具積分器之離散型全程擬滑動模式控制於非線性四軸旋翼機系統之應用

Application of Discrete Global Quasi-Sliding Mode Control with Integrator to a Nonlinear Quadcopter System

楊峻崴(Chun-Wei Yang)

指導教授 ： 陳建祥

國立清華大學/工學院/動力機械工程學系/碩士(2019年)

摘要

本文主旨在於藉由滑動模式控制的強健特性，將四軸旋翼機發展為一個強健且靈敏的應用平台。對於非線性欠驅動的四軸旋翼機系統，在串聯軸向子系統與轉向子系統的控制結構下，已經有許多前人在滑動模式控制的應用做出貢獻。但是這些滑動模式控制法不是設計在連續時間上就是在迫近階段有強健性不足的問題。對此，一種針對線性系統的離散型全程擬滑動模式控制法激勵了本文將其應用到非線性欠驅動的四軸旋翼機系統上。首先，本文改寫了四軸旋翼機的系統動態模型以提出串接無驅動子系統到全驅動子系統的串級控制架構。接著，本文提出了一種針對非線性系統的具積分器之離散型全程擬滑動模式控制法，其包含強制函數、Gao型離散迫近律、廣義飽和函數與積分控制項。強制函數用於改善迫近階段的強健性不足；Gao型離散迫近律用於確保擬滑動模式存在並收斂；廣義飽和函數用於取代傳統切換函數以降低切換控制項造成的顫震；積分控制項用於降低飽和函數與結構不確定性造成的系統誤差。最後，本文將四軸旋翼機用於室內環境的即時定位與地圖構建，證明本文的控制法能夠將四軸旋翼機發展為一個強健且靈敏的應用平台。

關鍵字

四軸旋翼機 ； 欠驅動系統 ； 全程擬滑動模式控制 ； 穩態誤差 ； ARW積分器

並列摘要

The main purpose of this thesis is to develop a robust and agile quadcopter control system by applying the sliding mode control scheme. A lot of research had applied sliding mode control schemes to quadcopter system, which was underactuated and nonlinear, with a control structure that connected a rotational subsystem to a translational subsystem. However, those sliding mode control schemes were either designed for a continuous-time system or suffered a robustness reduction problem during the reaching phase. Here a discrete global quasi-sliding mode control scheme for a linear system was proposed to solve the problem, and this thesis had been motivated to make it feasible for a nonlinear underactuated quadcopter system. Therefore, we first proposed a cascaded control structure for the underactuated quadcopter system by simply rewrote the dynamics model of a quadcopter to a form that cascaded a non-actuated subsystem to a fully-actuated subsystem. Then, we proposed a new design method of discrete global quasi-sliding mode control for the nonlinear system, which was designed to consist of forcing function, Gao’s reaching law, generalized smooth saturation function and integral control term as well. The forcing function was adopted to alleviate the robustness reduction problem of the reaching phase. Gao’s reaching law was adopted to guarantee the existence and finite-time convergence of quasi-sliding mode. The generalized smooth saturation function, which substituted for conventional switching function, was adopted to reduce the chattering phenomenon caused by switching control term. The integral control term was adopted to reduce the steady-state error caused by saturation function and structure uncertainty. Finally, a quadcopter was applied to doing an indoor simultaneous localization and mapping to prove the performance of the control scheme proposed by this thesis.

並列關鍵字

quadcopter ； underactuated system ； global quasi-sliding mode control ； steady-state error ； ARW integrator

參考文獻

[1] L. Breguet, "Breguet-Richet Gyroplane", En.wikipedia.org. [Online]. Available: https://en.wikipedia.org/wiki/Breguet-Richet_Gyroplane. [Accessed: 15- Oct- 2018].

[2] E. Altug, J. Ostrowski, and R. Mahony, “Control of a quadrotor helicopter using visual feedback,” Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292), pp. 72–77, May 2002.

[3] T. Hamel, R. Mahony, R. Lozano and J. Ostrowski, "Dynamic Modelling and Configuration Stabilization for an X4-Flyer.", IFAC Proceedings Volumes, vol. 35, no. 1, pp. 217-222, 2002.

[4] S. Bouabdallah, P. Murrieri, and R. Siegwart, “Design and control of an indoor micro quadrotor,” IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA 04. 2004, pp. 4393–4398, 2004.

[5] M. Rich, Model development, system identification, and control of a quadrotor helicopter, thesis, Iowa State University Digital Repository, United States., 2012.