Analysis of Transition Mode Operation and Characteristic Curves in a Buck–Boost Converter for Unmanned Guided Vehicles

Abstract

This study presents the development of a buck–boost converter for application in unmanned guided vehicles (UGVs). The converter was designed with its input connected to a lithium iron phosphate battery pack and its output connected to an inverter. This configuration enabled the inverter, which powered the drive motor, to receive a stable DC voltage, thereby mitigating the effects of battery voltage fluctuations and enhancing the overall system stability. A pulse-width modulation (PWM) controller was employed to regulate the developed buck–boost converter. During the transition from buck mode to buck–boost mode, both power MOSFETs were simultaneously turned on; however, the datasheet of the PWM controller did not provide operational details or characteristic curve analysis for this mode. Therefore, this study derived the relationship between voltage gain and duty cycle ratio for the transition mode. To analyze the input voltage versus duty cycle characteristics, the linear equation was employed. This analytical model was adjusted to meet different converter specifications developed for experimental validation. Furthermore, the external-connect test capacitor method was used to extract the equivalent parasitic inductance and capacitance present in the practical circuit of the buck–boost converter. Based on these parameters, a snubber circuit was designed and connected across the drain–source terminals of the power MOSFETs to suppress voltage spikes occurring at the junctions. Finally, the developed buck–boost converter prototype was installed on an unmanned guided vehicle to convert the power from the lithium battery pack into the input power required by two inverters. A computer host was used to control the motor speed. By measuring the output voltage and current of the buck–boost converter, its electrical functionality and performance specifications were verified. The dimensions of the developed UGV chassis prototype were 40 cm in length, 45 cm in width, and 18.3 cm in height.

1. Introduction

In switching power converter topologies, the buck–boost converter utilizes pulse-width modulation (PWM) to perform either buck or boost conversion, depending on variations in the input voltage and output load. As a result, the converter maintains a regulated output voltage, effectively functioning as a constant voltage source. In recent years, advancements in technology and cost reductions have made rechargeable lithium-ion batteries increasingly sophisticated and affordable, establishing them as a key power source, particularly in automotive electronic systems. Applications such as infotainment systems, dashboards, and headlights often require a stable operating voltage in the range of 5–12 V to ensure proper functionality of electronic modules. However, the floating voltage of a car battery varies from 9 to 32 V depending on its state of charge (SOC). As a result, a buck–boost converter is commonly employed between the car battery and the automotive electronic modules to regulate the output voltage, making this one of the most prevalent applications [1,2].

As the energy and power density of rechargeable lithium-ion batteries continue to improve, high-capacity batteries now support extended equipment operation while offering high charge/discharge efficiency and long cycle life. Consequently, unmanned guided vehicles (UGVs) or autonomous guide vehicles (AGVs) can effectively utilize rechargeable lithium-ion batteries as their primary power source. AGVs require specific guidance systems, such as the magnetic stripe, optical path, radio frequency identification (RFID) tag, quick response (QR) code, or simultaneous localization and mapping (SLAM)-based navigation to operate within a predefined environment. As a result, AGVs are categorized as industrial automation equipment and are primarily used for material handling in factories, warehouses, and logistics centers. Moreover, UGVs encompass all types of unmanned terrestrial vehicles. They feature more flexible navigation and control methods, including remote operation, semi-autonomous driving, and fully autonomous navigation based on artificial intelligence (AI) vision and sensors. Consequently, UGVs are widely employed as multi-purpose platforms in military, scientific research, agricultural, disaster relief, and inspection applications [3,4].

The UGV drive system is the powertrain, which consists of motors, inverters, and batteries. The battery supplies DC power, serving as the sole energy source for the UGV. The inverter (or motor driver) converts this DC power into AC power while regulating its frequency and voltage, thereby enabling precise control of motor speed and direction. As a result, the motor generates the required torque to propel the UGV [5,6,7,8].

