🎯 Objective
By the end of this lab, students will be able to:
- Understand the step-by-step procedure for designing a controller for a buck converter, including selecting gain and compensator structure (Type I vs Type II).
- Evaluate how controller design (Type I vs Type II) influences the transient response of a buck converter, focusing on rise time, overshoot, and settling time.
- Analyze the effect of controller gain variation, and identify how increasing gain impacts speed, damping, and stability of the system.
- Examine the influence of load resistance, and determine how changes in load affect system damping and overall transient behavior.
- Compare the performance of Type I and Type II controllers, and identify conditions under which Type II provides improved speed and reduced overshoot.
- Identify the trade-offs between fast response and stability, and understand the limitations imposed by both controller design and plant dynamics.
📚 Prerequisite
- Experiment A1, A2, A3, C1, and C2.
- Basic understanding of the Nyquist plot and the Nyquist Stability Criterion
- Concept of gain margin and phase margin
🧠 Theory
Measured Experimental Values
| Quantity | Measured Value |
|---|---|
| Core identification | T50-26 (yellow/white iron powder) |
| Inductance L | ~28.3 µH |
| DC resistance Rdc | ~35–38 mΩ |
| Estimated turns | ~29–30 turns |
| Wire diameter | 0.63 mm |
| Estimated wire gauge | AWG22 |
| Measured wire length | 21 7/16 in = 54.45 cm |
| Measured OD | 12.92 mm |
| Measured ID | 7.10 mm |
| Measured height | 5.26 mm |
Frequency Sweep Measurements
| Frequency | Inductance Ls | Series Resistance Rs |
|---|---|---|
| 100 Hz | 28.2665 µH | 0.03523 Ω |
| 500 Hz | 28.3412 µH | 0.03716 Ω |
| 1 kHz | 28.3736 µH | 0.03799 Ω |
| 5 kHz | 28.2852 µH | 0.04467 Ω |
| 10 kHz | 28.2395 µH | 0.05811 Ω |
| 50 kHz | 28.3282 µH | 0.24072 Ω |
| 100 kHz | 28.3157 µH | 1.67769 Ω |
Datasheet Values for Micrometals T50-26
| Parameter | Datasheet Value |
|---|---|
| Material mix | #26 |
| Color | Yellow / White |
| Initial permeability μi | 75 |
| AL | 33 nH/N² |
| Effective area Ae | 0.112 cm² |
| Effective path length le | 3.19 cm |
| Effective volume Ve | 0.358 cm³ |
| Mean length per turn (MLT) | 2.03 cm |
| OD | 12.7 mm |
| ID | 7.14 mm |
| Height | 4.83 mm |
Derived Quantities
Expected inductance for 30 turns
Using:
L=ALN2L=33×10−9×302 L≈29.7 μH
Very close to measured:
- ~28.3 µH.
Expected wire length
Using:MLT=2.03 cm
and N=30:l=30×2.03 l≈60.9 cm
Measured:
- 54.45 cm. (I had a cut section)
Reasonably close.
Expected AWG22 resistance
AWG22:
- ~53.5 mΩ/m.
For:
- l≈0.5445 m,
expected:R≈29 mΩ
Measured:
- ~35–38 mΩ.
Again very reasonable agreement.
🧰 Required Components
The components needed in this lab are:
- Red Board
- Blue Board
- Oscilloscope
- Signal Generator
- Multimeter
- Current probe (if interested in measuring inductor current)
🎥 Overview Video
This video gives you a quick glimpse of what you can expect from this lab.
🛡️ Safety
Watch out for potential safety issues.
- Confirm probe grounds are properly connected for each measurement.
- Don't power the blue board using both the USB-C cable and the power adapter.
- Always disconnect the power once you are done with the experiment.
⚠ Common Mistakes
- The gate of a MOSFET is directly connected to a microcontroller digital pin to perform switching actions without a gate driver.
- Incorrect grounding between comparator output, vref source, and carrier source. All of the signals are referenced relative to gnd of the blue board.
- Scope probe not set to dc-coupling.
- The reference of the scope channels are not properly set to zero at the start of the experiment. This will lead to incorrect reading of the signals.
