控制系统建模、分析、设计和仿真——计算机仿真课程设计

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1、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：0 7自动化1班指导教师：范杰起止时间：2010年6月2 8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=

2、tf(968 968*11 968*18,1 13 44 32 0 0)Transfer function:968 s-2+10648 s+17424s 5+13 s 4+44 s 3+32 s 2 sysgz=c2d(gs,0.2)Transfer function:1.165 z4+3.221 z-3-2.431 z 2-0.3256 z+0.1049z 5-3.47 z 4+4.564 z 3-2.792 z 2+0.7724 z-0.07427Sampling time:0.2 a b k=zpkdata(sysgz)a=4x1 doubleb=5x1 doublek=1.1651 s

3、ysgz=zpk(a,b,k,0.2,variable,z-T)Zero/pole/gain:1.1651 z-1(l+3.359zl)(1-0.6703z-l)(1-0.1654z-l)(1+0.2418zl)厂2(1-0.8187z-l)(1-0.4493z-l)(1-0.2019z-l)Sampling time:0.2 syms z hO hl gO gl1.1651*z-l*(l+3.359*z-l)*(l-0.6703*z=l)*(l-0.1654*z;l)*(l+0.2418*z-1)/(l-zl)2/(l-0.8187*21)/(1-0.4 4 9 3*z 2 0 1 9*z、

4、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+0.2418*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+3359/100

5、0/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)-1fl=4359/1000*h0+4359/1000*hl-l f2=subs(diff(hz),z,1)f2=-3859/5

6、00*h0-12077/l000*h1 hO hl=solve(f1,f2)hO=12077000/19000881hl=-7718000/19000881 h=hO;hlh=12077000/19000881-7718000/19000881 hz=z-l*(l+3.359*z*-l)*l z-l*hhz=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*

7、g0+19000881000/37899197279*gl gO gl=solve(f3,f4)gO=1gl=25924762/19000881 g=gO;glg=12 5 9 2 4 7 6 2/1 9 0 0 0 8 8 1 he=(l-z-l)2 *1he=(1-1/z)2+2 5 9 2 4 7 6 2/1 9 0 0 0 8 8 1*(1-1/z)2/z dz=hz/gz/hedz=1 0 0 0 0/1 1 6 5 1*(1 2 0 7 7 0 0 0/1 9 0 0 0 8 8 1/z*(l+3 3 5 9/1 0 0 0/z)-7 7 1 8 0 0 0/1 9 0 0 0 8

8、 8 1/z*2*(l+3 3 5 9/1 0 0 0/z)*z/(l+3 3 5 9/1 0 0 0/z)/(1-6 7 0 3/1 0 0 0 0/z)/(1-8 2 7/5 0 0 0/z)/(1+1 2 0 9/5 0 0 0/z)*(1-1/z)2*(l-8 1 8 7/1 0 0 0 0/z)*(l-4 4 9 3/1 0 0 0 0/z)*(1-2 0 1 9/1 00 0 0/z)/(1-1/z)-2+2 5 9 2 4 7 6 2/1 9 0 0 0 8 8 1*(1-1/z)2/z)sysy=zpk(-3.3 5 9 0.6 2 2 1,0 0 1 1,0.3 0 6 3,

9、0.2)Zero/pole/gain:0.3 0 6 3 (z+3.3 5 9)(z-0.6 2 2 1)z 2(z-1)2S ampling time:0.2 sysyc=d2 c(sysy,tustin()Zero/pole/gain:-0.2 9 3 0 2 (s-1 8.4 8)(sT O 厂2 (s+2.3 3)s*2 (s+1 0)2 hold on td=O:O.2:2td=0 0.2 0 0 0 0.4 0 0 0 0.6 0 0 0 0.8 0 0 01.0 0 0 01.2 0 0 01.4 0 0 0 1.6 0 0 0 1.8 0 0 0 2.0 0 0 0 ud=td

10、ud=0 0.2 0 0 0 0.4 0 0 0 0.6 0 0 0 0.8 0 0 01.4 0 0 0 1.6 0 0 0 1.8 0 0 0 2.0 0 0 0 lsim(sysy,ud,td)t=0:0.2:2t=1.0 0 0 01.2 0 0 00 0.2 0 0 0 0.4 0 0 0 0.6 0 0 0 0.8 0 0 01.0 0 0 01.2 0 0 01.4 0 0 0 1.6 0 0 0 1.8 0 0 0 2.0 0 0 0 u=tu=0 0.2 0 0 0 0.4 0 0 0 0.6 0 0 0 0.8 0 0 01.4 0 0 0 1.6 0 0 0 1.8 0

