Contents

clc
clear
close all

张峰2022年05月28日编写

初始化参数

t=0:0.01:10;
step_signal=ones(1,length(t));
line_width=4;

1 比例环节

k=[0.5,0.8];  % 增益
legend_str{1}='阶跃信号';
for i=1:length(k)
    s=tf(k(i),1);
    y(i,:)=step(s,t);
    legend_str{i+1}=strcat('增益K=',num2str(k(i)));
end
figure
plot(t,step_signal,t,y,'LineWidth',line_width)
legend(legend_str,'Location','best')
xlabel('时间/s')
ylabel('电压值/V')
set(gca,'FontSize',36)
set(gcf,'unit','normalized','position',[0.1,0.1,0.8,0.8]);
ylim([-0.3,1.3])
title('比例环节')

2 积分环节

voltage_t=1; %求输出信号1v时的时间
saturated=10; % 饱和电压
R0=200*1e3; % R0的电阻值
C=[1e-6,2e-6];  % 电容值
legend_str{1}='阶跃信号';
for i=1:length(C)
    s=tf(1,[R0*C(i),0]);
    ytemp=step(s,t);
    t_saturated=find(ytemp>voltage_t);
    if length(t_saturated)
        t_satu=t_saturated(1);
        t_sat(i)=t_satu;
        ytemp(ytemp>=saturated)=saturated;
    end
    y(i,:)=ytemp;
    legend_str{i+1}=strcat('电阻R0=200K,电容C=',num2str(C(i)*1e6),'uF');
end

figure
plot(t,step_signal,t,y,'LineWidth',line_width)
hold on
t1_s=t(t_sat(1));
t2_s=t(t_sat(2));
plot([t1_s,t1_s],[-0.1,saturated+1],'r--','LineWidth',3)
text(t1_s,saturated-1,strcat('t=',num2str(t1_s)),'Fontsize',36)
plot([t2_s,t2_s],[-0.1,saturated+1],'g--','LineWidth',3)
text(t2_s,saturated,strcat('t=',num2str(t2_s)),'Fontsize',36)
legend(legend_str,'Location','best')
xlabel('时间/s')
ylabel('电压值/V')
set(gca,'FontSize',36)
set(gcf,'unit','normalized','position',[0.1,0.1,0.8,0.8]);
xlim([0,4.5])
ylim([-0.3,11])
title('积分环节')

3 比例积分环节

voltage_t=2; %求输出信号1v时的时间
saturated=10; % 饱和电压
R0=200*1e3; % R0的电阻值
R1=200*1e3; % R0的电阻值
C=[1e-6,2e-6];  % 电容值
legend_str{1}='阶跃信号';
for i=1:length(C)
    s=tf([R1/R0*R0*C(i),1],[R0*C(i),0]);
    ytemp=step(s,t);
    t_saturated=find(ytemp>voltage_t);
    if length(t_saturated)
        t_satu=t_saturated(1);
        t_sat(i)=t_satu;
        ytemp(ytemp>=saturated)=saturated;
    end
    y(i,:)=ytemp;
    legend_str{i+1}=strcat('电阻R0=200K,R1=200K,电容C=',num2str(C(i)*1e6),'uF');
end
figure
plot(t,step_signal,t,y,'LineWidth',line_width)
hold on
t1_s=t(t_sat(1));
t2_s=t(t_sat(2));
plot([t1_s,t1_s],[-0.1,saturated+1],'r--','LineWidth',line_width)
text(t1_s,saturated-1,strcat('t=',num2str(t1_s)),'Fontsize',36)
plot([t2_s,t2_s],[-0.1,saturated+1],'g--','LineWidth',3)
text(t2_s,saturated,strcat('t=',num2str(t2_s)),'Fontsize',36)
legend(legend_str,'Location','best')
xlabel('时间/s')
ylabel('电压值/V')
set(gca,'FontSize',36)
set(gcf,'unit','normalized','position',[0.1,0.1,0.8,0.8]);
ylim([-0.3,11])
title('比例积分环节')

