本論文藉由以比例積分微分濾波器為基底之頻率塑型的方法，提出一種用於具有未知輸入和輸出干擾的連續時間系統之廣義最佳線性二次類比追蹤器。論文主要包括一、適用於非方陣極小相位連續時間系統的最佳追蹤器設計以及補償系統已知擾動的方法，二、探討系統同時具有輸入和輸出干擾時的等效輸入干擾以及等效輸入干擾與輸出干擾之間的關係，三、採用線性函數觀測器設計的改良擾動估測方法。同時將以一些說明性的例題來驗證本論文所提出之追蹤器以及應用的有效性。

This thesis presents a PID filter-based generalized optimal linear quadratic analog tracker (LQAT) with unknown input and output disturbance for the continuous-time systems. This includes (i) An optimal PI tracker design for non-square minimum phase continuous-time systems with known disturbances and direct-feedthrough term. (ii) Estimation of the Equivalent input disturbance (EID) of the system with unknown input and the output disturbance and the relationship between EID and output disturbance. (iii) The linear functional observer-based input disturbance estimation method.

[1] Anderson, B.D.O. and Moore, J.B. (1989). Optimal Control: Linear Quadratic Methods. Prentice-Hall, New Jersey.
[2] Anderson, B.D.O. and Moore, J.B. (1971). Linear Optimal Control. Englewood Cliffs: Prentice-Hal.
[3] Benallouch, M., Outbib, R., Boutayeb, M., and Laroche, E. (2009). A new scheme on robust unknown input nonlinear observer for PEM fuel cell stack system. 18th IEEE International Conference on Control Applications, Saint Petersburg, Russia, 613–618.
[4] Chang, J. L. (2006). Applying discrete-time proportional integral observers for state and disturbance estimations. IEEE Transactions on Automatic Control, 51(5), 814-8186.
[5] Chen, M. S. and Chen, C. C. (2010). Unknown input observer for linear non-minimum phase systems. Journal of The Franklin Institute, 347, 577-588.
[6] 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.
[7] 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.
[8] Fernando, T., and Trinh, H. (2007). Design of reduced-order state/unknown input observers based on a descriptor system approach. Asian Journal of Control, 9, 458–465.
[9] Hieu, T. and Tyrone, F. (2011). Functional Observers for Dynamical Systems. Berlin: Springer.
[10] Hunt, L. R., Mayer, G., and Su, R. (1996). Noncausal inverses for linear systems. IEEE Transactions on Automatic Control, 41(4), 608-611.
[11] Luenberger, D. (1971). An introduction to observers. IEEE Transactions on Automatic Control, 16, 596–602.
[12] Radke, A. and Gao, Z. (2006). A survey of state and disturbance observers for practitioners. Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, USA, June 14-26, 2006.
[13] Rao, C. and Mitra, S. (1971). Generalized Inverse of Matrices and Its Applications.
NY: John Wiley and Sons.
[14] She, J. H., Fang, M., Ohyama, Y., Hashimoto, H., and Wu, M. (2008). Improving disturbance-rejection performance based on an equivalent-input-disturbance approach. IEEE Transactions on Industrial Electronics, 55(1), 380-389.
[15] Shieh, L. S., Dib, H. M., and Ganesan, S. (1987). Continuous-time quadratic regulators and pseudo-continuous-time quadratic regulators with pole placement in a specific region. IEE Proceedings Part D, 134, 338-346.
[16] Tang, D., Chen, L., and Hu, E. (2014). A novel unknown-input estimator for disturbance estimation and compensation. Proceedings of Australasian Conference on Robotics and Automation, 2-4 Dec 2014, The University of Melbourne, Melbourne, Australia.
[17] Termehchy, A. and Afshar, A. (2014). A novel design of unknown input observer for fault diagnosis in non-minimum phase systems. The International Federation of Automatic Control, Cape Town, South Africa. August 24-29, 2014.
[18] Ting, H. C., Chang, J. I., and Chen, Y. P. (2011). Proportional-derivative unknown input observer design using descriptor system approach for non-minimum phase systems. International Journal of Control, Automation, and Systems, 9(5), 850-856.