- Forgetting to record Capacitances (C).
Arduino Code
Not applicable.Matlab Code for Plant Identification
plant
%% Experiment C3: Measured Bode Data and Identified Buck Plant
clear; clc; close all;
%% Paste measured data here: [Frequency_Hz, Magnitude_dB, Phase_deg]
data = [
10 20.0028223 -2.514754857
10.97498765 20.00192129 -2.334081822
12.0450354 20.00736401 -2.10876997
13.21941148 20.00611721 -1.93494749
14.50828778 20.00351947 -1.789560137
15.92282793 20.00275542 -1.659362344
17.475284 20.0038644 -1.544075211
19.17910262 20.0057258 -1.422055962
21.04904145 20.00056013 -1.322160504
23.101297 20.00080701 -1.227857342
25.35364494 20.00401021 -1.154408461
27.82559402 20.00373222 -1.08016905
30.53855509 19.99915776 -1.007779303
33.51602651 20.00317017 -0.99491473
36.78379772 20.0014183 -0.909566441
40.37017259 19.99515375 -0.893940297
44.30621458 19.99646451 -0.856481424
48.6260158 19.99514546 -0.856329911
53.36699231 19.99439037 -0.858631581
58.57020818 19.99287246 -0.84730729
64.28073117 19.99620909 -0.825148671
70.54802311 19.99490709 -0.859663326
77.42636827 19.99051543 -0.87835764
84.97534359 19.99662441 -0.912584419
93.26033469 19.99238194 -0.960391182
102.3531022 19.99228063 -0.987129883
112.3324033 19.99486346 -1.044530219
123.2846739 19.9930863 -1.109120723
135.3047775 19.99498788 -1.178728535
148.4968262 19.99544516 -1.231407361
162.9750835 19.99542994 -1.335523647
178.8649529 19.99500704 -1.439991206
196.304065 19.99825965 -1.531428402
215.443469 19.99859216 -1.666300596
236.4489413 19.99812763 -1.795908787
259.5024211 20.00134576 -1.963267746
284.8035868 20.00326148 -2.136931624
312.571585 20.00536279 -2.307941535
343.0469286 20.0071946 -2.516921969
376.4935807 20.01215251 -2.74077325
413.20124 20.01539413 -2.979072794
453.4878508 20.02284484 -3.248420057
497.7023564 20.03184002 -3.530978945
546.2277218 20.04397169 -3.861028676
599.4842503 20.05588639 -4.208155387
657.9332247 20.07378059 -4.58432299
722.0809018 20.09952528 -5.006182141
792.4828984 20.12367864 -5.445107522
869.7490026 20.15765561 -5.93330397
954.5484567 20.20077059 -6.485978256
1047.615753 20.25898346 -7.094798968
1149.756995 20.33183191 -7.76216431
1261.856883 20.42045559 -8.50035027
1384.886371 20.53282296 -9.368958098
1519.911083 20.67597488 -10.34902725
1668.100537 20.85631639 -11.51558022
1830.73828 21.07873075 -12.89674403
2009.233003 21.3620709 -14.57294662
2205.13074 21.71560334 -16.67577115
2420.128265 22.16091815 -19.37831645
2656.087783 22.71899453 -22.96179639
2915.053063 23.41330125 -27.93471712
3199.267138 24.2489123 -35.17245197
3511.191734 25.1655912 -46.07153871
3853.528594 25.8742802 -62.04661707
4229.242874 25.86179374 -82.06015176
4641.588834 24.84578755 -102.1868638
5094.138015 23.03693702 -119.0356483
5590.810183 20.84059288 -131.630477
6135.907273 18.54147972 -140.6648176
6734.150658 16.2776173 -147.0810646
7390.722034 14.09491242 -151.6560884
8111.308308 12.01395615 -154.8906836
8902.150854 10.0476177 -157.1025214
9770.099573 8.214444261 -158.6173597
10722.67222 6.520092064 -160.0575066
11768.11952 4.883409678 -161.9720076
12915.49665 3.21378201 -164.0918888
14174.74163 1.490956012 -165.95195
15556.76144 -0.240539188 -167.4130973
17073.52647 -1.955254743 -168.4898689
18738.17423 -3.644760251 -169.2819172
20565.12308 -5.332481132 -169.9946747
22570.1972 -6.98556958 -170.5509421
24770.76356 -8.647806069 -171.0273983
27185.88243 -10.31242669 -171.2604808
