基于Lyapunov稳定性的船舶航向保持控制器非线性反馈改进
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摘要
[目的]船舶航向保持是船舶自动导航的核心,其实现离不开非线性控制算法的设计。为了简化控制器的设计过程,提高系统鲁棒性,节省控制器的能量输出,提出一种基于Lyapunov函数改进的具有非线性反馈的控制器。[方法]首先,通过构建Lyapunov函数,简化控制器设计过程,避免非线性控制律对消系统的非线性项;然后,用指数函数处理后的航向误差代替航向误差本身的非线性反馈项,优化控制系统设计,减少能耗;最后,以实际船舶"育鹏"轮为例进行系统仿真。[结果]结果显示,采用上述方法设计的控制器控制效果良好,更加节能,且系统具有鲁棒性。[结论]研究表明,非线性反馈项的引入可以优化控制系统,其能节能的优点在实际工程应用中具有重要意义。
[Objectives] Course-keeping for ships is the core of automatic navigation in marine transportation, and it cannot be achieved without the design of the nonlinear controller. In order to simplify the design process, improve the robustness of the system and save the energy output of the controller, this paper proposes a nonlinear feedback controller based on the Lyapunov function. [Methods] By constructing a simplified Lyapunov function, the design process of the nonlinear controller is shortened and the cancellation of the nonlinear term of the control law avoided. The design of the control system can be optimized by replacing the course error with a nonlinear function of itself in the feedback loop. This optimization reduces energy consumption and improves the robustness of the system. [Results] Taking the ship 'Yu Peng' as an example,the simulation results show that the improved nonlinear control algorithm possesses good performance and robustness, and reduces energy consumption. [Conclusions] The results of this paper show that the introduction of a nonlinear feedback term can optimize the control system, and the energy saving advantages of such a measure are of great significance for practical engineering application.
[Objectives] Course-keeping for ships is the core of automatic navigation in marine transportation, and it cannot be achieved without the design of the nonlinear controller. In order to simplify the design process, improve the robustness of the system and save the energy output of the controller, this paper proposes a nonlinear feedback controller based on the Lyapunov function. [Methods] By constructing a simplified Lyapunov function, the design process of the nonlinear controller is shortened and the cancellation of the nonlinear term of the control law avoided. The design of the control system can be optimized by replacing the course error with a nonlinear function of itself in the feedback loop. This optimization reduces energy consumption and improves the robustness of the system. [Results] Taking the ship 'Yu Peng' as an example,the simulation results show that the improved nonlinear control algorithm possesses good performance and robustness, and reduces energy consumption. [Conclusions] The results of this paper show that the introduction of a nonlinear feedback term can optimize the control system, and the energy saving advantages of such a measure are of great significance for practical engineering application.
引文
[1]张显库.船舶运动简捷鲁棒控制[M].北京:科学出版社,2012:1-10.Zhang X K.Simple and robust control of ship motion[M].Beijing:Science Press,2012:1-10(in Chinese).
[2]张显库,郭晨,杜佳璐.船舶航向不对称信息理论与非线性逆推鲁棒控制算法[J].交通运输工程学报,2006,6(2):47-50.Zhang X K,Guo C,Du J L.Asymmetric information theory and nonlinear backstepping robust control algorithm of ship navigation[J].Journal of Traffic and Transportation Engineering,2006,6(2):47-50(in Chinese).
[3]Krstic M,Kanellakopoulos I,Kokotovic P V.Nonlinear and adaptive control design[M].New York:Wiley,1995:89-108.
[4]Do K D,Pan J.Global robust adaptive path following of underactuated ships[J].Automatica,2006,42(10):1713-1722.
[5]董文瀚,孙秀霞,林岩,等.一类直接模型参考Backstepping自适应控制[J].控制与决策,2008,23(9):981-986,993.Dong W H,Sun X X,Lin Y,et al.Direct model reference Backstepping adaptive control[J].Control and Decision,2008,23(9):981-986,993(in Chinese).
[6]郭源博,张晓华,陈宏钧.基于双线性系统理论的PWM整流器非线性控制[J].西南交通大学学报,2009,44(2):232-237.Guo Y B,Zhang X H,Chen H J.Nonlinear control of PWM rectifier based on bilinear system theory[J].Journal of Southwest Jiaotong University,2009,44(2):232-237(in Chinese).
[7]张显库.船舶航向保持的非线性逆推鲁棒控制算法[J].大连海事大学学报,2007,33(2):80-83.Zhang X K.Nonlinear backstepping robust control algorithm for ship's course-keeping[J].Journal of Dalian Maritime University,2007,33(2):80-83(in Chinese).
[8]张显库.基于Lyapunov稳定性的船舶航向保持非线性控制[J].西南交通大学学报,2010,45(1):140-143.Zhang X K.Nonlinear control for ship course-keeping based on Lyapunov stability[J].Journal of Southwest Jiao Tong University,2010,45(1):140-143(in Chinese).
[9]贾欣乐,张显库.船舶运动智能控制与H∞鲁棒控制[M].大连:大连海事大学出版社,2002:273-275.Jia X L,Zhang X K.Ship motion intelligent control and H∞robust control[M].Dalian:Dalian Maritime University Press,2002:273-275(in Chinese).
[10]马超,张显库.基于指数函数非线性反馈的船舶航向保持控制[J].船舶工程,2017,39(增刊1):162-165.Ma C,Zhang X K.Ship course keeping control based on nonlinear feedback of exponential function[J].Ship Engineering,2017,39(Supp 1):162-165(in Chinese).
