控制系统建模、分析、设计和仿真-计算机仿真课程设计

控制系统建模、分析、设计和仿真

——计算机仿真课程设计

学生姓名：薛伟煌

学号：070104011035

学院：信息科学技术学院

专业/班级：07自动化1班

指导教师：范杰

起止时间：2010年6月28日——2010年7月2日

离散控制系统建模、分析、设计和仿真[5号]

设被控对象的传递函数G(s)=~v幽上辿主出一,用零阶保持器离散化，采

s2(s+l)(s+4)(s+8)

样周期取0.2秒，以MATLAB为工具，分别设计一单位速度信号输入时的最少有

波纹控制器DY(z)和一阶跃信号输入时的最少拍无波纹控制器DW(z)o要求通过

仿真证实设计结果。

离散有波纹的运行结果：

»gs=tf([968968*11968*18],[113443200])

Transferfunction:

968s-2+10648s+17424

s5+13s4+44s3+32s2

>>sysgz=c2d(gs,0.2)

Transferfunction:

1.165z'4+3.221z-3-2.431z2-0.3256z+0.1049

z5-3.47z4+4.564z3-2.792z2+0.7724z-0.07427

Samplingtime:0.2

>>[abk]=zpkdata(sysgz)

a=

[4x1double]

b=

[5x1double]

k=

1.1651

>>sysgz=zpk(a,b,k,0.2,'variable','z-T)

Zero/pole/gain:

1.1651z^-1(l+3.359z'l)(1-0.6703z^-l)(1-0.1654z^-l)(1+0.2418z'l)

厂2(1-0.8187z^-l)(1-0.4493z^-l)(1-0.2019z^-l)

Samplingtime:0.2

>>symszhOhlgOgl

»

1.1651*z^-l*(l+3.359*z^-l)*(l-0.6703*z=l)*(l-0.1654*z;l)*(l+0.2418*

z^-1)/(l-z^l)^2/(l-0.8187*2^1)/(1-0.4493*z2019*z、l)

ans=

11651/10000/z*(1+3359/1000/z)*(l-6703/10000/z)*(l-827/5000/z)*(1+1209

/5000/z)/(1-1/z)*2/(1-8187/10000/z)/(1-4493/10000/z)/(1-2019/10000/z)

»

gz=l.1651*z*-l*(l+3.359*z'-l)*(l-o.6703*z*-l)*(l-0.1654*z'-l)*(l+0.24

18*z"-l)/(l-z--l)"2/(l-0.8187*z"-l)/(l-0.4493*z"-l)/(l-0.2019*z--l)

gz=

11651/10000/z*(1+3359/1000/z)*(l-6703/10000/z)*(l-827/5000/z)*(1+1209

/5000/z)/(1-1/z)*2/(1-8187/10000/z)/(1-4493/10000/z)/(1-2019/10000/z)

>>hz=z'-l*(l+3.359*z--l)*(hO+hl*z--l)

hz=

1/z*(1+3359/1000/z)*(hO+hl/z)

>>he=(l-z'-l)~2*(gO+gl*z'-l)

he=

(1-1/z)'2*(g0+gl/z)

>>fl=subs(hz,z,1)-1

fl=

4359/1000*h0+4359/1000*hl-l

>>f2=subs(diff(hz),z,1)

f2=

-3859/500*h0-12077/l000*h1

»[hOhl]=solve(f1,f2)

hO=

12077000/19000881

hl=

-7718000/19000881

»h=[hO;hl]

h=

[12077000/19000881]

[-7718000/19000881]

>>hz=z"-l*(l+3.359*z*-l)*[lz'-l]*h

hz=

12077000/19000881/z*(1+3359/1000/z)-7718000/19000881/z*2*(1+3359/1000

/z)

>>f3=l-limit(he,z,Inf)

f3=

1-gO

>>f4=l-subs(he,z,-3.359)

f4=

1-19000881/11282881*g0+19000881000/37899197279*gl

>>[gOgl]=solve(f3,f4)

gO=

1

gl=

25924762/19000881

»g=[gO;gl]

g=

[1]

[25924762/19000881]