11、0 0 2.0 0 0 0 lsim(sysyc,u,t)1.0 0 0 01.2 0 0 0Linear Simulation Resuts16离散无波纹的运行结果：gs=tf(l968 968*ll 968*18J,1 13 44 32 0 0)Transfer function:968 sA2+10648 s+17424sA5+13s八4+44 sA3+32 sA2 sysgz=c2d(gs,0.2,zoh,)Transfer function:1.165 zA4+3.221 zA3-2.431 zA2-0.3256 z+0.1049zA5-3.47 zA4+4.564 zA3-2.79

12、2 zA2+0.7724 z-0.07427Sampling time:0.2 a b kl=zpkdata(sysgz)a=f4xl doubleb=5x1 doublek=1.1651 sysgz=zpk(a,b,k,0.2,variable7zA-1)Zero/pole/gain:1.1651 zA-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)Sampling time:0.2 syms z hO hl gO glgz

13、=13473/100000/z*(l+3403/1000/z)*(l-8187/10000/z)*(l-1213/2000/z)*(1+301/1250/z)/(M/z)A2/(l-1131/l 250/z)/(l-463/625/z)/(l-2483/5000/z)g z=1.1651*2八-1 *(1+3.359*zA-1 )*(1 0.6703*2八-1 )*(1-0.1654*z 1 )*(1+0.2418*zA 1)/(1 2八-1)A2/(I-0.8187*zA-1)/(1-0.4493*zA-l)/(1-0.2019*z 人-1)gz=l 1651/10000/z*(l+3359

14、/1000/z)*(l-6703/10000/z)*(l-827/5000/z)*(l+1209/5000/z)/(l-l/z)A2/(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+h 1 *zA-l)hz=l/z*(l+3359/1000/z)*(l-6703/10000/z)*(l-827/5000/z)*(l+1209/5000/z)*(h0+hl/z)syms g2 g3 g4 he=(1

15、 -zA-1 )A2*(gO+g 1 *zA-l+g2*zA-24-g3*zA-3+g4*zA-4)he=(1-1/z)A2*(gO+g 1 /z+g2/zA2+g3/zA3+g4/zA4)fl=subs(hz,z,l)-lfl=372371008274811/250000000000000*h0+372371008274811/250000000000000*h 1 -1 f2=subs(diff(hz),z,1)f2=19805087962989/500000000000900-136672784229933/125000000000000*h 1 h0hl=solve(fl,f2)hO=

16、361568212248500000000000000/733651681500525726108450189hl=130986031501250000000000000/733651681500525726108450189 h=hO;hlh=361568212248500000000000000/733651681500525726108450189130986031501250000000000000/733651681500525726108450189J hz=zA-1*(1 +3.359*zA-1)*(1-0.6703*zA-1 )*(1-0.1654*zA-1)*(1+0.241

17、8*zA-1 )*(hO+h 1 *zA-1)hz=l/z*(l+3359/1000/z)*(1-6703/10000/z)*(1-827/5000/z)*(1+1209/5000/z)*(361568212248500000000000000/733651681500525726108450189+130986031501250000000000000/733651681500525726108450189/z)he=(1 -l/z)A2*(gO+gl/z+g2/zA2+g3/zA3+g4/zA4)he=(1 -l/z)A2*(gO+g l/z+g2/zA2+g3/zA3+g4/zA4)f3

18、=1 -limit(he,z,Inf)f3=l-g0 f4=1 -subs(he,z,-3.359)f4=l-l 9000881/11282881*g0+19000881000/37899197279*g 1-19000881000000/127303403660161*g2+19000881000000000/427612132894480799*g3-19000881000000000000/143634915439256100384 Pg4 f5=l-subs(he,z,0.1654)f5=l-17413929/68392尹g0-87069645000/565609283*g 1 -43

19、5348225000000/467758877041*g2-2176741125000000000/386836591312907*g3-l 0883705625000000000000/319913861015774089*g4 f6=1 -subs(he,z,-0.2418)f6=1-3855I681/146168I*g0+192758405000/176717232尹g 1 -963792025000000/21365H 345761*g2+4818960125000000000/2583042217025049*g3-24094800625000000000000/3122898040

