有界扰动多变量Hammerstein系统输入到状态稳定模型预测控制
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摘要
考虑具有状态和控制约束的有界未知扰动多变量Hammerstein系统,提出一种具有输入到状态稳定和有限L_2增益性能的鲁棒非线性模型预测控制策略.基于多变量线性子系统H_∞控制律,滚动预测非线性代数方程的解算误差,继而在线优化计算满足系统约束条件的预测控制量.利用输入到状态稳定性概念和L_2增益思想,建立闭环系统关于该扰动信号具有鲁棒稳定性和L_2增益的充分条件,使闭环系统不仅满足系统约束,而且对不确定扰动输入和解算误差具有鲁棒性.最后以工业聚丙烯多牌号切换过程控制为例,仿真验证本文算法的有效性.
A robust nonlinear model predictive control strategy, with guaranteed input-to-state stability and finite L_2-gain, is proposed for multi-variable Hammerstein systems subject to unknown but bounded disturbances and constraints on the state and control. Based on H_∞ control laws of the multi-variable linear subsystem of the Hammerstein model,the solution errors of the nonlinear algebra equation are predicted over a receding horizon. Then the predictive control actions are computed by online optimization. Using the concepts of input-to-state stability and L_2-gain, some sufficient conditions are established to guarantee the robust stability and L_2-gain properties of the closed-loop system with respect to the disturbance signal. This implies that the closed-loop system not only satisfies the constraints but also has robustness with respect to the disturbance input and the solution errors. Finally, the example of industrial polypropylene multi-grade transition control is used to illustrate the effectiveness of the strategy presented here.
A robust nonlinear model predictive control strategy, with guaranteed input-to-state stability and finite L_2-gain, is proposed for multi-variable Hammerstein systems subject to unknown but bounded disturbances and constraints on the state and control. Based on H_∞ control laws of the multi-variable linear subsystem of the Hammerstein model,the solution errors of the nonlinear algebra equation are predicted over a receding horizon. Then the predictive control actions are computed by online optimization. Using the concepts of input-to-state stability and L_2-gain, some sufficient conditions are established to guarantee the robust stability and L_2-gain properties of the closed-loop system with respect to the disturbance signal. This implies that the closed-loop system not only satisfies the constraints but also has robustness with respect to the disturbance input and the solution errors. Finally, the example of industrial polypropylene multi-grade transition control is used to illustrate the effectiveness of the strategy presented here.
引文
[1]BHANDARI N,ROLLINS D.Continuous-time Hammerstein nonlinear modeling applied to distillation.AIChE Journal,2004,50(2):530-533.
[2]LAWRYNCZUK M.Nonlinear predictive control of dynamic systems represented by winer-hammerstein models.Nonlinear Dynamics,2016,86(2):1193-1214.
[3]HE Defeng,ZOU Tao,YU Li.Receding horizon control of grade transition of large-scale polypropylene production plants.CIESCJournal,2010,61(2):405-412.(何德峰,邹涛,俞立.大型聚丙烯生产装置牌号切换滚动时域控制.化工学报,2010,61(2):405-412.)
[4]FENG Shaohui,QIAN Feng.The application of model prediction control based on Hammerstein model in Chemical Process.Automation in Petro-Chemical Industry,2004(3):25-27.(冯少辉,钱锋.基于Hammerstein模型的预测控制在化工过程中的应用.石油化工自动化,2004(3):25-27.)
[5]KHANI F,HAERI M.Robust model predictive control of nonlinear processes represented by wiener or Hammerstein models.Chemical Engineering Science,2015,129:223-231.
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[8]DING B C,XI Y G,LI S Y.Stability analysis on predictive control of discrete-time systems with input nonlinearity.Acta Automatica Sinica,2003,29(6):827-834.
[9]XU Xiangyuan,MAO Zongyuan.The analysis and reseaerch of predictive control based on Hammerstein model.Control Theory&Applications,2000,17(4):529-532.(徐湘元,毛宗源.基于Hammerstein模型的预测控制的分析与研究.控制理论与应用,2000,17(4):529-532.)
[10]DING BC,PING XB.Dynamic output feedback model predictive control for nonlinear systems represented by Hammerstein-Wiener model.Journal of Process Control,2012,22(9):1773-1784.
[11]DING Baocang,LI Shaoyuan.Design and analysis of Hammerstein nonlinear control systems with constraints.Control and Decision,2003,18(1):24-28.(丁宝苍,李少远.具有约束的Hammerstein非线性控制系统的设计与分析.控制与决策,2003,18(1):24-28.)
