.④二階系統阻尼比越大,系統超調量越小,系統穩定性越好。且最佳阻尼比在0.7左右時,二階系統為最佳狀態。4個人總結附錄實驗程序：%%求階躍響應的典型指標

functionmain_GetPerformanceOfStepResponseclc

clearall

closeallglobalgTolerance

gTolerance=0.05;%調整時間的偏差容許圍%%test

wn=X;

xi=Y;X,Y的值視具體情況而定

g=tf<wn^2,[1,2*xi*wn,wn^2]>;

t=0:0.01:;

y=step<g,t>;%%計算階躍響應的指標

stepvalue=1;

[OverShoot,RiseTime,PeakTime,AdjustTime,SteadyStateError]=GetPerformanceOfStepResponse<t,y,stepvalue>;%繪圖

figure

plot<t,y>

gridonline<[PeakTime,PeakTime],[0,<1+OverShoot/100>*stepvalue],'color','r'>

text<PeakTime,stepvalue*0.05,sprintf<'峰值時間%.2f',PeakTime>>

text<PeakTime,<1+OverShoot/100+0.05>*stepvalue,sprintf<'超調量%.2f%%',OverShoot>>line<[RiseTime,RiseTime],[0,stepvalue],'color','r'>

text<RiseTime,-stepvalue*0.05,sprintf<'上升時間%.2f',RiseTime>>line<[AdjustTime,AdjustTime],[0,stepvalue*<1+gTolerance>],'color','r'>

text<AdjustTime,stepvalue*0.05,sprintf<'調整時間%.2f',AdjustTime>>line<[AdjustTimet<end>],stepvalue*[<1-gTolerance>,<1-gTolerance>],'color','r','linestyle','--'>

text<AdjustTime,stepvalue*<1-gTolerance-0.05>,sprintf<'容許圍%.2f',1-gTolerance>>

line<[AdjustTimet<end>],stepvalue*[<1+gTolerance>,<1+gTolerance>],'color','r','linestyle','--'>

text<AdjustTime,stepvalue*<1+gTolerance+0.05>,sprintf<'容許圍%.2f',1+gTolerance>>

text<t<end>*0.9,stepvalue*1.05,sprintf<'穩態誤差%f',SteadyStateError>>end%%求階躍響應的典型指標

function[OverShoot,RiseTime,PeakTime,AdjustTime,SteadyStateError]=GetPerformanceOfStepResponse<t,y,stepvalue>globalgTolerance%超調量和峰值時間

[OSValue,OSIndex]=max<y>;

OverShoot=<OSValue-stepvalue>/stepvalue*100;

PeakTime=t<OSIndex>;%上升時間

index=find<y>=stepvalue,1,'first'>;

RiseTime=t<index>;%調整時間和穩態誤差

index1=find<y<=stepvalue*<1-gTolerance>,1,'last'>;%容許圍由全局變量指定

index2=find<y>=stepvalue*<1+gTolerance>,1,'last'>;ifisempty<index2>%如果沒有超調量,此值為空

index=index1;

else

index=max<index1,index2>;

end

index=max<index1,index2>;

AdjustTime=t<index>;SteadyStateError=mean<y<index:end>>-stepvalue;%這里的穩態誤差計算為調整時間后的數據平均值與給定輸入的差,概念上是最后時刻的值與給定輸入的差end參考文獻[1]勤賢,王培良,郭永洪,等.