1、 1滑?？刂葡到y(tǒng)A=兀2屯=兀大3=f(x)+gu+d=(一a內(nèi)一a2x2一a3Xj)+gu+d其中a.=a.o+A.,|A.|.(/),Vr；g=g+Ag,gW0(f),0f；dD(t)yto、go為系統(tǒng)的標(biāo)稱參數(shù)，卜、Ag為系統(tǒng)參數(shù)的不確定部分，q(f)、0(/)分別為Aq和Ag的上界，(/)為擾動d的上界。5=4=一xid=x2-xld嚴(yán)=入一昭=心一九1-1未加入邊界層的滑?？刂七x擇滑動模態(tài)為s=qq+c2e2+幺$控制器為Ue.u(0=g；工4。兀一C&2-C2+鬲/=!,(0|兀|+Q|%|+d(i)+“從)=K肋=_r肋1-2加入邊界層的滑模控制其它式子不變，將1節(jié)中冷(/)的用

2、下式代替3un(t)=K(t)sign(s)=-式中,go-0(/)工%(0kI+0(/)1%I+D+i=i1.3PID控制控制器為ii=-Kpei-Kie,dt-Kde11-4參數(shù)選擇0=0,a20=8873.64,=37.68,g=179425,d=0.86+9.73M,M=M/o+M”,MfQ=3000+1000sin,Md=500+100sinInt,q=0.5a/osin(2r),Ag=0.2gosin(2r),at(t)=Q.5aiQ,0(f)=0.2go,D=60000,xld=sin(2r),初始狀態(tài)x(0)=100r,q=3600,c2=120,=300,=1。PID控制器參

3、數(shù)：K“=0.8,Kt=0.01,K/=0.0001。2仿真結(jié)果2.1未加邊界層 # #50-5x2dx2100 xix1dx151501.0.xpX # #0000.511.520.511.52time/s圖2-1x仁x1d跟蹤曲線time/s圖22x2、x2d跟蹤曲線2.! 005x3dx3coxpexo00-5CLO圖2-3x3.x3d跟蹤曲線21110.511.52time/s圖2-4滑?？刂菩盘柷€10.80.6r(D0.40.200.511.5time/s圖2-5跟蹤誤差曲線 2.2加入邊界層 # #x1dx1505o.0LX-OLXx2dx21050d-5-10 # #0.511

4、.52time/s圖2-6x1.x1d跟蹤曲線圖0.511.52time/s2-7x2.x2d跟蹤曲線 # #40co20 x3dx300000-20-400.40.200.20.4000.60.8 #OCLO-8O0.511.52time/s圖2-8x3.x3d跟蹤曲線0.511.5time/s圖2-9滑?？刂菩盘柷€ # 1|0.80.60.4-0.2-o1x1d跟蹤曲線圖0.511.5time/s2-12x2.x2d跟蹤曲線expex0.511.52time/so00-50050.200.20.40.6圖2-13x3.x3d跟蹤曲線0.511.5time/s圖2-14PID控制信號 0.

5、511.5time/s圖2-15跟蹤誤差曲線21.210.80.60.40.20023Matlab程序3.1滑?？刂瞥绦騝learclca10=0,a20=8873.64,a3O37.68?g0=l79425,cl=3600,c2=120,fea=300,N=l,xl=l,x2=0,x3=0,n=l,t=o,DA0.001,for1=1:2000%指令信號xld=sin(2*pi*t),xldl=2*pi*cos(2*pL*t),xld2=-(2*pi)A2*sin(2*pi*t),xId3=-(2*pi)A3*cos(2*pi*t),Mf0=3000+1000*sm(2*pi*t),DMfO

6、=1000*2*pi*cos(2*pL*t);Md=500+100*sm(2*pi*t),DMd=100*2*pi*cos(2*pL*t);M=NfO+Md,DM=DMfO+DMd,d=0.86*DM+9.73*M,da1=0.5*sin(2*pL*t)*a10,da2=0.5*sm(2*pi*t)*a20,da3=05*sm(2*pi*t)*a30,dg=0.2*sin(2*pL*t)*g0,f=-(alO+dal)*xl-(a2O+da2/)*x2-(a3CH-da3)*x3,g=gO+dg,el=xl-xld,e2=x2-xldl,e3=x3-xld2,u_equ=l/g0al0*xl+

7、a20*x2+a30*x3-cl*e2-c2*e3+xld3力s=cl*el+c2*e2+e3,%加入邊界層控制ifabs(s/fea)=lss=s/fea,elsess=sign(s/fea),endK=(Ka10+da1)*abs(x1J+(a20+da2)*absx2)+(a3Oda3)*abs(x3)+0.2*g0*abs(u_equ)+60000+1/(g0-0.2*g0),u_n=K*ss,%加入邊界層控制%u_n=K*sign(s力u=u_equ+ujn,Dxl=x2,Dx2=x3,Dx3=f+g*u+d,xl=xl+Dxl*Dt,x2=x2+Dx2*Dt,x3=x3+Dx3*D

8、t,x_store(:q尸x1d,xId1,x1d2,x1x2,x3;u_store(n)=u,e_stoi:e(ii尸el,t=t+Dt,n=n+l,endfigug)plot(l:n-l)*Dt_store(1,1mJ)*Dt/_stoi:e(4,J)legendxld/xr)xlabelCtime/sJylabeKxldjXT)figure(2)plot(l:n-l)*Dtc_store(2/1:n-1)*Dt_store(5,:)legendCx2d；x2JxlabelCtime/sJylabel(x2dx2Jfigure(3)plot(l:n-l)*Dtc_store(31:n-1)

9、*Dt_store(6/)Iegend(x3d；x3jxlabel(time/sjylabel(x3d3*)figure(4)plot(l:n-l)*Dt,e_store)xlabel(time/sjvlabel(er)figure(5)plot(l:n-l)*Dt,u_store)xlabel(time/sjylabel(U)3.2PID控制程序clearclca10=0,a20=8873.64,a3O=37.68?g0=l79425,kp=0.8,1Md=500+100*sin(2*pi*t),DMd=100*2*pi*cos(2*pi*t);M=NfO+Md,DM=DMfO+DMd,d=

10、086*DM+973*M,da1=0.5*sin(2*pi*t)*a10,da2=0.5*sm(2*pi*t廣a20,da3=05*sm(2*pi*t丿怙3(dg=0.2*sin(2*pi*t)*g0f=-(alO+dal)*xl-(a2CH-da2/)*x2-(a3O+da3)*x3,g=g0+dg,el=xl-xld,e2=x2-xldle3=x3-xld2,sumel=sumel+el*Dtzu=-kp*e1ki*sum_e1kd*e2,Dxl=x2,Dx2=x3,Dx3=f+g*u+d，xl=xl+Dxl*Dt,x2=x2+Dx2*Dt,x3=x3+Dx3*Dt,x_store(:q尸x1d,xId1,x1d2,x1,x2,x3,u_store(n)=u,e_store(n)=el,t=t+Dt,11=11+1,endfigure(l)plot(l:n-l)*Dtc_store(11:n-1)*Dtc_store(4,:)legendxldxr)xlabel(time/sjylabel(xld,xr)figure(2)plot(l:n-l)*Dtc_store(2rXl:n-l)*Dt_store(5,:)Iegend(,x2d,x2,)xlabelCtime/sJylabelCx2djX2Jfigug)plot(l:n-l)*Dtc_store(3r)l:n