本論文針對含有直接傳輸項之未知線性系統提出新型的線性二次觀測器與追蹤器，本文利用觀測/卡爾曼濾波器鑑別方法計算出具有直接傳輸項之資料取樣線性模型的適當階數的線性觀測器。再根據此模型，開發出具有高增益特性及最佳化之線性二次型類比觀測型追蹤器，使之有效率的獲得高品質狀態估測以及追蹤軌跡。此外，在含有直接傳輸項之線性系統下，採用具有預估特性之數位重新設計方法將具有高增益類比觀測器與追蹤器轉換得到一低增益且可執行的數位觀測器與追蹤器。為了降低控制力來滿足輸入飽和限制的需要，提出修正型的線性二次式數位軌跡追蹤器。藉此控制力可以有效地被壓縮，而且不會損失原本良好的軌跡追蹤效果。

This thesis develops a new linear quadratic observer and tracker for the linear unknown system with a direct transmission term from input to output. The off-line observer/Kalman filter identification (OKID) method is used to determine the sampled-data linear model with a direct feedthrough term. Based on this model, a high-gain optimal linear quadratic analogue observer-based tracker are proposed, so that it can effectively induce a high quality performance on the state estimation and the trajectory tracking design. Besides, the prediction-based digital redesign method is utilized to obtain a relatively low-gain and implementable observer and digital tracker from the theoretically well-designed high-gain analogue observer and tracker for the linear system with a direct transmission term from input to output. To reduce the magnitude of control input, which is caused by the high-gain property to fit the requirement of the input constraint, the modified linear quadratic analogue tracker (LQAT) is proposed. Thus, the control input can be compressed effectively without losing the original high performance of tracking much.

[1] Chen, C. H., Tsai, J. S. H., Lin, M. J., Guo, S. M., and Shieh, L. S., “A novel linear quadratic obersver and tracker for the linear sampled-data regular system with a direct feedthrough term: digital redesign approach,” IMA Journal of Mathematical Control and Information. (Accept for publication)
[2] Guo, S. M., Shieh, L. S., Chen, G., and Lin, C. F., “Effective chaotic orbit tracker a prediction based digital redesign approach,” IEEE Transaction on Circuits and System-I, Fundamental Theory and Applications, vol. 47, pp. 1557-1570, 2000.
[3] Hu, T., Teel, A. R., and Zaccarian, L., “Anti-windup synthesis for linear control systems with input saturation: Achieving regional, nonlinear performance,” Automatica, vol. 44(2), pp. 512-519, 2008.
[4] Juang, J. N., Applied System Identification. New Jersey: Prentice-Hall, 1994.
[5] Kuo, B. C., Digital Control Systems, New York, 1980.
[6] Lin, P. H., A Modified NARMAX Model-based Self-tuner with Fault Tolerance for Unknown Nonlinear Stochastic Hybrid Systems with An Input-output Direct Feed-through Term and Input Constraint, Master Thesis, National Cheng Kung University, 2013.
[7] Mertzios, B. G., Christodoulou, M. A., Syrmos, B. L., and Lewis, F. L., “Direct controllability and observability time domain conditions of singular systems,” IEEE Transactions Automatic Control, vol. 33, pp. 788-791, 1988.
[8] Shieh, L. S., Zho, X. M., and Zhang, J. L., “Locally optimal-digital redesign of continuous-time systems,” IEEE Transactions Automatic Control, vol. 36, pp. 511-515, 1989.
[9] Solmaz, S. K. and Faryar, J., “Modified anti-windup compensators for stable plants,” IEEE Transactions on Automatic Control, vol. 54, pp. 1934-1939, 2009.
[10] Tsai, J. S. H., Shieh, L. S., Zhang, J. L., and Coleman, N. P., “Digital redesign of pseudo continuous-time suboptimal regulators for large-scale discrete systems,” Control Theory Advance Technology, vol. 5, pp. 37-65, 1989.
[11] Tsai, J. S. H., Chien, T. H., Guo, S. M., Chang, Y. P., and Shieh, L. S., “State-space self-tuning control for stochastic fractional-order chaotic systems,” IEEE Transactions on Circuits and Systems I-Regular Papers, vol. 54, pp. 632-642, Mar. 2007.
[12] Tiwari, P. Y., Mulder, E. F., and Kothare, M. V., “Synthesis of stabilizing antiwindup controllers using piecewise quadratic Lyapunov functions,” IEEE Transactions on Automatic Control, vol. 52(12), pp. 2341-2345, 2007.
[13] Tsai, J. S. H., Du, Y. Y., Zhuang, W. Z., Guo, S. M., Chen, C. W., and Shieh, L. S., “Optimal anti-windup digital redesign of multi-input multi-output control systems under input constraints,” IET Control Theory Applications, vol. 5(3), pp. 447-464, 2011.
[14] Wu, F., and Lu, B., “Anti-windup control design for exponentially unstable LTI systems with actuator saturation,” Systems & Control Letters, vol. 52(4), pp. 305-322, 2004.
[15] Zaccarian, L., and Teel, A. R., “Nonlinear scheduled anti-windup design for linear systems,” IEEE Transactions on Automatic Control, vol. 49(11), pp. 2055-2061, 2004.