MATLAB PID Controller Tuning Example: Buck Converter Loop Design

Learn how to model, tune, and simulate a closed‑loop controller with this practical MATLAB PID controller tuning example that uses a DC-DC buck converter voltage loop.

Introduction to Plant Modeling in MATLAB

Feedback control is needed to keep voltage steady in power‑electronics circuits. To show a practical MATLAB PID controller tuning example, we will design a voltage‑loop controller for a DC-DC buck converter. The buck converter takes an unregulated input voltage and produces a lower, stable output voltage even when the load resistance or the input supply changes. When a buck converter works in continuous conduction mode (CCM), its dynamic behavior looks like a second‑order low‑pass filter. The transfer function G(s) connects the duty‑cycle command to the output voltage.

This function depends on the inductance (L), the capacitance (C), the equivalent series resistance (ESR), and the load resistance (R). In this example, we use a simplified second‑order transfer function, assuming the output voltage is controlled by changing the duty cycle.

For a closely related example, see Applying Ant Lion Optimization Technique to Enhance Power Converters Performance via Effective Controller Tuning.

Defining the Transfer Function in MATLAB

Before we tune the controller, we need to create the plant transfer function in the MATLAB workspace with the Control System Toolbox. First, we set the basic parameters: an inductance L of 100 microhenries, a capacitance C of 220 microfarads, and a load resistance R of 10 ohms.
The buck converter’s continuous‑time transfer function is G(s) = 1 / (L*C*s^2 + (L/R)*s + 1). In the MATLAB command window, we enter these values and build the model using the ‘tf’ command. This object‑oriented model lets MATLAB run frequency and time‑domain analyses.

For a closely related example, see Enhancing ride comfort of semi-active suspension through collaboration control using dung beetle optimizer optimized Fuzzy PID controller.

The MATLAB PID Controller Tuning Example Script

To perform the tuning, we use the automated 'pidtune' command. This function optimizes the proportional (Kp), integral (Ki), and derivative (Kd) gains to satisfy specified crossover frequency and phase margin targets. It also includes a first-order filter on the derivative term to suppress high-frequency sensor noise.
Below is the complete, executable MATLAB script to define the plant, tune the PID controller, construct the closed-loop system, and plot the transient step response:

% MATLAB PID Controller Tuning Example
% Step 1: Define physical parameters
L = 100e-6;  % Inductance (H)
C = 220e-6;  % Capacitance (F)
R = 10;      % Load Resistance (Ohms)
% Step 2: Create the plant transfer function G(s)
num = [1];
den = [L*C, L/R, 1];
G = tf(num, den);
% Step 3: Define target loop bandwidth (rad/s) and tune
target_bandwidth = 2 * pi * 1500; % 1.5 kHz crossover frequency
[C_pid, info] = pidtune(G, 'pidf', target_bandwidth);
% Step 4: Construct the closed-loop transfer function T(s)
T = feedback(C_pid * G, 1);
% Step 5: Display calculated controller parameters
disp('Tuned PID Parameters:');
disp(C_pid);
disp('Tuning Info:');
disp(info);
% Step 6: Plot step response
figure;
step(T);
title('Closed-Loop Step Response of Buck Converter');
grid on;

For a closely related example, see An Adaptive Frequency Multi-Resonant Current Controller for Grid-Tied Single-Phase Cascaded H-Bridge Photovoltaic Inverters.

Analyzing the Tuned Controller Performance

Running the script gives you the controller gains and the main loop characteristics. The 'pidf' controller type in the script is a PID controller that includes a derivative filter coefficient (N). The filter stops sudden spikes in the control signal that can be caused by measurement noise.
The returned 'info' structure holds the achieved crossover frequency and the phase margin. In power systems, a phase margin of 45 to 60 degrees is usually desired because it gives a quick response with little overshoot. If the step response has too much ringing, you can change the phase‑margin target by supplying a custom options structure to the 'pidtune' function with 'pidtuneOptions'.

Closed-Loop Frequency Domain Validation

Although the step response shows how the system behaves over time, we also need to check frequency‑domain margins to be sure the system stays stable when conditions change. In MATLAB, we use the ‘margin’ command to find the gain and phase margins of the open-loop system (C_pid * G). When we run `margin(C_pid * G)`, MATLAB displays a Bode plot with the gain and phase curves. The gain margin tells us how much we can increase the loop gain before the system becomes unstable. The phase margin tells us how much extra phase delay the system can tolerate.

For a buck converter, a gain margin larger than 6 dB gives confidence that the converter will keep working even as components age or temperature changes.

Transitioning from Script to Simulink Simulation

For complex electrical systems, engineers often move from MATLAB scripts to Simulink. You can bring the tuned controller values straight into the Simulink PID Controller block. In the block’s dialog box, choose “External” as the source, or point to the workspace variables C_pid.Kp, C_pid.Ki, C_pid.Kd, and C_pid.N.
Simulink also lets you add physical limits, such as duty‑cycle saturation (usually kept between 0 and 0.95 for a buck converter) and anti‑windup features. These nonlinear effects are hard to capture with pure transfer functions, but they are essential to prevent integrator windup during large transients.