Design and Analysis of DC Buck Converter

Controller using Matlab and Simulink

Control Systems: Honors Project

Project Sponsor: Dr. Daniel Geiger

Abstract

The dc-dc buck converter is a favoured method for efficiently stepping down a higher voltage to a lower one. This is achieved by implementing a controller onto a transistor driven RLC circuit that switches the voltage source for the load between the constant dc source and a charged capacitor. This paper explores a generalized buck converter model simulated in Simulink in order to design and analyze a controller that has no steady state error and minimized overshoot and settling time. The design is verified using MATLAB and the results are published from Simulink.

Index Terms

buck converter, source switching, input voltage, output voltage, MATLAB, Simulink, settling time, percentage overshoot, controller design

I. Background Information

An electrical buck converter is a type of DC-DC converter that can step down a DC voltage to a lower level. It is commonly used in power supply applications to convert a higher voltage to a lower voltage, while maintaining a high efficiency. The buck converter works by controlling the duty cycle of a switch, typically a MOSFET or a transistor. The switch is turned on, and the input voltage is applied to the inductor. The inductor resists the change in current, causing the current to increase linearly with time. During the on-time of the switch, energy is stored in an inductor, which causes the current to increase. The energy is proportional to the square of the current and the inductance of the inductor. The switch is turned off, and the inductor is now connected to the output load. The current in the inductor begins to decrease, as the inductor releases its stored energy to the output load. During the off-time of the switch, the energy stored in the inductor is transferred to the output load, causing the voltage to decrease. This output voltage is equal to the sum of the voltage across the inductor and the voltage across the load. The voltage across the inductor is proportional to the rate of change of current in the inductor, which is negative during the off-time. To regulate the output voltage, the duty cycle of the switch is adjusted. If the output voltage is too high, the duty cycle is decreased, which reduces the time the switch is on and the energy stored in the inductor. If the output voltage is too low, the duty cycle is increased, which increases the time the switch is on and the energy stored in the inductor. The efficiency of the buck converter is high because the energy is transferred from the input to the output in discrete packets, rather than being continuously dissipated as heat in a linear regulator.

II. Tools Utilized

MATLAB and Simulink

The following add-ons and tool boxes for MathWorks MATLAB and Simulink are required to design and analyze a dc-dc buck converter PID controller.

• Control System Tool Box

• Simscape Electrical

• Simulink Control Design

• System Identification Toolbox

III. Design Parameters

The following design parameters are considered in the design and analysis of the dc-dc buck converter.

IV. Design of DC Buck Converter Model

The dc buck converter is designed using Simulink to step down a constant 20V source to a 12V reference.The circuit is driven with two n-channel mosfets that are coupled with diodes. The inductor is designed to operate at 1mH in parallel with a 10kΩ resistor, and a smoothing capacitor is implemented with a value of 22µF. The fixed load value in the system is 3.75Ω, while the cyclic load operates at 200Hz. A scope is used to measure the output reference voltage and mosfet power and load current.

V. Open-Loop Performance

Figure 1 demonstrates the Simulink model for the dc-dc buck converter. The resultant scope output is shown in Figure 2. The output of the buck converter settles close to the 12V reference output.

VI. Design of PID Controller

Once open-loop performance has been established, the controller for the system is designed to stabilize a switching voltage between 15V and 12V. The controller takes an input reference voltage from a 15V to 12V step function. A standard modeled feedback controller is used to contain the designed PID controller, as can be seen in Figure 3. Once the controller model is establish, the PID controller is tuned using a transfer function base. The PID tuner app is used to establish an under-damped pair plant identification resulting in a model parameter function Eq.1 plotted in Figure 4.

Then, the controller is tuned in order to meet the design parameters specified in Table 1. The tuned controller results in the step plot response shown in Figure 5, and design parameters are detailed in Table 2.

VII. Closed-Loop Performance

After the controller and the plant have both been modeled, the closed loop performance can be modeled. Figure 7 demonstrates the scope output for the final controller-plant model laid out in Figure 6.

VIII. Conclusions

The dc-dc buck converter is an essential application of power electronics to modern, every-day use, and MATLAB and Simulink tools provide a robust platform for controller and converter design by utilizing the control system tool boxes. With these tools, a buck-converter that steps 20V down to a 15V-12V switch can be modeled that achieves a steady-state error of 0, an overshoot percentage of 3.56$\%$, and a 2$\%$ settling time of .98ms. Future applications of this modeling study include more advanced control systems for power electronics as well as more detailed analysis of plants and controllers.

References

1. S. Palanidoss and T. V. S. Vishnu, "Experimental analysis of conventional buck and boost converter with integrated dual output converter," 2017 International Conference on Electrical, Electronics, Communication, Computer, and Optimization Techniques (ICEECCOT), Mysuru, India, 2017, pp. 323-329

2. H. Y. Kanaan and K. Al-Haddad, "Modeling and Simulation of DC-DC Power Converters in CCM and DCM Using the Switching Functions Approach: Application to the Buck and C ù k Converters," 2005 International Conference on Power Electronics and Drives Systems, Kuala Lumpur, Malaysia, 2005, pp. 468-473

3. P. Azer and A. Emadi, "Generalized State Space Average Model for Multi-Phase Interleaved Buck, Boost and Buck-Boost DC-DC Converters: Transient, Steady-State and Switching Dynamics," in IEEE Access, vol. 8, pp. 77735-77745, 2020

4. J. H. Jose and K. Pramelakumari, "A positive output buck boost converter combining KY and SR-buck converters," 2015 International Conference on Power, Instrumentation, Control and Computing (PICC), Thrissur, India, 2015, pp. 1-5

5. Mohan, Ned. Power Electronics. Wiley, 2011. 

6. Erickson, Robert Warren, and Maksimovic Dragan. Fundamentals of Power Electronics. Springer, 2020. 

7. “Buck Converter.” Buck Converter - MATLAB & Simulink, MathWorks

8. “Pid Tuner.” MATLAB & Simulink, MathWorks