全程滑模控制器的设计

1、 1全程滑模控制器设计考虑如卜的三阶非线性系统y=f(y,y,y;0+gV,+(y,V,y;0+d(t)其中，y=yy2儿丘疋，d(/)=o,“=(坷u23)rg/?3一1.5y；cos(3y2)、/(y,j,y；/)=3%sm(3儿)、cos)1sin儿；100)g(y,y,y；/)=oio101丿sin/sincos(3yj、V(y,y,y;t)=ecosysin儿cos/siny2为了表示成状态方程形式，引入状态变量人1、人2、召3、“21、兀22Ns-耳、心八xn,且X=xn,y2=x21,儿=心，于是得到卜面三组状态方程1=人212=X13若3=-l.SjcosGXzJ+sm/sin

2、xIcosGXiJ+iq=X23*23=x2isin(3x31)+cosx13sinx31+u2B=心232=“3大33=X33C0SXliS111X21+COS/SillX23+M3设计滑模面函数为$(/)=CE(/)CP400400100、其中,c=Gc2G)=04004001004004001;E(t)=(e7e1KJ,=(qxlld.为期望轨迹；P(f)=(Pi(f)P2(0P3(0)r其中nnn(ipM=；+/r+l工存化0)4工E-r(O)tk=oky=oI/=o/丿 # TOC o 1-5 h zet(0)+(0+*(o)尸+(0)尸+骨q(0)+怜勺(0)+2勺(。)JJj+如

3、石(0)+终弓(0)+也乂(0)+缪(0)+躲(0)片TfT；TfTfT；0tTfbJ函数p,(t)是一个在f=7；时刻三阶可微的连续函数，由此可以得到四组四元一次方程组：i+doo+qo+Eo+d)%+5坷0+6a2O+7a3O=012aw+20alo+30a2O+42ax=0248+60alo+120a2O+210a%=0l+a0l+an+a2l+a3l=01+4a0l+5an+6a2l+7an=012f/01+20an+30仙+42an=024a01+60an+120au+210a31=00.5+6/02+al2+a22+=01+4a01+5al2+6a22+7a52=01+1202+2

4、0al2+30幻+42=024a02+60al2+120an+210.=0-+aO3+a13+a23+33=00.5+4。03+5d3+6冬3+7。33=01+12aQi+20an+30a23+42a33=01+24a03+60a13+120a23+210an=0 # #解得aoo=-3510=846o=-70。30=20oi=-20n=45a、=3631=10aoi=-5fl12=10=7.5.an=2仙=-2/33=1知=-2/3仙=1/6 #控制器为w(0=-2)_厉_龙3sin(龙f)厲cosxnsinx21+4(x32-必)+4(禺3-/3)-A # #F(x)+f(川_1)+k(1

5、_严|严 式中,F(x)=2+k|AT(X,f)|。参数选取：a=2,0=1,k=0.02p=59g=3,Tf=3=0.05,=2。2仿真结果 # #1.5x11x11d # #50515QQ1.P二a20=-70,a3O20,a01=-20,all=45,a21=-36,a31=10,a02=-5,al2=10,a22=-7.5,a32=2,a03=-2/3,al3=l;a23=-2/3,a33=l/6,xll=0.5,xl2=0,xl3=0,x21=-l,x22=0,x23=0,x31=-0.2,x32=0,x33=0,el_0=xll-0, Del_0=xl2-pL/2,DDel_0=x

6、l3-0,DDDel_O04pi/2)A3,e2_0=x21丄De2_0=x22-0,DDe2_0=x23+pS2,DDDe2_O=sin(l)-pLA3e3_O=x31-l,De3_0=x32-0,DDe3_O=x33O,DDDe3_0=0OAl=a00/Tr4*el_(Ha0inr3*Del_0+a02/Tr2*DDel-0+a03/Tf*DDDeC0,Bl=al0/Tr5*el_0+all/Tfx4*Del_0+al2/TfA3*DDeC0+al3/Tr2*DDDeC0,Cl=a20/Tr6*el_0+a21/TfA5*Del_0+a22/TfA4*DDel-0+a23/rfx3*DDD