29836.4724 -11.97512677 -172.0175216
32745.49163 -13.59989048 -171.6701965
35938.13664 -15.29292232 -171.6620848
39442.06059 -17.00928283 -172.3587968
43287.61281 -20.2148371 -168.6489977
47508.10162 -17.97964985 -164.0527226
52140.08288 -22.11576173 -162.450398
57223.67659 -19.62620262 -176.3029059
62802.91442 -22.45053991 -178.2410966
68926.12104 -24.22665661 -179.4248315
75646.33276 -25.79800333 179.8752848
83021.75681 -27.31825429 178.8774177
91116.27561 -29.13800895 176.4789999
100000 -29.34048478 -135.4607238
];
%% Extract measured data
f_meas = data(:,1);
mag_meas_dB = data(:,2);
phase_meas_deg = data(:,3);
%% Identified plant model
Kdc = 10; % DC gain, 20 dB
f0 = 3900; % resonant frequency in Hz
zeta = 0.28; % damping ratio
w0 = 2*pi*f0;
G = tf(Kdc*w0^2, [1 2*zeta*w0 w0^2]);
%% Evaluate identified model at measured frequency points
w_meas = 2*pi*f_meas;
[mag_model, phase_model] = bode(G, w_meas);
mag_model = squeeze(mag_model);
phase_model = squeeze(phase_model);
mag_model_dB = 20*log10(mag_model);
phase_model_deg = squeeze(phase_model);
%% Plot measured data and identified plant
figure;
subplot(2,1,1);
semilogx(f_meas, mag_meas_dB, 'o', 'LineWidth', 1.2); hold on;
semilogx(f_meas, mag_model_dB, '-', 'LineWidth', 2);
grid on;
ylabel('Magnitude (dB)');
title('Measured Bode Plot and Identified Buck Converter Plant');
legend('Measured Data', 'Identified Plant', 'Location', 'Best');
subplot(2,1,2);
semilogx(f_meas, phase_meas_deg, 'o', 'LineWidth', 1.2); hold on;
semilogx(f_meas, phase_model_deg, '-', 'LineWidth', 2);
grid on;
xlabel('Frequency (Hz)');
ylabel('Phase (deg)');
legend('Measured Data', 'Identified Plant', 'Location', 'Best');
%% Display plant transfer function
disp('Identified plant transfer function G(s):');
GMatlab Code for Controller Design
%% Experiment C3: Controller Comparison for Voltage-Mode Buck Converter
clear; clc; close all;
%% Formatting
set(groot,'defaultAxesFontSize',14);
set(groot,'defaultTextFontSize',14);
set(groot,'defaultLineLineWidth',2.5);
s = tf('s');
%% Plant transfer function
G = 7.07e9/(s^2 + 1.28e4*s + 7.07e8);
%% Measurement block
H = 1/4;
%% Desired output and reference
Vout_desired = 5;
Vref = H*Vout_desired; % 1.25 V
%% Common axes for loop-gain plots
w = logspace(1,6,1500); % rad/s
f = w/(2*pi);
bode_mag_lim = [-80 40];
bode_phase_lim = [-300 0];
nyquist_x_lim = [-6 6];
nyquist_y_lim = [-6 6];
%% Controllers to compare
controllers(1).name = 'Unity Gain Controller';
controllers(1).K = tf(1);
controllers(1).t_final = 0.01;
controllers(1).time_ylim = [0 8];
controllers(2).name = 'Pure Integral Controller with Unity Gain';
controllers(2).K = 1/s;
controllers(2).t_final = 10;
controllers(2).time_ylim = [0 8];
controllers(3).name = "Integral Controller with |K|=1000";
controllers(3).K = 1000/s;
controllers(3).t_final = 0.01;
controllers(3).time_ylim = [0 8];
controllers(4).name = "Integral Controller with |K|=4000";
controllers(4).K = 4000/s;
controllers(4).t_final = 0.01;
controllers(4).time_ylim = [0 8];
controllers(5).name = "Integral Controller with |K|=10000";
controllers(5).K = 10000/s;
controllers(5).t_final = 0.01;
controllers(5).time_ylim = [0 8];
controllers(6).name = 'Type II Controller';
% Extract parameters from:
% 21813 (s + 2.143e04) / [ s (s + 1.522e05) ]
wz = 2.143e4; % zero (rad/s)
wp = 1.522e5; % pole (rad/s)
fz = wz/(2*pi); % zero in Hz (for reference)
fp = wp/(2*pi); % pole in Hz (for reference)
% Base Type II structure
