零极点对系统性能的影响分析报告

1、零极点对系统性能的影响分析1任务步骤1）分析原开环传递函数GO （s）的性能，绘制系统的阶跃响应曲线得到系统的暂态性能（包括上升时间，超调时间，超调量，调节时间）；2） 在GO（ s）上增加零点，使开环传递函数为 G1 （ s），绘制系统的根轨 迹，分析系统的稳定性。绘制系统的阶跃响应曲线得到系统的暂态性能（包括上 升时间，超调时间，超调量，调节时间）；3） 在GO（ s）上增加极点，使开环传递函数为 G2（ s），绘制系统的根轨 迹，分析系统的稳定性；绘制系统的阶跃响应曲线得到系统的暂态性能（包括上 升时间，超调时间，超调量，调节时间）；4） 同时在GO（ s）上增加零极点，使开环传递函数为

2、 G3（s），绘制系统 的根轨迹，分析系统的稳定性；绘制系统的阶跃响应曲线得到系统的暂态性能（包 括上升时间，超调时间，超调量，调节时间）；5）综合数据，分析零极点对系统性能的影响。2开环传递函数GO (s)的性能分析2.1原GO (s)性能分析取原开环传函数为：G 0(s)1(s + 0.25)( s + 0.52 )2,1.1分析系统稳定性在M指令中输入：gO二zpk(,-0.25,-0.52,1) g二feedback(gO,1);z,p,k=zpkdata(g, V) 按Enter回车得：Zero/pole/ga in:1(s+0.25) (s+0.52) z =Empty matri

3、x: O-by-1p =-0.2500-0.5200k =1即闭环系统两个极点均具有负实部，系统稳定2.1.2系统的根轨迹Matlab 指令：G0=zpk(，-0.25,-0.52,1)g=feedback(g0,1);rlocus(g)得到图形：根据原函数的根轨迹可得:2 1O-1-9XJLSanocesvQXA VFanma nLitL!1LSystem: gGai n: 0.101Pole: -0.385 + 1.04iDamp ing: 0.347Overshoot (%): 31.3Freque ncy (rad/s): 1.11System: g-Gai n: 0.0369二Pol

4、e: -0.385 - 1.01iDamp ing: 0.356Overshoot (%): 30.2Freque ncy (rad：1.08rrtiiftt-3-4543Root Locus-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1-1Real Axis (sec onds)0 0.1图1原函数G0(s)的根轨迹系统的两个极点分别是-0.52和-0.25，零点在无限远处2.1.3G0 ( s)的阶跃响应Matlab 指令：g0二zpk(,-0.25,-0.52,1) g二feedback(g0,1);step(g)得到图形：Step Response1.40.8

5、0.40.2Time (sec on ds)System: gTime (seco nds): 3.18Amplitude: 1.15System: gTime (sec on ds): 11.3Amplitude: 0.887System: gTime (secoqds): 1.97Amplitude: 0.888图2原函数的阶跃响应曲线0.6由阶跃响应曲线分析系统暂态性能： 曲线最大峰值为1.15，稳态值为0.887，上升时间tr=1.97s超调时间tp=3.18s调节时间ts=11.3s，厶=2超调量 p%=29.505%2.2增加零点后的开环传递函数G1 （s）的性能分析传递函数的表达

6、式上单独增加一个零点 S=-a,并改变a值大小，即离虚轴的 距离，分析比较系统性能的变化。所以增加零点后为了分析开环传递函数的零点 对系统性能的影响，现在在原开环的开环传递函数为：2.2.1G（s+0.2；）（：+0.52）当a分别为0.01,0.1,1,10,100时，G1（s）的根轨与阶跃响应如下excel0.010.110100G _s401_(s 40.25(s 40.52s -0.1G(s，=(s 0.2(s 0.52)G(s)=(s40.2(s+0.52s 10G(s)：s02)(s0.52s100G(s(s0.25)(s0.52)传递函数g0=zpk(-0.01,-M旨令0.25

7、,-o.52,1)g=feedback(g0,1);z,p,k=zpkdata(g,v)g0=zpk(-0.1,-0.25,- 0.52,1) g=feedback(g0,1); z,p,k=zpkdata(g,v)g0=zpk(-1,-0.25,- 0.52,1) g=feedback(g0,1); z,p,k=zpkdata(g,v)g0=zpk(-10,-0.25,-0.52,1) g=feedback(g0,1);z,p,k=zpkdata(g,v)g0=zpk(-100,-0.25,-0.52,1) g=feedback(g0,1); z,p,k=zpkdata(g,v)结果系统稳定

8、性根轨迹Zero/pole/gai n:(s+0.01)Zero/pole/ga in:(s+0.1)Zero/pole/ga in:(s+1)Zero/pole/ga in:(s+10)Zero/pole/ga in:(s+100)(s+0.25) (s+0.52)(s+0.25) (s+0.52)(s+0.25) (s+0.52)(s+0.25) (s+0.52)(s+0.25) (s+0.52)z =z =z =z =z =-0.0100-0.1000-1.0000-10.0000-100.0000p =p =p =p =p =-1.6870-1.6288-0.8850 + 0.5889

9、i-0.8850 + 3.0572i-0.8850 + 9.9673i-0.0830-0.1412-0.8850 - 0.5889i-0.8850 - 3.0572i-0.8850 - 9.9673ik =k =k =k =k =1.00001.00001.00001.00001.0000是是否稳定g0=zpk(-0.01,- 0.25,-0.52,1) 指令 g=feedback(g0,1);rlocus(g)g0=zpk(-0.1,-0.25,-0.52,1) g=feedback(g0,1);rlocus(g)g0=zpk(-1,-0.25,- 0.52,1) g=feedback(g0