7、el_0D130/TfA7*el_CH-a31/rfA6*Del_0+a32/rfA5*DDel-CH-a33/TfA4*DDDel_0A2=a00/TP4牲2_(HaOinr、3水De2_0+a02/TF2水DDe2_O+aO3ZTf*DDDe2_O，E2=alO/TP5轻2_0+all/TH4水DeZOlZ/rfTDDO+aW/Tf水DDDe2_0,C2=a20/TH6轻2_O+a21/TP、5水De2_0+a22/Tf八炉DDe2_0+a23/T&3水DDDe2_0,D2=a30/rfA7*e2_0+a3irrfA6*De2.0+a32ZrfA5*DDe2_0+a33/TfA4*DDDe

8、2_05A3=a00/TH4*e3_OHi01/TF/、3水De3_0+a02/TH2*DDe3_0+a03/Tf*DDDe3_0,B310/Tr5*e3_(ll/Tr4*De3_(H-al2/rfA3*DDe3-0+al3/TfA2*DDDe3_0,C3=a20/Tr6*e3_0+a21/Tr5*De3_0+a22ZTfA4*DDe3-0+a23/Tfv3*DDDe3_0D3=a3O/TfA7*e3_O+a31/TfA6*De3.O+a32rrfA5*DDe3_O+a33/TfA4*DDDe3_O?n=l,t=0,Dt=O.OOl,for1=18000%参考信号及其一、二阶导数xlld=si

9、iXpi/2*t),Dx1ld=pi/2*cos(pL/2*t),DDxlld=-(pL/2)A2*SLn(pL/2*t),x21d=cos(pi*t),Dx21d=-pi*smpi*t),DDx21d=-piA2*cos(pi*t),x31d=l,Dx31d=0,DDx31d=0,%跟踪误差及其一、二阶导数e=xll-xlld,x21-x21dx31-x31dDe=xl2-Dxlldx22-Dx21dx32-Dx31d,DDe=xI3DDxlld,x23DDx21d,x33DDx31d,Lft=Tfpl=el_O+Del_O*叶1/2水DDelOT+l/DDDelOT+AFrM+El*护5+

10、Cl*V6+Dl*T7,Dpl=Del_0+DDel_0*t+l/2*DDDel_0*tA2+Al*4*tA3+Bl*5*tA4+Cl*6*tA5+Dl*7*tA6,DDpl=DDel_(HDDDel_0*t+xl*4*3*tA2+Bl*5*4*r34-01*6*5*4+01*7*6*5,DDDpl=DDDel_0+Al*4*3*2*t+Bl*5*4*3*tA2+Cl*6*5*4*tA3+Dl*7*6*5*tA4,p2=e2_0+De2_0*叶1/2水。02_0*广2+1/6*。02_0升/、3+人2七、4+2水护5+2呛八6+。2打人7,Dp2=De2_0+DDe2_0*t+l/2*DDDe

11、2_0*tA2+A2*4*tA3+B2*5*tA4+C2*6*tA5+D2*7*tA6,DDp2=DDe2_(HDDDe2_0*t+x2*4*3*tA2+B2*5*4*r34-02*6*5*4+02*7*6*5,DDDp2=DDDe2_0+A2*4*3*2*t+B2*5*4*3*tA2+C2*6*5*4*tA3+D2*7*6*5*tA4,p3=e3_O+De3_O*叶1/2水。03_0*广2+1/6*。63_0升/、3+人3%八4+珀*护5+3牡八6+。3人7,Dp3=De3_0+DDe3_0*t+l/2*DDDe3_0*tA2+A3*4*tA3+B3*5*tA4+C3*6*tA5+D3*7*