K_base = (s + wz)/(s*(s + wp));
% Gain from given controller
K_gain = 21813;
controllers(6).K = K_gain * K_base;
controllers(6).t_final = 0.02;
controllers(6).time_ylim = [0 6];
%% Run controllers one by one
for idx = 1:1:length(controllers)
K = controllers(idx).K;
controller_name = controllers(idx).name;
L = K*G*H;
T = feedback(K*G,H); % Vout/Vref
T_meas = H*T; % H*Vout/Vref
t_final = controllers(idx).t_final;
[y,t] = step(Vref*T,t_final);
[yh,~] = step(Vref*T_meas,t);
%% Error and control input
e = Vref - yh;
if isequal(K,tf(1))
u = e;
else
u = lsim(K,e,t);
end
Vout_ss = dcgain(Vref*T);
ess_out = Vout_desired - Vout_ss;
[Gm,Pm,Wcg,Wcp] = margin(L);
if isinf(Gm)
Gm_dB_text = 'Inf';
else
Gm_dB_text = sprintf('%.2f dB',20*log10(Gm));
end
if isnan(Pm)
Pm_text = 'NaN';
else
Pm_text = sprintf('%.2f deg',Pm);
end
fprintf('\n==============================================================\n');
fprintf('%s\n',controller_name);
fprintf('==============================================================\n');
fprintf('Reference voltage = %.4f V\n',Vref);
fprintf('Desired output voltage = %.4f V\n',Vout_desired);
fprintf('Steady-state output voltage = %.6f V\n',Vout_ss);
fprintf('Output steady-state error = %.6e V\n',ess_out);
fprintf('Gain margin = %s\n',Gm_dB_text);
fprintf('Phase margin = %s\n',Pm_text);
fprintf('Gain crossover frequency = %.2f Hz\n',Wcp/(2*pi));
fprintf('Phase crossover frequency = %.2f Hz\n',Wcg/(2*pi));
%% 1. Bode plot with GM and PM
local_bode_margin_plot(L,w,f,bode_mag_lim,bode_phase_lim, ...
'Loop Gain Bode Plot');
%% 2. Nyquist plot
local_nyquist_plot(L,nyquist_x_lim,nyquist_y_lim, ...
'Nyquist Plot');
%% 3. Time-domain response
local_step_plot(t,y,Vout_desired,Vout_ss,ess_out, ...
controllers(idx).time_ylim,t_final, ...
'Closed-Loop Step Response');
%% 4. Control input response
local_control_plot(t,u,t_final, ...
'Control Input');
%% Pause before next controller
if idx < length(controllers)
disp(' ');
disp('==============================================================');
disp('Press any key to continue to the next controller.');
disp('The Nyquist and Bode axes will remain the same.');
disp('The time-domain axis will be adjusted to show the main feature.');
disp('==============================================================');
pause;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Local functions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function local_bode_margin_plot(L,w,f,mag_lim,phase_lim,title_text)
figure('Color','w');
margin(L);
grid on;
title(title_text,'FontSize',18);
% Make lines thick
h = findall(gcf,'Type','line');
set(h,'LineWidth',3);
% Set fonts and axes
ax = findall(gcf,'Type','axes');
set(ax,'FontSize',16,'LineWidth',1.5);
% Force same x-axis for all controllers
for k = 1:length(ax)
xlim(ax(k),[1e3 1e6]); % rad/s
end
% Force same y-axis for magnitude and phase
for k = 1:length(ax)
yl = get(get(ax(k),'YLabel'),'String');
if contains(yl,'Magnitude')
ylim(ax(k),[-60 20]);
elseif contains(yl,'Phase')
ylim(ax(k),[-180 0]);
end
end
end
function local_nyquist_plot(L,x_lim,y_lim,title_text)
figure('Color','w');
nyquist(L);
grid on;
title(title_text,'FontSize',18);
hline = findall(gcf,'Type','line');
set(hline,'LineWidth',3);
ax = findall(gcf,'Type','axes');
set(ax,'FontSize',16,'LineWidth',1.5);
xlim(x_lim);
ylim(y_lim);
hold on;
plot(-1,0,'rx','MarkerSize',14,'LineWidth',3);
text(-1,0.25,'-1 + j0','FontSize',16, ...
