H∞ Control using Tensor Product Model Transformation
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- 英文论文题名：H∞ Control using Tensor Product Model Transformation
- 论文作者：Zhen Chen ; Si Chen ; Xing Xin ; Zhen Li ; Zhuoyue Song ; Xiangdong Liu
- 英文论文作者：Zhen Chen ; Si Chen ; Xing Xin ; Zhen Li ; Zhuoyue Song ; Xiangdong Liu ; School of automation ; Beijing Institute of Technology
- 年：2017
- 作者机构：School of automation,Beijing Institute of Technology;
- 英文论文关键词：H∞ control ; tensor product(TP) ; linear matrix inequality ; integral sliding mode(ISM) control
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：344k
- 原文格式：D
- 会议级别：全国
摘要
In this paper a combined controller composed of the H∞ virtual controller and the sliding mode controller is proposed to improve the rigid spacecraft robustness. Considering the strong nonlinearity of the spacecraft dynamics, tensor product(TP)transformation is applied on the linear parameter varying(LPV) model which is obtained from the attitude kinematics system.The TP-based H∞ controller can be optimized by linear matrix inequality(LMI) tools off-line. Moreover, an integral sliding mode(ISM) attitude controller which enhances the robustness of the whole system is designed to track the output of the proposed H∞ virtual controller. The global stability of the nonlinear system can be guaranteed in large attitude maneuver with external disturbance and inertia uncertainties. Simulation results verified the effectiveness of the proposed algorithms.
In this paper a combined controller composed of the H_∞ virtual controller and the sliding mode controller is proposed to improve the rigid spacecraft robustness. Considering the strong nonlinearity of the spacecraft dynamics, tensor product(TP)transformation is applied on the linear parameter varying(LPV) model which is obtained from the attitude kinematics system.The TP-based H_∞ controller can be optimized by linear matrix inequality(LMI) tools off-line. Moreover, an integral sliding mode(ISM) attitude controller which enhances the robustness of the whole system is designed to track the output of the proposed H_∞ virtual controller. The global stability of the nonlinear system can be guaranteed in large attitude maneuver with external disturbance and inertia uncertainties. Simulation results verified the effectiveness of the proposed algorithms.
In this paper a combined controller composed of the H_∞ virtual controller and the sliding mode controller is proposed to improve the rigid spacecraft robustness. Considering the strong nonlinearity of the spacecraft dynamics, tensor product(TP)transformation is applied on the linear parameter varying(LPV) model which is obtained from the attitude kinematics system.The TP-based H_∞ controller can be optimized by linear matrix inequality(LMI) tools off-line. Moreover, an integral sliding mode(ISM) attitude controller which enhances the robustness of the whole system is designed to track the output of the proposed H_∞ virtual controller. The global stability of the nonlinear system can be guaranteed in large attitude maneuver with external disturbance and inertia uncertainties. Simulation results verified the effectiveness of the proposed algorithms.
引文
[1]X.Yang and Y.Jia,Adaptive nonlinear attitude tracking control for rigid spacecraft with input constraints,harmonic disturbances and parameter uncertainties,in Proceedings of the International Conference on Information and Automation,2015:2632-2637.
[2]C.Li,B.Jiang,Q.Zhu and C.Yu,Non-singular terminal sliding mode controller for spacecraft attitude stabilization,in Proceedings of the 34th Chinese Control Conference,2015:907-912.
[3]L.Show,J.Juang and C.Yang,Nonlinear H∞robust control for satellite large angle attitude maneuvers,in Proceedings of the,2011:1357-1362.
[4]H.Beikzadeh and H.D.Taghirad,Robust H∞filtering for nonlinear uncertain systems using state-dependent riccati equation technique,in Proceedings of the 48th IEEE Conference on Decision and Control,jointly with the 28th Chinese Control Conference(CCC),2009:4438-4445.
[5]M.Zhu and S.Xu,Stability-based SDRE controller for spacecraft momentum management,Acta Astronautica,89(8):71-82,2013.
[6]P.Baranyi,TP model transformation as a way to LMI-based controller design,IEEE Transactions on Industrial Electronics,51(2):387-400,2004.
[7]K.Tanaka and H.O.Wang,Fuzzy control systems design and analysis:a linear matrix inequality approach,John Wiley&Sons,2004.
[8]P.Baranyi,P.Korondi,R.J.Patton and H.Hashimoto,Tradeoff between approximation accuracy and complexity for TSfuzzy models,Asian Journal of control,6(1):21-33,2004.
[9]X.Liu,Y.Yu,Z.Li and H.H.Iu,Polytopic H∞filter design and relaxation for nonlinear systems via tensor product technique,Signal Processing,127:191-205,2016.
[10]X.Liu,X.Xin,Z.Li,and Z.Chen,Near Optimal Control based on Tensor-Product Technique,IEEE Transactions on Circuits and Systems II:Express Briefs,accepted.
[11].Ile,F.Koloni and J.Matuko,Linear matrix inequalities based H∞control of gantry crane using tensor product transformation,in Proceedings of the 18th International Conference on Process Control,2011.