20、383284241*g4 f7=1 -subs(he,z,0.6703)17=1-10870209/44930209*g0-l 08702090000/301167190927*g 1 -1087020900000000/2018723680783681*g2 10870209000000000000/13531504832293013743*g3-l 08702090000000000000000/90701676890860071119329*g4 gO gl g2 g3 g4=solve(13,f4,f5,f6,f7)gO=lgl=1105735150752551452216900378

21、/733651681500525726108450189g2=ll 5686774938333276108450189/244550560500175242036150063g3=-19531199739613777676199244/733651681500525726108450189g4=-302434549395200528374745/18811581576936557079703851 he=(l-zA-l)A2*(gO+g 1 *zA-1 +g2*zA-2+g3*zA-3+g4*zA-4)he=(l-l/z)A2*(1+1105735150752551452216900378/7

22、33651681500525726108450189/z+115686774938333276108450189/244550560500175242036150063/zA2-19531199739613777676199244/733651681500525726108450189/zA3-302434549395200528374745/l 8811581576936557079703851/zA4)dz=hz/gz/hedz=10000/11651*(361568212248500000900000000/733651681500525726108450189+130986031501

23、250000000000000/733651681500525726108450189/z)*(1 -8187/10000/z)*(1-4493/10000/z)*(1 -2019/1 OOOO/z)/(l+ll 05735150752551452216900378/733651681500525726108450189/z+ll5686774938333276108450189/244550560500175242036150063/zA2-19531199739613777676199244/733651681500525726108450189/zA3-30243454939520052

24、8374745/1881158157693655707970385 l/zA4)361568212248500000000000000/733651681500525726108450189ans=0.4928 130986031501250000000000000/733651681500525726108450189ans=0.1785 0.1785/0.4928ans=0.3622 sysy=zpk(-3,359 0.6221,0 0 1 1,0.3063,0.2)Zero/pole/gain:0.3063(z+3.359)(z-0.6221)zA2(z-l)A2Sampling tim

25、e:0.2 sysyc=d2c(sysy,tustin,)Zero/pole/gain:-0.29302(s-18.48)(s-10)A2(s+2.33)sA2(s+10)A2 hold on td=0:0.2:2td=Columns 1 through 80 0.2000 0.4000 0.6000Columns 9 through 111.6000 1.8000 2.0000 ud=tdud=Columns 1 through 80 0.2000 0.4000 0.6000Columns 9 through 111.6000 1.8000 2.0000lsim(sysy,ud,td)t=0

26、:02:2t=Columns 1 through 80 0.2000 0.4000 0.6000Columns 9 through 111.6000 1.8000 2.0000 u=tu=Columns 1 through 80 0.2000 0.4000 0.6000Columns 9 through 111.6000 1.8000 2.00000.80001.00001.20001.40000.80001.00001.20001.40000.80001.00001.20001.40000.80001.00001.20001.4000lsim(sysyc,u,t)连续控制系统建模、分析、设计

27、和仿真 5 号设有连续线性时不变被控对象G(s)=(1-5)(5+4)s(s+0.45)(s 0.45)试 以 MATLAB为工具设计-模拟控制器D(s),将单位反馈闭环系统的主导极点配置在.%=3+j3,s2=-3-j 3,其余极点都在主导极点的左边；单位加速度信号输入时闭环系统稳态误差为零。要求通过SIMULINK仿真证实设计结果。运行结果：syms s h0 hl h2 h3 h4 gOhs=(l-s)*(hO+h 1 *s+h2*sA2+h3*sA3+h4*sA4);hg=(sA2+6*s-18)*(s+3)A2*(s+4)A2-sA3*(s+0.45)*(s-0.45)*(g0+s)

28、;fl=subs(hs,s,O)-subs(hg,s,O);f2=subs(diff(hs),s,0)-subs(diff(hg),s,0);f3=subs(diff(hs,2),s,0)-subs(diff(hg,2),s,0);f4=subs(hs,s,-0.45)-subs(hg,s,-0.45);f5=subs(hs,s,0.45)-subs(hg,s,0.45);hO hl h2 h3 h4=solve(fl,f2,f3,f4,f5);f6=subs(hg,s,1)g0=solve(f6)h=h4 h3 h2hl hOg=l gOhs=(l-s)*sA4 sA3 sA2s l*h*he=sA3*(s+0.45)*(s-0.45)*s l*ggs=(l-s)*(s+3)/s/(s+0.45)/(s-0.45)ds=simplify(hs/gs/he)