本論文主要針對以分散式自適應法則控制之大尺度資料採樣系統，提出數位再設計控制器。研究對象由數組子系統組成，各子系統之特徵未知，且彼此間存在相互作用，但一子系統之控制器無法取得其他子系統之資訊，此一限制形成本研究之先天條件。經由模型參考的導入，分散式自適應控制可利用參考模型提供之資訊，使受控系統漸近式追蹤參考模型，達到零誤差的境地。該架構之本質，讓控制系統之設計可拆分為兩部分，一是使系統完美地追蹤參考模型，一是使模型狀態緊隨參考訊號。而數位再設計，將可分別針對此二部分進行設計。利用脈幅調變及脈寬調變法則，可設計出與類比控制等效之控制器，簡化控制設計之複雜度，並可降低控制器設計及實作之成本。在本論文中將舉列證明，經數位再設計之控制器，使受控系統呈現出的追蹤軌跡，可近似類比控制下之表現。

A novel model-reference-based decentralized adaptive controller is proposed for a continuous-time large scale multivariable system consisting of N interconnected linear subsystem with unknown parameters. The adaptation of the analog controller gain is derived by using model reference adaptive control theory based on Lyapunov's method. In this paper, it is shown that in the sampled-data decentralized adaptive control systems, it is theoretically possible to asymptotically track desired outputs with zero error. It is assumed that all the controllers share their prior information and the principal result is derived assuming that they cooperate implicitly. The optimal digital redesign of PAM and PWM controllers for sampled-data decentralized adaptive control systems is newly proposed. The prediction-based digital redesign methodology is utilized to find the new pulse-amplitude-modulated (PAM) and pulse-width-modulated (PWM) digital controllers for effective digital control of the analog plant. An illustrative example of MIMO interconnected linear system is presented to demonstrate the effectiveness of the proposed design methodology.

[1] Hansheng wv, Decentralized Robust Control for a class of Large-Scale Interconnected Systems with Uncertainties, Int. J. System Sci, vol.20, no.12, pp.2597-2608, 1989.
[2] Mohammed Jamshidi, LargeScale System: Modeling and Control, New York, Elserier Science Publishing Co., Inc., 1983.
[3] E. J. Davison, The Robust Decentralized Control of Servomechanism Problem for Composite System with Input-Output Interconnection, IEEE Trans. On Automatic Control AC 248, no.2, 1979.
[4] P. A. Ioannou and J. Sun, Robust Adaptive Control, Prentice Hall, 1996.
[5] D. T. Gavel and D. D. Siljak, “Decentralized adaptive control: Structural conditions for stability,” IEEE Trans. Automat. Contr., vol. 34, pp.413–426, Apr. 1989.
[6] L. Shi and S. K. Singh, “Decentralized adaptive controller design of large-scale systems with higher order interconnections,” IEEE Trans. Automat. Contr., vol. 37, pp. 1106–1118, Aug. 1992.
[7] R. Ortega and A. Herrera, “A solution to the decentralized adaptive stabilization problem,” Syst. Control Lett., vol. 20, pp. 299–306, 1993.
[8] A. Datta, “Performance improvement in decentralized adaptive control: A modified model reference scheme,” in Proc. 31st Conf. Decision Control, Tucson, AZ, Dec. 1992, pp. 1346–1351.
[9] Y. H. Chen, G. Leitmann, and Z. K. Xiong, “Robust control design for interconnected systems with time-varying uncertainties,” Int. J. Control, vol. 54, pp. 1119–1124, 1991.
[10] C. Wen, “Direct decentralized adaptive control of interconnected systems having arbitrary subsystem relative degrees,” in Proc. 33rd Conf. Decision Control, Lake Buena Vista, FL, Dec. 1994, pp. 1187–1192.
[11] -----, “Indirect robust totally decentralized adaptive control of continuous-time interconnected systems,” IEEE Trans. Automat. Contr., vol. 40, pp. 1122–1126, June 1995.
[12] K. Ikeda and S. Shin, “Fault tolerant decentralized control systems using backstepping,” in Proc. 34th Conf. Decision Control, New Orleans, LA, Dec. 1995, pp. 2340–2345.
[13] P. R. Pagilla, “Robust decentralized control of large-scale interconnected systems: General interconnections,” in Proc. Amer. Control Conf., San Diego, CA, June 1999, pp. 4527–4531.
[14] O Huseyin, M. E. Sezer, and D. D. Siljak, “Robust decentralized control using output feedback,” in IEE Proc., vol. 129, Nov. 1982, pp. 310–314.
[15] P. A. Ioannou and A. Datta, “Decentralized indirect adaptive control of interconnected systems,” Int. J. Adapt. Control Signal Processing, vol.5, pp. 259–281.
[16] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems. Upper Saddle River, NJ: Prentice-Hall, 1989.
[17] K. S. Narendra and N. O. Oleng’, “Exact Output Tracking in Decentralized Adaptive Control Systems,” Center for Systems Science, Yale University, New Haven, CT, Tech. Rep. 0104, 2001.
[18] G. C. Goodwin and K. S. Sin, Adaptive Filtering Prediction and Control. Prentice Hall, 1984.
[19] Boris M. Mirkin, Decentralized adaptive controller with zero residual tracking errors, Proceedings of the 7th Mediterranean Conference on Control and Automation (MED99) Haifa, Israel - June 28-30, 1999.
[20] B. M. Mirkin, Proportional-integral-delayed algorithms of adaptation, Automation, no. 5, pp. 13-20, 1991.
