權重H2降階控制器設計及硬體迴路模擬

Design and Hard ware-in-the-loop Simulation of Weighted H2 Reduced-order Controllers

吳達太(Da-Tai Wu)

指導教授 ： 周永山

共同指導教授 ： 李世安(Shih‐An Li)

淡江大學/工學院/電機工程學系碩士班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.01019

摘要

本文研究權重 降階控制器設計之問題。傳統方法引入權重函數會造成控制器階數增加，並且在擴增系統內產生一些無法移動的極點，造成閉迴路極點配置的困難。本文針對這兩點提出改善的方法，利用僅併入權重函數的一部分而非全部，配合特殊之變數設定，推導出權重 性能之充分條件。如此，可彈性調整控制器階數使其介於受控體階數以及受控體與權重函數階數總和之間。另外，本文所提的方法，不管權重函數的極點是否落在指定的極點配置區域中，仍能進行區域極點配置。
本論文所提出的設計條件皆為線性矩陣不等式(Linear Matrix Inequalities，LMIs)，可利用MATLAB軟體求解以及數值模擬驗證。最後，本文在FPGA(DE2-115)開發板上，運用硬體描述語言將所設計出之控制器實現在硬體上。再與Simulink作結合，透過硬體迴路模擬證實我們所提方法之可行性。

關鍵字

權重函數 ； H2控制 ； 降階 ； 區域極點配置 ； FPGA ； 硬體迴路模擬

並列摘要

This thesis investigates the problem of weighted reduced-order controller design. Traditional method introduces weighting functions into the design procedure, which increases the order of the controllers. Furthermore, it leads to the situation that some poles of the augmented plant (i.e., the weighted plant) are fixed, causing difficulty in closed-loop pole placement. To make improvements concerning the two questions, only a part but not all of the weighting function is incorporated into the plant. Sufficient conditions for the problem are derived utilizing a particular choice of variables. As a result, in the affirmative case the order of the controller is equal to the sum of the plant's order and the order of the part of the weighting function incorporated into the plant, which in total lies between the plant's order and that of the weighted plant. In addition, the proposed method is capable of performing regional pole placement, regardless of the poles of the weighting function falling within the specified region in the complex plane or not.
The solvability conditions derived for the problem are in terms of linear Matrix Inequalities (LMIs), which can be solved efficiently using MATLAB. Finally, the controller is implemented on FPGA(DE2-115) development board. When integrated with Simulink the results of the hardware-in-the-loop simulation validate the effectiveness of the proposed method.

並列關鍵字

weighting functions ； loop shaping ； control ； reduced-order ； regional pole placement ； Hardware-in-the-loop

參考文獻

[2]M.C. de Oliveira, J.C. Geromel and J. Bernussou, “Extended and norm characterizations and controller parameterizations for discrete-time systems,” Int. J. Control, vol. 75,no. 9, 2002, pp. 666-679.

[3]C.W. Scherer, “An efficient solution to multi-objective control problems with LMI objectives,” System & Control Letters, vol. 40, 2000, pp. 43-57.

[4]J.S. Lim, J.R. Ryoo, Y.I. Lee, and S.Y. Son, “Design of a Fixed-Order Controller for the Track-Following Control of Optical Disc Drives,” IEEE Trans. Control System Tech, vol. 20, 2012, pp. 205-213.

[5]楊景富，“ 迴路整形技術之研究”， 淡江大學電機工程學系碩士班碩士論文，民103年。

[7]C.W. Scherer, P. Gahinet and M. Chilali, “Multiobjective output-feedback control via LMI optimization,” IEEE Trans. Aut. Control, vol. 42, 1997, pp. 896-911.