The PWM controller (Model number: LM5118, Texas Instruments, Dallas, USA) used in this study includes a characteristic curve of input voltage versus duty cycle ratio, as provided in the original datasheets [9,10]. However, the data presented were plotted based solely on the specifications of an example circuit, without any explanation or derivation of how the curve was obtained. As a result, the information cannot meet the requirements of different application scenarios. Moreover, the original datasheet neither analyzed the operating principles of the PWM controller during the transition from buck mode to buck–boost mode, nor provided a derivation of the relationship between voltage gain and duty cycle ratio. Therefore, this study employed the linear function to establish a characteristic curve relating input voltage to duty cycle ratio. This curve was then extended to meet the design specifications of the proposed buck–boost converter, and its accuracy was validated through experimental results. The reasons for adopting linear equations are summarized as follows:

• Advantage: A linear simple model is simple, easy to derive and compute, enables fixed-slope analysis, and supports monotonically decreasing or increasing trends.
• Disadvantage: It requires piecewise analysis, and the overall process can become complex.

Both the printed circuit board (PCB) traces and power MOSFETs inherently possess parasitic inductance and capacitance, which can lead to resonant voltage surges during high-current and high-frequency switching operations. If these surges exceed the rated breakdown voltage of the power switch, device degradation or catastrophic failure may occur. A common mitigation method involves connecting a resistor–capacitor (RC) snubber circuit across the terminals where the surge appears, effectively suppressing transient voltages. The snubber circuit is a widely adopted protection technique in switching power supply designs. It serves to absorb or suppress high-voltage transients, oscillations, and electromagnetic interference (EMI) generated during the switching operations of power transistors. Most snubber circuits are composed of passive components such as resistors, capacitors, and diodes. When high-voltage spikes and oscillations are generated by the power switch during operation, the resistor dissipates the surge energy to suppress oscillatory behavior, while the capacitor absorbs the voltage spike generated at the moment when the power transistor is turned off. When voltage surges exceed the voltage stress limits of power transistors, a transient voltage suppression (TVS) diode can be employed to clamp the surge within a safe range. Accordingly, the use of snubber circuits in power electronic systems offers several advantages, including suppression of voltage surges, reduction of EMI, prevention of oscillations, and extension of the power transistor’s operational lifespan [11,12]. However, the resistors in snubber circuits dissipate the electrical energy of voltage surges as heat, resulting in a temperature rise that can accelerate component aging. Consequently, in high-power applications, it becomes necessary to either increase the power rating of the resistors or incorporate heat sinks for thermal management. These requirements hinder hardware miniaturization and increase both component and assembly costs. Moreover, the snubber circuit extends the voltage rise and fall times during power switch transitions, thereby reducing the switching speed and increasing switching losses. The snubber circuit must be tailored to the actual circuit conditions to achieve optimal performance. Common types include resistor–capacitor (RC) snubbers, resistor–capacitor–diode (RCD) snubbers, and transient voltage suppression (TVS) diode clamp snubbers. For RC and RCD snubbers, the appropriate resistor and capacitor values must be designed based on practical operating conditions and estimated parasitic parameters. In contrast, TVS diode clamp snubbers rely on the diode’s breakdown characteristics to suppress voltage spikes, thereby eliminating the need to calculate resistor and capacitor values. Both RC and RCD snubbers dissipate voltage surge energy as heat through resistors, resulting in significant energy loss and reduced switching speed of the power transistor. In contrast, TVS diode clamp snubbers offer rapid response and effective suppression of voltage surges with minimal impact on switching performance [12,13,14].

