本論文提出適用於有著未知干擾的方陣非極小相位彈性臂系統之強健數位追蹤器設計。主題包含了基於觀測/卡爾曼濾波器方法之具挑戰性的一軸以及多軸非極小相位彈性臂系統建模，暨針對未知雜訊之未知方陣系統，提出整合了具有著等效未知雜訊估測所建構的強健追蹤器。設計步驟過程中，本論文提出了零點配置之模型追蹤設計方法論。最後以數值範例說明所提出設計方法的優越性。

A robust digital tracker design for unknown square non-minimum phase (NMP) flexible systems with disturbances have been proposed in this thesis. This includes the observer/Kalman filter method-based modellings of the challenging one-link and multi-link non-minimum phase flexible arm systems and the state estimator integrated with the equivalent-input-disturbance (EID) estimate robust tracker for the unknown square systems with unknown disturbances. During the design procedures, a zero-assignment reference model is also proposed in this thesis for the model following design methodology. Numerical examples are given to demonstrate the superiority of the proposed design.

[1] Aoustin, Y., Chevallereau, C. and Glumineau, A. (2006). Experimental results for the end-effector control of a single flexible robotic arm. IEEE Transactions on Control Systems Technology, 2(4), 371-381.
[2] Cannon, R.H., and Schmitz, E. (1984). Initial experiments on the end-point control of a flexible one-link robot. International Journal of Robotics Research, 3(3), 62-75.
[3] Chang, J.L. (2006). Applying discrete-time proportional integral observers for state and disturbance estimations. IEEE Transactions on Automatic Control, 51(5), 814-818.
[4] Chang, J.L., Ting, H.C., and Chen, Y.P. (2008). Robust discrete-time output tracking controller design for non-minimum phase systems. Journal of System Design and Dynamics, 2(4), 950-961.
[5] Chen, B.S., and Yang, T.Y. (1993). Robust optimal model matching control design for flexible manipulators. Journal of Dynamic Systems, Measurement, and Control, 115(1), 173-178.
[6] Chen, M.S., and Chen, C.C. (2010). Unknown input observer for linear non-minimum phase systems. Journal of the Franklin Institute, 347(2), 577-588.
[7] Davison, E.J., and Wang, S.H. (1975). On pole assignment in linear multivariable systems using output feedback. IEEE Transactions on Automatic Control, 20(4), 516-518.
[8] Davison, E.J., and Wonham, W.M. (1968). On pole assignment in multivariable linear systems. IEEE Transactions on Automatic Control, 13(6), 747-749.
[9] Davison, E.J. (1970). On pole assignment in linear systems with incomplete sate feedback. IEEE Transactions on Automatic Control, 15(3), 348-351.
[10] Davison, E.J., and Chatterjee, R. (1971). A note on pole assignment in linear systems with incomplete sate feedback. IEEE Transactions on Automatic Control, 16(1), 98-99.
[11] Ding, F., and Chen, T. (2005). Gradient based iterative algorithms for solving a class of matrix equation. IEEE Transactions on Automatic Control, 50(8), 216-221.
[12] Ebrahimzadeh, F., Tsai, J.S.H., Liao, Y.T., Chung, M.C., Guo, S.M., Shieh, L.S., and Wang, L. (2017). A generalized optimal linear quadratic tracker with universal applications－Part 1: Continuous-time systems. International Journal of Systems Science, 48(2), 376-396.
[13] Ebrahimzadeh, F. Tsai, J.S.H., Chung, M.C., Liao, Y.T., Guo, S.M., Shieh, L.S., and Wang, L. (2017). A generalized optimal linear quadratic tracker with universal applications－Part 2: Discrete-time systems. International Journal of Systems Science, 48(2), 397-416.
[14] Ebrahimzadeh, F. Tsai, J.S.H., and Lin Y.Y. (2017). An efficient robust servo design for non-minimum phase discrete-time systems with unknown matched/mismatched input disturbances. Automation, Control and Intelligent Systems, 5(2), 14-28.
[15] Fallside, F., and Seraji, H. (1971). Pole-shifting procedure for multivariable systems using output feedback. Electrical Engineers, Proceedings of the Institution, 118(11), 1648-1654.
[16] Juang, J.N. (1994) Applied System Identification. Prentice-Hall, Englewood Cliffs.
[17] Kimura, H., (1975). Pole assignment by gain output feedback. IEEE Transactions on Automatic Control, 20(4), 509-516.
[18] Mertzios, B.G., Christodoulou, M.A., Syrmos, B.L., and Lewis, F.L. (1988). Direct controllability and observability time domain conditions of singular systems. IEEE Transactions Automatic Control, 33(8), 788-791.
[19] Miminis, G.S., and Paige, C.C. (1982). An algorithm for pole assignment of time-invariant linear systems. International Journal of Control, 35(2), 341-354.
[20] Popescu, D., Sendrescu, D., and Bobasu, E. (2008). Modelling and robust control of a flexible beam Quanser experiment. Acta Montanistica Slovaca, 13(1), 127-135.
[21] Talebi H.A, Patel R.V., and Khorasani K. (2001). Control of Flexible-Link Manipulators Using Neural Networks. Springer, London.
[22] Tsai, J.S.H., Chien, T.H., Guo, S.M., Chang, Y.P., and Shieh, L.S. (2007). State-space self-tuning control for stochastic fractional-order chaotic systems. IEEE Transactions on Circuits and Systems I-Regular Papers, 54(3), 632-642.
[23] Smagina, Ye. M. (2002). “Zero assignment in multivariable system using pole assignment method,” [Online]. Available: http://arxiv.org/abs/math/0207094.