Page 99 - Mechatronics with Experiments

CLOSED LOOP CONTROL 85
data is to plot the 20 log |G(jw)| as y-axis versus ∠(G(jw)) as the x-axis, where w is
10
parameterized along the plot. A frequency response can be expressed as
G(jw) = |G(jw)|∠(G(jw)) (2.89)

Log magnitude (20 log |G(jw)|)versus phase angle (∠(G(jw))) plots of various elements
10
®
are shown in Figure 2.32. A MATLAB program to generate the plot for Figures 2.30–2.32
is shown below.
K0 = 10.0 ;
z1 = 1.0 ;
p1 = 1.0 ;

num1 = [K0] ; den1 = [1] ; sys1=tf(num1,den1) ; % Ko
num2 = [1] ; den2 = [1 0] ; sys2=tf(num2,den2) ; % 1/s
num3 = [1 0] ; den3 = [1] ; sys3=tf(num3,den3) ; % s
num4= [1] ; den4 = [1/p1 1]; sys4=tf(num4,den4) ; % 1/(s/p1+1)
num5= [1/z1 1] ; den5 = [1] ; sys5=tf(num5,den5) ; % (s/z1+1)
psi = 0.25; w_n = 1.0 ;
num6=[w_nˆ2] ; den6=[1 2*psi*w_n w_nˆ2]; sys6=tf(num6,den6) ;
psi = 0.5; w_n = 1.0 ;
num7=[w_nˆ2] ; den7=[1 2*psi*w_n w_nˆ2]; sys7=tf(num7,den7) ;
psi = 0.75; w_n = 1.0 ;
num8=[w_nˆ2] ; den8=[1 2*psi*w_n w_nˆ2]; sys8=tf(num8,den8) ;
psi = 0.25; w_n = 1.0 ;
num9=[1 2*psi*w_n w_nˆ2]; den9=[w_nˆ2] ; sys9=tf(num9,den9) ;
psi = 0.5; w_n = 1.0 ;
num10=[1 2*psi*w_n w_nˆ2]; den10=[w_nˆ2] ; sys10=tf(num10,den10) ;
psi = 0.75; w_n = 1.0 ;
num11=[1 2*psi*w_n w_nˆ2]; den11=[w_nˆ2] ; sys11=tf(num11,den11) ;
figure(1) ; grid on; % Bode Plots
subplot(3,3,1) ; bode(sys1); grid on;
subplot(3,3,2) ; bode(sys2); grid on;
subplot(3,3,3) ; bode(sys3); grid on;
subplot(3,3,4) ; bode(sys4); grid on;
subplot(3,3,5) ; bode(sys5); grid on;
subplot(3,3,7) ; bode(sys6); hold on; bode(sys7); hold on;
bode(sys8); hold on;grid on;
subplot(3,3,8) ; bode(sys9); hold on; bode(sys10); hold on;
bode(sys11); hold on;grid on;
figure(2) ; grid off; % Nyquist (Polar) plots
subplot(3,3,1) ; nyquist(sys1); grid off;
subplot(3,3,2) ; nyquist(sys2); grid off;
subplot(3,3,3) ; nyquist(sys3); grid off;
subplot(3,3,4) ; nyquist(sys4); grid off;
subplot(3,3,5) ; nyquist(sys5); grid off;
subplot(3,3,7) ; nyquist(sys6); hold on; nyquist(sys7); hold on;
nyquist(sys8); hold on; grid off;
subplot(3,3,8) ; nyquist(sys9); hold on; nyquist(sys10); hold on;
nyquist(sys11); hold on; grid off;

figure(3) ; grid off; % Log Magnitude versus Phase plots
subplot(3,3,1) ; nichols(sys1); grid off;
subplot(3,3,2) ; nichols(sys2); grid off;
subplot(3,3,3) ; nichols(sys3); grid off;
subplot(3,3,4) ; nichols(sys4); grid off;
subplot(3,3,5) ; nichols(sys5); grid off;