一阶非线性系统的自适应控制资料来源：程代展，应用非线性控制,例例设计自适应控制器控制不稳定系统：yy+y2+3u假定对象参数a，1，b3对于自适应控制器是未知的。pp参考模型选择为：x，4x+4r4，b4。取自适应增益Y2。两个控制器参数的初值均取为m即am仿真中使用了两种不同的参考信号：(1)r(t)=4。从图8.9中知跟踪误差收敛到零，但参数误差不收敛。()r(t)=4sin(3t)从图8.10中知跟踪误差和参数误差都收敛到零。KXTENSIOWTONONLINEARPLANTS(832)ThesamemettiedofadpttvcontroltlesigncanbeusedforChenonlinearfirsr-orderplantdesenbidbyIhtdifftFentialequation2-陀-中f*映where/isanyknownnonlinearftineiion.Thenonliiwdrityinth&礙djTiamicsischaracterizedbyitslinearparametrizetioinrmsofiheunknownconsiantc.InsteadofU5ingtlwcontnoJlaw(E2Z)*wettowusethecontrolhw(8.33)u=&yy+菊-iafrwhe惟thesccord忙rmisintroducedwitlirheintenttonofadaptivelycancelingthenonlinearterm.Subs4iluiiiig由相comiroElawintoik0h#Generallyspeakhig,forlinear占丫咅杞u屏theconvergentestinvatifwofmparaiticicrsrequireat皿sinusoidsin(hete-fcrcnce$igEd曲、aswHlbediscussedinmoredelailinsections83and8AHoweverforthisnonlinearcaseb3uchsimplereluLicMimaynolbevalid.Ustially,thequati(aliverehliont(we*nr(0andvf)isifcpcntienionEheparticiihrnonlinearfuncdoiis/(yXsunclearfcowmanystnusflidsmH/)anenecesaiytogaranteidiepersistentesdtafionofv(tjhefollowingexampleiihisirates赴思belisivicryflite-arinpiivesystemfor3nonlinearplant.ExuiripkS.4:simuhtikmofafirt-ordcrnwituiearplaiklAsuiineihpi3nwline&rplanie.describedbycheequation#This-dtfTersitimtheunstablepLantinEiampUinLhaiaquadralk址门口治in山此nEMiidVDrnii.?.5,04.34J)3-53JJ152“L.5JJ.O/IVW181.6141.2IOOS(r.40.2051.0LS2.02.53.0HQ_il.，”.、0.0t.5I刈1.52.02.5M)rimafMc)XU44-o.s-L0L2-L4d_6itmcfsccgXU4).6船1-0L24d.6I一_一100a.5LO152j02.53.0timc(sci)E-.亠一.j0.00.51.0152.02-5剂linwfSK)#upperrihcpjrsmeifT玄:l(n*trleftrpurauieierav;lowerriglri:FigureKJJ:Adaptivecntrulofalir-Qrifcrnonlinear础寻出tn呦-4upperk!L(TidingpiFitirmafncefs=16A2sii?(3f+fl.vj1+亠7+二”#图8.9跟踪性能和参数估计，r(t)=4#图8.10跟踪性能和参数估计，r(t)=4sin(3t)clearclcgamma=2;x=0;xm=0;a_r=0;a_y=0;a_f=0;t=0;Dt=0.001;n=1;fori=1:10000r=4;%r=4*sin(3*t);Dxm=-4*xm+4*r;xm=xm+Dxm*Dt;f=xA2;e=x-xm;Da_r=-gamma*e*r;Da_y=-gamma*e*x;Da_f=-gamma*e*f;a_r=a_r+Da_r*Dt;a_y=a_y+Da_y*Dt;a_f=a_f+Da_f*Dt;u=a_r*r+a_y*x+a_f*f;Dx=x+xA2+3*u;x=x+Dx*Dt;x_store(:,n)=x;xm;a_store(:,n)=4/3;(-1-4)/3;-1/3;a_r;a_y;a_f;n=n+1;t=t+Dt;endfigure(1)plot(1:n-1)*Dt,x_store(1,:),(1:n-1)*Dt,x_store(2,:)legend(x,xm)xlabel(time/s)figure(2)plot(1:n-1)*Dt,a_store(1,:),(1:n-1)*Dt,a_store(4,:),(1:n-1)*Dt,a_store(2,:),(1:n-1)*Dt,a_store(5,:),(1:n-1)*Dt,a_store(3,:),(1:n-1)*Dt,a_store(6,:)xlabel(time/s)#