[12]DING B C,XI Y G.A two-step model predictive control of Hammerstein model.International Journal of Robust and Nonlinear Control,2006,16(7):353-367.
[13]NIU Yongxiao,DING Baocang,SUN Hexu.Robust stability of twostep predictive control for systems with input nonlinearitis.Control and Decision,2006,21(4):457-462.(牛永肖,丁宝苍,孙鹤旭.输入非线性系统的两步法预测控制的鲁棒稳定性.控制与决策,2006,21(4):457-462.)
[14]ZHANG H T,LI H X,CHEN G R.Dual-model predictive control algorithm for constrained Hammerstein systems.International Journal of Control,2008,81(10):1609-1625.
[15]LI Yan,MAO Zhizhong,WANG Yan,et al.Predictive control of Hammerstein-Wiener nonlinearity based on polytopic terminal region.Acta Automatica Sinica,2011,37(5):629-638.(李妍,毛志忠,王琰,等.基于多面体终端域的Hammerstein-Wiener非线性预测控制.自动化学报,2011,37(5):629-638.)
[16]HE Defeng,YU Li.Nonlinear predictive control of constrained Hammerstein systems and its research on simulation of polypropylene grade transition.Acta Automatica Sinica,2009,35(12):1558-1563.(何德峰,俞立.约束Hammerstein系统非线性预测控制及在聚丙烯牌号切换中的仿真研究.自动化学报,2009,35(12):1558-1563.)
[17]XI Yugeng,LI Dewei.Fundamental philosophy and status of qualitative synthesis of model predictive control.Acta Automatica Sinica,2008,34(10):1225-1234.(席裕庚,李德伟.预测控制定性综合理论的基本思路和研究现状.自动化学报,2008,34(10):1225-1234.)
[18]KHALIL HK.Nonlinear Systems[M].3rd Edition.New York:Prentice Hall,2002.
[19]MAGNI L,RAIMONDO DM,SCATTOLINI R.Regional input-tostate stability for nonlinear model predictive control.Regional Inputto-State Stability for Nonlinear Model Predictive Control,2006,51(9):1548-1553.
[20]LAZAR M,PENA D M,HEEMELS WPMH,et al.On input-to-state stability of min-max nonlinear model predictive control.Systems&Control Letter,2008,57(1):39-48.
[21]HE Defeng,JI Haibo,ZHENG Tao.Nonlinear H∞robust predictive control with bounded persistent disturbances.Acta Automatica Sinica,2008,34(2):215-219.(何德峰,季海波,郑涛.持续有界扰动下的非线性H∞鲁棒预测控制.自动化学报,2008,34(2):215-219.)
[22]HE Defeng,DING Baocang,YU Shuyou.Review of fundamental properties and topics of model predictive control for nonlinear systems.Control Theory&Applications,2013,30(3):274-288.(何德峰,丁宝苍,于树友.非线性系统模型预测控制若干基本特点与主题回顾.控制理论与应用,2013,30(3):274-288.)
[23]LIN W,BYRNES CI.H∞Control of discrete-time nonlinear systems.IEEE Transactions on Automatic Control,1996,41(4):494-510.
[24]RICHARDS J R,CONGALIDIS J P.Measurement and control of polymerization reactors.Computers and Chemical Engineering,,2006,30(10/12):1447-1463.
[2]LAWRYNCZUK M.Nonlinear predictive control of dynamic systems represented by winer-hammerstein models.Nonlinear Dynamics,2016,86(2):1193-1214.
[3]HE Defeng,ZOU Tao,YU Li.Receding horizon control of grade transition of large-scale polypropylene production plants.CIESCJournal,2010,61(2):405-412.(何德峰,邹涛,俞立.大型聚丙烯生产装置牌号切换滚动时域控制.化工学报,2010,61(2):405-412.)
[4]FENG Shaohui,QIAN Feng.The application of model prediction control based on Hammerstein model in Chemical Process.Automation in Petro-Chemical Industry,2004(3):25-27.(冯少辉,钱锋.基于Hammerstein模型的预测控制在化工过程中的应用.石油化工自动化,2004(3):25-27.)
[5]KHANI F,HAERI M.Robust model predictive control of nonlinear processes represented by wiener or Hammerstein models.Chemical Engineering Science,2015,129:223-231.
[6]BLOEMEN H H J,BOOM T J J V,VERBRUGGEN H B.Modelbased predictive control for Hammerstein-wiener systems.International Journal of Control,2001,74(5):482-495.
