本論文主要研究邊界熱源之銅棒熱傳導偏微分系統參數辨識，運用德州儀器(Texas Instruments)生產之 TMS320LF 2407A 數位信號處理器(DSP)及周邊設備，透過撰寫程式以PWM模組控制固定輸入邊界熱源，利用ADC模組內建取樣和保持(sample-and-hold)功能，收集銅棒熱傳之溫度分佈情形，所得之數據運用Matlab軟體繪製時間與溫度曲線圖。另外將第四章推導之銅棒熱傳導方程式的動態模型，利用座標平移及透過取樣資料系統(sampled-data system)零階保持器(zero-order-hold)轉換程序，把連續時間的邊界控制規則轉變成離散固定信號，再應用變數轉換法，將熱傳導方程式轉變為齊次的邊界條件，進而以Matlab pdepe.m功能模擬動態模型來近似實驗曲線，進而對照比較分析獲得邊界熱源之銅棒熱傳導偏微分系統參數。

This thesis is on PDE parameters identification of a heat conductive copper rod with a boundary heat source. A copper rod, 400mm in length and 38mm in diameter, is heated by an electrical heater with a pulse-width-modulated (PWM) solid state relay (SSR) control module from one boundary point. The temperature distribution of the copper rod is sampled and collected into a TMS320LF 2407A digital signal processor (DSP) manufactured by Texas Instruments (TI). The data is then plotted and analyzed by using Matlab software packages. In addition, the copper heat conduction equation and the derived dynamic model in Chapter IV will be applied to the conversion process of the continuous-time boundary control into the discrete-time sampled-data representation by using the Zero-Order-Hold (Z.O.H) process. The boundary conditions of the heat conduction equation are converted into homogeneous boundary conditions before applying the Matlab pdepe.m simulation functions. Finally, the experimental data are compared against the simulation data for confirmation of the PDE system parameters identification for the copper rod heat conduction system.

中文摘要.....................................ⅰ
英文摘要....................................ⅱ
誌謝辭......................................ⅲ
目次.......................................ⅳ
圖目錄......................................ⅵ
表目錄......................................ⅸ
符號說明....................................ⅹ
第一章 緒論...................................1
1.1研究動機與目的..............................1
1.2相關文獻回顧...............................1
1.3論文架構...................................2
第二章 系統硬體架構.............................4
2.1規格及整體架構..............................4
2.2溫度感測器.................................4
2.2.1熱電偶...................................5
2.2.2電阻式...................................8
2.2.3熱敏電阻..................................8
2.3 K Type 溫度試驗.............................9
2.4線性轉換..................................11
第三章 DSP TMS320LF 2407簡介...................12
3.1 DSP TMS320LF 2407A架構介紹..................12
3.2 DSP 系統核心(core)中央處理單元.................13
3.2.1 中央算術邏輯單元(CALU) .....................14
3.2.2 累積器(ACC) ...............................14
3.2.3 乘法器...................................15
3.2.4 輸入倍率部份..............................15
3.3 記憶體架構..................................15
3.4 事件管理模組.................................17
3.5 類比/數位轉換模組.............................18
第四章 熱傳導系統之數學模式建構.....................20
4.1熱傳導方程式................................20
4.2系統之數學式建模..............................22
4.3固定輸入的分析解..............................24
第五章 實驗結果與模擬分析討論......................29
5.1實驗方法介紹................................29
5.2實驗結果....................................33
5.3模擬方法介紹................................37
5.4模擬結果....................................37
5.5實際量測與Matlab模擬之各點溫度分佈比較誤差分析.....40
5.6誤差分析....................................46
5.7 Q值之近似曲線..............................51
5.8實驗與模擬結果討論............................55
5.8.1實驗結果討論..............................55
5.8.2模擬結果討論..............................56
第六章 結論與展望..............................57
6.1結論......................................57
6.2未來展望....................................58
參考文獻.......................................59

