倒立摆系统与自动控制实验实验指导书

᩼㌱㔕ф㠠ࣞ᧝࡬ᇔ僂PIDMATLABPIDBorlandC+3.1CIIIIII⌞ᝅӁ亯1.2.IVV目录内容简介..........................................................I序言............................................................II注意事项.........................................................IV第一章直线一级倒立摆的牛顿－欧拉方法建模.........................1微分方程的推导.........................................................1传递函数................................................................3状态空间方程............................................................3开环系统仿真............................................................4实验步骤................................................................4第二章直线一级顺摆的建模........................................6微分方程的推导.........................................................6系统的状态空间模型......................................................8系统开环响应仿真........................................................8实验步骤...............................................................8第三章固高倒立摆系统MATLAB实验软件............................10固高倒立摆系统MATLAB实验软件的安装...................................10MATLAB以及SIMULINK应用的基本介绍....................................11固高倒立摆系统工具箱................................................14第四章经典控制理论实验.........................................18实验一PID控制器设计与调节.............................................19实验二根轨迹法控制器设计与调节.........................................23实验三频域响应法控制器设计与调节......................................29第五章现代控制理论实验—状态空间极点配置........................38第六章最优控制理论—LQR控制器设计与调节........................45第七章PID神经网络控制理论与实验.................................49附录1固高摆控制系统的硬件和软件.................................53A.1控制系统硬件......................................................53A.2控制系统软件.......................................................53ㅢжㄖ⴪㓵ж㓝و㄁᩼Ⲻ⢑亵ι⅝᣿ᯯ⌋ᔰ⁗1-11-1MmblIFx1NP(a)PImgN(b)1-2abNxbFxMsincos:)sin(222mlmlxmNlxdtdmNFmlmlxbxmMsincos)(2cossin)cos(222mlmlmgPldtdmmgPINlPlcossinsinsin,coscos,PN2cossin)(2xmlmglmlIcos1sin0)2dtd(uF umlxbxmMxmlmglmlI)(2 )()()()()()()()(22222sUssmlssbXssXmMssmlXsmglssmlI)(])([)(22ssgmlmlIsX)()()()()()()(22222sUssmlsssgmlmlIbsssgmlmlImMsqbmglsqmglmMsqmlIbssqmlsUs23242)()()()(])())([(22mlmlImMq3DuCXyBuAXX,xuMmlmMImlMmlmMImMmglxMmlmMImlbuMmlmMImlIMmlmMIglmxMmlmMIbmlIxxx2222222222)()()()()()()()()(uMmlmMImlMmlmMImlIxxMmlmMImMmglMmlmMImlbMmlmMIglmMmlmMIbmlIxx2222222222)(0)(00)()()(010000)()()(00010uxxxy0001000001:M1.096Kgm0.109Kgb0.1N/m/secl0.25mI0.0034kg*m*m70.0050$7/$%0$7/$%&RPPDQG0$7/$%SOBRSHQBWP4SOBRSHQBVP5ㅢㄖ⴪㓵ж㓝亰᩼Ⲻᔰ⁗1-1M1m1lx1),(),(),(qqVqqTqqLLqTViqLiiifqLqLdtdin3,2,11,xif21mmTTTMT1mT221xMTM6212111111212112111'121cos21)cos()sin(21lmxlmxmdtlddtlxdmTm212112121121''161312121lmlmJTpm21211111121''1'1132cos21lmxlmxmTTTmmm21211111121232cos2121lmxlmxmxMT 111cos1glmV 111212111111212cos132cos2121glmlmxlmxmxML1011LLdtd0sin34cos1111211111glmlmxlmxu  0,0,0,0,,,11xxXullgux111143437141321xxxxxxulxxxxlgxxxx14321143214301004300100000000010uxxxxxy000100000143211:M1.096Kgm0.109Kg1l0.25mI0.0034kg*m*m70.0050$7/$%0$7/$%&RPPDQG0$7/$%SFBRSHQBVP89ㅢㄖര儎و㄁᩼㌱㔕MATLABᇔ僂䖥ԬWindows2000Windows9895MATLAB6Release12.1SIMULINK4.1MATLABsetup.exe”,3-13-1MATLABBrowse…”3-2MATLAB3-2setup10MATLAB\Toolbox\pendPCISIMULINKMATLABSIMULINKLQRMATLABM=.5;//m=0.2;b=0.1;I=0.006;g=9.8;l=0.3;p=(M+m)*(I+m*l^2)-(m*l)^2;%simplifiesinputA=[0100;//0-(I+m*l^2)*b/p(m^2*g*l^2)/p0;0001;0-(m*l*b)/pm*g*l*(M+m)/p0]B=[0;(I+m*l^2)/p;0;m*l/p]C=[1000;0010]D=[0;0]%closeloopsystemresponseforstepsignalx=20;y=100;Q=[x000;0000;00y0;0000];R=1;K=lqr(A,B,Q,R)//lqrAc=[(A-B*K)];Bc=[B];Cc=[C];Dc=[D];T=0:0.005:5;11U=0.2*ones(size(T));Cn=[1000];Nbar=rscale(A,B,Cn,0,K)//Bcn=[Nbar*B];[Y,X]=lsim(Ac,Bcn,Cc,Dc,U,T);//plot(T,Y)//legend('Cart','Pendulum')m3-33-3MATLABEditorF:/pend/m/rascale.mMATLABMATLABSIMULINKSIMULINKLibrarybrowserFileFile/New/ModelCtrl-NSIMULINKLibrarySIMULINK/Sources/SignalOperatorSIMULINK/Sinks/ScopeSIMULINK/Subsystems/Subsystem”in1out1ControlSystemToolbox/LMISystem3-4123-4SIMULINK 103122ssssG3-5113-5ABEditorSFunctionS-FunctionBuilderS-FunctionSIMULINKMATL13S-FunctionMATLABLQRPIDLQRWindows20001.2.5.6.7.LQRSIMULINKSIMUrtedPedulum3.4.Windows2000MATLABCommandWindowsSIMULINKToolbox”3-6SIMULINKLINKInven14StartRealPendulSFunctionProfileModeConstantSFunction3-6SFunctionCMATLABCMEXcSinglePendulumLQRControlDemos”3-7LQRPendulumInitializaton,Enb