Please wait a minute...
J4  2009, Vol. 43 Issue (11): 1945-1950    DOI: 10.3785/j.issn.1008-973X.2009.11.001
    
Grey-box modeling of small-scale unmanned helicopter based on Bayesian technique
FANG Zhou, LI Ping, HAN Bo, HOU Xin
(Institute of Industrial Process Control, Zhejiang University, Hangzhou 310027, China)
Download:   PDF(997KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

This work presented a synthesized method for identification and modeling of a small-scale unmanned helicopter in grey-box modeling framework. A nonlinear first principle model was simplified and divided into longitudinal and lateral motions using some reasonable assumptions, and then linearized around the hover point to get two parameterized models for both motion directions. The unknown parameters were explicitly expressed as prior uniform distributions on certain intervals. A Bayesian maximum A posteriori (MAP) estimation was formed and translated into a restricted nonlinear optimization problem, which was solved by a Lagrange multiplier method using a DFP-based quasi-Newton recursive algorithm. The identification procedures were done in discrete-time domain, and a “sinch” algorithm was applied to map the direct continuous-time domain parameterization problem into the discrete-time domain. This method effectively reduces the complexity and costs of identification experiments. The acquired continuous-time state-space model shows good prediction performance and is fit for controller design.



Published: 01 November 2009
CLC:  TP 27  
Cite this article:

FANG Zhou, LI Beng, HAN Bei, et al. Grey-box modeling of small-scale unmanned helicopter based on Bayesian technique. J4, 2009, 43(11): 1945-1950.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2009.11.001     OR     http://www.zjujournals.com/eng/Y2009/V43/I11/1945


基于Bayes技术的小型无人直升机灰箱建模

高精度的动态模型是实现小型无人直升机高性能自主飞行控制的基础.给出了在灰箱建模框架下辨识小型无人直升机动态模型的系统性方法.在合理的假设下,将非线性机理运动方程简化并进行横、纵向解耦,在悬停点附近线性化得到横、纵向的参数化状态空间模型,以区间均匀分布的方式合理表达了待辨识参数的先验分布.将辨识问题构造成Bayes的极大后验(MAP)估计问题,并进一步转化为约束非线性优化问题,采用拟牛顿法求解.辨识步骤在离散时域中进行,利用sinch算法将连续时域的状态空间参数化问题映射到离散域.提出的小型无人直升机灰箱建模方法有效减少了对辨识实验的要求,获得的对象连续域状态空间模型具有良好的预报精度,并适用于控制器的设计.

[1] GAVRILETS V. Autonomous aerobatic maneuvering of miniature helicopters [D]. Cambridge: Massachusetts Institute of Technology, 2003.
[2] METTLER B. Modeling small-scale unmanned rotorcraft for advanced flight control design [D]. Pittsburgh: Carnegie Mellon University, 2001.
[3] LACIVITA M. Integrated modeling and robust control for full-envelope flight of robotic helicopters [D]. Pittsburgh: Carnegie Mellon University, 2002.
[4] TULLEKEN H J A F. Grey-box modeling and identification using physical knowledge and Bayesian techniques [J]. IFAC Journal of Automatica, 1991, 29(2): 285-308.
[5] BOHLIN T, GRAEBE S F. Issues in nonlinear stochastic grey box identification [J]. International Journal of Adaptive Control and Signal Processing, 1995, 9(6): 465-490.
[6] SOHLBERG B. Grey box modeling for model predictive control of a heating process [J]. Journal of Process Control, 2002, 13(3): 225-238.
[7] KRISTENSEN N R, MADSEN H, JORGENSEN S B. Parameter estimation in stochastic grey-box models [J]. IFAC Journal of Automatica, 2003, 40(2): 225-237.
[8] PRESS S J.贝叶斯统计学:原理、模型及应用\[M\].廖文,陈安贵,译.北京:中国统计出版社,1992: 1-7.
[9] 张贤达.矩阵分析与应用[M]. 北京:清华大学出版社, 2004:55.
[10] WILSON D A, KUMAR A. Derivative computations for the log likelihood function [J]. IEEE Transactions on Automatic Control, 1982, 27: 230-232.
[11] NAJFELD I, HAVEL T F. Derivatives of the matrix exponential and their computation [J]. Advances in Applied Mathematics, 1995, 16(3): 321-375.
[12] LJUNG L. System identification: theory for the user [M]. 2nd ed. Upper Saddle River: Prentice Hall PTR, 1999: 412-414.

No related articles found!