[7]ZHU X F,SEBORG D E.Nonlinear predictive control based on Hammerstein models.Control Theory&Applications,1994,11(5):564-575.
[8]DING B C,XI Y G,LI S Y.Stability analysis on predictive control of discrete-time systems with input nonlinearity.Acta Automatica Sinica,2003,29(6):827-834.
[9]XU Xiangyuan,MAO Zongyuan.The analysis and reseaerch of predictive control based on Hammerstein model.Control Theory&Applications,2000,17(4):529-532.(徐湘元,毛宗源.基于Hammerstein模型的预测控制的分析与研究.控制理论与应用,2000,17(4):529-532.)
[10]DING BC,PING XB.Dynamic output feedback model predictive control for nonlinear systems represented by Hammerstein-Wiener model.Journal of Process Control,2012,22(9):1773-1784.
[11]DING Baocang,LI Shaoyuan.Design and analysis of Hammerstein nonlinear control systems with constraints.Control and Decision,2003,18(1):24-28.(丁宝苍,李少远.具有约束的Hammerstein非线性控制系统的设计与分析.控制与决策,2003,18(1):24-28.)
[12]DING B C,XI Y G.A two-step model predictive control of Hammerstein model.International Journal of Robust and Nonlinear Control,2006,16(7):353-367.
[13]NIU Yongxiao,DING Baocang,SUN Hexu.Robust stability of twostep predictive control for systems with input nonlinearitis.Control and Decision,2006,21(4):457-462.(牛永肖,丁宝苍,孙鹤旭.输入非线性系统的两步法预测控制的鲁棒稳定性.控制与决策,2006,21(4):457-462.)
[14]ZHANG H T,LI H X,CHEN G R.Dual-model predictive control algorithm for constrained Hammerstein systems.International Journal of Control,2008,81(10):1609-1625.
[15]LI Yan,MAO Zhizhong,WANG Yan,et al.Predictive control of Hammerstein-Wiener nonlinearity based on polytopic terminal region.Acta Automatica Sinica,2011,37(5):629-638.(李妍,毛志忠,王琰,等.基于多面体终端域的Hammerstein-Wiener非线性预测控制.自动化学报,2011,37(5):629-638.)
[16]HE Defeng,YU Li.Nonlinear predictive control of constrained Hammerstein systems and its research on simulation of polypropylene grade transition.Acta Automatica Sinica,2009,35(12):1558-1563.(何德峰,俞立.约束Hammerstein系统非线性预测控制及在聚丙烯牌号切换中的仿真研究.自动化学报,2009,35(12):1558-1563.)
[17]XI Yugeng,LI Dewei.Fundamental philosophy and status of qualitative synthesis of model predictive control.Acta Automatica Sinica,2008,34(10):1225-1234.(席裕庚,李德伟.预测控制定性综合理论的基本思路和研究现状.自动化学报,2008,34(10):1225-1234.)
[18]KHALIL HK.Nonlinear Systems[M].3rd Edition.New York:Prentice Hall,2002.
[19]MAGNI L,RAIMONDO DM,SCATTOLINI R.Regional input-tostate stability for nonlinear model predictive control.Regional Inputto-State Stability for Nonlinear Model Predictive Control,2006,51(9):1548-1553.
[20]LAZAR M,PENA D M,HEEMELS WPMH,et al.On input-to-state stability of min-max nonlinear model predictive control.Systems&Control Letter,2008,57(1):39-48.
[21]HE Defeng,JI Haibo,ZHENG Tao.Nonlinear H∞robust predictive control with bounded persistent disturbances.Acta Automatica Sinica,2008,34(2):215-219.(何德峰,季海波,郑涛.持续有界扰动下的非线性H∞鲁棒预测控制.自动化学报,2008,34(2):215-219.)
[22]HE Defeng,DING Baocang,YU Shuyou.Review of fundamental properties and topics of model predictive control for nonlinear systems.Control Theory&Applications,2013,30(3):274-288.(何德峰,丁宝苍,于树友.非线性系统模型预测控制若干基本特点与主题回顾.控制理论与应用,2013,30(3):274-288.)
[23]LIN W,BYRNES CI.H∞Control of discrete-time nonlinear systems.IEEE Transactions on Automatic Control,1996,41(4):494-510.
[24]RICHARDS J R,CONGALIDIS J P.Measurement and control of polymerization reactors.Computers and Chemical Engineering,,2006,30(10/12):1447-1463.