二維倒單擺非線性控制器設計

Abstract

本文以靜態Tustin摩擦力模型及干擾觀測器，補償台車和軌道間的摩擦力及外部干擾，以改善二維倒單擺系統的穩態誤差；其次依倒單擺的角度，分為三區，設計一個三階段的控制器，使倒單擺由靜止上甩並維持直立。 此三階段控制器分別為：(1)上甩，將倒單擺由靜止狀態( )甩入 的範圍內。 (2)倒單擺角度介於 ~ 時，以順滑模態控制器含回饋線性化，專注於倒單擺角度的直立性，此時不控制台車的位置，使倒單擺的最大操作角擴大2倍。 (3)倒單擺角度小於 時，同時控制倒單擺的角度及台車的位置，此階段分別為順滑模態控制器和 控制器，以穩定此單擺車系統。 實驗顯示，Tustin摩擦力模型及干擾觀測器補償前後，若第三區為順滑模態控制器，其穩態誤差改善超過6倍；而若第三區為 控制器，其穩態誤差改善超過4倍。 最後，以定性(實驗影片)和定量(實驗數據)兩種方式，呈現、歸納、及比較順滑模態控制器和 控制器的控制性能，也彰顯此三階段控制律含摩擦力及干擾觀測器補償架構的優越性及強健性。

This study presents the use of static Tustin friction model and a disturbance observer to compensate for frictional force between cart-rail and external disturbance so as to reduce the steady-state error (SSE) of a bi-axial inverted pendulum cart system (IPCS). Furthermore, a three-phase controller switching varied according to the angle of the pendulum is employed to swing-up and stabilize the IPCS. The three-phase controller contains: (1) a swing-up control to swing-up the pendulum angle from rest ( ) into ; (2) a sliding-mode with feedback linearization control for pendulum angle in the region of to double enlarge the maximum angle of operation, while the control of the position of the cart is temporarily ignored; (3) A sliding-mode control (SMC) and a control are employed in the region of to stabilize the IPCS, respectively. Experimental results reveal that the SSE of the IPCS is improved more than 6 times for SMC and 4 times for control. Finally, two methods, qualitative (experimental films) and quantitative (experimental data), are used to present, conclude and compare the control performances of SMC and control. The results also show the effectiveness and robustness of the proposed control schema.