基于T-S模型集装箱桥吊防摇控制方法的研究
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摘要
集装箱桥吊的防摇就是指集装箱吊具带着提升载荷的主小车在运行到预定位置时,依靠减摇装置使吊着的提升载荷围绕悬吊点的摇摆幅度在规定的时间内或规定的摇摆周期内减到规定的数值内。
集装箱桥吊是一个十分复杂的不确定非线性系统,所以系统防摇控制变得非常困难,因此,给出集装箱桥吊的防摇控制方法具有重要的意义。但是现行的研究方法中把集装箱桥吊作为一个不确定系统的研究很少,并且防摇时间较长,所以针对这些问题做一些有益的探索很有必要。
首先通过对集装箱桥吊运动特性的研究,根据拉格朗日方程,以长度和角度为自由度建立方程,得出集装箱桥吊运动的数学模型;再依据集装箱桥吊的数学模型求解出桥吊的T-S模糊模型。在此基础上针对桥吊系统的不确定性,给出了一种基于T-S模型的桥吊防摇H_∞控制方法,把系统可稳和H_∞控制存在的条件转化为解一系列矩阵不等式(LMI: Linear Matrix Inequality)的问题,得出最优反馈H_∞控制律,它使得桥吊闭环系统内部稳定,且不确定性对桥吊系统的输出影响最小。然而这种控制方法还存在施加干扰时不能保住某些性能的缺点,所以提出了基于T-S模型的桥吊防摇保性能控制,通过解一个具有线性矩阵不等式约束的凸优化问题,求得一个性能指标的上界和保证这一性能的PDC (Parallel Distributed Compensation)结构模糊控制器的状态反馈增益矩阵,得到了基于T-S模型的保性能控制器。所设计的控制器不仅使得系统闭环稳定而且使得某个或某些性能指标值不超过规定的上界。
仿真结果表明上述两种方法在系统模型发生变化和外界干扰施加时都能在很短时间抑制摆动和干扰,具有很强的鲁棒性。
The anti-swing control of the container crane is that the main trolley carries the load by the container spreader arrive at the goal and the anti-swing device makes the swing range of load get the prescribe range in the prescribe time.
The container crane is a complex and nonlinear system with uncertainty. So the anti-swing control is very difficult. The research of the anti-swing system is very important. But there are only a few methods researched on the container crane as an uncertain system. And the anti-swing time is much longer. Therefore some useful researches have been done in this dissertation. Firstly, container crane kinematical characteristic and Lagrange Equation are investigated. Then utilizing the freedom of position and theta, establish the system equations. Thus container crane kinematical model is educed. From this model, the container crane T-S model is got. To deal with uncertainty of container crane system, a H_∞controller based on the T-S model is obtained. Transforms the system stabilizability and the existence condition of the H_∞controller to solving a problem of LMI (Linear Matrix Inequality). Then gets the optimal feedback matrix, this method makes the system inner stable and the effect by the uncertain factor minimum. But it has a disadvantage that it can’t reserve some performance when system disturbances exit. So the cost guaranteed controller is designed. By solving the convex optimization problem with a set of LMI constrains, the performance upper boundary and the state feedback matrix of PDC (Parallel Distributed Compensation) fuzzy logic controller are obtained. the container crane system can be robust stabilized and the closed loop performance is guaranteed.
The simulation results indicate that these two approaches can restrain the swing and disturbance in short time. Thus, with the uncertainty and disturbance of system, it is approved that the anti-swing controller of the container crane is effective and robust.
集装箱桥吊是一个十分复杂的不确定非线性系统,所以系统防摇控制变得非常困难,因此,给出集装箱桥吊的防摇控制方法具有重要的意义。但是现行的研究方法中把集装箱桥吊作为一个不确定系统的研究很少,并且防摇时间较长,所以针对这些问题做一些有益的探索很有必要。
首先通过对集装箱桥吊运动特性的研究,根据拉格朗日方程,以长度和角度为自由度建立方程,得出集装箱桥吊运动的数学模型;再依据集装箱桥吊的数学模型求解出桥吊的T-S模糊模型。在此基础上针对桥吊系统的不确定性,给出了一种基于T-S模型的桥吊防摇H_∞控制方法,把系统可稳和H_∞控制存在的条件转化为解一系列矩阵不等式(LMI: Linear Matrix Inequality)的问题,得出最优反馈H_∞控制律,它使得桥吊闭环系统内部稳定,且不确定性对桥吊系统的输出影响最小。然而这种控制方法还存在施加干扰时不能保住某些性能的缺点,所以提出了基于T-S模型的桥吊防摇保性能控制,通过解一个具有线性矩阵不等式约束的凸优化问题,求得一个性能指标的上界和保证这一性能的PDC (Parallel Distributed Compensation)结构模糊控制器的状态反馈增益矩阵,得到了基于T-S模型的保性能控制器。所设计的控制器不仅使得系统闭环稳定而且使得某个或某些性能指标值不超过规定的上界。
仿真结果表明上述两种方法在系统模型发生变化和外界干扰施加时都能在很短时间抑制摆动和干扰,具有很强的鲁棒性。
The anti-swing control of the container crane is that the main trolley carries the load by the container spreader arrive at the goal and the anti-swing device makes the swing range of load get the prescribe range in the prescribe time.
