二轴框架视线指向系统的凸优化反馈镇定

上海交通大学学报（自然版） ›› 2013, Vol. 47 ›› Issue (08): 1312-1318.

二轴框架视线指向系统的凸优化反馈镇定

詹世涛1，闫维新1，付庄1,2，潘根1，于锦江3，赵言正1

(1. 上海交通大学机械系统与振动国家重点实验室，上海 200240； 2. 哈尔滨工业大学机器人技术与系统重点实验室，哈尔滨 150001；3. 上海航天技术研究院控制所，上海 200233)

收稿日期:2012-08-12 出版日期:2013-08-29 发布日期:2013-08-29
基金资助:
国家自然科学基金(61075086),机械系统与振动国家重点实验室研究基金(MSVMS201003)资助项目

Feedback Stabilization of a Two-axis Gimbal System via Convex Optimization

ZHAN Shitao1,YAN Weixin1,FU Zhuang1,2,PAN Gen1,YU Jinjiang3,ZHAO Yanzheng1

(1. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai 200240, China; 2. State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China; 3. Institute of Control Engineering Shanghai Academy of Spaceflight Technology, Shanghai 200233, China)

Received:2012-08-12 Online:2013-08-29 Published:2013-08-29

摘要/Abstract

摘要：

以一类偏航-俯仰二自由度框架结构为研究对象，探讨执行元件存在输出饱和的条件下此类不确定系统的最优镇定问题.在框架动力学模型的基础上，分析了基座角运动、结构耦合和惯性不平衡力矩等干扰因素对系统动力学特性的影响.针对干扰条件下执行元件非线性饱和导致的稳定性问题，基于线性矩阵不等式组的凸优化方法，得到了镇定系统的状态反馈矩阵的最优值，为设计稳定的导引头回路控制系统提供了理论依据.仿真结果表明，最优反馈控制器对该类系统中的结构不确定性、饱和非线性和外界干扰力矩等因素具有较强的鲁棒性.

关键词: 框架平台, 状态反馈, 线性矩阵不等式组, 凸优化

Abstract:

This paper discussed the optimal feedback stabilization problem of a yaw-pitch gimbaled system with structure uncertainties, actuator saturation and disturbance torques in its control channels. The influence modes of platform angular motion, kinematics & geometrical coupling and unbalance moments on system dynamics were analyzed from the perspective of gimbal dynamics. Optimal feedback controllers were synthesized by means of Linear Matrix Inequalities (LMIs) and convex optimization to prevent the system from the instability caused by disturbance torques and actuator saturation. Simulation results prove the robustness of the derived optimal feedback controllers against system uncertainties, actuator saturation and disturbance torques.

Key words: gimbal system, state feedback, linear matrix inequalities （LMIs）, convex optimization

中图分类号:

TJ 76

詹世涛1，闫维新1，付庄1,2，潘根1，于锦江3，赵言正1. 二轴框架视线指向系统的凸优化反馈镇定[J]. 上海交通大学学报（自然版）, 2013, 47(08): 1312-1318.

ZHAN Shitao1,YAN Weixin1,FU Zhuang1,2,PAN Gen1,YU Jinjiang3,ZHAO Yanzheng1. Feedback Stabilization of a Two-axis Gimbal System via Convex Optimization[J]. Journal of Shanghai Jiaotong University, 2013, 47(08): 1312-1318.

参考文献

［1］Waldmann Jacques. Lineofsight rate estimation and linearizing control of an imaging seeker in a tactical missile guided by proportional navigation ［J］. IEEE Trans on Control Systems Technology, 2002, 10(4): 556567.

［2］Rue A K. Precision stabilization systems ［J］. IEEE Trans on Aerospace and Electronics Systems, 1974, 10(1): 3443.

［3］Kennedy P J, Kennedy R L. Direct versus indirect line of sight (LOS) stabilization ［J］. IEEE Trans on Control Systems Technology, 2003, 11(1): 315.

［4］Yu S, Zhao Y Z. A new measurement method for unbalanced moments in a twoaxis gimbaled seeks ［J］. Chinese Journal of Aeronautics, 2010,23(1): 117122.

［5］Yu S, Zhao Y Z. Simulation study on friction compensation method for inertial platform based on disturbance observer ［J］. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering March 1, 2008,222(3): 341346.

［6］Adegbege A A, Heath W P.Internal model control design for inputconstrained multivariable processes［J］.American Institute of Chemical Engineers, 2011,57(12): 34593472.

［7］Wang L K, Liu X D. Gain scheduled state feedback control for discretetimevarying polytopic systems subject to input saturation ［J］. Circuits System Signal Processing, 2011(30): 11651182.

［8］Adegbege A A, Heath W P. Twostage multivariable antiwindup design for internal model control constraints［C］//Proceedings of 9th International Symposium on Dynamics and Control of Process Systems. Leuven, Belgium： The International Federation of Automatic Control，2010: 276281.

［9］Zuo Z Q, Wang Y J. An improved set invariance analysis and gainscheduled control of LPV systems subject to actuator saturation［J］. Circuits System Signal Processing, 2007(26): 635649.

［10］Hu T S, Lin Z L, Chen B M. An analysis and design method for linear systems subject to actuator saturation and disturbance ［J］. Automatica,2002(38): 351359.

［11］Gahinet P, Apkarian P. A linear matrix inequality approach to H∞ control ［J］. Robust and Nonlinear Control, 1994(4): 421448.

［12］Zhang J H, Xia Y Q. New LMI approach to fuzzy H∞ filter designs ［J］. IEEE Transactions on Circuits and Systems II: Express Briefs, 2009, 56(9): 739743.

［13］Choi H C, Chwa D Y, Hong S K. An LMI approach to robust reducedorder H∞ filter design for polytopic uncertain systems ［J］. International Journal of Control, Automation and Systems, 2009, 7(3): 487494.

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