基于粒子群算法倒立摆分数阶PID参数优化
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摘要
来旋转式倒立摆是一种单输入双输出、强耦合、非线性不稳定系统。为实现对该系统在稳定阶段进行有效控制,采用分数阶PID(PI~γD~μ,FOPID)分别对倒立摆摆角、转角的位置和速度进行闭环控制。因为FOPID控制器数目和参数较多,手动调节各控制器参数极为繁琐且不易实现,故采用改进多目标粒子群(IMOPSO)算法整定各个FOPID控制器参数。通过QUBE-Servo旋转式倒立摆上验证了IMOPSO-FOPID算法的有效性,并使倒立摆获得优于PID控制系统的良好的动态品质,同时具备良好的稳定性和鲁棒性。
The rotary inverted pendulum is a strong coupling, nonlinear and unstable system which has one input and two outputs. In order to realize the effective control of the system in the stable stage, fractional order PID, PI~γD~μ, and FOPID are used in the pendulum angle and rotation angle's position and speed closed-loop control, respectively. Because of the large number of FOPID controllers and parameters, manual setting of the controller parameters is very complicated and not easy to achieve. Therefore, this paper uses the improved multi-objective particle swarm algorithm(IMOPSO) to adjust FOPID controller parameters. The effectiveness of the IMOPSO-FOPID algorithm is verified by the QUBE-Servo the rotary inverted pendulum. The inverted pendulum obtains good dynamic quality and stability, better than PID.
The rotary inverted pendulum is a strong coupling, nonlinear and unstable system which has one input and two outputs. In order to realize the effective control of the system in the stable stage, fractional order PID, PI~γD~μ, and FOPID are used in the pendulum angle and rotation angle's position and speed closed-loop control, respectively. Because of the large number of FOPID controllers and parameters, manual setting of the controller parameters is very complicated and not easy to achieve. Therefore, this paper uses the improved multi-objective particle swarm algorithm(IMOPSO) to adjust FOPID controller parameters. The effectiveness of the IMOPSO-FOPID algorithm is verified by the QUBE-Servo the rotary inverted pendulum. The inverted pendulum obtains good dynamic quality and stability, better than PID.
引文
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[12]杨景明,马明明,车海军,等.多目标自适应混沌粒子群优化算法[J].控制与决策,2015,30(12):2168-2174.Yang J M,Ma M M,Che H J,et al.Multi-object adaptive chaotic particle swarm optimization alogorithm[J].Control and Decision,2015,30(12):2168-2174.
[13]Xue B,Zhang M,Browne W N.Particle Swarm Optimization for Feature Selection in Classification:A Multi-objective Approach[J].IEEE Transactions on Cybernetics,2013,43(6):1656-1671.
[14]王生生,杨娟娟,柴胜.基于混沌鲶鱼效应的人工蜂群算法及应用[J].电子学报,2014,42(9):1731-1737.Wang S S,Yang J J,Chai S.Artificial Bee Colony Algorithm with Chaotic Catfish Effect and Its Application[J].ACTAELECTRONICA SINICA,2014,42(9):1731-1737.
[15]Deb K,Pratap A,Agarwal S,et al.A fast and elitist multi-objective genetic algorithm:NSGA-II[J].Evolutionary Computation,IEEETransactions on,2002,6(2):182-197.
[2]Mason P,Broucke M,Piccoli B.Time optimal swing-up of the planar pendulum.IEEE Transactions on Automatic Control,2008,53(8):1876-1886.
[3]张永立,李洪兴,苗志宏,等.基于变增益LQR控制方法的二级倒立摆自动摆起[J].系统工程理论与实践,2011,31(7):1341-1355.Zhang Y L,Li H X,Miao Z H,et al.Swing-up of double inverted pendulum baused on variable gain LQR technique[J].Systems Engineering-Theory&Practice,2011,31(7):1341-1355.
[4]刘成,张万绪,张志勇,等.具有环境自适应能力的旋转倒立摆控制方法[J].西北大学学报:自然科学版,2015,45(1):45-48.Liu C,Zhang W X,Zhang Z Y,et al.Control method of rotary inverted pendulum with environment adaptive capacity ability[J].Journal of Northwestern University:Natural Science Edition,2015,45(1):45-48.
[5]Md.Akhtaruzzaman,A.A.Shafie.Modeling and control of a rotary inverted pendulum using various methods,comparative assessment and result analysis[J].Mechatronics and Automation(ICMA),2010International Conference on.IEEE 2010:1342-1347.
[6]PODLUBNY I.Fractional-order systems and PIγDμcontrollers[J].IEEE Transactions on automat control,1999,44(1):208-214.
[7]柳志远,张湘平.基于遗传算法PID的旋转式倒立摆控制[J].计算机技术与发展,2008,18(2):180-183.Liu Z Y,Zhao X P.Rational Function Approximation for Fractional Order Differential and Integral Operators[J].COMPUTERTECHNOLOGY AND DEVELOPMENT,2008,18(2):180-183.
[8]李文,赵慧敏.一种分数阶微积分算子的有理函数逼近方法[J].自动化学报,2011,37(8):999-1005.Li W,Zhao H M.Rational Function Approximation for Fractional Order Differential and Integral Operators[J].ACTA AUTOMATICASINICA,2011,37(8):999-1005.
[9]刘景艳,王福忠,李玉东,等.基于粒子群网络的提升机制动系统故障诊断[J].控制工程,2016,23(2):294-298.Liu J Y,Wang Y Z,Li Y D,et al.Fault Diagnosis of Hoist Braking System Based on Neural Network Optimized by Particle Swarm[J].Control Engineering of China,2016,23(2):294-298.
[10]叶永伟,王晓恩,林海,等.改进协同粒子群算法的汽车涂装线调度[J].控制工程,2012,19(6):47-51.Ye Y W,Wang X E,Lin H,et al.Improved Cooperative Particle Swarm Algorithm for Automobile Painting Line Scheduling[J].,Control Engineering of China,2012,19(6):47-51
[11]谢承旺,邹秀芬,夏学文,等.一种多策略融合的多目标粒子群优化算法[J].电子学报,2015,43(8):1538-1544.Xie C W,Zou X F,XIA X W,et al.A Multi-Objective Particle Swarm Optimization Algorithm Integrating Multiply Strategies[J].ACTAELECTRONICA SINICA,2015,43(8):1538-1544.
[12]杨景明,马明明,车海军,等.多目标自适应混沌粒子群优化算法[J].控制与决策,2015,30(12):2168-2174.Yang J M,Ma M M,Che H J,et al.Multi-object adaptive chaotic particle swarm optimization alogorithm[J].Control and Decision,2015,30(12):2168-2174.
[13]Xue B,Zhang M,Browne W N.Particle Swarm Optimization for Feature Selection in Classification:A Multi-objective Approach[J].IEEE Transactions on Cybernetics,2013,43(6):1656-1671.
[14]王生生,杨娟娟,柴胜.基于混沌鲶鱼效应的人工蜂群算法及应用[J].电子学报,2014,42(9):1731-1737.Wang S S,Yang J J,Chai S.Artificial Bee Colony Algorithm with Chaotic Catfish Effect and Its Application[J].ACTAELECTRONICA SINICA,2014,42(9):1731-1737.
[15]Deb K,Pratap A,Agarwal S,et al.A fast and elitist multi-objective genetic algorithm:NSGA-II[J].Evolutionary Computation,IEEETransactions on,2002,6(2):182-197.
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