>>he=(l-z--l)"2*[1

he=

(1-1/z)~2+25924762/19000881*(1-1/z)~2/z

>>dz=hz/gz/he

dz=

10000/11651*(12077000/19000881/z*(l+3359/1000/z)-7718000/19000881/z*2

*(l+3359/1000/z))*z/(l+3359/1000/z)/(1-6703/10000/z)/(1-827/5000/z)/(

1+1209/5000/z)*(1-1/z)~2*(l-8187/10000/z)*(l-4493/10000/z)*(1-2019/10

000/z)/((1-1/z)-2+25924762/19000881*(1-1/z)"2/z)

»sysy=zpk([-3.3590.6221],[0011],[0.3063],0.2)

Zero/pole/gain:

0.3063(z+3.359)(z-0.6221)

z2(z-1)2

Samplingtime:0.2

>>sysyc=d2c(sysy,'tustin()

Zero/pole/gain:

-0.29302(s-18.48)(sTO厂2(s+2.33)

s*2(s+10)"2

>>holdon

»td=O:O.2:2

td=

00.20000.40000.60000.80001.00001.2000

1.40001.60001.80002.0000

>>ud=td

ud=

00.20000.40000.60000.80001.00001.2000

1.40001.60001.80002.0000

>>lsim(sysy,ud,td)

>>t=0:0.2:2

t=

00.20000.40000.60000.80001.00001.2000

1.40001.60001.80002.0000

>>u=t

u=

00.20000.40000.60000.80001.00001.2000

1.40001.60001.80002.0000

>>lsim(sysyc,u,t)

LinearSimulationResuts

16

离散无波纹的运行结果：

»gs=tf(l968968*ll968*18J,[113443200])

Transferfunction:

968sA2+10648s+17424

AAA

s5+13s八4+44s3+32s2

»sysgz=c2d(gs,0.2,,zoh,)

Transferfunction:

1.165zA4+3.221zA3-2.431zA2-0.3256z+0.1049

zA5-3.47zA4+4.564zA3-2.792zA2+0.7724z-0.07427

Samplingtime:0.2

»[abkl=zpkdata(sysgz)

a=

f4xldouble]

b=

[5x1double]

k=

1.1651

»sysgz=zpk(a,b,k,0.2,'variable7zA-1')

Zero/pole/gain:

1.1651zA-l(1+3.359zA-l)(l-0.6703zA-l)(1-0.1654zA-l)(l+0.2418zA-l)

(l-zA-l)A2(l-0.8187zA-l)(l-0.4493zA-l)(l-0.2019zA-l)

Samplingtime:0.2

»symszhOhlgOgl

gz=13473/100000/z*(l+3403/1000/z)*(l-8187/10000/z)*(l-1213/2000/z)*(1+301/1250/z)/(M/z)

A2/(l-1131/l250/z)/(l-463/625/z)/(l-2483/5000/z)

A

»gz=1.1651*2八-1*(1+3.359*zA-1)*(1・0.6703*2八-1)*(1-0.1654*z^・1)*(1+0.2418*z・1)/(1・2八-1)

AAA

2/(I-0.8187*z-1)/(1-0.4493*z-l)/(1-0.2019*z人-1)

gz=l1651/10000/z*(l+3359/1000/z)*(l-6703/10000/z)*(l-827/5000/z)*(l+1209/5000/z)/(l-l/z)A

2/(1-8187/10000/z)/(l-4493/10000/z)/(l-2019/10000/z)

»hz=zA-l*(1+3.359*zA-1)*(1-0.6703^-1)*(1-0.1654*zA-1)*(1+0.2418*zA-l)*(hO+h1*zA-l)

hz=l/z*(l+3359/1000/z)*(l-6703/10000/z)*(l-827/5000/z)*(l+1209/5000/z)*(h0+hl/z)

»symsg2g3g4

»he=(1-zA-1)A2*(gO+g1*zA-l+g2*zA-24-g3*zA-3+g4*zA-4)

he=(1-1/z)A2*(gO+g1/z+g2/zA2+g3/zA3+g4/zA4)

»fl=subs(hz,z,l)-l

fl=372371008274811/250000000000000*h0+372371008274811/250000000000000*h1-1

»f2=subs(diff(hz),z,1)

f2=19805087962989/50000000000090^^0-136672784229933/125000000000000*h1

»[h0hl]=solve(fl,f2)

hO=361568212248500000000000000/733651681500525726108450189

hl=130986031501250000000000000/733651681500525726108450189

»h=[hO;hl]

h=[361568212248500000000000000/733651681500525726108450189]

