Distributed parameter modeling and finite-frequency loop-shaping of electromagnetic molding machine

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• 作者：Takayuki Ishizaki ; Kenji Kashima ; Jun-ichi Imura ; Atsushi Katoh ; Hiroshi Morita ; Kazuyuki Aihara
• 关键词：Industrial applications of optimal control ; Modeling for control optimization ; Infinite-dimensional systems ; Generalized KYP lemma ; Electromagnet
• 刊名：Control Engineering Practice
• 出版年：December, 2013
• 年：2013
• 卷：21
• 期：12
• 页码：1735-1743
• 全文大小：1493 K

文摘

We derive a mathematical model for an electromagnet inside a molding machine, and propose a novel loop-shaping method of the proportional-integral (PI) controller design for the system based on the generalized KYP (GKYP) lemma. The behavior of the molding machine is difficult to capture by using finite-dimensional models owing to eddy currents spatially distributed throughout the electromagnet. To analyze fundamental properties of the system both theoretically and experimentally, we first derive a mathematical model of the machine in terms of a partial differential equation (PDE). An analysis using the PDE model shows that a low-dimensional approximation performed by standard spatial discretization results in a spillover effect, which makes the behavior of the closed-loop system oscillatory. Then, to develop an easily tunable and implementable control system, we propose a novel loop-shaping method for PI control on the basis of the GKYP lemma. In this control system design, we use multiple low-dimensional models, which work simultaneously in specified finite frequency ranges. The proposed method successfully suppresses the spillover effect despite the use of low-dimensional approximants. Finally, we show the efficiency of the proposed control design method through numerical and experimental verification and discuss a performance limitation of the PI control.