'HorizontalAlignment','center');
end
function local_step_plot(t,y,Vout_desired,Vout_ss,ess_out,y_lim,t_final,title_text)
figure('Color','w');
plot(t,y,'LineWidth',3); hold on;
plot(t,Vout_desired*ones(size(t)),'--','LineWidth',2.5);
plot(t,Vout_ss*ones(size(t)),':','LineWidth',2.5);
grid on;
xlabel('Time (s)');
ylabel('Output Voltage V_{out} (V)');
title(title_text,'FontSize',18);
legend('V_{out}(t)', ...
'Desired output = 5 V', ...
'Steady-state output', ...
'Location','best');
ylim(y_lim);
xlim([0 t_final]);
set(gca,'FontSize',16,'LineWidth',1.5);
%% Highlight steady-state error
t_arrow = 0.85*t_final;
if abs(ess_out) > 1e-3
plot([t_arrow t_arrow],[Vout_ss Vout_desired],'k','LineWidth',3);
text(t_arrow*0.65,(Vout_ss + Vout_desired)/2, ...
sprintf('Steady-state error = %.3f V',ess_out), ...
'FontSize',15);
else
text(0.45*t_final,0.85*y_lim(2), ...
sprintf('Steady-state error \\approx %.2e V',ess_out), ...
'FontSize',15, ...
'BackgroundColor','w', ...
'EdgeColor','k');
end
end
function local_control_plot(t,u,t_final,title_text)
figure('Color','w');
plot(t,u,'LineWidth',3);
grid on;
xlabel('Time (s)');
ylabel('Control Input u(t)');
title(title_text,'FontSize',18);
xlim([0 t_final]);
set(gca,'FontSize',16,'LineWidth',1.5);
endMatlab Code for using Control System Designer Toolbox
%% Open Control System Designer for Experiment C3
clear; clc; close all;
s = tf('s');
%% Plant: buck converter duty-to-output transfer function
G = 7.07e9/(s^2 + 1.28e4*s + 7.07e8);
%% Sensor / measurement gain
H = 0.25;
%% Controller: Start here and gradually add zero and poles.
C = 1;
%% Explicit sensor architecture, if supported
controlSystemDesigner('bode',G,C,H)🧷 Jumper Settings
For this experiment, we will be using only the black board.