10、,1);rlocus(g)g0=zpk(-10,-0.25,- 0.52,1) g=feedback(g0,1);rlocus(g)g0=zpk(-100,-0.25,- 0.52,1) g=feedback(g0,1);rlocus(g)Root Locus0.8System: gGain: 0.0102Pole:-0.89 + 0.589iDamping: 0.834100150.18Rot LocusSystem gSysterrgGain: 397Gain: InfFole: -200Pole: -100Drping: 1Danping:1Overshoot (%): Overshoo

11、t (%): 0Frequency (rad/iJiStjCency (rad/s): 100System gGain: 0.358 Pole: -1.07 + 11.6iDamping: 0.0915 Overshoot (%): 74. Frequency (rad/s):50.7g0=zpk(-0.01,-M指令 O.25，-。.521) 指令 g=feedback(g0,1);step(g)g0=zpk(-0.1,-0.25,- 0.52,1) g=feedback(g0,1);step(g)g0=zpk(-1,-0.25,- 0.52,1) g=feedback(g0,1);step

12、(g)g0=zpk(-10,-0.25,- 0.52,1) g=feedback(g0,1);step(g)g0=zpk(-100,-0.25,- 0.52,1) g=feedback(g0,1);step(g)阶跃响应):256 ad/s): 0.893Root LocusRoot Locus根轨迹绘根轨迹2ystem: gGai 0System: g，Gni0Pel -1.310 ； Daimpi1Overshoot (%): 0Frequency (rad/s):Ga: 0Pee 0.218 +Damg: -0.24Overshoot (Frequency (0.853i%): 223a

13、d/s): 0.881.System: gGa: 0Damg: -0.28Overshoot (Frequency iad254s): 0.884-10.-1.Damg: -0.24OvershootFrequency ( ad/s): 0.881):223-0-1-1 -0.System: gGni0.026Pel -1.65Dampi1Overshoot (%): 0Frequency (rad/s): 1.65System: gGai: 0.00198Pel -0.0641 + 0.8Damp: 0.0772Overshoot (%):Frequency (rad/8.4 ):0.832

14、5300200Root LocusSystem: gGni: 0Pel -0.0644 - 8 Damg: 0.0776 Overshoot (% Frequency (rad/27i8.3 ):0.8320T-S-1-0.525System: gGan 4.54Pel -10.1Damgi 1Overshoot (%)Frequency (rad/s): 10.1System: gGa: 0Pel -0.38 - 0.293Damg: 0.792Overshoot (%):Frequency (rad/.7.):0.479150000)0-20(System: gGai2.21e+004Pe

15、l -102Dampi1Overshoot (%): 0Frequency (rad/s): 102System: gGn: 0Pol -0.475Damg: 1Overshoot (%)Frequency (ra(0s): 0.475-300-200-100100200系统是否稳定否g0=zpk(，-0.25,-g0=zpk(，-0.25,-g0=zpk(，-0.25,-00=Zpk(，-0.25,-0g52=zpk(，-0.25,-0.52,-M指令令-52,-0.01,1); 0.52,-0.1,1);1,1)；10,1)；100,1)；E=feedback(g0,1g=feedback

16、(g0,1g=feedback(g0,1g=feedback(g0,1);g=feedback(g0,1);step(g)step(g)step(g)Tire (seconds)System: gSystem: gTie (seconds): 8.52Tie (seconds): 15.9$Ampude: 0.S卿 Responsmpde: 0.436 TZTSystem: g4Tire (seconds): 10.8Amplde: 0.44253( 15d li 10.Step Response0.0.Tie (seconds)Tie (seconds)Tine (seconds)0.Sys

17、tem: gTie (seconds): 2.59Amude: 0.887iSystem: gTm (seconds): 4.22Amplje:49Step Responsex 10System: gTime (seconds): 76.5Amplde: 0.87918step(g)0.080 )60 050 030 0201Step Response0 - -05101520Tin (seconds)System: gTire (secondAmpde: 0.0725):21.41130增加极点对系统性能的影响结论:1.增加不同的极点对系统参数有不同的影响;2.比较观察增加零点时的系统参数(

18、以上升时间tr为例)的变化，可以发现,在某些区间(x1a=px2 )内,存在：，则，说明了极点与零点对系统系能的影响的差别;3同时可以预见，当零点与原点的距离趋近于无穷远时，系统性能受到的影 响趋近于0。2.4偶极子对系统性能的影响原函数不十分接近原点的偶极子十分接近原点的偶极子传递函数G (s) 一(s 讦0.25)( s 讦0.52 )(s .2.01)G(s)( s .2)( s .0.25)(s .0.52)(s 亠0.01)G(s)=S(S 0.25)(s .0.52)根轨迹阶跃响应Root LocusRoot LocusRoot Locus2i)1-reqpency (rad/s.

19、0-1-3Real Axis (secondsReal Axis (secondsStep Response1.41.2System: gT ime (seconds)Time (seconds)Tirie (seccAmplitude: 0.888System : gTime (seconds): 11.4Amplitude: 0.887System: gGain: 0.0369Pole:-0.385- 1.01iDamping: 0.356Overshoot (%): 30.2Frequency (rad/s): 1.08Damping: 0.333Overshoot (%): 30Frequency (rad/s): 1.07m -2System : gGain: InfPole: 0.01Damping:-Overshoot (%): 0Frequency (rad/s): 0.0-Gain: 0.0166 Pole: -0.384 + 1iSystem : gTim e (seconds): 1.97A