一阶保持器FOH

一阶保持器是一种按照线性规律外推的保持器

一阶保持器的单位脉冲响应可以分解为若干阶跃函数和斜坡函数之和

其单位脉冲响应的拉普拉斯变换可以表示为

s = tf('s');

T = 2 ;%  采样周期T=2s

G = T*(1+T*s)*((1-exp(-T*s))/(T*s))^2 ;

bode(G)

w = 0:0.001:500;

T = 0.1;

G = T*(1+1j*T*w).*(sin(w*T/2)./(T*w/2)).^2.*exp(-1j*w*T);

plot(w,abs(G))

title("FOH的相频特性")

xlabel('w/(rad/s)')

ylabel('|G(jw)|')

figure

plot(w,angle(G))

title("FOH的幅频特性")

xlabel('w/(rad/s)')

ylabel('\angleG(jw)')

w = logspace(1,3,1000);

T = 0.1;

G = T*(1+1j*T*w).*(sin(w*T/2)./(T*w/2)).^2.*exp(-1j*w*T);

plot(w,[abs(G);angle(G)])

axis([0 1000 -5 5])

title('the Frequency Characteriistic of FOH')

xlabel('w (rad/s)')

ylabel('Amplitude-Phase-frequency characteristic') 

w = logspace(1,3,1000);

T = 0.1; %sample time

G = T*(1+1j*T*w).*((1-exp(-1j*w*T))./(1j*T*w)).^2;

figure % new figure

[hAx,hLine1,hLine2] = plotyy(w,abs(G),w,angle(G));

title('the Frequency Characteriistic of FOH')

xlabel('w (rad/s)')

ylabel(hAx(1),'Amplitude-frequency characteristic') % left y-axis 

ylabel(hAx(2),'Phase-frequency characteristic') % right y-axis

与ZOH的幅频特性相比，FOH的幅频特性的幅值较大，高频分量较大，相位滞后比ZOH更大，对系统稳定性不利

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