Blue Board:
| Jumper | Function | Setting | Note |
|---|---|---|---|
| JP4 | Carrier waveform selection (Option 1: Constant, Option 2: External Carrier, Option 3: Sawtooth waveform internally generated) | Position 3 (we will use internal sawtooth) | - |
| JP5 | Reference signal selection (Option 1: a dc, whose magnitude can be varied using the potentiometer Rduty1, Option 2: any external signal that ranges between 0 and 5 V, Option 3: Voltage mode (we will use this later on for closed-loop control) | Position 3 (Analog voltage mode controller drives the reference signal to the PWM) | - |
| JP3 | The PWM input signal to the deadtime generation circuit can be provided in three ways. (Option 1: Using an external PWM source, for example, an Arduino generating PWM pulses, Option 2: Internal PWM that is generated by the PWM generation circuit, and Option 3: Using current-mode control.) | Position 2. We will generate PWM using the internal comparator | - |
| JP1 | The gate of the high-side MOSFET [qH (in Blue Board) or PWM_H(in Red Board)] can be fed three signals. (Option 1: q1 signal from the dead time compensation circuit, Option 2: gnd, Option 3: q2 signal from the dead time compensation circuit). Note that q1 follows q(t) and q2 is complementary. | Position 1. We will use the half-bridge in synchronous mode. | |
| JP2 | The gate of the low-side MOSFET [qL (in Blue Board) or PWM_L(in Red Board)] can be fed three signals. (Option 1: q2 signal from the dead time compensation circuit, Option 2: gnd, Option 3: q1 signal from the dead time compensation circuit). Note that q1 follows q(t) and q2 is complementary. | Position 1. We will use the half-bridge in synchronous mode. | |
| JP6 | Filter selection for the onboard measured inductor current. (Option 1: RC filter with a cut-off frequency at 159 Hz, Option 2: RC filter with a cut-off frequency at 1.59 MHz, Option 3: No filter). | Position 3. We are interested in measuring the unfiltered inductor current in this experiment. | |
| JP7 | Selection between only voltage mode or outer-loop voltage mode and inner loop current mode control. (Option 1: Only voltage mode. Option 2: Outer-loop voltage-mode control sends the reference to the inner-loop current-mode control. | Position 1. We will use only the voltage mode controller in this experiment | |
| JP8 | Selection between Type I or Type II voltage mode control. (Option 1: Type I, Option 2: Type II) | We will start with Type I (Position 1) and move to Type II when asked (Position 2). | |
| JP9 | Current mode control. The clock pulse (rising edge) is internally generated (position 1) or externally provided (position 2). This indirectly determines the switching frequency in current-mode control. | X. | |
| JP10 | Voltage feedback to the analog controller. Option 1. Vhigh_sns is fed back (useful for Boost converter voltage control, Option 2. Vmid_sns is fed back (useful for Buck converter voltage control) | Position 2. We will be sending back the output voltage of the buck converter to the controller. |
Red Board:
| Jumper | Function | Setting | Note |
|---|---|---|---|
| J7 | Populating this jumper provides the 12 V supply to the gate driver. (Option 1: 12 V is internally generated, Option 2: An External supply is needed) | Position 1. We will provide the internally generated 12V supply to the gate driver. | - |
| J10 and J11 | These jumpers allow changing the direction of current measurement through the Rsense resistor. (Option 1: Current can be measured flowing from L2 to Vmid terminals, Option 2: Current can be measured flowing from Vmid to L2 terminals) | Position 1. (We will set it up to measure the buck converter current.) |
Keep all the other jumpers unpopulated.
⚙️ Circuit Configuration & Setting up the experiment
We will configure the red and blue boards to operate as a synchronous buck converter by connecting an external inductor (recommended value: 30 µH) and a load resistor using Bank A and Bank B in parallel. This configuration allows the load resistance to be varied by adding parallel resistors, enabling operation from no-load to the following approximate values: 51 Ω, 8.36 Ω, 4.55 Ω, 3.13 Ω, and 2.38 Ω. If a current probe is available, the inductor current should also be measured. The system is powered via USB. The reference signal to the controller can be provided either through the on-board potentiometer and tactile switch or using a signal generator. Please be extra cautious: The signal Vref. should always stay between 0 and 5 V, else we will destroy the voltage controller IC on the blue board.
Use the checklist below to mark each step as you complete it. You can download it later on to verify that you have performed all the steps.
Startup & Setup Checklist
Word of caution: the signal generator output must remain between 0 V and 5 V under all conditions. Exceeding this limit can destroy the opamp for voltage mode control on the Blue Board. Always ensure V_ref is within 0 and 5V before connection.
Red Board + External Components
Blue Board
Blue Board
Red Board
All signals are measured with respect to GND (black test points).
V_ref(t) is now provided either from Ext. Vref within the blue board or by the external signal generator.
Blue Board
Red Board
Initial Power-Up (Before Signal Injection)
Signal Generator Setup (Before Connecting to Blue Board)
Ext. Ref Setup
Connect and Verify
🧪 Experiment
Download the checklist above and ensure you have completed all steps before we power on. We will go through the following steps:
- Probe the following signals on the oscilloscope: Analog Cnt. D (controller output, Blue Board) q(t) (PWM signal, Blue Board) Vmid (Red Board) and Ch4 Inductor current (using external current probe or using iL_filt1 onboard measurement). Ensure all signals share a common ground reference and are properly scaled for clear observation on the oscilloscope.