A review of journal articles published over the past decade in electronic databases reveals that few studies have examined UGV powertrains incorporating power converters. Therefore, this study developed a buck–boost converter for integration into the powertrain of a UGV. Moreover, this paper extends the research presented in [9,10,15,16]; the technical contributions and characteristics are summarized as follows:

• The converter input was connected to a lithium iron phosphate (LiFePO₄) battery pack, and its output was connected to a motor driver (inverter). This configuration ensured that the motor driver consistently received a stable DC power supply, even under varying battery voltage levels or motor speed conditions, thereby enhancing the overall system stability;
• This study derived and analyzed the voltage gain of the buck–boost converter during buck-to-buck-boost transitional operation, as the mathematical model was not presented in [9,10]. To meet the rated specification of the developed prototype, a linear equation was employed to model and analyze the characteristic curve between the input voltage to duty cycle ratio;
• The power switches in the buck–boost converter were equipped with an RC snubber in conjunction with a TVS diode to achieve enhanced suppression of voltage surges. To cope with the effects of parasitic components in the circuit, the method of adding a test capacitor was adopted to estimate their values. Based on these estimations, suitable resistance and capacitance values for the snubber circuit were determined and applied; thus, the design procedure and considerations derived from the snubber design data were verified;
• The developed buck–boost converter prototype was integrated into a UGV, where it converted the lithium-ion battery power into the operating power required by two inverters to drive motors under varying speed conditions;
• The experimental measurements and results reported in [15,16] were updated and expanded in this study.

This paper is organized into five sections: Section 2 presents the system configuration and buck–boost converter. Section 3 describes the design consideration. Section 4 provides the experimental results. Finally, the conclusions of this study are presented in Section 5.

2. Powertrain Architecture and Buck–Boost Converter

The motor drive architecture of the two-wheel UGV powertrain is illustrated in Figure 1. As shown in Figure 1a, the system comprises a lithium iron phosphate battery pack, two inverters, two motors, and a pair of wheels (left and right) [5,17,18,19]. In this configuration, the lithium battery pack directly supplies power to inverters, which then drive the motors to rotate the two wheels. The primary advantage of this architecture lies in its simplicity of hardware implementation, which helps reduce the time and cost associated with wiring and assembly [19]. However, the battery pack voltage varies with its SOC. When the inverter driving the motor is powered directly by the battery pack, the magnitude of the input DC-link voltage V_bat directly affects the phase/line voltage amplitude, output power, and waveform quality of the inverter, as illustrated Figure 1b [20,21,22]. The relationship can be summarized as follows:

• High-SOC region: Higher V_bat → higher inverter phase/line voltage → higher deliverable power → excellent waveform quality → lower total harmonic distortion.
• Low-SOC region: Lower V_bat → lower inverter phase/line → reduced deliverable power → poor waveform quality → higher total harmonic distortion.

The motor drive architecture of the two-wheel UGV powertrain adopted in this study is illustrated in Figure 1b. In this configuration, a DC–DC converter was inserted between the LiFePO₄ battery pack and the inverter. This setup allows the inverter to receive a stable input power supply, unaffected by changes in battery voltage due to varying states of charge. Consequently, in inverter design, a fixed input voltage can be assumed, disregarding battery voltage fluctuations across different SOCs. This architecture ensures that the inverter is capable of driving the motor at its rated maximum speed in practical operations [19,23].

2.1. Buck–Boost Converter

The DC–DC converter employed in this study adopts a buck–boost topology, as illustrated in Figure 2. The circuit comprises two power MOSFETs (M₁ and M₂), two power diodes (D₁ and D₂), an inductor (L_bb), and an output capacitor (C_o). The input of the buck–boost converter is connected to a lithium iron phosphate battery pack, where the input voltage V_i corresponds to the battery voltage V_bat (i.e., V_i = V_bat). The load connected to the converter’s output is an inverter, which receives the output voltage V_o and output current I_o. A PWM controller is used to generate gate-drive signals v_gs1 and v_gs2 for the two power MOSFETs, thereby regulating their switching states to achieve the desired voltage conversion.

• Boost mode operation

When the input voltage is lower than the output voltage (V_i < V_o), the power MOSFETs M₁ and M₂ are turned on and off synchronously, effectively operating as a conventional boost converter to achieve voltage step-up. Therefore, this study does not delve into the detailed operation of this mode.

• Buck mode operation

When the input voltage is higher than the output voltage (V_i > V_o), the power MOSFET M₂ remains continuously turned off, while M₁ operates in a switching mode. This operating mode functions as a conventional buck converter to achieve voltage step-down. Therefore, the detailed operation of this mode is not elaborated in this study.

