本文介紹了一種新設計的火箭構型無人機 (Rocket-type unmanned aerial vehicle, Rocket-type UAV)，並設計姿態與高度控制系統。該火箭構型無人機由一個基於萬向環的同軸轉子系統 (gimbal-based coaxial rotor system, GCRS) 驅動，以實現推力與感應力矩的向量控制 (thrust vector control, TVC)。由於 GCRS 是操縱無人機方向的唯一致動器，這將是火箭構型無人機控制系統穩定的設計挑戰。近年來，隨著太空科技與產業的發展，可回收是火箭被廣泛討論與研究。利用向量推進的不穩定構型載具被討論。為了研究其物理行為與控制策略，火箭構型無人機可以作為前期研究，並用於討論可行性。為了解決火箭構型無人機的穩定性問題，此論文提出了詳細的飛行動力學方程式。結果表明，高度非線性的耦合控制輸入問題是主要的難關。因此，本研究提出了一種控制策略來進行追蹤控制。本文設計比例-積分-微分控制器 (Proportional-Integral-Derivative, PID) 控制演算法，並基于線性矩陣不等式 (linear matrix inequality, LMI) 保證控制系統的強健性與性能。針對 GCRS 系統產生的非線性控制輸入映射的問題，必須設計一種高效率與高可靠度的非線性方程解算的方法。文中比較梯度下降法 (Gradient Decent Method)、高斯牛頓法 (Gauss Newton Method) 與 Levenberg-Marquardt（LM）方法等三種最佳化演算法以解決非線性映射的問題。依據結果可知 LM 方法的強健性與效率遠高於另外兩種方法。結合控制律設計並利用 LM 方法求解致動器控制量。為了驗證火箭構型無人機的飛行特性並驗證結合最佳化問題的控制策略是否能在嵌入式系統中運行，本文提供了一些模擬結果與實作測試結果。在具有干擾與模型不確定性的情況下，控制策略與最佳化方法具有一定的強健性。控制演算法可以在要求的取樣時間內在 Teensy 4.0 上完成計算，根據模擬的結果控制律也可處理複雜軌跡並使追蹤誤差收斂。經由 LMI 可以確定控制增益保證的追蹤性能。實作結果清楚的表明這一結果。對於同軸雙槳馬達的建模則需要考慮更細緻的空氣動力學動態，使得螺旋槳的感應力矩能更好的平衡。而在另外兩個姿態角與高度上可以很好的保證穩定，最佳化演算法也可以對抗實作中馬達運作產生的噪訊。

This paper presents a newly designed rocket-type unmanned aerial vehicle (UAV) altitude and attitude control system. The rocket-type UAV is driven by a gimbal-based coaxial rotor system (GCRS) to realize the thrust vector control (TVC). Since the GCRS is the only actuating source to manipulate the orientation of the UAV, it causes a challenge on the rocket-type UAV stabilization.

To deal with the stabilization problem of the rocket-type UAV, the detailed derivations of the attitude flight dynamics is presented. The result shows that the main control difficulty comes from the highly nonlinear tightly coupled control distribution problem. Therefore, this study proposes a control strategy to track the desired attitude trajectory. First, a Proportional-Integral-Derivative (PID) control algorithm is designed based on the formulation of the linear matrix inequality (LMI) to guarantee the robust stability and performance of the control system. Second, due to the nonlinear coupled control input distribution, a nonlinear inverse mapping problem between the control law and real actuator outputs is formulated. To solve the nonlinear inverse mapping problem of the GCRS, an optimization algorithm applying Levenberg-Marquardt (LM) method is developed. Finally, to validate the flight properties of the rocket-type UAV and the performance of the proposed control algorithm, a couple of numerical simulations are conducted. The numerical results indicate that the tightly coupled control input nonlinear inverse problem can be solved successfully and the attitude stabilization in the presence of disturbance is well achieved accordingly.

The control strategy and optimization method are robust in the presence of external disturbances and model uncertainties. The control algorithm can be computed on Teensy 4.0 within the required sampling time. According to the simulation results, the control law can also handle complex trajectories and allow the tracking error to be reduced. The tracking performance is guaranteed by the control gain that can be determined by the LMI. The results of the implementation clearly demonstrated this point. For the modeling of a coaxial rotor motor system, a more detailed aerodynamic dynamics model needs to be considered, so that the induced torque of the propellers can be better balanced for the heading angle. The stability of the other two attitude angles and altitudes can be well ensured and the optimization algorithm can counteract the noise generated by the motor operation in practice.

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