[12]P.V′arkonyi,D.Tikk,P.Korondi and P.Baranyi,A new algorithm for RNO-INO type tensor product model representation,in Proceedings of the 2005 IEEE International Conference on Intelligent Engineering Systems,5:263-266,2005.
[13]Y.Yam,Fuzzy approximation via grid point sampling and singular value decomposition,IEEE Transactions on Systems,Man,and Cybernetics,Part B,27(6):933-951,1997.
[14]Z.Petres,Polytopic decomposition of linear parametervarying models by tensor-product model transformation,Ph.D.dissertation,2006.
[15]M.Ge,M.-S.Chiu,and Q.-G.Wang,Robust PID controller design via LMI approach,Journal of process control,12(1):3-13,2002.
[16]Y.Zhou and J.Zeng,Robust H∞dynamic output feedback controller design for a class of flexible spacecraft,in Proceedings of the 29th Chinses Control Conference(CCC),2010:1917-1922.
[17]S.Xu and T.Chen,An LMI approach to the H∞filter design for uncertain systems with distributed delays,IEEE Transactions on Circuits and Systems II:Express Briefs,51(4):195-201,2004.
[18]Z.Chen,B.Cong,X.Liu,Robust control of spacecraft eigenaxis maneuver via integral sliding mode,in Proceedings of the25th Chinese Control and Decision Conference,2013:1758-1763.
[19]B.Ding and C.Ding,Recurrence and La Salle invariance principle,Systems&Control Letters,93:64-68,2016.
[2]C.Li,B.Jiang,Q.Zhu and C.Yu,Non-singular terminal sliding mode controller for spacecraft attitude stabilization,in Proceedings of the 34th Chinese Control Conference,2015:907-912.
[3]L.Show,J.Juang and C.Yang,Nonlinear H∞robust control for satellite large angle attitude maneuvers,in Proceedings of the,2011:1357-1362.
[4]H.Beikzadeh and H.D.Taghirad,Robust H∞filtering for nonlinear uncertain systems using state-dependent riccati equation technique,in Proceedings of the 48th IEEE Conference on Decision and Control,jointly with the 28th Chinese Control Conference(CCC),2009:4438-4445.
[5]M.Zhu and S.Xu,Stability-based SDRE controller for spacecraft momentum management,Acta Astronautica,89(8):71-82,2013.
[6]P.Baranyi,TP model transformation as a way to LMI-based controller design,IEEE Transactions on Industrial Electronics,51(2):387-400,2004.
[7]K.Tanaka and H.O.Wang,Fuzzy control systems design and analysis:a linear matrix inequality approach,John Wiley&Sons,2004.
[8]P.Baranyi,P.Korondi,R.J.Patton and H.Hashimoto,Tradeoff between approximation accuracy and complexity for TSfuzzy models,Asian Journal of control,6(1):21-33,2004.
[9]X.Liu,Y.Yu,Z.Li and H.H.Iu,Polytopic H∞filter design and relaxation for nonlinear systems via tensor product technique,Signal Processing,127:191-205,2016.
[10]X.Liu,X.Xin,Z.Li,and Z.Chen,Near Optimal Control based on Tensor-Product Technique,IEEE Transactions on Circuits and Systems II:Express Briefs,accepted.
[11].Ile,F.Koloni and J.Matuko,Linear matrix inequalities based H∞control of gantry crane using tensor product transformation,in Proceedings of the 18th International Conference on Process Control,2011.
[12]P.V′arkonyi,D.Tikk,P.Korondi and P.Baranyi,A new algorithm for RNO-INO type tensor product model representation,in Proceedings of the 2005 IEEE International Conference on Intelligent Engineering Systems,5:263-266,2005.
[13]Y.Yam,Fuzzy approximation via grid point sampling and singular value decomposition,IEEE Transactions on Systems,Man,and Cybernetics,Part B,27(6):933-951,1997.
[14]Z.Petres,Polytopic decomposition of linear parametervarying models by tensor-product model transformation,Ph.D.dissertation,2006.
[15]M.Ge,M.-S.Chiu,and Q.-G.Wang,Robust PID controller design via LMI approach,Journal of process control,12(1):3-13,2002.
[16]Y.Zhou and J.Zeng,Robust H∞dynamic output feedback controller design for a class of flexible spacecraft,in Proceedings of the 29th Chinses Control Conference(CCC),2010:1917-1922.
[17]S.Xu and T.Chen,An LMI approach to the H∞filter design for uncertain systems with distributed delays,IEEE Transactions on Circuits and Systems II:Express Briefs,51(4):195-201,2004.
[18]Z.Chen,B.Cong,X.Liu,Robust control of spacecraft eigenaxis maneuver via integral sliding mode,in Proceedings of the25th Chinese Control and Decision Conference,2013:1758-1763.
[19]B.Ding and C.Ding,Recurrence and La Salle invariance principle,Systems&Control Letters,93:64-68,2016.