- Reference Tracking and Transient Observation: As you vary the Ref. potentiometer, observe that q(t) is automatically adjusted by the controller to meet the reference. Verify that Vmid follows the reference set by the Ref. potentiometer. Adjust the Ref. potentiometer such that Vmid≈5V. Ensure that the load resistance is 10 Ohm||10 Ohm||51 Ohm (~4.33 Ohm).
- Transient Response Measurement: Configure the oscilloscope to single trigger on the rising edge of Analog Cnt. D. Set the time scale to approximately 400 µs (adjust as needed). Using the tactile switch, press and release it to generate a step change on the reference signal. Observe the transient response of Vmid as it transitions from 0 V to 5 V. Capture the scope shot.
- Effect of Controller Gain: Vary the gain using the Rp1 potentiometer on the Blue Board. Observe the effect on transient response: at low gain, the response is sluggish (slow rise, minimal overshoot). At high gain, the response is faster (reduced rise time, increased overshoot or ringing). Use the “G” marking and arrows on the blue board to identify the direction for increasing or decreasing gain.
- Next, let us turn off the 10 V power supply. Disconnect the USB.
- Replace the input to V_ref from Ext. Ref. to the signal generator. Probe the signal generator output one more time before feeding it to the Blue Board using the control port. Replace q(t) measurement with that of V_ref measurement on the scope.
- Plug the USB back in and then gradually increase the 10 V power supply. We are ready to do some measurements. If you trigger the scope using the V_ref signal, you should observe a clean transient response of Vmid and inductor current, as well as the controller output.
- Data Collection: We will repeat the transient measurement across multiple gain settings and loads, and use the table below to capture the data. For each test case, measure the following transient performance metrics from the Vmid waveform:
- Rise Time: Time taken for to rise from 10% to 90% of its final value.
- Overshoot: Percentage by which exceeds its final steady-state value, defined as
- Settling Time: Time taken for to remain within ±5% of its final value.
- Often, the scope can directly provide you with rise-time and overshoot measurements.
- Adjust the Rp1 potentiometer to obtain at least 5 distinct data points, spanning: Lowest overshoot (well-damped response) to largest overshoot (underdamped response)
- Adjust the Rp1 potentiometer such that the overshoot is 15%. Next, vary the loads, going from a heavy load (2.38 Ohm) to the lightest load (51 Ohm). Again, record the above-mentioned features of the transient waveform.
- Turn off the 10 V power supply. Move on to the Type II controller by setting jumper JP8 to position 2. Ensure that the load resistance is 10 Ohm||10 Ohm||51 Ohm (~4.33 Ohm).
- Turn on the 10 V power supply gradually.
- Repeat Steps 9 and 10.
- If you have access to soldering stations and 1206 package surface-mount capacitors and resistors, design a controller that outperforms the on-board controller. The performance metric is to limit the overshoot to 15% while increasing the settling time faster than the onboard controller for the 4.55 Ohm load case.
C3 Transient Response Data Collection Tool
Record rise time, overshoot, and settling time for Type I and Type II controllers under gain variation and load variation.
Measurement guidelines: Measure Vmid during the step response.
Rise time is measured from 10% to 90% of the final value. Overshoot is measured relative to the final value.
Settling time is the time required for Vmid to remain within ±5% of the final value.
