基于ADMM算法的航空发动机模型预测控制
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摘要
为了提升航空发动机非线性模型预测控制(MPC)的实时性,将交替方向乘子法(ADMM)应用于模型预测控制的滚动优化中。基于状态空间模型构造预测方程,通过引入辅助变量和对偶变量,将二次型性能指标和发动机约束改写为适合ADMM算法求解的形式。在航空发动机部件级模型上开展的仿真结果表明,基于ADMM算法的单变量模型预测能够实现对指令信号的高性能跟踪和约束的有效管理。相比于内点法(IPM),ADMM算法在滚动优化过程中,在不同控制指令下,均具有更高的实时性,且在预测时域增加的情况下,计算耗时增加更少,验证了其在模型预测控制中应用的有效性。
In order to improve the real time performance of the nonlinear model predictive control( MPC)for aero-engine,an alternating direction method of multipliers( ADMM) was applied to the receding horizon optimization of MPC. The predictive equation was constructed based on the state space model. The auxiliary variables and dual variables were introduced to rewrite the quadratic control performance index and engine constraints into a new form which could be solved by ADMM. Simulations on a component level model show that the single input variable model predictive control based on ADMM achieves both high-quality reference tracking performance and efficient limit management of aero-engine. Compared with interior point method( IPM),the real time performance of ADMM is much better than that of IPM at different magnitude control commands,and the increment of time consumption is much less than that of IPM with the increase of the predictive horizon. The effectiveness of the ADMM in MPC is valid.
In order to improve the real time performance of the nonlinear model predictive control( MPC)for aero-engine,an alternating direction method of multipliers( ADMM) was applied to the receding horizon optimization of MPC. The predictive equation was constructed based on the state space model. The auxiliary variables and dual variables were introduced to rewrite the quadratic control performance index and engine constraints into a new form which could be solved by ADMM. Simulations on a component level model show that the single input variable model predictive control based on ADMM achieves both high-quality reference tracking performance and efficient limit management of aero-engine. Compared with interior point method( IPM),the real time performance of ADMM is much better than that of IPM at different magnitude control commands,and the increment of time consumption is much less than that of IPM with the increase of the predictive horizon. The effectiveness of the ADMM in MPC is valid.
引文
[1]BRUNELL B J,BITMEAD R R,CONNOLLY A J.Nonlinear model predictive control of an aircraft gas turbine engine[C]∥41st IEEE Conference on Decision and Control.Piscataway,NJ:IEEE Press,2003,4:4649-4651.
[2]BRUNELL B J,VIASSOLO D E,PRASANTH R.Model adaptation and nonlinear model predictive control of an aircraft engine[C]∥ASME Turbo Expo 2004:Power for Land,Sea,and Air,2004:673-682.
[3]BRUNELL B J,MATHEWS H K,KUMAR A.Adaptive modelbased control systems and methods for controlling a gas turbine:US6823675[P].2004-11-30.
[4]RICHTER H,SINGARAJU A V,LITT J S.Multiplexed predictive control of a large commercial turbofan engine[J].Journal of Guidance,Control,and Dynamics,2008,31(2):273-281.
[5]VROEMEN B G,VAN ESSEN H A,VAN STEENHOVEN AA,et al.Nonlinear model predictive control of a laboratory gas turbine installation[J].Journal of Engineering for Gas Turbines and Power,1999,121(4):629-634.
[6]杜宪.滑模与预测控制在航空发动机限制管理中应用研究[D].西安:西北工业大学,2016.DU X.Application of sliding mode control and model predictive control to limit management for aero-engines[D].Xi’an:Northwestern Polytechnical University,2016(in Chinese).
[7]LAU M S K,YUE S P,LING K V,et al.A comparison of interior point and active set methods for FPGA implementation of model predictive control[C]∥European Control Conference.Piscataway,NJ:IEEE Press,2009:156-161.
[8]SHAHZAD A,KERRIGAN E C,CONSTANTINIDES G A.Awarm-start interior-point method for predictive control[C]∥UKACC International Conference on Control.London:IET,2010:949-954.
[9]ECKSTEIN J.Splitting methods for monotone operators with applications to parallel optimization[D].Cambridge:Massachusetts Institute of Technology,1989.
[10]BOYD S,PARIKH N,CHU E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations and Trends in Machine Learning,2011,3(1):1-122.
[11]ECKSTEIN J,WANG Y.Understanding the convergence of the alternating direction method of multipliers:Theoretical and computational perspectives[J].Pacific Journal of Optimization,2015,11(4):619-644.
[12]GHADIMI E,TEIXEIRA A,SHAMES I,et al.Optimal parameter selection for the alternating direction method of multipliers(ADMM):Quadratic problems[J].IEEE Transactions on Automatic Control,2015,60(3):644-658.
[13]王曦,党伟,李志鹏,等.1种N-dot过渡态PI控制律的设计方法[J].航空发动机,2015,41(6):1-5.WANG X,DANG W,LI Z P,et al.A design method of N-dot transient state PI control laws[J].Aeroengine,2015,41(6):1-5(in Chinese).
[14]JAW L C,MATTINGLY J D.Aircraft engine controls:Design,system analysis,and health monitoring[M].Reston:AIAA,2009:119-141.
[15]RICHTER H.A multi-regulator sliding mode control strategy for output-constrained systems[J].Automatica,2011,47(10):2251-2259.
[16]RICHTER H,LITT J.A novel controller for gas turbine engines with aggressive limit management[C]∥47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference&Exhibit.Reston:AIAA,2011:1-17.
