磁盘驱动读取系统的分析设计一、闭环系统的性能分析(1)确定使闭环系统稳定的Ka的取值范围>>G1=tf([5000],[1,1000]);>>G2=tf([1],conv([1,0],[1,20]));>>G=series(G1,G2)Transferfunction:5000------------------------s^3+1020s^2+20000sg3=一一开环传函G3=一一闭环传函>>symsKden>>den=[11020200005000*K];>>K=den(2)*den(3)/den(1)/5000K=4080有劳斯判据可得k的范围是0>g=100*Gg1=feedback(g,1)C=dcgain(g1)Transferfunction:500000------------------------s^3+1020s^2+20000sTransferfunction:500000---------------------------------s^3+1020s^2+20000s+500000C=1[c,t]=step(g1);>>[y,k]=max(c);>>percentovershoot=100*(y-C)/Cpercentovershoot=21.6918>>t=setllingtime(g1)t=0.3697K=1000时>>g=1000*GTransferfunction:5e006--------------------------------s^3+1020s^2+20000s>>g2=feedback(g,1)Transferfunction:5e006------------------------------------------s^3+1020s^2+20000s+5e006>>[c,t]=step(g2);>>C=dcgain(g2)C=1>>[y,k]=max(c)y=1.7109k=11>>percentovershoot=100*(y-C)/C调节时间函数percentovershoot=71.0891t=setllingtime(g2)t=0.4989超调量调节时间0.3697(s)K=1000时超调量调节时间0.4989(s)(3)考察扰动信号为单位阶跃时,上述两个Ka取值情况下,系统的抗干扰能力,并进行分析>>g2=tf([1],conv([10],[120]))Transferfunction:1----------s^2+20s>>g1=tf([5000],[11000])Transferfunction:5000-----------s+1000>>symsk>>g3=feedback(g2,g1,1)Transferfunction:s+1000-------------------------------s^3+1020s^2+20000s-5000>>g3=feedback(g2,-g1,1)Transferfunction:s+1000-------------------------------s^3+1020s^2+20000s+5000>>g4=-g3Transferfunction:-s-1000-------------------------------s^3+1020s^2+20000s+5000--------------------扰动输入的传递函数当K=100时>>g=tf([-1-1000],[1102020000500000])Transferfunction:-s-1000---------------------------------s^3+1020s^2+20000s+500000>>[c,t]=step(g);>>[y,k]=min(c)y=-0.0024k=15c(t)=2.4*10-3(s)当K=1000时>>g=tf([-1-1000],[11020200005000000])Transferfunction:-s-1000--------------------------------s^3+1020s^2+20000s+5e006>>[c,t]=step(g);>>[y,k]=min(c)y=-3.4308e-004k=11c(t)=0.34*10-3(s)(4)针对如下的性能指标要求,折中选取一个合适的Ka值取Ka=100二、速度反馈系统的性能分析(1)运用第3章中所学的劳斯判据,确定要使闭环系统稳定,Ka和K1应如何选取?Ka=100,K1=0.03(2)针对你选取的Ka和K1,仿真闭环系统的阶跃响应,并计算超调量、调节时间和对单位阶跃扰动的最大响应值。>>g1=tf([5000],[11000])Transferfunction:5000--------s+1000>>g2=tf([1],[120])Transferfunction:1------s+20>>g3=tf([1],[120])Transferfunction:1------s+20>>g0=feedback(g3*feedback(100*g1*g2,0.03,-1),1)Transferfunction:500000--------------------------------------------s^3+1020s^2+35000s+500000>>t=setllingtime(g0)t=0.2300>>[c,t]=step(g0);>>C=dcgain(g0)C=1>>[y,k]=max(c)y=1.0206k=38>>percentovershoot=100*(y-C)/Cpercentovershoot=2.0650超调量调节时间0.2300(s)>>g10=-feedback(g2*g3,-g1*100*(0.03*1/g3+1),1)Transferfunction:-s-1000----------------------------------------------------------------扰动输入传递函数s^3+1020s^2+35000s+500000>>step(g10)>>[c,t]=step(g10);>>[y,k]=max(c)y=0k=1>>[y,k]=min(c)y=-0.0020k=38对单位阶跃扰动的最大响应值:c(t)=2.0*10-3(s)。三、PD控制器的性能分析——根轨迹法利用根轨迹图,分析K3的变化对系统性能指标的影响,选取能够满足下列指标要求的K3值>>G3=series(G,tf([11],1))Transferfunction:5000s+5000------------------------s^3+1020s^2+20000s>>rlocus(G3)K3=14时GK3=feedback(G3*58,1);step(GK3,0.5)调节时间216ms超调量0对单位阶跃扰动的最大响应值