2.2. Transition from Buck Operation Mode to Buck–Boost Operation Mode

The PWM controller used in this study includes a characteristic curve of input volt-age versus duty cycle ratio, as provided in the original datasheets [9,10]. During the transition from buck mode to buck–boost mode, both power MOSFETs were simultaneously turned on; however, the datasheet of the PWM controller did not provide operational details or characteristic curve analysis for this mode. Therefore, this study implemented a reverse engineering process to derive the relationship between voltage gain and duty cycle ratio for the transition mode. To analyze the input voltage versus duty cycle characteristics, the linear equation was employed. This analytical model was adjusted to meet different converter specifications developed for experimental validation.

The circuit operation and corresponding timing diagram for this mode are illustrated in Figure 3. During the interval t₀ to t₁, both v_gs1 and v_gs2 are at a high-voltage level, turning on MOSFETs M₁ and M₂ while diodes D₁ and D₂ remain off. As a result, the inductor L_bb is charging, and the output capacitor C_o is discharges to the load. During this interval, the voltage across the inductor is v_Lbb = V_i, and the inductor current can be expressed as:

i_Lbb (t₀ to t₁) = V_i d_on1 t_s/L_bb,

(1)

where d_on1 denotes the duty cycle ratio corresponding to the interval t₀ to t₁, and t_s represents the switching period.

During the interval t₁ to t₂, v_gs1 remains at a high-voltage level, keeping M₁ turning on, while v_gs2 drops to a low-voltage level, turning off M₂. As a result, diode D₁ remains off and D₂ turns on, allowing the inductor L_bb to discharge power into the output capacitor C_o and the load. During this interval, the inductor voltage is v_Lbb = V_i − V_o, and the inductor current can be expressed as:

i_Lbb (t₁ to t₂) = (V_i − V_o) d_on2 t_s/L_bb,

(2)

where d_on2 denotes the duty cycle ratio corresponding to the interval t₁ to t₂.

During the interval t₂ to t₃, both v_gs1 and v_gs2 are at low-voltage levels, turning off M₁ and M₂. As a result, both diodes D₁ and D₂ are turned on, allowing L_bb to discharge power into C_o and the load. During this interval, v_Lbb = −V_o, and the inductor current can be expressed as:

i_Lbb (t₂ to t₃) = −V_o d_off t_s/L_bb,

(3)

where d_off denotes the duty cycle ratio corresponding to the interval t₂ to t₃.

By substituting (1)–(3) into the volt-second balance method, expressed as v_Lbb (t₀ to t₁) + v_Lbb (t₁ to t₂) + v_Lbb (t₂ to t₃) = 0, the voltage gain and the duty cycle ratio under this operating mode can be derived as follows:

V_o/V_i = d_on/(1 − d_on + d_on2),

(4)

where d_on = d_on1 + d_on2.

The PWM controller employed in this study was the LM5118. According to its original datasheet, a characteristic curve illustrating the relationship between the duty cycle ratio and the input voltage during the transition from buck mode to buck–boost mode was provided, as shown in Figure 4a [9]. In Figure 4a, when the input voltage exceeded the output voltage and subsequently decreased, the duty cycle ratio d_M1 of power MOSFET M₁ increased to maintain a stable output voltage through the coordinated operation of the PWM controller and the buck–boost converter. When d_M1 increased to 0.75, the duty cycle ratio d_M2 of power MOSFET M₂ began to increase from zero (with d_M1 and d_M2 defined as shown in Figure 3). As the input voltage continued to decrease, the duty cycle ratio d_M2 gradually increased until it became equal to d_M1. When the input voltage approached the output voltage, d_M1 and d_M2 operated with approximately equal duty cycle ratios, indicating that the converter had entered buck–boost mode operation. This control method allowed the buck–boost converter to transition smoothly from buck mode to buck–boost mode.