[17]杜宪,郭迎清,孙浩,等.基于滑模控制的航空发动机多变量约束管理[J].航空学报,2016,37(12):3657-3667.DU X,GUO Y Q,SUN H,et al.Sliding mode control based multivariable limit management for aircraft engine[J].Acta Aeronautic et Astronautica Sinica,2016,37(12):3657-3667(in Chinese).
[18]RICHTER H.Multiple sliding modes with override logic:Limit management in aircraft engine controls[J].Journal of Guidance,Control,and Dynamics,2015,35(4):1132-1142.
[19]BERTSEKAS D P.Convex optimization algorithms[M].Nushua:Athena Scientific,2016:280-285.
[20]BOLEY D.Local linear convergence of the alternating direction method of multipliers on quadratic or linear programs[J].SIAMJournal on Optimization,2013,23(4):2183-2207.
[21]赵辉.基于平衡流形展开模型的航空发动机非线性控制方法研究[D].哈尔滨:哈尔滨工业大学,2011.ZHAO H.Research on nonlinear control for aeroengines based on equlibrium manifold expansion model[D].Harbin:Harbin Institute of Technology,2011(in Chinese).
[22]NOCEDAL J,WRIGHT J.Numerical optimization[M].Berlin:Springer,2006:481-485.
[2]BRUNELL B J,VIASSOLO D E,PRASANTH R.Model adaptation and nonlinear model predictive control of an aircraft engine[C]∥ASME Turbo Expo 2004:Power for Land,Sea,and Air,2004:673-682.
[3]BRUNELL B J,MATHEWS H K,KUMAR A.Adaptive modelbased control systems and methods for controlling a gas turbine:US6823675[P].2004-11-30.
[4]RICHTER H,SINGARAJU A V,LITT J S.Multiplexed predictive control of a large commercial turbofan engine[J].Journal of Guidance,Control,and Dynamics,2008,31(2):273-281.
[5]VROEMEN B G,VAN ESSEN H A,VAN STEENHOVEN AA,et al.Nonlinear model predictive control of a laboratory gas turbine installation[J].Journal of Engineering for Gas Turbines and Power,1999,121(4):629-634.
[6]杜宪.滑模与预测控制在航空发动机限制管理中应用研究[D].西安:西北工业大学,2016.DU X.Application of sliding mode control and model predictive control to limit management for aero-engines[D].Xi’an:Northwestern Polytechnical University,2016(in Chinese).
[7]LAU M S K,YUE S P,LING K V,et al.A comparison of interior point and active set methods for FPGA implementation of model predictive control[C]∥European Control Conference.Piscataway,NJ:IEEE Press,2009:156-161.
[8]SHAHZAD A,KERRIGAN E C,CONSTANTINIDES G A.Awarm-start interior-point method for predictive control[C]∥UKACC International Conference on Control.London:IET,2010:949-954.
[9]ECKSTEIN J.Splitting methods for monotone operators with applications to parallel optimization[D].Cambridge:Massachusetts Institute of Technology,1989.
[10]BOYD S,PARIKH N,CHU E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations and Trends in Machine Learning,2011,3(1):1-122.
[11]ECKSTEIN J,WANG Y.Understanding the convergence of the alternating direction method of multipliers:Theoretical and computational perspectives[J].Pacific Journal of Optimization,2015,11(4):619-644.
[12]GHADIMI E,TEIXEIRA A,SHAMES I,et al.Optimal parameter selection for the alternating direction method of multipliers(ADMM):Quadratic problems[J].IEEE Transactions on Automatic Control,2015,60(3):644-658.
[13]王曦,党伟,李志鹏,等.1种N-dot过渡态PI控制律的设计方法[J].航空发动机,2015,41(6):1-5.WANG X,DANG W,LI Z P,et al.A design method of N-dot transient state PI control laws[J].Aeroengine,2015,41(6):1-5(in Chinese).
[14]JAW L C,MATTINGLY J D.Aircraft engine controls:Design,system analysis,and health monitoring[M].Reston:AIAA,2009:119-141.
[15]RICHTER H.A multi-regulator sliding mode control strategy for output-constrained systems[J].Automatica,2011,47(10):2251-2259.
[16]RICHTER H,LITT J.A novel controller for gas turbine engines with aggressive limit management[C]∥47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference&Exhibit.Reston:AIAA,2011:1-17.
[17]杜宪,郭迎清,孙浩,等.基于滑模控制的航空发动机多变量约束管理[J].航空学报,2016,37(12):3657-3667.DU X,GUO Y Q,SUN H,et al.Sliding mode control based multivariable limit management for aircraft engine[J].Acta Aeronautic et Astronautica Sinica,2016,37(12):3657-3667(in Chinese).
[18]RICHTER H.Multiple sliding modes with override logic:Limit management in aircraft engine controls[J].Journal of Guidance,Control,and Dynamics,2015,35(4):1132-1142.
[19]BERTSEKAS D P.Convex optimization algorithms[M].Nushua:Athena Scientific,2016:280-285.
[20]BOLEY D.Local linear convergence of the alternating direction method of multipliers on quadratic or linear programs[J].SIAMJournal on Optimization,2013,23(4):2183-2207.
[21]赵辉.基于平衡流形展开模型的航空发动机非线性控制方法研究[D].哈尔滨:哈尔滨工业大学,2011.ZHAO H.Research on nonlinear control for aeroengines based on equlibrium manifold expansion model[D].Harbin:Harbin Institute of Technology,2011(in Chinese).
[22]NOCEDAL J,WRIGHT J.Numerical optimization[M].Berlin:Springer,2006:481-485.
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