[21] Kumpati S. Narendra and Nicholas O. Oleng’, Exact Output Tracking in Decentralized Adaptive Control Systems, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 47, NO. 2, FEBRUARY 2002.
[22] Houpis, C. H. and Lamont, G. B., Digital Control Systems, McGraw Hill, New York, 1985.
[23] Kuo, B. C., Digital Control Systems, Holt, Rinehart and Winston, NY, 1980.
[24] Chen, T. and Francis, B. A., Optimal Sampled-Data Control Systems, Spring-Verlag, New York, 1995.
[25] Fujimoto, H., Hori, J. and Kawamura, A., “Perfect tracking control based on multirate feedforward control with generalized sampling periods”, IEEE Trans. on Industrial Electronics, vol. 48, no. 3, pp. 636-644, 2001.
[26] Fujimoto, H., Kawamura, A. and Tomizuka, M., “Generalized digital redesign method for linear feedback system based on n-delay control”, IEEE/ASME Trans. Mechaton., vol. 4, pp. 101-109, 1999.
[27] Ieko, T., Ochi, Y. and Kanai, K., “Digital redesign of linear state-feedback law via principle of equivalent area”, J. of Guidance, Control and Dynamics, vol. 24, pp. 857-859, 2001.
[28] Shieh, L. S., Wang, W. M. and Panicker, M. K. A., “Design of PAM and PWM digital controllers for cascaded analog systems”, ISA Transaction, vol. 37, pp. 201-213, 1998.
[29] Yang, T. and Chua, L.O., “Control of chaos using sampled-data feedback control”, Int. J. Bifurcation and Chaos, vol. 8, pp. 2433-2438, 1998.
[30] Rafee, N., Chen, T. and Malik, O. P., “A technique for optimal digital redesign of analog controllers”, IEEE Trans. Control Systems Technology, vol. 5, no. 1, pp. 89-99, 1997.
[31] D. T. Gavel and D. D. Siljak, “Decentralized adaptive control: Structural conditions for stability,” IEEE Trans. Automat. Contr., vol. 34, pp.413–426, Apr. 1989.
[32] I.H.Suh and Z.Bien (1980). Use of time delay action tn the controller design, IEEE Transactions on Automatic Control, 25, pp.600-603.
[33] Guo, S. M., Shieh, L. S., Chen, G. and Lin, C. F., “Effective chaotic orbit tracker: a prediction-based digital redesign approach”, IEEE Trans. on Circuits and Systems – I, Fundamental Theory and Applications, vol. 47, no. 11, pp. 1557-1570, 2000.
[34] Kuo, B. C., Digital Control Systems, Holt, Rinehart and Winston, NY, 1980.
[35] Lancaster, P., Lambda-matrices and vibrating systems, Pergamon Press, New York, 1966.
[36] Lewis, F. L. and Syrmos, V. L., Optimal Control, edition, Wiley, New York, 1995.
[37] Rafee, N., Chen, T. and Malik, O. P., “A technique for optimal digital redesign of analog controllers”, IEEE Trans. Control Systems Technology, vol. 5, no. 1, pp. 89-99, 1997.
[38] Shieh, L. S., Chang, F. R. and Mcinnis, B. C., “The block partial fraction expansion of a matrix fraction description with repeated block poles”, IEEE Trans. Automat. Contr., vol. AC-31, no. 3, 1986.
[39] Shieh, L. S. and Tsay, Y. T., “Algebra-geometric approach for the model reduction of large-scale multivariable systems”, Proc. IEE, vol. 131, part D., no. 1, pp. 23-36, 1984.
[40] Shieh, L. S. and Tsay, Y. T., “Block modal matrices and their applications to multivariable control systems”, Proc. IEE, vol. 129, part D., no. 2, pp. 41-48, 1982.
[41] Shieh, L. S. and Tsay, Y. T., “Transformations of a class of multivariable control systems to block companion forms”, IEEE Trans. Automat. Contr., vol. AC-27, pp.199-203, 1982.
[42] Shieh, L. S. and Tsay, Y. T., “Transformations of solvents and spectral factors of matrix polynomials and their applications”, Int. J. Contr., vol. 34, no. 4, pp. 813-823, 1981.
[43] Shieh, L. S., Tsay, Y. T. and Yates, R. E., “State-feedback decomposition of multivariable systems via block-pole placement”, IEEE Trans. Automat. Contr., vol. AC-28, no. 8, pp. 850-852, 1983.
[44] Shieh, L. S., Wang, W. M. and Panicker, M. K. A., “Design of PAM and PWM digital controllers for cascaded analog systems”, ISA Transaction, vol. 37, pp. 201-213, 1998.
[45] Tsay, Y. T. and Shieh, L. S., “Block decompositions and block modal controls of multivariable control systems”, Automatica, vol. 19, no. 1, pp. 29-40, 1983.
[46] Tsay, Y. T. and Shieh, L. S., “Irreducible divisors of λ-matrices and their applications to multivariable control systems”, Int. J. Contr., vol. 37, no. 1, pp. 17-36, 1983.
[47] Tsay, Y. T., Shieh, L. S., Yates, R. E. and Barnett, S., “Block partial fraction expansion of a rational matrix”, Linear and Multilinear Algebra, Vol. 11, pp.225-241, 1982.
[48] Yang, T. and Chua, L.O., “Control of chaos using sampled-data feedback control”, Int. J. Bifurcation and Chaos, vol. 8, pp. 2433-2438, 1998.
[49] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems. Upper Saddle River, NJ: Prentice-Hall, 1989.