目	OEST-EMPC	传统切换EMPC(t_s=6 min)
控制性能(终端状态到控制目标区间边界的最短距离)	-0.04	-0.04
经济性能(平均经济性能指标)	0.564	0.837

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