4 比例积分

saturated=10; % 0.632电压
voltage_t=0.632; % 0.632电压
R0=200*1e3; % R0的电阻值
R1=200*1e3; % R0的电阻值
C=[1e-6,2e-6];  % 电容值
legend_str{1}='阶跃信号';
for i=1:length(C)
    s=tf(R1/R0,[R1*C(i),1]);
    ytemp=step(s,t);
    t_saturated=find(ytemp>voltage_t);
    if length(t_saturated)
        t_satu=t_saturated(1);
        t_sat(i)=t_satu;
        ytemp(ytemp>=saturated)=saturated;
    end
    y(i,:)=ytemp;
    legend_str{i+1}=strcat('电阻R0=200K,R1=200K,电容C=',num2str(C(i)*1e6),'uF');
end
figure
plot(t,step_signal,t,y,'LineWidth',line_width)
hold on
t1_s=t(t_sat(1));
t2_s=t(t_sat(2));
plot([t1_s,t1_s],[-0.1,saturated+1],'r--','LineWidth',line_width)
text(t1_s,voltage_t,strcat('t=',num2str(t1_s)),'Fontsize',36)
plot([t2_s,t2_s],[-0.1,saturated+1],'g--','LineWidth',line_width)
text(t2_s,0,strcat('t=',num2str(t2_s)),'Fontsize',36)
plot([-1,t2_s],[voltage_t,voltage_t],'b--','LineWidth',line_width)
text(-1,voltage_t,strcat(num2str(voltage_t)),'Fontsize',36)
legend(legend_str,'Location','best')
xlabel('时间/s')
ylabel('电压值/V')
set(gca,'FontSize',36)
set(gcf,'unit','normalized','position',[0.1,0.1,0.8,0.8]);
y_in_max=max(step_signal);
y_out_max=max(y(:));
y_max=max(y_in_max,y_out_max);
xlim([0,4])
ylim([-0.3,1.15*y_max])
title('比例积分环节')

5 比例微分

saturated=10; % 0.632电压
R0=100*1e3; % R0的电阻值
R2=100*1e3; % R2的电阻值
R3=10*1e3; % R3的电阻值
C=1e-6;  % 电容值
R1=[100*1e3,200*1e3]; % R1的电阻值
legend_str{1}='阶跃信号';
for i=1:length(R1)
    P=(R1(i)+R2)/R0;
    num = [R1(i)*R2*C, 0];
    den = [R0*R3*C, R0];
    G1= tf(num, den);
    G2= P+G1;
    ytemp=step(G2,t);
    ytemp(ytemp>=saturated)=saturated;
    y(i,:)=ytemp;
    legend_str{i+1}=strcat('电阻R1=',num2str(R1(i)));
end
figure
plot(t,step_signal,t,y,'LineWidth',line_width)
legend(legend_str,'Location','best')
xlabel('时间/s')
ylabel('电压值/V')
set(gca,'FontSize',36)
set(gcf,'unit','normalized','position',[0.1,0.1,0.8,0.8]);
y_in_max=max(step_signal);
y_out_max=max(y(:));
y_max=max(y_in_max,y_out_max);
ylim([-0.3,1.15*y_max])
xlim([0,0.3])
title('比例微分环节')

5 比例积分微分

saturated=10; % 10v饱和电压
R0=100*1e3; % R0的电阻值
R2=10*1e3; % R2的电阻值
R3=10*1e3; % R3的电阻值
C1=1e-6;  % 电容值
C2=1e-6;  % 电容值
R1=[100*1e3,200*1e3]; % R1的电阻值
legend_str{1}='阶跃信号';
for i=1:length(R1)
    G1=R2/R0;
    num2 = [R1(i)*C1, 1];
    den2 = [R0*C1, 0];
    G2= tf(num2, den2);
    num3 = [R1(i)*R2*C1*C2, R2*C2,0];
    den3 = [R0*R3*C1*C2,R0*C1,0];
    G3= tf(num3, den3);
    G= G1+G2+G3;
    ytemp=step(G,t);
    ytemp(ytemp>=saturated)=saturated;
    y(i,:)=ytemp;
    legend_str{i+1}=strcat('电阻R1=',num2str(R1(i)/1000),'K');
end
figure
plot(t,step_signal,t,y,'LineWidth',line_width)
legend(legend_str,'Location','best')
xlabel('时间/s')
ylabel('电压值/V')
set(gca,'FontSize',36)
set(gcf,'unit','normalized','position',[0.1,0.1,0.8,0.8]);
y_in_max=max(step_signal);
y_out_max=max(y(:));
y_max=max(y_in_max,y_out_max);
ylim([-0.3,1.15*y_max])
xlim([0,5])
title('比例微分积分环节')

Published with MATLAB® R2021b