質量不確定之剛體六自由度運動非線性H∞強健控制研究與模擬

The Study and Simulation of Nonlinear H(subscript ∞) Robust Control for Six DOF Equations of Motion of Rigid Body with Mass Uncertainty

孔健君(Chien-Chun Kung)

《航空太空及民航學刊.系列B》 39卷2期 (2007/10) Pp. 53-60

https://doi.org/10.6124/JAAA.200710_39(2).01

摘要

本文嘗試推導在質量與慣性矩有不確定性的情形下，系統之非線性H(下標 ∞)強健控制器解析解。剛體六自由度運動被完整的考慮，並依平衡點的不同區分?非線性體軸速度角速度控制與非線性體軸速度姿態角控制兩種模式，進一步轉化?狀態空間表示式，以非線性H∞ 控制理論進行求解。理論上求解非線性H(下標 ∞)強健控制器的關鍵，在於該系統之Hamilton-Jacobi不等式的解，本文求得一具有不確定性質量與慣性矩之Lyapunov函數?其解，再利用質量與慣性矩不確定性之上界，可求出一狀態回授之非線性H(下標 ∞)強健控制器。模擬結果顯示，系統質量與慣性矩增加，將促使剛體六自由度運動逐漸不穩定；傳統的非線性H(下標 ∞)控制器無法保證系統強健穩定，而非線性H(下標 ∞)強健控制器不但可保證強健穩定，並有良好的性能。

關鍵字

非線性H(下標 ∞)強健控制 ； 系統不確定性 ； Hamilton-Jacobi不等式

並列摘要

In this paper, we derive the analytic solution of nonlinear H(subscript ∞) robust controller for a system with mass and moment inertia uncertainties. The complete six degree-of-freedom nonlinear equations of motion are considered directly to recast into the standard state-space form to apply the nonlinear H(subscript ∞) control theory. The nonlinear velocity and body-rate control mode and nonlinear velocity and attitude control mode are introduced by different trim conditions and the associated Hamilton-Jacobi partial differential inequality (HJPDI) is expressed. The key point to obtain the nonlinear H(subscript ∞) robust controller is the solution of HJPDI. A special Lyapunov function with mass and moment inertia uncertainties is introduced to solve the HJPDI. Numerical simulation is carried out and the results show that the system will be getting unstable with increasing mass and moment inertia and the nonlinear H(subscript ∞) robust controller occupies a more dominant position than the traditional nonlinear H(subscript ∞) controller.

並列關鍵字

Nonlinear H(subscript ∞) robust control ； Model uncertainty ； Hamilton-Jacobi partial differential inequality