In [9], only the characteristic curve and the accompanying text description shown in Figure 4a were provided, without any explanation of how the curve was derived. Furthermore, as observed from Equation (4), during the transition from buck mode to buck–boost mode, it was necessary to determine both d_M1 = d_on and d_M2 = d_on1 to derive the ratio of d_M1 to V_o/V_i. Therefore, this study defined five linear segments based on Figure 4a, analyzed each segment, and derived its corresponding linear equations to develop the design specifications of the buck–boost converter proposed in this work. As shown in Figure 4a, the following observations were found:

• The output voltage V_o was set to 12 V, and the duty cycle ratios of power MOSFETs M₁ and M₂ were denoted as d_M1 and d_M2, respectively. In buck–boost mode operation, the maximum duty cycle ratio of d_M1 was set to 0.75.
• When the buck–boost converter operated in buck mode, the duty cycle ratio of M₁, as well as the input and output voltages, were expressed as follows:

d_M1 = V_o/V_i,

(5)

• The characteristic curve of the duty cycle ratio versus input voltage exhibited an approximately linear behavior; therefore, each line segment was modeled using a linear equation expressed as:

  d_M1 = d_M2 = a (V_i/k) + b,

  (6)

  where both a and b represented constants. Additionally, k was defined as k = V_o/12, where k ≧ 1.

• The linear equation analysis of line segments 1 to 5 is conducted as follows.

• Segment 1: d_M1 vs. V_i (16.4 to 18 V)

  1.

  Substituting V_o = 12 V and V_i = 16.4 V into (5) can obtain d_M1 = 75%, substituting V_o = 12 V and V_i = 16.4 V into (5) yields d_M1 = 66.67%.

  2.

  Substituting V_i = 16.4 V and d_M1 = 75%, and V_i = 18 V and d_M1 = 66.67% into (6), the linear equation for this segment can be derived as follows:

$$\left\{\begin{array}{c}75\%=16.4 a+b\\ 66.67\%=18 a+b\end{array}\right.$$

Solving this simultaneous equations, the linear equation for Segment 1 can be obtained as follows:

d_M1 = −5.1875 (V_i/k) + 160.075,

(7)

• Segment 2: d_M2 vs. V_i (16.4 to 18 V)

Since V_o = 12 V and V_i ranges from 16.4 V to 18 V, the buck–boost converter operates in buck mode. In this mode, when d_M1 < 75%, d_M2 is zero, i.e., d_M2 = 0.

• Segment 3: d_M1 vs. V_i (13.2 to 16.4 V)

(1)

Substituting V_i < 16 V and V_o = 12 V into (5) can yields d_M1 > 75%; however, according to the setting specification in [9], the PWM controller limits d_M1 to no more than 75%.

(2)

Substituting V_i = 16.4 V and d_M1 = 75%, as well as V_i = 13.2 V and d_M1 = 50% into (6), the linear equation for this segment can be derived as follows:

$$\left\{\begin{array}{c}75\%=16.4 a+b\\ 50\%=13.2 a+b\end{array}\right.$$

Solving this simultaneous equations, the linear equation for Segment 3 can be obtained as follows:

d_M1 = 7.8125 (V_i/k) − 53.125,

(8)

• Segment 4: d_M2 vs. V_i (13.2 to 16.4 V)

Substituting V_i = 16 V and d_M2 = 0, as well as V_i = 13.2 V and d_M2 = 50% into (6), the linear equation for this segment can be derived as follows:

$$\left\{\begin{array}{c}0 = 16.4 a + b\\ 50\% = 13.2 a + b\end{array}\right.$$

Solving this simultaneous equations, the linear equation for Segment 4 can be obtained as follows:

d_M2 = −15.625 (V_i/k) + 256.25,

(9)

• Segment 5: d_M1 and d_M2 vs. V_i (12 to 13.2 V)

d_M1 = d_M2 = 50%,

(10)

The characteristic curve derived from Equations (5)–(10) and plotted using MATLAB R2021a is shown in Figure 4b. The ranges of d_M1 and d_M2 ranges for V_o = 12 V are listed in

Table 1. Characteristic curve for V_o = 12 V.

