現今三維圖形系統已廣泛的運用在可攜式電子產品，如筆記型電腦、個人數位助理(Personal Digital Assistant, PDA)以及智慧型手機上。然而這些嵌入式系統的電池所儲存的電能是有限的，不像桌上型系統可以無限制的供電。再者，現在製程進步的速度飛快，導致了同樣面積的積體電路(IC)上，電晶體數目大量的增加，相對地功率的消耗也更為驚人。況且三維圖形系統所需要的運算極其複雜，為了完成這些運算所造成的功\率消耗自然不在話下，如果想要有效地利用電池所提供的有限能源，電源管理將是一項不可或缺的設計。

動態電壓與頻率調整(Dynamic Voltage and Frequency Scaling, DVFS)是最常用的電源管理方法之一。在動態電壓與頻率調整方法中，需要使用一個準確的工作量預測器來預測每一個frame的工作量，並以此預測結果動態地調整下一個frame的電壓與頻率。電壓與頻率的層級數量以及各層級的電壓與頻率是固定的，由設計者依照不同的應用採用不同的層級數量與電壓頻率值。預測器預估出下一個frame的工作量之後，依照此工作量對電壓與頻率表進行查表的動作即可獲知下一個frame即將使用的電壓與頻率。

本論文提出一個以卡爾曼濾波器為主控制器、模糊控制器為輔助控制器的工作量預測器，透過模糊控制器的模糊概念調整卡曼濾波器中的參數，修正傳統卡爾曼濾波器需要事先知道系統特性的缺點。此外，我們也提出一個嶄新的概念---延遲顯示機制。透過這個延遲顯示機制，我們可以在不修改原本預測器架構的前提下，改變顯示控制訊號的時序，就可以大幅減少frame的預測失誤率。

In modern life, 3D graphics system is widely applied to portable product like Notebook, PDA and smart phone. Unlike desktop system, the capacity of batteries of these embedded systems is finite. Furthermore, rapid improvement of IC process leads to quick growth in the transistor count of a chip. According to above-mentioned reason and the complex computation of 3D graphics system, the power consumption will be very large. To efficiently lengthen the lifetime of battery, power management is an indispensable technique.

Dynamic voltage and frequency scaling (DVFS) is one of the popular power management policy. In the scheme of DVFS, an accurate workload predictor is needed to predict the workload of every frame. According to these predictions a specific voltage and frequency level is applied to each frame of the 3D graphics system. The number of the voltage/frequency levels and the voltage/frequency of each level are fixed, the voltage/frequency table is decided according to the application of power management. Whenever the workload predictor completes the workload prediction of next frame, the voltage/frequency level of next frame will be found by looking up the voltage/frequency table.

In this thesis, we propose a power management scheme with a framework composed of mainly Kalman filter and an auxiliary fuzzy controller to predict the workload of next frame. This scheme amends the shortcomings of traditional Kalman filter that needs to know the system features beforehand. And we propose a brand new concept named ”delayed display” to massively reduce the miss rate of prediction without changing the framework of predictor.

第一章 緒論.................................................................................................................. 1
1.1研究動機 ......................................................................................................... 1
1.2論文架構與大綱 ............................................................................................. 2
第二章 背景.................................................................................................................. 3
2.1功率消耗的種類 ............................................................................................. 3
2.2低功率元件設計 ............................................................................................. 5
2.3維圖形晶片系統 ........................................................................................... 12
第三章 預測器的選擇與設計.................................................................................... 15
3.1 預測器的必要性 .......................................................................................... 15
3.2 Uniform Window-size One(UW1) .................................................................. 15
3.3 Uniform Window-size Five(UW5) .................................................................. 16
3.4 Uniform Window-size One-Five (UW15)........................................................ 18
3.5 Frame structure-based預測器 ...................................................................... 20
3.6 比例積分微分 (PID) 控制器 ........................................................................ 23
3.7 混合型(Hybrid)控制器 ................................................................................. 26
3.8 卡爾曼濾波器(Kalman Filter) ....................................................................... 31
第四章 模糊混合型預測器........................................................................................ 39
4.1 模糊(Fuzzy)控制器 ....................................................................................... 39
4.2 應用卡爾曼濾波器於工作量預測 .............................................................. 45
4.3 混合型模糊卡爾曼濾波器 .......................................................................... 47
4.4 延遲顯示機制(delayed display scheme) ...................................................... 51
4.5 Inter-Compensation ....................................................................................... 56
4.6 C 模組 ........................................................................................................... 57
4.7 硬體架構 ...................................................................................................... 59
4.8Benchmarks ..................................................................................................... 64
4.9效能的評估 ................................................................................................... 65
4.10實驗結果 ..................................................................................................... 68
第五章 結論與未來工作............................................................................................ 73
參考文獻...................................................................................................................... 74

