Modeling and control strategy for packing-stage of injection molding process based on PWA fusion model

doi:10.11949/0438-1157.20191539

Abstract

Abstract:

The injection molding is a typical batch process and consists of three stages: filling, packing-holding and cooling. Packing-holding is an important stage to determine product quality and has obvious nonlinear and time-varying characteristics. Piece-wise affine (PWA) model can effectively describe the dynamics of packing-holding stage, but the hard switching of PWA model will lead to the output jump problem. Therefore, we propose a novel time-partitioned PWA fusion model, in which the switching regionis introduced between adjacent sub-models and model fusion is realized by linear weighting method. Then, an identification algorithm based on separable nonlinear least-squares is developed to estimate model parameters. Based on this, a multi-model PID control method based on internal model tuning is designed.Experimental results of injection molding machine show the effectiveness of the algorithm.

Key words: injection molding process, PWA fusion model, separable least-squares, multi-model PID control

摘要：

注塑过程是典型的批次过程，由注射、保压、冷却等阶段构成。保压段是决定制品质量的一个重要阶段，且具有较大的非线性和时变性。分段仿射(piece-wise affine, PWA)模型能够有效描述保压段的特性，但是PWA模型硬切换方式会导致输出跳变问题，因此提出一种基于时间划分的PWA融合模型，在子模型切换过程中引入切换区间，通过线性加权方法进行模型融合，并采用基于分离最小二乘的辨识方法进行参数估计。在此基础上，设计了基于内模整定的多模型PID控制方法。注塑机实验结果表明了算法的有效性。

关键词: 注塑过程, PWA融合模型, 分离最小二乘, 多模型PID控制

CLC Number:

TP 13

Yaobo HUANG, Jiaxin LIU, Zuhua XU, Jun ZHAO, Zhijiang SHAO. Modeling and control strategy for packing-stage of injection molding process based on PWA fusion model[J]. CIESC Journal, 2020, 71(3): 1103-1110.

黄耀波, 刘佳新, 徐祖华, 赵均, 邵之江. 基于PWA融合模型的注塑过程保压段建模及控制策略[J]. 化工学报, 2020, 71(3): 1103-1110.

Figures/Tables 11

Fig.1 Weighting function of linear weighting

Fig.2 Process of identification algorithm

Fig.3 Rotation, expansion and shrinkage of MDS

Fig.4 Diagram of multi-model PID controller

Fig.5 Appearance of injection molding machine

Fig.6 GBN test near nominal trajectory

Table 1 Switching intervals and loss function for order=1

区间个数	次序					J
区间个数	1	2	3	4	5	J
1	328/329					0.9067
2	136/154	329/329				0.9002
3	136/154	329/329	573/580			0.8975
4	143/191	216/218	404/433	500/503		0.8819
5	136/154	278/278	318/320	404/434	500/503	0.8862

Fig.7 CIC criterion for different structure of PWA fusion model

Fig.8 Switching intervals of PWA fusion model

Table 2 Parameters of multi-model PID controller

PID参数	PWA子模型
PID参数	1	2	3	4	5
$K c$	0.7250	0.7607	0.6497	0.6390	0.5930
$τ i$	0.0904	0.1168	0.0892	0.0959	0.0855
$τ d$	0.0457	0.0829	0.0489	0.0800	0.0480

Table 2 Parameters of multi-model PID controller

PID参数	PWA子模型
PID参数	1	2	3	4	5
$K c$	0.7250	0.7607	0.6497	0.6390	0.5930
$τ i$	0.0904	0.1168	0.0892	0.0959	0.0855
$τ d$	0.0457	0.0829	0.0489	0.0800	0.0480

Fig.9 Multi-model PID control experiment for packing stage

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