[1] 吳朗，感測與轉換－原理、元件與應用，全欣資訊圖書股份有限公司，81年3月2日二版
[2] 杜光宗，感測器應用電路的設計、製作，建宏出版社，81年11月出版
[3] 董勝源，DSP TMS320LF2407與C語言控制實習，長高科技圖書，93年6月初版
[4] 龔應時、陳建武、徐永松，TMS320F/C24×DSP控制器原理與應用，滄海書局，94年2月初版
[5] 張仲卿,侯順雄,張進寬,杜鳳棋,熱傳遞第4版,高立圖書有限公司,民國86年
[6] 王鎮雄、朱朝煌、李世榮、劉傳仁、蔡豐欽譯,熱傳遞學第八版,美商麥格羅、希爾國際股份有限公司,2008
[7] 張忠誠,金屬細線邊界溫度控制之取樣資料形式推導,國立中興大學/電機工程學系,2005年
[8] F. P. Incropera, and D. P. Dewiit,“Introduction to Heat Transfer”, 4th ed New York, Wiley, 2002.
[9] J. P. Holman,“Heat Tranfr”, New York, McGraw-Hill, 1990.
[10] A. Bejan, “Heat Tranfr”, New York, John Wiley&Sons, 1993.
[11] E. kreyszig, “Advanced Engineering Mathematics”, New York, John Wiley&Sons, 1999.
[12] J.P.Holman, “Heat Transfer”, 6th ed, New York, McGraw-Hill,1986.
[13] M.Necati Ozişik,“Heat Conduction”,New York ,John Wiley and Sons,1980.
[14] E. Zauderer, “Partial Dferential Equalions of Applied Mathematics”, New York, Wiley-Interscience, 1989.
[15] J. L. Lions, “Optimal Control Of System Governed by Partial Differential Equations”, New York, Springer-Verlag, 1972.
[16] M. Renardy, and R. C. Rogers, “An Introduction to Partial Differential Equations”, New York, Springer-Verlag, 2004.
[17] D. M. Boŝković, M. Kristic and W. Liu, “Boundary control of an unstable heat equation via measurement of domain-averaged temperature”,IEEE Trans. Autom. Control, vol.46, pp.2022–2028, Dec. 2001.
[18] A. Smyshlyaev and M. Kristic, “Explicit state and output feedback boundary controllers for partial differential equations”, J. Autom.Control, vol.13, no.2, pp.1–9, 2003.
[19] A. Smyshlyaev and M. Krstic, “On control design for PDEs with space-dependent diffusivity or time-dependent reactivity”, Automatica, vol. 41, no.9, pp. 1601–1608, 2005
[20] B. Bhikkaji, K. Mahata and T. Soderstrom, “Reduced order models for a two-dimensional heat diffusion system” ,Int. J. Control, vol.77, pp.1532-1548, 2004.
[21] A. Smyshlyaev and M. Kristic, “Backstepping boundary control for PDEs with non-constant diffusivity and reactivity” , Proceedings of the American Control Conference, pp.4557-4562, 2005.
[22] S. V. Drakunov, and V. Utkin, “Sliding Mode Control in Dynamic System”, Internation Journal of Control, Vol. 55, no.4, pp.1029-1037, 1992.
[23] S. V. Drakunov, and U.Ozguner, “Generalized Sliding Modes for Manifold Control of Distributed Parameter System, chapter in the book Variable Structure and Lyapunov Control ”, Springer Verlog., pp.109-132, 1993.
[24] S. Stojanovic,“Optimal damping control and nonlinear parabolic system”, Numer. Funct. And. And Optimiz, pp.573-591, 1989.
[25] H. E. Lee,and O. W. C. Shen,”Optimalcontrol of a class of distributed-parameter systems using gradient methods”, Inst. Electr. Volume 116, Issue 7, pp.1237–1244,1969.
[26] Meng-Bi Cheng, Verica Radisavljevic, Chung-Cheng Chang,Chia-Fu Lin, and Wu-Chung Su, “A Sampled-Data Singularly Perturbed Boundary Control for a Heat Conduction System With Noncollocated Observation”, IEEE Transactions On Automatic Control, vol. 54, no. 6, June 2009.
[27] B. S. Mordukhovich,and K. Zhang,” Feedback control for state-constrained heat equations with uncertain disturbances”,Proc. IEEE 33rd. Control Decision Conf., pp.1774-1775,1994.
[28] S. Lenhart, and D. G. Wilson,”Optimal Control of a heat equation with convective boundary condition,” Proc. IEEE 29th. Control Decision Conf., pp.142-143,1990.
[29] W. N. Everitt, and A. Zettl, “Sturm-Liouville differential operators in direct sum spaces.” Rocky Mountain J. Math. 16, pp.495-516,1986.
[30] W. N. Everitt, and A. Zettl, “Differential operators generated by a countable number of quasi-differential expressions on the real line,” Proc. London Math. Soc.(3) 64, pp.524-544,1992.
[31] C. S.Christ, and G. Stolz, ”Spectral theory of one-dimensional Schrodinger operators with point interactions,” J. Math. Anal. Appl. 184, pp491-516,1994.
[32] P. B. Bailey, W. N. Everitt and A. Zettl, “Regular and singular Sturm-Liouville problems with coupled boundary conditions,” Proc. Roy. Soc. Edinb. (A) 126, pp.505-514,1996.
[33] “The User Manual of TMS320LF2407A”,TI Inc. The User Manual of TMS320F2407, TI Inc.
[34] http://zh.wikipedia.org/zh-tw/%E7%83%AD%E7%94%B5%E5%81%B6.
[35] http://www.mathworks.com/access/helpdesk/help/techdoc/ref/pdepe.html.