火箭发动机燃烧过程的鲁棒非脆弱H_∞控制
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摘要
针对某液体火箭发动机燃烧室的燃烧过程,设计了鲁棒非脆弱H_∞状态反馈控制器。首先,基于一种新型的时滞分割法和交互式凸组合技术,借助于构造一个包含四重积分项的Lyapunov-Krasovskii泛函(LKF),并利用新的积分不等式方法给出了LMI形式的时滞相关有界实判据;其次,在有界实判据的基础上,采用矩阵的合同变换以及变量替代技巧将燃烧过程非线性矩阵不等式线性化,通过求解线性矩阵不等式得到相应的非脆弱H_∞控制器的可行解。模拟结果验证了本文设计方法的有效性。
In this study we dealt with the robust non-fragile H_∞ controller for the combustion process in liquid propellant rocket motor chambers. In developing a less conservative H_∞ performance analysis criterion, we introduced a Lyapunov-Krasovskii functional comprising quadruple-integral term. Then, based on a new delay-partitioning method, the reciprocally convex combination technique and the integral inequality approach (ⅡA), we formulated the bounded real criterion in terms of linear matrix inequalities(LMIs). Furthermore, based on this bounded real criterion, we translated the nonlinear matrix inequality into the linear matrix inequality by using the matrix congruent transformation and the variable substitution technique, and obtained the parameter expression of non-fragile H_∞ controller by solving the feasible linear matrix inequality. The numerical examples we provided showed the effectiveness of the proposed theoretical results.
In this study we dealt with the robust non-fragile H_∞ controller for the combustion process in liquid propellant rocket motor chambers. In developing a less conservative H_∞ performance analysis criterion, we introduced a Lyapunov-Krasovskii functional comprising quadruple-integral term. Then, based on a new delay-partitioning method, the reciprocally convex combination technique and the integral inequality approach (ⅡA), we formulated the bounded real criterion in terms of linear matrix inequalities(LMIs). Furthermore, based on this bounded real criterion, we translated the nonlinear matrix inequality into the linear matrix inequality by using the matrix congruent transformation and the variable substitution technique, and obtained the parameter expression of non-fragile H_∞ controller by solving the feasible linear matrix inequality. The numerical examples we provided showed the effectiveness of the proposed theoretical results.
引文
[1]CROCCO L.Aspects of combustion stability in liquid propellant rocket motors,part I:fundamentals-low frequency instability with monopropellants[J].Journal of the American Rocket Society,1951,21(2):163-178.
[2]钱学森,宋健.工程控制论[M].北京:科学出版社,1980:343-365.
[3]ZHANG Jin,PENG Chen,ZHENG Min.Improved results for linear discrete-time systems with an interval time-varying input delay[J].International Journal of Systems Science,2015,47(2):492-499.
[4]ZHANG X M,HAN Q L.A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays[J].International Journal of Robust and Nonlinear Control,2009,19(17):1922-1930.
[5]LEE W I,PARK P G.Second-order reciprocally convex approach to stability of systems with interval time-varying delays[J].Applied Mathematics and Computation,2014,229(1):245-253.
[6]张合新,惠俊军,周鑫,等.基于时滞分割法的区间变时滞不确定系统鲁棒稳定新判据[J].控制与决策,2014,29(5):907-912.ZHANG Hexin,HUI Junjun,ZHOU Xin,et al.New robust stability criteria for uncertain systems with interval time-varying delay based on delay-partitioning approach[J].Control and Decision,2014,29(5):907-912.
[7]FARNAM A,REZA M E.Improved linear matrix inequality approach to stability analysis of linear systems with interval time-varying delays[J].Journal of Computational and Applied Mathematics,2016,294(1):49-56.
[8]聂万胜,丰松江.液体火箭发动机燃烧动力学模型与数值计算[M].北京:国防工业出版社,2011:25-31.
[9]李涛,张合新,孟飞.火箭发动机燃烧过程无记忆鲁棒镇定的积分不等式方法[J].宇航学报,2010,31(12):2788-2793.LI Tao,ZHANG Hexin,MENG Fei.Integral inequality approach to memoryless robust stabilization of combustion process in rocket motor[J].Journal of Astronautics,2010,31(12):2788-2793.
[10]惠俊军,张合新,周鑫,等.基于时滞分割方法的火箭发动机燃烧过程有记忆反馈控制[J].航空学报,2014,35(4):948-956.HUI Junjun,ZHANG Hexin,ZHOU Xin,et al.Delay-decomposition approach to memory state feedback controller for stabilization of combustion process in rocket motor[J].Acta Aeronautica ET Astronautica Sinica,2014,35(4):948-956.
[11]SHEN Yi,LIU Hao.Robust control system design for missiles based on theory of time-delay and uncertainty[J].Acta Aeronautica Astronautica Sinica,2011,32(3):473-479.
[12]XIAO L,SAN Y,ZHU Y.Delay-dependent robust stabilization by states feedback for linear systems with uncertainties[J].Systems Engineering and Electronics,2013,35(4):802-806.
[13]LIU P L.State feedback stabilization of time-varying delay uncertain systems:A delay decomposition approach[J].Linear Algebra and its Applications,2013,438(5):2188-2209.
[14]LI C F,WANG Z S,WANG Y J,et al.Robust H∞delay control for glide vehicles via LMI[J].Systems Engineering and Electronics,2011,33(9):2060-2065.