[11]同济大学应用数学系.高等数学[M].北京:高等教学出版社,2005:215-220.Department of Applied Mathematics,Tongji University.Advanced mathematics[M].Beijing:Higher Education Press,2005:215-220(in Chinese).
[12]Deng H,Krsti C M.Stochastic nonlinear stabilization-I:a backstepping design[J].Systems&Control Letters,1997,32(3):143-150.
[13]贾欣乐,张显库.风力等效舵角及应用[J].中国造船,2015,56(3):116-123.Jia X L,Zhang X K.Equivalent rudder angle to wind force and its application[J].Shipbuilding of China,2015,56(3):116-123(in Chinese).
[14]涂武.船舶航向最优控制与仿真研究[D].哈尔滨:哈尔滨工程大学,2008.Tu W.Research of optimal control of ship heading and using Simulink for simulation[D].Harbin:Harbin Engineering University,2008(in Chinese).(下转第161页)155155
[15]张显库,杨光平,张强.一种双极性S函数修饰的非线性船舶航向保持算法[J].大连海事大学学报,2016,42(3):15-19.Zhang X K,Yang G P,Zhang Q.A kind of bipolar Sigmoid function decorated nonlinear ship course keeping algorithm[J].Journal of Dalian Maritime University,2016,42(3):15-19(in Chinese).
[16]Zhang X K,Zhang G Q.Design of ship coursekeeping autopilot using a sine function-based nonlinear feedback technique[J].The Journal of Navigation,2016,69(2):246-256.
[2]张显库,郭晨,杜佳璐.船舶航向不对称信息理论与非线性逆推鲁棒控制算法[J].交通运输工程学报,2006,6(2):47-50.Zhang X K,Guo C,Du J L.Asymmetric information theory and nonlinear backstepping robust control algorithm of ship navigation[J].Journal of Traffic and Transportation Engineering,2006,6(2):47-50(in Chinese).
[3]Krstic M,Kanellakopoulos I,Kokotovic P V.Nonlinear and adaptive control design[M].New York:Wiley,1995:89-108.
[4]Do K D,Pan J.Global robust adaptive path following of underactuated ships[J].Automatica,2006,42(10):1713-1722.
[5]董文瀚,孙秀霞,林岩,等.一类直接模型参考Backstepping自适应控制[J].控制与决策,2008,23(9):981-986,993.Dong W H,Sun X X,Lin Y,et al.Direct model reference Backstepping adaptive control[J].Control and Decision,2008,23(9):981-986,993(in Chinese).
[6]郭源博,张晓华,陈宏钧.基于双线性系统理论的PWM整流器非线性控制[J].西南交通大学学报,2009,44(2):232-237.Guo Y B,Zhang X H,Chen H J.Nonlinear control of PWM rectifier based on bilinear system theory[J].Journal of Southwest Jiaotong University,2009,44(2):232-237(in Chinese).
[7]张显库.船舶航向保持的非线性逆推鲁棒控制算法[J].大连海事大学学报,2007,33(2):80-83.Zhang X K.Nonlinear backstepping robust control algorithm for ship's course-keeping[J].Journal of Dalian Maritime University,2007,33(2):80-83(in Chinese).
[8]张显库.基于Lyapunov稳定性的船舶航向保持非线性控制[J].西南交通大学学报,2010,45(1):140-143.Zhang X K.Nonlinear control for ship course-keeping based on Lyapunov stability[J].Journal of Southwest Jiao Tong University,2010,45(1):140-143(in Chinese).
[9]贾欣乐,张显库.船舶运动智能控制与H∞鲁棒控制[M].大连:大连海事大学出版社,2002:273-275.Jia X L,Zhang X K.Ship motion intelligent control and H∞robust control[M].Dalian:Dalian Maritime University Press,2002:273-275(in Chinese).
[10]马超,张显库.基于指数函数非线性反馈的船舶航向保持控制[J].船舶工程,2017,39(增刊1):162-165.Ma C,Zhang X K.Ship course keeping control based on nonlinear feedback of exponential function[J].Ship Engineering,2017,39(Supp 1):162-165(in Chinese).
[11]同济大学应用数学系.高等数学[M].北京:高等教学出版社,2005:215-220.Department of Applied Mathematics,Tongji University.Advanced mathematics[M].Beijing:Higher Education Press,2005:215-220(in Chinese).
[12]Deng H,Krsti C M.Stochastic nonlinear stabilization-I:a backstepping design[J].Systems&Control Letters,1997,32(3):143-150.
[13]贾欣乐,张显库.风力等效舵角及应用[J].中国造船,2015,56(3):116-123.Jia X L,Zhang X K.Equivalent rudder angle to wind force and its application[J].Shipbuilding of China,2015,56(3):116-123(in Chinese).
[14]涂武.船舶航向最优控制与仿真研究[D].哈尔滨:哈尔滨工程大学,2008.Tu W.Research of optimal control of ship heading and using Simulink for simulation[D].Harbin:Harbin Engineering University,2008(in Chinese).(下转第161页)155155
[15]张显库,杨光平,张强.一种双极性S函数修饰的非线性船舶航向保持算法[J].大连海事大学学报,2016,42(3):15-19.Zhang X K,Yang G P,Zhang Q.A kind of bipolar Sigmoid function decorated nonlinear ship course keeping algorithm[J].Journal of Dalian Maritime University,2016,42(3):15-19(in Chinese).
[16]Zhang X K,Zhang G Q.Design of ship coursekeeping autopilot using a sine function-based nonlinear feedback technique[J].The Journal of Navigation,2016,69(2):246-256.