Casey Petersen
EECS460; HW12
Part a....................................................................................................................................................... 1
Part b ...................................................................................................................................................... 1
Part c ....................................................................................................................................................... 2
close all
clear all
clc
Part a
s = tf('s');
num = exp(-2*s);
den = (10*s+1)*(25*s+1);
Ga = num/den;
margin(Ga);
hold on;
Part b
n =
T =
num
den
2;
2;
= (1-s*T/2/n)^n;
= (1+10*s)*(1+25*s)*(1+s*T/2/n)^n;
Casey Petersen
EECS460; HW12
Gb = num/den;
margin(Gb);
Part c
n = 1;
num = (1-s*T/2/n)^n;
den = (1+10*s)*(1+25*s)*(1+s*T/2/n)^n;
Gc = num/den;
margin(Gc);
figure;
nyquist(Ga);
hold on;
n = 1000;
r = 1;
th = linspace(0,2*pi,n);
x = r*cos(th);
y = r*sin(th);
plot(x,y,'g');axis equal;
Casey Petersen
EECS460; HW12
Casey Petersen
EECS460; HW12
close all
clear all
clc
% Part a
% syms Kp Ki s
s = tf('s');
Ki=2;
den = (s*(1+0.25*s));
Kp=1;
i=1;
num = ((Kp*s+Ki)*exp(-0.2*s));
Gp = tf(num/den);
[Gm,Pm,Wgm,Wpm] = margin(Gp);
for Kp = 0.9:0.0001:1
num = ((Kp*s+Ki)*exp(-0.2*s));
Gp = tf(num/den);
% stepinfo(Gp)
close all
[Gm,Pm,Wgm,Wpm] = margin(Gp);
gainMargin(:,i)=([Kp,Gm]);
phaseMargin(:,i)=([Kp,Pm]);
i=i+1;
end
% [val col]=max(gainMargin(2,:));
% gainMargin(:,col)
[val col]=max(phaseMargin(2,:));
phaseMargin(:,col)
% [val col]=min(phaseMargin(2,:));
% phaseMargin(:,col)
% gainMargin(:,col)
ans =
0.9597
77.1679
close all
clear all
clc
Part a syms Kp Ki s
Casey Petersen
EECS460; HW12
s = tf('s');
Ki=2;
den = (s*(1+0.25*s));
Kp=1;
i=1;
num = ((Kp*s+Ki)*exp(-0.2*s));
Gp = tf(num/den);
[Gm,Pm,Wgm,Wpm] = margin(Gp);
for Kp = 2.5552:0.000001:2.5554
num = ((Kp*s+Ki)*exp(-0.2*s));
Gp = tf(num/den);
% stepinfo(Gp)
close all
[Gm,Pm,Wgm,Wpm] = margin(Gp);
gainMargin(:,i)=([Kp,Gm]);
phaseMargin(:,i)=([Kp,Pm]);
i=i+1;
end
phaseMargin;
Published with MATLAB® R2016a
Casey Petersen
EECS460; HW12
Problem 4
Step 1 ...................................................................................................................................................... 6
Step 2 ...................................................................................................................................................... 7
Step 3 ...................................................................................................................................................... 7
Step 4 ...................................................................................................................................................... 8
close all
clear all
clc
Step 1
s = tf('s');
num = 100;
den = (s^2+10*s+100);
Gp = num/den;
margin(Gp);
Casey Petersen
EECS460; HW12
Step 2
K=10^(18.65/20)
Gp2 = K*Gp;
figure(2)
margin(Gp2);
[Gm,Pm,Wgm,Wpm] = margin(Gp2);
K =
8.5605
Step 3
Gc = 1/1.455*((1+0.0485*s)/(1+0.0229*s));
phi_m = 50-Pm
a = (1+sind(phi_m))/(1-sind(phi_m))
T = 1/(30*sqrt(a))
aT = a*T
Gc = 1/sqrt(a)*((1+a*T*s)/(1+T*s))
phi_m =
Casey Petersen
EECS460; HW12
29.4657
a =
2.9362
T =
0.0195
aT =
0.0571
Gc =
0.03333 s + 0.5836
-----------------0.01945 s + 1
Continuous-time transfer function.
Step 4
figure(3)
margin(Gc);
figure(4)
G=Gc*Gp2
margin(G);
stepinfo(G)
G =
28.54 s + 499.6
--------------------------------------0.01945 s^3 + 1.195 s^2 + 11.95 s + 100
Continuous-time transfer function.
ans =
RiseTime:
SettlingTime:
SettlingMin:
SettlingMax:
0.1367
0.7836
4.6383
5.9785
Casey Petersen
EECS460; HW12
Overshoot: 19.6718
Undershoot: 0
Peak: 5.9785
PeakTime: 0.3132
Casey Petersen
EECS460; HW12
Published with MATLAB® R2016a