[1] 葉家惠, “An adaptive Fuzzy proportional-Integral predictor for power management of 3D Graphics System-on-chip,”國立中山大學資訊工程系碩士論文,2010.
[2] Y. Gu, S. Chakraborty, and W. T. Ooi, “Games are up for DVFS,” in Proc. Design Autom. Conf., 2006, pp. 598–603.
[3] Yan Gu and Chakraborty S., “A hybrid DVS scheme for interactive 3D games,” in Proc. Real-Time and Embedded Technology and Applications Symposium, 2008.
[4] Greg Welch and Gary Bishop, “An introduction to the kalman filter,” ACM, 2001.
[5] 吳志賢, “嵌入式適應模糊比例積分微分控制器設計與實現,” 中華技術學院電子工程系碩士論文,2006.
[6] 孫宗瀛、楊英魁編著, “Fuzzy控制理論、實作與應用,” 全華科技圖書，1994.
[7] Sung-Yong Bang, Kwanhu Bang, Sungroh Yoon, and Eui-Young Chung, “Run-Time Adaptive Workload Estimation for Dynamic Voltage Scaling,” IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, Sept. 2009.
[8] Greg Welch and Gary Bishop, “Fuzzy Controller: Choosing an Appropriate and Smallest Rule Set,” International journal of computational cognition, Dec. 2005.
[9] Yung-Hsiang Lu and Giovanni De Micheli, “Comparing system level power management policies,” IEEE Design & Test,, Vol. 18, pp.10-19, 2001.
[10] Shujjat Khan, Donald Bailey, and Gourab Sen Gupta, “Simulation of Triple Buffer Scheme,” in Proc. Second International Conference on Computer and Electrical Engineering, 2009.
[11] M. G. Jibukumar, Raja Datta, and P. K. Biswas, “Kalman filter based variable bit rate video frame size prediction,” in 3rd International Symposium, Wireless Pervasive Computing, ISWPC 2008. May. 2008.
[12] Huifeng Ji, Aigong Xu, Xin Sui, and Lanyong Li, “The applied research of kalman in the dynamic travel time prediction,” International Conference on Geoinformatics, 2010.
[13] http://zh.wikipedia.org/wiki/%E5%8D%A1%E5%B0%94%E6%9B%BC%E6%BB%A4%E6%B3%A2
[14] Kihwan Choi, Wei-Chung Cheng, and M Pedram, “Frame-based dynamic voltage and frequency scaling for a MPEG player”, Journal of Low Power Electronics, 2005.
[15] L. Benini, A. Bogliolo, G.A. Paleologo, and G. De Micheli, “Policy optimization for dynamic power management” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1999.
[16] 郭煒, “SOC嵌入式系統晶片設計從理論邁向實務”, 碩博文化, 2008.
[17] Dimitrios Soudris, C. Piguet, and C. Goutis, “Designing CMOS Circuits for Low Power”, Boston, MA :Kluwer Academic Press, 2002.
[18] Bren Mochocki, Kanishka Lahiri and Srihari Cadambi, “Power Analysis of Mobile 3D Graphics,” IEEE Design Automation Conference, pp.592-597, 2006.
[19] P.M. Larsen, “Industrial applications of fuzzy logic control,” Int. J.Man, Mach, Studies, vol.12, no.1, pp.3-10, 1980.
[20] 許華山, “三維圖形系統晶片電源管理策略之設計與實作,” 國立中山大學資訊工程學系碩士論文,2008.
[21] 鄭浩逸, “應用在三維圖形系統晶片電源管理之適應性比例積分控制器,” 國立中山大學資訊工程學系碩士論文,2009.