12、tA6,DDp3=DDe3_(HDDDe3_0*t+x3*4*3*tA2+B3*5*4*r34-03*6*5*4+03*7*6*5,DDDp3=DDDe3_0+A3*4*3*2*t+B3*5*4*3*tA2+C3*6*5*4*tA3+D3*7*6*5*tA4,elsepl=O,Dpl=O,DDpl=O,DDDpl=O,p2=0,Dp2=0,DDp2=0,DDDp2=0,p3=0,Dp3=0,DDp3=0,DDDp3=0,end%全程滑模而函数KDDDDpl-4*Dpl-4*pl,DDe(2)+4*De(2)+4*e(2/)-DDp2-4*Dp2-4*p2,DDe(3)+4*De(3)+4*e(

13、3)-DDp3-4*Dp3-4*p3J,delta=delta0+delta1*norm(e人F=2+exp-t),ul=-(-1.5*xl3A2*cos(3*x21)+4*(xl2-pL/2*cos(pi/2*t)-Dpl)+4*(xl3+piA2/4*sin(pL/2*t)-DDpl)-DDDpl+piA3/8*cos(pi/2*t)XF+alpha/k*(exp(k*norm(s)-l)+beta/k*(1-exp(-k*nonn(s)A(q/p)*exp(k*nomxs/(noms)+delta),u2=-(3*x22*SLn(3*x31)+4*(x22+pi*sm(pL*t)-Dp2

14、)+4*(x23+cos(pi*t)*piA2-DDp2)-DDDp2-pLA3*sin(pi*t)HF+alpha/k*(exp(k*nomXs”J)+beta/k*(l-exp(-k*nomxsexp(k*nomxs2y(norm(s)+delta),u3=-(x33*cosx11)*smx21)+4*(x32Dp3)+4*(x33DDp3)DDDp3HF+aLpha/k*(exp(k*iionn(s/)-1)+beta/k*(1exp(-k*nomxsD/Xq/p)*exp(k*iiomxs“(noms)+delta方Dxll=xl2,Dxl2=xl3,Dxl3=-1.5*xl3A2*c

15、os(3*x21)+sin(t)*sin(x22A2)*cos(3*x11)+u1;xll=xll+Dxll*Dt,xl2=xl2+Dxl2*Dt,xl3=xl3+Dxl3*Dt,Dx21=x22,Dx22=x23,Dx23=3*x22*sii3*x31)+exp(-t)*cos(x13)*sin(x31)+u2,x21=x21+Dx21*Dt,x22=x22+Dx22*Dt,x23=x23+Dx23水Dt,Dx31=x32,Dx32=x33,Dx33=x33*cos(x11)*sin(x21)+cos(t)*sin(x23)+u3,x31=x31+Dx31*Dt,x32=x32+Dx32水D

16、t,x33=x33+Dx33水Dt,y1_store(:i)=xlllld,v2_store(:q尸x2l,x21d,v3_store(:q尸x3l,x31d,u_store(:q尸u1卩2卩3s_sroi:e(尸s,t=t+Dt,11=11+1,endfigure(l)plot(l:n-l)*Dt,yl_store(l,:)Xl：n-l)*Bt,yl_store(2,:)legend(,xU,xlld,)xlabelCtime/sJylabelCxlllld)figure(2)plot(l:n-l)*Dt,y2store(l,：Xl：n-l)*Bt,y2_store(2,:)legend(x21；x2IdJxlabelCtime/sJylabel(x2121d,)figure(3)plot(l:n-l)*Dt,y3_store(l,:)Xl：n-l)*Bt,y3_store(2,:)legendCx31；x31dJxlabelCtime/sJylabel(,x31pc31d,)figure(4)plot(l:n-l)*Dt,u_store(11:n-1)*Dt,u_store(2,:),(1：n-1)*Dt,u_store(3,:)legendCur；u2*；u3jxlabelCtime/sJylabel(U)figure(5