The container crane is a complex and nonlinear system with uncertainty. So the anti-swing control is very difficult. The research of the anti-swing system is very important. But there are only a few methods researched on the container crane as an uncertain system. And the anti-swing time is much longer. Therefore some useful researches have been done in this dissertation. Firstly, container crane kinematical characteristic and Lagrange Equation are investigated. Then utilizing the freedom of position and theta, establish the system equations. Thus container crane kinematical model is educed. From this model, the container crane T-S model is got. To deal with uncertainty of container crane system, a H_∞controller based on the T-S model is obtained. Transforms the system stabilizability and the existence condition of the H_∞controller to solving a problem of LMI (Linear Matrix Inequality). Then gets the optimal feedback matrix, this method makes the system inner stable and the effect by the uncertain factor minimum. But it has a disadvantage that it can’t reserve some performance when system disturbances exit. So the cost guaranteed controller is designed. By solving the convex optimization problem with a set of LMI constrains, the performance upper boundary and the state feedback matrix of PDC (Parallel Distributed Compensation) fuzzy logic controller are obtained. the container crane system can be robust stabilized and the closed loop performance is guaranteed.
The simulation results indicate that these two approaches can restrain the swing and disturbance in short time. Thus, with the uncertainty and disturbance of system, it is approved that the anti-swing controller of the container crane is effective and robust.
引文
[1]蒋国仁，岸边集装箱起重机，湖北：湖北科学技术出版社，2001，180-182
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[4]Liang Chunyan, Xie Jianying, A Zero-placement Method to Design Robust Time Delay Filter,Proceedings of the 3th world Congress on Intelligence Control and Automation,june28,2000:3403-3407
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[11]Hongjun Chen, Bingtuan Gao, Xiaohua Zhang, Dynamical Modelling and Nonlinear Control of a 3D Crane,Control and Automation,2005.ICCA’05.International Congerence on Volume 2,26-29 June 2005:1085-1090
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[28]交通部水运司，港口起重运输机械设计手册，北京：人民交通出版社，2001：512-530
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[41]Liu Guoyi; Zhang Qingling; Zhai ding; Non-fragile H-Infinite Control For T-S FuzzySystems via LMI, Control and Automation, 2005. ICCA '05. International Conference on Volume 1, 26-29 June 2005 Page(s):171 - 175
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[2]严云福，超巴拿马型岸边集装箱起重机发展的新趋势，港口装卸，2001（1）：12-15
[3]彭传圣，岸边集装箱起重机技术新进展，港口装卸，2001（2）：1-5
[4]Liang Chunyan, Xie Jianying, A Zero-placement Method to Design Robust Time Delay Filter,Proceedings of the 3th world Congress on Intelligence Control and Automation,june28,2000:3403-3407
[5]郭建明，新型集装箱起重机防摇控制系统研究，交通科技，2000（6）：27-28
[6]周勇 ，集装箱起重机防摇的模糊智能控制研究及仿真，[硕士学位论文]，湖北，武汉理工大学，2003
[7]Jianqiang YI and Naoyoshi YUBAZAKI, anti-swing Fuzzy Control of Overhead Traveling Crane,IEEE,2002: 1298-1303
[8]Diantong Liu, Jianqiang Yi, Min Tan,Proposal of GA-based two-stage fuzzy control of overhead crane,TENCON’02,Proceedings,2002 IEEE Region 10 congerence on Computers,Communications, Control and Power Engineering. Volume 3,28-31 Oct,2002:1721-1724
[9]Diantong Liu, Jiangqiang Yi, Dongbin Zhao, Swing-free transporting of two-dimensional overhead crane using sliding mode fuzzy control, American Control Conference,2004,Proceedings of the 2004 Volume 2,30 June-2 July 2004:1764-1769
[10]Xiaohua Zhang, Bingtuan Gao, Nonlinera controller for a gantry crane based on partial feedback linearization, Control and Automation,2005.ICCA’05.International Conference on Volume 2,26-29 June 2005:1074-1078
[11]Hongjun Chen, Bingtuan Gao, Xiaohua Zhang, Dynamical Modelling and Nonlinear Control of a 3D Crane,Control and Automation,2005.ICCA’05.International Congerence on Volume 2,26-29 June 2005:1085-1090
