模拟电路二阶系统模型设计与仿真(PID参数调节)

.④二阶系统阻尼比越大,系统超调量越小,系统稳定性越好。且最佳阻尼比在0.7左右时,二阶系统为最佳状态。4个人总结附录实验程序：%%求阶跃响应的典型指标

functionmain_GetPerformanceOfStepResponseclc

clearall

closeallglobalgTolerance

gTolerance=0.05;%调整时间的偏差容许围%%test

wn=X;

xi=Y;X,Y的值视具体情况而定

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

t=0:0.01:;

y=step<g,t>;%%计算阶跃响应的指标

stepvalue=1;

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

figure

plot<t,y>

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

text<PeakTime,stepvalue*0.05,sprintf<'峰值时间%.2f',PeakTime>>

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

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

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

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

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

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

text<t<end>*0.9,stepvalue*1.05,sprintf<'稳态误差%f',SteadyStateError>>end%%求阶跃响应的典型指标

function[OverShoot,RiseTime,PeakTime,AdjustTime,SteadyStateError]=GetPerformanceOfStepResponse<t,y,stepvalue>globalgTolerance%超调量和峰值时间

[OSValue,OSIndex]=max<y>;

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

PeakTime=t<OSIndex>;%上升时间

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

RiseTime=t<index>;%调整时间和稳态误差

index1=find<y<=stepvalue*<1-gTolerance>,1,'last'>;%容许围由全局变量指定

index2=find<y>=stepvalue*<1+gTolerance>,1,'last'>;ifisempty<index2>%如果没有超调量,此值为空

index=index1;

else

index=max<index1,index2>;

end

index=max<index1,index2>;

AdjustTime=t<index>;SteadyStateError=mean<y<index:end>>-stepvalue;%这里的稳态误差计算为调整时间后的数据平均值与给定输入的差,概念上是最后时刻的值与给定输入的差end参考文献[1]勤贤,王培良,郭永洪,等.