輸入修正法可以有效降低系統因運動所引起的殘餘振動，特別適用於低阻尼的結構。其運作原理是針對一動態系統之輸入，依所需之目的作修正而分成數個分部輸入，以啟動破壞性干涉來消除系統主要振動模態，使系統之整體殘餘振動明顯地減少。
　　現存針對輸入修正法之研究，大多是針對單自由度或低自由度系統的探討，針對無限自由度之連續系統的研究並不多；本文即希望對此方向做更完整的論述。首先本文探討不同的輸入修正法在連續系統的適用性及其功效。在系統的選擇方面，我們分別以單一端固定之彈性棒及懸臂樑為系統來進行殘餘振動抑制效果之討論，並且探討末端負載對減振效能的影響。
　　根據我們得到的數值結果，輸入修正法對於動態連續系統的殘餘振動抑制確實有不錯的成效。此外，我們也提出一種附加配重的方法，可同時消去第一及第二主要模態之振動，以進一步減低殘餘振動。

　　Input shaping has been demonstrated to be an effective means for suppressing motion-induced residual vibration of lightly damped structures. In essence, for linear systems, input shaping simply means decomposing the input of a dynamical system into a series of properly calculated partial inputs, so as to annihilate the dominate vibration mode of the system through destructive interference. The overall residual vibration of the system can then be significantly reduced.
　　Existing research on input shaping schemes, however, is largely based on the simplified dynamical models having single or low degrees of freedom (DOFs). The purpose of this thesis is to discuss the design methodology of input shaping by considering continuous systems having infinite DOFs. First, we will discuss the efficiency and robustness of various input shaping schemes when they are applied to continuous system. Specifically, in this thesis we consider two different models of continuous systems─namely a fixed-free bar and a cantilever beam; in particular, the effects of system payload on the robustness of various input shaping schemes are discussed.
　　Our results indicate that it is effective to suppress the residual vibration of continuous dynamical systems by input shaping. Also, we propose a counterweight addition method for suppressing the first and second dominant vibration modes simultaneously, so that the residual vibration amplitude can be further reduced.

[1] Connor, J. J., Introduction to Structural Motion Control, Pearson Education, Inc. (2003).

[2] O. J. M. Smith, “Posicast control of damped oscillatory systems.”Proc. of the IRE, pp. 1249-1255, (1957).

[3] L. Y. Pao and M. A. Lau,“Robust input shaper control design for parameter variations in flexible structures.” ASME J. Dyn. Syst. Meas., Control 122, pp. 63-70, (2000).

[4] T.-C. Lin, “Design an input shaper to reduce operation-induced vibration.” In: Proceedings of the 1993 American Control Conference. Piscataway, NJ: Institute of Electrical and Electronics Engineers, pp. 2502~2505, (1993).

[5] N. C. Singer and W. P. Seering, “Design and comparison of command shaping methods for controlling residual vibration.” In: Proceedings of the IEEE International Conference on Robotics and Automation. Piscataway, NJ: Institute of Electrical and Electronics Engineers, pp. 888~893, (1989).

[6] N. C. Singer and W. P. Seering, “Preshaping Command Inputs to Reduce System Vibration,” J. of Dynamic Systems, Measurement, and Control, pp. 76-82, (1990)

[7] W. E. Singhose, Command Generation for Flexible Systems, Ph.D. thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, pp. 285, (1997).

[8] D.O. Popa, Byoung Hun Kang, J.T. Wen, H.E. Stephanou, G. Skidmore and A. Geisberger, “Dynamic modeling and input shaping of thermal bimorph MEMS actuators,” Proceedings: ICRA 2003 IEEE international Conference on Robotics and Automation, Vol. 1, no. 14-19, pp. 1470-1475, (Sept, 2003).

[9] P. F. van Kessel, L. J. Hornbeck, R. E. Meier and M. R. Douglass, MEMS-Based projection display. Proc. IEEE 86, pp. 1687-1704, (1998).

[10] W. E. Singhose, L. J. Porter, and W. P. Seering, “Input Shaped Control of a Planar Gantry Crane with Hoisting.” In: Proceedings of the 1997 American Control Conference. Albuquerque, NM.

[11] T.-S. Yang and W.-L. Liang, “Suppression of nonlinear forced waves by input shaping.” Wave Motion 37, pp. 101~117, (2003).

[12] S.-P. Su and T.-S. Yang, “Suppression of nonlinear forced waves by error-insensitive input shaping.” J. Chinese Soc. Mech. Eng. 23, pp. 507-516, (2002).

[13] T.-S Yang, K.-S. Chen and J.-F. Yin, “Design of input shapers for vibration control in Duffing nonlinear systems.” J. Sound and Vibration, submitted, (2004).

[14] 尹瑞豐，非線性輸入修正法之研究與其在機電系統減振上之應用，國立成功大學機械系碩士論文，(2004)。

[15] S. D. Senturia, “Microsystem Design,” Kluwer Academic Publication, (2000).

[16] P. Van Kessel, L. Hornbeck, R. Meier, M. Douglass, A MEMS-Based Projection Display, Proc. IEEE, Vol. 86, no. 8, pp. 1687-1704, (1998).

[17] T. R. Akylas and T.-S. Yang, “On Short-scale Oscillatory Tails of Long-wave Disturbances.” Stud. Appl. Maths, Vol. 94, pp. 1-20, (1995).

[18] K.-S. Chen, T.-S. Yang, J.-F. Yin, “Residual vibration suppression for Duffing nonlinear systems with electromagnetic actuation.” Precision Engineering, to appear (2004).

[19] 陳敬元，輸入修正法結合回授控制之研究與其在長距離移動之機電系統定位最佳化與減振之應用，國立成功大學機械系碩士論文，(2005)。

[20] 李佳昌，利用輸入修正手段抑制因連續系統運動而引起之殘餘振動之理論研究，國立成功大學機械系碩士論文，(2004)。

[21] T.-S. Yang, K.-S. Chen, C.-C. Lee and J.-F. Yin, “Suppression of motion induced residual vibration of cantilever beam by input shaping.” The 27th Conference on Theoretical and Applied Mechanics, Taiwan, (Dec. 2003)

[22] K.-S. Chen, J.-F. Yin, T.-S. Yang and K.-S. Ou, “Vibration suppression of a piezoelectrically driven cantilever beam by input shaping.” J. Chinese Society of Mechanical Engineers, vol. 25, no. 1, pp. 59-67, (Feb., 2004).

[23] T.-S. Yang, K.-S. Chen, C.-C. Lee and I. Hu, “Suppression of motion induced vibration of an elastic rod by input shaping.” The 28th national conference on theoretical and applied mechanics, Taiwan, (2004)

[24] 胡逸群、楊天祥、陳國聲，“以附加配重增進輸入修正法應用於連續結構時之減振效能.”中華民國第二十九屆全國力學會議，(2005)