[12] Chin,T.C and H0,Y.K. Optimal overhead crane control. proc. of Int. conf. on Automation, Rohotics and Computer Vision ICARV’90,1990:312-316
[13]Sakawa, Y and Shindo, Y. Optimal control of container cranes. IEEE, Automatic, vol. 18-3, 1996:245-247
[14]Yoshida, K. and Kawabe, H. A design of saturating control with a guaranteed cost and its application to the crane control system. IEEE Trans. On Automatic Control system,vol.37-1,1992:121-127 [15]Osamu Itoh and Hirohisa Migita Jun Itoh esc. Application of fuzzy control to automatic crane operation. On Automatic Control system IEEE vol.91-3, 1993：161-164
[16]Y.Kijima and R.Ohtsubo and S.Yamada esc. An Optimization of Fuzzy Controller and It’s Application to Overhead Crane IEEE. vol 26-9, 1995：1508-1513
[17]Bahram Kimiaghalam and Abdollah Homaifar. Genetic Algorithm Based Gain Scheduling. IEEE，2002:540-545
[18]Bahram Kimiaghalam and Abdollah Homaifar.Genetic Algorithms Solution For Unconstrained Optimal Crane Control，IEEE，1999，:2124-2130
[19]Amel Ouezri and Nabil Derbel. On The Intelligent Control Of A Rotary Crane, Neural Network and Fuzzy Logic Approaches. Proceedings of the 2003 IEEE，2003: 586-591
[20]Leonardo Azevedo Scardua and Jose Jaime Da Cruz , Optimal control of ship unloadersusing reinforcement learning. Advanced Engineering Informatics 16，IEEE，2002: 217-227
[21]Chunshien Li and Chun-Yi Lee. Soft Computing System for Motion Control. IEEE，2001:364-369
[22]Chunshien Li and Chun-YI Lee. Fuzzy Motion Control of an Auto-Warehousing Crane System.IEEE,VOL48,NO5 ，2001: 983-994
[23]L.F.Mendonca and J..M.Sousa, Optimization problems in multivariable fuzzy predictivecontrol. International Journal of Approximate Reasoning 36，IEEE，2004: 199-221
[24]Ho-Hoon Lee and Sung Kun Cho. A New Fuzzy-Logic Anti-swing Control for Industrial Three-Dimensional Overhead Cranes. International Conference on Robotics & Automation Seoul, Korea system IEEE ,2001：2956-2961
[25]Sung-kun Cho and Ho-Hoon Lee, An Anti-Swing Control of a 3-Dimensional Overhead Crane, Proceedings of the American Control Conference Chicago, June, [22000: 1037-1041
[26]Dal-Young Ha, Design of container crane controller using intelligence algorithms. IEEE，2001: 1507-1513
[27]Kunihito Matsuhi and Noriyuki kikuti the control system Design of a Traveling Crand using H∞ Control Theory. IEEE，2000: 131-134
[28]交通部水运司，港口起重运输机械设计手册，北京：人民交通出版社，2001：512-530
[29]胡宗武，起重机动力学，北京：机械工业出版社，1988 ：60-75
[30]蔡自兴，智能控制，北京：国防工业出版社，2005， 229-250
[31]诸静，模糊控制原理与应用，北京：机械工业出版社，2001，371-386
[32]佟绍成，模糊控制系统的设计及稳定性分析，北京：科学出版社，2004，22-54
[33]胡寿松，最优控制理论与系统，北京：科学出版社，2005，231-254
[34]Chang, B.-C.;A stable state-space realization in the formulation of H∞ norm computation, Automatic Control, IEEE Transactions on Volume 32, Issue 9, Sep 1987 Page(s):811 - 815
[35]Conte, G.; Automatic Control, A course in H∞ control theory, IEEE Transactions on Volume 32, Issue 12, Dec 1987 Page(s):1144 – 1145
[36]Petersen, I.; Disturbance Attenuation and H∞ Optimization: a design method based on thealgebraic Riccati equation, Automatic Control, IEEE Transactions on Volume 32, Issue 5,May 1987 Page(s):427 - 429
[37]关新平，赵宇翔，一类非线性系统的H∞鲁棒控制，控制理论与应用，第19卷第1期，2002（2）：126-130
[38]曾建平，程鹏，基于LMI可行解的所有状态反馈H∞控制器，控制与决策，第15卷第1期，2000（1）：89-94
[39]刘晓东，张庆灵，模糊H∞控制器的设计的LMI方法，控制理论与应用，第21卷第1期，2004（2）：120-124
[40]Chong-Hong，Wang; Hong-Ru，Robust fault detection for uncertain system with time-delay in state, Machine Learning and Cybernetics, 2005,Proceedings of 2005 InternationalConference on Volume 2,18-21,Aug. 2005 Page(s):1110 - 1115
[41]Liu Guoyi; Zhang Qingling; Zhai ding; Non-fragile H-Infinite Control For T-S FuzzySystems via LMI, Control and Automation, 2005. ICCA '05. International Conference on Volume 1, 26-29 June 2005 Page(s):171 - 175
[42]Abu-Khalaf, M.; Lewis, F.L.; Neural Network H∞ State Feedback Control with actuator saturation; Control and Automation, 2005. ICCA '05. International Conference on Volume 1,26-29 June 2005 Page(s):1 - 9
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