第1期 吴晓威，等：基于灰色预测的自适应内模PD双重控制器设计 ·75 [2]周涌，陈庆伟，胡维礼.内模控制研究的新发展[U]. 控制理论与应用，2004,21(3)：475482。 ZHOU Yong,CHEN Qingwei,HU Weili.New develop- ments of research on internal model control [J].Control Theory Applications,2004,21(3):475-482. [3]LI S,LIJ H.IMC-PID control of ultrar sonic motor ser- vo system based on neural network[C]//Proceedings of the 6th World Congress on Control and Automation. 0.04 0.080.120.160.20 Dalian,China,2006. 1/s [4 ]LI H X,DENG H.An approximate internal model-based neural control for unknown nonlinear discrete processes b)参数b的变化曲线图 [J].IEEE Transactions on Neural Networks,2006,17 图7参数a、b的变化曲线图 (3):695670. Fig.7 The change of the parameters of a and b (5]HABER R E,AL IQUE J R.Nonlinear internal model 图8中可实现因子选为入=0.7.PD控制器的参数 control using neural networks:an application for machi- 为kp=0.01,k=0.1,ka=0.01.实线为文中方法， ning processes[J].Neural Comput&Applic,2004,13: 虚线为文献[4]采用基于神经网络的逼近内模控制 4755 方法.从图中可以看出文中方法响应速度快，控制效 [6]吕朝霞，吴晓蓓，郭建，等.基于小波网络的非线性内 模控制[J].控制与决策，2001,16(1)：6568 果明显改善 LU'Zhaoxia,WU Xiaobei,GUO Jian,et al.Nonlinear 2.0 internal model control based on wavelet network [J]. 6 Control and Decision,2001,16(1):65-68. [7]HABER R E.Nonlinear internal model control using 12 neural networks and fuzzy logic:application to an elec- 0.8 tromechanical process [J].LNCS,2006,2657:351- 360. 0.4 [8]党映农，韩崇昭.基于Volterra级数模型的内模控制方 法0].西安交通大学学报，2001,35(4)：385389 1/s DANG Yingnong,HAN Chongzhao.Internal model con trol for uncertain Volterra series system [J ]Journal of 图82种挖制方案的输出比较图 Xian Jiaotong University,2001,35(4):385-389. Fig.8 Simulation results of the different controller [9]刘士荣，林卫星，俞金寿，等.非线性动态系统神经模糊 建模与内模/PD双重控制系统设计[J],控制理论与应 4结束语 用，2004,21(4)：553-560. LIU Shirong,L IN Weixing,YU jinshou,et al.Neuro- 针对非线性系统，提出一种基于灰色预测的自 fuzzy modeling for nonlinear dynamic systems and double 适应内模/PD双重控制方法.该控制方法结合了灰 control system design with internal model control and 色预测、内模控制和PD控制器的优点.与基本内 PID control [J ]Control Theory Applications,2004 模控制相比，在满足鲁棒稳定前提下，可使得跟踪误 21(4):553-560. 差较快收敛.如果系统存在输出扰动时候，通过PD [10]HE MJ,CAI WJ,WU B F.Design of decentralized 反馈控制，也可以抑制这种干扰的影响.仿真结果表 IMC-PID controller based on dRi analysis[J].American 明该方法的有效性 Institute of Chemical Engineers,2006,52(11):3852- 3863. 参考文献： [11]LI C Y,HUANG T L.Optimal design for the grey prediction PID controller for power system stabilizers by [1]赵曜.内模控制发展综述[U].信息与控制，2000,29 evolutionary programming [C]//Proceedings of the (6):526531. 2004 IEEE International Conference on Networking, ZHAO Yao.A survey of development of internal model Sensing Control.Taipei,China,2004. control[J ]Information and Control,2000,29(6):526- [12]DINGC C,LEE K T.Optimal design for power system 531 dynamic stabilizer by grey prediction PID control[C]// 1994-2008 China Academic Journal Electronic Publishing House.All rights reserved.http://www.cnki.net(b) 参数 b的变化曲线图 图 7 参数 a、b的变化曲线图 Fig. 7 The change of the parameters of a and b 图 8 中可实现因子选为λ= 017. PID 控制器的参数 为 k p = 0101 , ki = 011 , k d = 0101. 