[15]SUN J,LIU G P,CHEN J.Delay-dependent stability and stabilization of neutral time-delay systems[J].International Journal of Robust and Nonlinear Control,2009,19(1):1364-1375.
[16]KEEL L H,BHATTACHARYYA S P.Robust,fragile,or optimal[J].IEEE trans on automatic control,1997,42(8):1098-1105.
[17]WU M,XIAO S P,ZHANG X M,et al.Non-fragile delay-dependent H∞control for linear neutral systems[J].Systems Engineering and Electronics,2008,30(9):1768-1773.
[18]ZHANG J H,SHI P,YANG H J.Non-fragile robust stabilization and H∞control for uncertain stochastic nonlinear time-delay systems[J].Chaos,Solitons Fractals,2009,42(5):3187-3196.
[19]HUI J J,ZHANG H X,KONG X Y.Delay-dependent non-fragile H∞control for linear systems with interval time-varying delay[J].International Journal of Automation and Computing,2015,12(1):109-116.
[20]RAMAKRISHNAN K,RAY G.Robust stability criteria for uncertain linear systems with interval time-varying delay[J].Journal of Control Theory and Applications,2011,9(4):559-566.
[21]KIM J H.Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays[J].International Journal of Control,Automation,and Systems,2009,7(3):357-364.
[2]钱学森,宋健.工程控制论[M].北京:科学出版社,1980:343-365.
[3]ZHANG Jin,PENG Chen,ZHENG Min.Improved results for linear discrete-time systems with an interval time-varying input delay[J].International Journal of Systems Science,2015,47(2):492-499.
[4]ZHANG X M,HAN Q L.A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays[J].International Journal of Robust and Nonlinear Control,2009,19(17):1922-1930.
[5]LEE W I,PARK P G.Second-order reciprocally convex approach to stability of systems with interval time-varying delays[J].Applied Mathematics and Computation,2014,229(1):245-253.
[6]张合新,惠俊军,周鑫,等.基于时滞分割法的区间变时滞不确定系统鲁棒稳定新判据[J].控制与决策,2014,29(5):907-912.ZHANG Hexin,HUI Junjun,ZHOU Xin,et al.New robust stability criteria for uncertain systems with interval time-varying delay based on delay-partitioning approach[J].Control and Decision,2014,29(5):907-912.
[7]FARNAM A,REZA M E.Improved linear matrix inequality approach to stability analysis of linear systems with interval time-varying delays[J].Journal of Computational and Applied Mathematics,2016,294(1):49-56.
[8]聂万胜,丰松江.液体火箭发动机燃烧动力学模型与数值计算[M].北京:国防工业出版社,2011:25-31.
[9]李涛,张合新,孟飞.火箭发动机燃烧过程无记忆鲁棒镇定的积分不等式方法[J].宇航学报,2010,31(12):2788-2793.LI Tao,ZHANG Hexin,MENG Fei.Integral inequality approach to memoryless robust stabilization of combustion process in rocket motor[J].Journal of Astronautics,2010,31(12):2788-2793.
[10]惠俊军,张合新,周鑫,等.基于时滞分割方法的火箭发动机燃烧过程有记忆反馈控制[J].航空学报,2014,35(4):948-956.HUI Junjun,ZHANG Hexin,ZHOU Xin,et al.Delay-decomposition approach to memory state feedback controller for stabilization of combustion process in rocket motor[J].Acta Aeronautica ET Astronautica Sinica,2014,35(4):948-956.
[11]SHEN Yi,LIU Hao.Robust control system design for missiles based on theory of time-delay and uncertainty[J].Acta Aeronautica Astronautica Sinica,2011,32(3):473-479.
[12]XIAO L,SAN Y,ZHU Y.Delay-dependent robust stabilization by states feedback for linear systems with uncertainties[J].Systems Engineering and Electronics,2013,35(4):802-806.
[13]LIU P L.State feedback stabilization of time-varying delay uncertain systems:A delay decomposition approach[J].Linear Algebra and its Applications,2013,438(5):2188-2209.
[14]LI C F,WANG Z S,WANG Y J,et al.Robust H∞delay control for glide vehicles via LMI[J].Systems Engineering and Electronics,2011,33(9):2060-2065.
[15]SUN J,LIU G P,CHEN J.Delay-dependent stability and stabilization of neutral time-delay systems[J].International Journal of Robust and Nonlinear Control,2009,19(1):1364-1375.
[16]KEEL L H,BHATTACHARYYA S P.Robust,fragile,or optimal[J].IEEE trans on automatic control,1997,42(8):1098-1105.
[17]WU M,XIAO S P,ZHANG X M,et al.Non-fragile delay-dependent H∞control for linear neutral systems[J].Systems Engineering and Electronics,2008,30(9):1768-1773.
[18]ZHANG J H,SHI P,YANG H J.Non-fragile robust stabilization and H∞control for uncertain stochastic nonlinear time-delay systems[J].Chaos,Solitons Fractals,2009,42(5):3187-3196.
[19]HUI J J,ZHANG H X,KONG X Y.Delay-dependent non-fragile H∞control for linear systems with interval time-varying delay[J].International Journal of Automation and Computing,2015,12(1):109-116.
[20]RAMAKRISHNAN K,RAY G.Robust stability criteria for uncertain linear systems with interval time-varying delay[J].Journal of Control Theory and Applications,2011,9(4):559-566.
[21]KIM J H.Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays[J].International Journal of Control,Automation,and Systems,2009,7(3):357-364.