[130986031501250000000000000/733651681500525726108450189J

»hz=zA-1*(1+3.359*zA-1)*(1-0.6703*zA-1)*(1-0.1654*zA-1)*(1+0.2418*zA-1)*(hO+h1*zA-1)

hz=l/z*(l+3359/1000/z)*(1-6703/10000/z)*(1-827/5000/z)*(1+1209/5000/z)*(361568212248500

000000000000/733651681500525726108450189+130986031501250000000000000/7336516815

00525726108450189/z)

»he=(1-l/z)A2*(gO+gl/z+g2/zA2+g3/zA3+g4/zA4)

he=(1-l/z)A2*(gO+gl/z+g2/zA2+g3/zA3+g4/zA4)

»f3=1-limit(he,z,Inf)

f3=l-g0

»f4=1-subs(he,z,-3.359)

f4=l-l9000881/11282881*g0+19000881000/37899197279*g1-19000881000000/1273034036601

61*g2+19000881000000000/427612132894480799*g3-19000881000000000000/1436349154392

56100384Pg4

»f5=l-subs(he,z,0.1654)

f5=l-17413929/68392尹g0-87069645000/565609283*g1-435348225000000/467758877041*g2-

2176741125000000000/386836591312907*g3-l0883705625000000000000/31991386101577408

9*g4

»f6=1-subs(he,z,-0.2418)

f6=1-3855I681/146168I*g0+192758405000/176717232尹g1-963792025000000/21365H345761

*g2+4818960125000000000/2583042217025049*g3-24094800625000000000000/312289804038

3284241*g4

»f7=1-subs(he,z,0.6703)

17=1-10870209/44930209*g0-l08702090000/301167190927*g1-1087020900000000/201872368

0783681*g2・10870209000000000000/13531504832293013743*g3-l08702090000000000000000

/90701676890860071119329*g4

»[gOglg2g3g4]=solve(13,f4,f5,f6,f7)

gO=l

gl=1105735150752551452216900378/733651681500525726108450189

g2=ll5686774938333276108450189/244550560500175242036150063

g3=-19531199739613777676199244/733651681500525726108450189

g4=-302434549395200528374745/18811581576936557079703851

»he=(l-zA-l)A2*(gO+g1*zA-1+g2*zA-2+g3*zA-3+g4*zA-4)

he=(l-l/z)A2*(1+1105735150752551452216900378/733651681500525726108450189/z+115686

774938333276108450189/244550560500175242036150063/zA2-19531199739613777676199244/

733651681500525726108450189/zA3-302434549395200528374745/l8811581576936557079703

851/zA4)

»dz=hz/gz/he

dz=10000/11651*(361568212248500000900000000/733651681500525726108450189+13098603

1501250000000000000/733651681500525726108450189/z)*(1-8187/10000/z)*(1-4493/10000/z)

*(1-2019/1OOOO/z)/(l+ll05735150752551452216900378/733651681500525726108450189/z+ll

5686774938333276108450189/244550560500175242036150063/zA2-1953119973961377767619

9244/733651681500525726108450189/zA3-302434549395200528374745/1881158157693655707

970385l/zA4)

»361568212248500000000000000/733651681500525726108450189

ans=0.4928

»130986031501250000000000000/733651681500525726108450189

ans=0.1785

»0.1785/0.4928

ans=0.3622

»sysy=zpk([-3,3590.6221],[0011],[0.3063],0.2)

Zero/pole/gain:

0.3063(z+3.359)(z-0.6221)

zA2(z-l)A2

Samplingtime:0.2

»sysyc=d2c(sysy,,tustin,)

Zero/pole/gain:

-0.29302(s-18.48)(s-10)A2(s+2.33)

sA2(s+10)A2

»holdon

»td=0:0.2:2

td=

Columns1through8

00.20000.40000.60000.80001.00001.20001.4000

Columns9through11

1.60001.80002.0000

»ud=td

ud=

Columns1through8

00.20000.40000.60000.80001.00001.20001.4000

Columns9through11

1.60001.80002.0000

»lsim(sysy,ud,td)

»t=0:02:2

t=

Columns1through8

00.20000.40000.60000.80001.00001.20001.4000

Columns9through11

1.60001.80002.0000

»u=t

u=

Columns1through8

00.20000.40000.6000