Nonlinear and Adaptive Control Design for the Translational Oscillator with Rotating Actuator System

[[abstract]]平移式震盪滑車(TORA)系統是改良來自航空器上的一個平衡裝置，後來在學術上獲得廣泛的研究與討論。在本論文中，將對平移式震盪滑車系統的控制進行相關的設計，並採用非線性與適應性遞迴步階控制設計方法來控制平移式震盪滑車系統，而我們主要的控制目標，不僅要令滑車回到原點並且要維持旋轉軸回到原始的位置也就是角度為零。 由於直接對原始系統利用遞迴步階控制設計，有一定程度上的複雜與困難。所以我們先對系統做線性化的動作，並且對其做分析與控制器的設計，經過幾次的設計失敗，最後我們成功的設計出控制器，再來我們將此設計概念套入非線性系統做設計，最後成功的設計出非線性控制器，並達到我們所要求的目標。接下來，我們加入適應性控制以克服未知的干擾與當系統有參數未知的情形，而控制結果一樣能夠達成我們的控制目標，且由模擬驗證得知當系統有未知的干擾與參數未知時，有加適應性控制會有比較好的控制效果。[[abstract]]The problem of the translational oscillator with rotating actuator (TORA) system has been widely discussed and investigated. The TORA system was developed as a simplified model of a dual-spin spacecraft. In this thesis, the nonlinear and adaptive controllers based on backstepping design schemes are developed for the manipulation of the TORA system. The main control objective here is not only to return the cart to the origin, but also to drive the rotating proof mass back to its starting point. In the procedure of nonlinear backstepping design, the direct analysis of this nonlinear system is complex and difficult for control design. In order to analyze and realize the system properties of the TORA system, in the beginning, the linearized system model is studied and investigated. Furthermore, according to the information obtained from the design of the linearized system, the nonlinear backstepping controllers can be successfully developed to achieve our control objectives for the original system. In addition, the zero dynamics would be investigated to guarantee the stability of the closed-loop system. Next, an adaptive backstepping design scheme is proposed to cope with the unknown spring coefficient and disturbance for the control of this TORA system. With backstepping design schemes, our proposed nonlinear and adaptive controllers are not only to achieve control objectives, but also to possess system robustness. Finally, some simulation results are given to illustrate the excellent performance of the proposed controllers applied to the TORA system.[[note]]碩