Lines of magnitude plot of bode diagram

Hi MATLAB community. I have the following code:

%% Parameters
w = 2*pi*50;        % [rad/s]
Lf = 2.5e-3;        % [H]
Rf = 0.1*w*Lf;      % [Ohm]
Cf = 15e-6;         % [F]
Lg = 12e-3;         % [H]
Rg = 0.1*w*Lg;      % [Ohm]

s = tf('s');
plantg_ol = 1/((Cf*Lg)*s^2 + (Cf*Rg)*s)
plantg_cl = feedback(plantg_ol,1)
H = s*Lg + Rg
plant_v = plantg_cl*H
Cont_v = 0.07601*(s+2593)/s % THIS IS GOOD!

Gv_ol = Cont_v*plant_v;
Gv_cl = feedback(Gv_ol,1);

figure(3);
bode(Gv_cl,'k'); grid on; title('Compensated IVL Bode Diagram');
hold on;
yline(0.707); xline(200);
l=legend({' $G\_{c,IVL}^{CL} (s)$'}); set(l, 'Interpreter', 'latex','FontSize',12,'Location','northeast');
hold off

Which yields the following output:

I'm trying to empasize the bandwidth of the system. Therefore the lines (and preferable the legend as well although this I can just move manually) should be plotted on the mangitude plot. However it is automatically added to the phase plot. What can I do?

Thank you! Best regards.

Answer 1

[Mathieu NOE]

hello

try this - hope it helps

I opted for the convention of 3 dB below the peak amplitude point (which is not the 0 dB) but if you prefer -3 dB below 0 dB you can easily change that in the code at this line

threshold = 0 - 3;

instead of

threshold = max(g_dB) - 3;

full code :

%% Parameters
w = 2*pi*50;        % [rad/s]
Lf = 2.5e-3;        % [H]
Rf = 0.1*w*Lf;      % [Ohm]
Cf = 15e-6;         % [F]
Lg = 12e-3;         % [H]
Rg = 0.1*w*Lg;      % [Ohm]
s = tf('s');
plantg_ol = 1/((Cf*Lg)*s^2 + (Cf*Rg)*s);
plantg_cl = feedback(plantg_ol,1);
H = s*Lg + Rg;
plant_v = plantg_cl*H;
Cont_v = 0.07601*(s+2593)/s; % THIS IS GOOD!
Gv_ol = Cont_v*plant_v;
Gv_cl = feedback(Gv_ol,1);

freq = logspace(0,4,300);
[g,p] = bode(Gv_cl,2*pi*freq);
g = g(:);
g_dB = 20*log10(g);
p = p(:);

% find the BW by searching the  max - 3 dB point
threshold = max(g_dB) - 3;
[ZxP,ZxN] = find_zc(freq,g_dB',threshold);
BW_3dB = ZxN(end);  % -3 dB bandwith
g_3dB = interp1(freq,g_dB,BW_3dB);
p_3dB = interp1(freq,p,BW_3dB);

figure(1)
subplot(2,1,1)
semilogx(freq,g_dB,BW_3dB,g_3dB,'dr'); grid on;
title('Compensated IVL Bode Diagram');
xlabel('Frequency (Hz)')
ylabel('Gain (dB)')
l=legend([{' $G\_{c,IVL}^{CL} (s)$'};{['   BW = ' num2str(BW_3dB) ' Hz ']}]);
set(l, 'Interpreter', 'latex','FontSize',12,'Location','northeast');
% yline(0.707); xline(200);

subplot(2,1,2)
semilogx(freq,p,BW_3dB,p_3dB,'dr'); grid on;
xlabel('Frequency (Hz)')
ylabel('Phase (°)')

% yline(0.707); xline(200);



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [ZxP,ZxN] = find_zc(x,y,threshold)

% positive slope "zero" crossing detection, using linear interpolation
y = y - threshold;
zci = @(data) find(diff(sign(data))>0);  %define function: returns indices of +ZCs
ix=zci(y);                      %find indices of + zero crossings of x
ZeroX = @(x0,y0,x1,y1) x0 - (y0.*(x0 - x1))./(y0 - y1); % Interpolated x value for Zero-Crossing 
ZxP = ZeroX(x(ix),y(ix),x(ix+1),y(ix+1));

% negative slope "zero" crossing detection, using linear interpolation
zci = @(data) find(diff(sign(data))<0);  %define function: returns indices of +ZCs
ix=zci(y);                      %find indices of + zero crossings of x
ZeroX = @(x0,y0,x1,y1) x0 - (y0.*(x0 - x1))./(y0 - y1); % Interpolated x value for Zero-Crossing 
ZxN = ZeroX(x(ix),y(ix),x(ix+1),y(ix+1));

end

[Mathieu NOE]

hello again

do you mind accepting my answer (if it has fullfiled your expectations ) ? tx

Answer 2

[Brahmadev]

Hi @Asger Hebsgaard,

I understand that you would like to add plots and legends to the Magnitude axes of the Bode plot. Using "hold on" plots the curve in the current active plot. Hence the legend and the line plots appear in the phase plot. The magnitude axes can be made active by modifying your code after defining "Gv_cl" as following:

figHandle = figure;                   % create a handle to new figure
plotName = bodeplot(Gv_cl,'k'); 
grid on; 
title('Compensated IVL Bode Diagram');
childrenHandle = get(figHandle, 'Children') % use this handle to obtain list of figure's children
magChild = childrenHandle(3);          % Pick a handle to axes of magnitude in bode diagram
axes(magChild)                   % Make this axes active
hold on;
yline(0.707); xline(200);
l=legend({' $G\_{c,IVL}^{CL} (s)$'}); set(l, 'Interpreter', 'latex','FontSize',12,'Location','northeast');
hold off

The output will look like:

Hope this helps in resolving your query!

[Asger Hebsgaard]

This worked wonders! Thank you so much @Brahmadev