实线为文中方法 , 虚线为文献[4 ]采用基于神经网络的逼近内模控制 方法. 从图中可以看出文中方法响应速度快 ,控制效 果明显改善. 图 8 2 种控制方案的输出比较图 Fig. 8 Simulation results of the different controller 4 结束语 针对非线性系统 ,提出一种基于灰色预测的自 适应内模/ PID 双重控制方法. 该控制方法结合了灰 色预测、内模控制和 PID 控制器的优点. 与基本内 模控制相比 ,在满足鲁棒稳定前提下 ,可使得跟踪误 差较快收敛. 如果系统存在输出扰动时候 ,通过 PID 反馈控制 ,也可以抑制这种干扰的影响. 仿真结果表 明该方法的有效性. 参考文献 : [1 ]赵 曜. 内模控制发展综述[J ]. 信息与控制 , 2000 , 29 (6) : 5262531. ZHAO Yao. A survey of development of internal model control[J ]. Information and Control , 2000 , 29 (6) :5262 531. [2 ]周 涌 , 陈庆伟 , 胡维礼. 内模控制研究的新发展[J ]. 控制理论与应用 , 2004 , 21 (3) : 4752482. ZHOU Yong ,CHEN Qingwei , HU Weili. New develop2 ments of research on internal model control[J ]. Control Theory & Applications , 2004 , 21 (3) : 4752482. [3 ]L I S , L IJ H. IMC2PID control of ultra2sonic motor ser2 vo system based on neural network[ C]/ / Proceedings of the 6th World Congress on Control and Automation. Dalian , China , 2006. [ 4 ]L I H X , DEN G H. An approximate internal model2based neural control for unknown nonlinear discrete processes [J ]. IEEE Transactions on Neural Networks , 2006 , 17 (3) : 6952670. [5 ] HABER R E , AL IQU E J R. Nonlinear internal model control using neural networks: an application for machi2 ning processes[J ]. Neural Comput & Applic , 2004 ,13 : 47255. [6 ]吕朝霞 ,吴晓蓓 , 郭 建 , 等. 基于小波网络的非线性内 模控制[J ]. 控制与决策 ,2001 ,16 (1) :65268. LU¨Zhaoxia , WU Xiaobei , GUO Jian , et al. Nonlinear internal model control based on wavelet network [J ]. Control and Decision ,2001 ,16 (1) :65268. [ 7 ] HABER R E. Nonlinear internal model control using neural networks and fuzzy logic : application to an elec2 tromechanical process [J ]. LNCS , 2006 , 2657 : 3512 360. [8 ]党映农 ,韩崇昭. 基于 Volterra 级数模型的内模控制方 法[J ] . 西安交通大学学报 ,2001 ,35 (4) :3852389. DAN G Yingnong , HAN Chongzhao. Internal model con2 trol for uncertain Volterra series system [J ]. Journal of Xi’an Jiaotong University , 2001 ,35 (4) :3852389. [9 ]刘士荣 ,林卫星 ,俞金寿 ,等. 非线性动态系统神经模糊 建模与内模/ PID 双重控制系统设计[J ]. 控制理论与应 用 ,2004 ,21 (4) :5532560. L IU Shirong , L IN Weixing , YU jinshou , et al. Neuro2 fuzzy modeling for nonlinear dynamic systems and double control system design with internal model control and PID control[J ]. Control Theory & Applications ,2004 , 21 (4) :5532560. [10 ] HE M J , CAI W J ,WU B F. Design of decentralized IMC2PID controller based on dRi analysis[J ]. American Institute of Chemical Engineers , 2006 , 52 ( 11) : 38522 3863. [11 ]L I C Y , HUAN G T L. Optimal design for the grey prediction PID controller for power system stabilizers by evolutionary programming [ C ]/ / Proceedings of the 2004 IEEE International Conference on Networking , Sensing & Control. Taipei , China ,2004. [12 ]DIN G C C , L EE K T. Optimal design for power system dynamic stabilizer by grey prediction PID control[ C]/ / 第 1 期 吴晓威 ,等 :基于灰色预测的自适应内模 PID 双重控制器设计 · 57 ·