Subgroup 1: Gain Variation - Type I Controller
Fixed condition: Load = 10 Ω || 10 Ω || 51 Ω ≈ 4.55 Ω.
| Case | Controller | Gain Setting | Load R (Ω) | Rise Time (µs) | Overshoot (%) | Settling Time (µs) | Observations |
|---|---|---|---|---|---|---|---|
| 1 | Type I | Lowest Overshoot | |||||
| 2 | Type I | Low-Medium | |||||
| 3 | Type I | Medium | |||||
| 4 | Type I | Medium-High | |||||
| 5 | Type I | Largest Overshoot |
Subgroup 2: Load Variation - Type I Controller
Adjust Rp1 such that overshoot is approximately 15% for 4.55 Ω Load. Then keep gain fixed.
| 1 | Type I | Fixed | |||||
| 2 | Type I | Fixed | |||||
| 3 | Type I | Fixed | |||||
| 4 | Type I | Fixed | |||||
| 5 | Type I | Fixed |
Subgroup 3: Gain Variation - Type II Controller
Fixed condition: Load = 10 Ω || 10 Ω || 51 Ω ≈ 4.55 Ω.
| 1 | Type II | Lowest Overshoot | |||||
| 2 | Type II | Low-Medium | |||||
| 3 | Type II | Medium | |||||
| 4 | Type II | Medium-High | |||||
| 5 | Type II | Largest Overshoot |
Subgroup 4: Load Variation - Type II Controller
Adjust Rp1 such that overshoot is approximately 15% for 4.55 Ω Load. Then keep gain fixed.
| 1 | Type II | Fixed | |||||
| 2 | Type II | Fixed | |||||
| 3 | Type II | Fixed | |||||
| 4 | Type II | Fixed | |||||
| 5 | Type II | Fixed |
Turn off Checklist
Before we close the experiment, please ensure:
Turn-Off & Shutdown Checklist
🧠 Observations & Analysis
Now, let us analyze the data you collected to write a brief report that solidifies our understanding. Structure the report to include the following:
- Restate the objectives of this experiment in your own words. Your response should address the following: How does controller design (Type I vs Type II) influence the transient response of a buck converter? What is the effect of controller gain on rise time, overshoot, and settling time? How does the load resistance influence the transient response, and how does this compare to the effect of controller design?
- Theory: Explain the role of the controller in shaping transient response: Why does increasing gain generally reduce rise time but increase overshoot? What is the role of the integrator (Type I) in steady-state accuracy? What additional feature does a Type II controller introduce, and how does it improve performance? Discuss how phase margin is related to: Overshoot, Damping, and Robustness.
- Using the scope shot of Step 3, explain the controller action and switching signal. Explain how the inductor current transients during the step change. Can you identify the effect of the reference feedforward on the controller output?
- Gain Variation Analysis (Type I Controller): Using the data collected in Subgroup 1, analyze the effect of increasing gain: As gain increases, how does rise time change? How does overshoot vary? Does the system transition from overdamped → underdamped behavior?
- Load Variation Analysis (Type I Controller) Using the data collected in Subgroup 2, analyze the effect of load variation: As load resistance increases (heavy → light load), how does: Does the system become more or less damped at light load?
- Gain Variation Analysis (Type II Controller)
- Using the data collected in Subgroup 3, repeat the same analysis: Compare rise time and overshoot trends with Type I. For the same overshoot, does Type II achieve faster response? For the same rise time, does Type II reduce overshoot? Explain why Type II outperforms Type I, referring to: Phase boost, improved phase margin near crossover.
- Using the data collected in Subgroup 4, repeat the analysis and compare the results with those from Type I. At which load condition does Type II provide the most benefit? At which load condition do Type I and Type II behave similarly? Explain why controller influence reduces at heavy load.
- Controller vs Plant Dominance: Based on your observations, when does the controller dominate system behavior? When does the plant (LC + load) dominate behavior? Explain how this depends on: Load resistance and Damping
- What would be the trade-off of changing the controller structure from Type II to Type III?
- If you have step 14, show your theoretical calculations along with experimental results and compare them.
- Write a short conclusion summarizing the main findings of the experiment. Your conclusion should address: How does controller design influence transient performance? Why does Type II provide improved performance over Type I? The role of load in determining system damping. The importance of balancing speed and stability in control design.
✔ Conclusion
The experiment demonstrates that controller design and gain strongly shape the transient response, with Type II control achieving a superior balance between speed and damping, while load conditions ultimately determine the system’s inherent performance limits.
🔍 References & further reading
- Erickson, R.W. and Maksimovic, D. (2020). Fundamentals of Power Electronics. 3rd Edition, Springer, Berlin.