Input Voltage (V)	dM1 Range	dM2 Range
16.4 to 18	0.67 to 0.75	0
13.2 to 16.4	0.75 to 0.5	0 to 0.5
12 to 13.2	0.5	0.5

.

2.3. Calculation of Component Values and Rated Specification

The output power P_o of the buck–boost converter can be expressed as:

P_o = η P_i,

(11)

where η represents the conversion efficiency, and P_i represents the input power; they can be expressed as:

P_i = V_i I_i,

(12)

Substituting (12) into (11), the input current expression can be obtained as:

I_i = P_o/(η V_i),

(13)

• Calculation of inductance value

In [9], it has been calculated and demonstrated that the required inductance value under buck-mode operation was greater than that under buck–boost mode. However, considering system stability and compatibility with the control strategy of the PWM controller, this study adopted the inductance calculation based on the buck–boost mode of operation. Therefore, the expression used to calculate the inductor L_bb is given as follows:

L_bb = V_i(min) V_o/[(V_o + V_i(min)) α i_L f_s],

(14)

where α represents the percentage value, i_Lbb is the inductor current, and f_s is the switching frequency of the power MOSFET. The term α × i_L denotes the peak-to-peak ripple current of the inductor during charging and discharging.

• Rated specifications of power MOSFET and diode

The input-side power MOSFET M₁ and diode D₁ must withstand the voltage stress imposed by the input voltage V_i [23]. Therefore, the maximum voltage across the drain-to-source terminals of M₁ and across D₁ can be expressed as:

v_ds1(max)= v_d1(max)= V_i(max),

(15)

The output-side power MOSFET M₂ and diode D₂ must withstand the voltage stress imposed by the output voltage V_o [24]. Therefore, the maximum voltage across the drain-to-source terminal of M₂ and across D₂ can be expressed as:

v_ds2(max) = v_d2(max) = V_o,

(16)

The currents i_ds1 and i_ds2 flowing through the two power MOSFETs, as well as the diode currents i_d1 and i_d2, must withstand the input current I_i under the condition of the lowest input voltage. Therefore, the maximum withstand current for each component is given by:

i_ds1 = i_ds2 = i_d1 = i_d2 = I_i,

(17)

• Output capacitor

The output capacitor C_o must store sufficient power to supply the load during buck-boost operation. Therefore, its required value can be calculated using the following expression [9]:

C_o = I_o d_M1/(β V_o f_s),

(18)

where β represents the percentage value, i_Lbb is the inductor current, the term β × V_o denotes the peak-to-peak value of the output voltage ripple.

2.4. Snubber Circuit

The parasitic inductances (L_p1 and L_p2) and capacitances (C_p1 and C_p2) can induce resonant voltage surges across the drain-source terminals of M₁ and M₂, as illustrated in Figure 5. When both M₁ and M₂ are turned off, the terminal voltage v_ds = v_ds1 = v_ds2 exhibits the voltage spike shown in Figure 5a.

At this time, the first resonant surge frequency f_r1 can be observed and measured. Its corresponding expression is given by:

$${f_r}_1 = 1/(2 \pi \sqrt{L_p{C}_p}),$$

(19)

where L_p represents the equivalent parasitic inductance, C_p represents the equivalent parasitic capacitance.

Using the external-connection capacitor test method, a test capacitor C_test is connected in parallel across the drain-source terminals of the power MOSFET. This setup allows for the measurement of the terminal voltage v_ds = v_ds1 = v_ds2 of either M₁ or M₂ during their cut-off state. The second resonant surge frequency f_r2, as illustrated in Figure 5b, can then be observed. Its corresponding calculation expression is:

$${f_r}_2 = 1/(2 \pi \sqrt{L_p (C_p+C_{test})},$$

(20)

To calculate f_r1 and f_r2, L_p and C_p can be replaced by L_p1, L_p2, C_p1, and C_p2, respectively.

Using (19) and (20), the parasitic elements at the drain-source terminals of the power MOSFET can be determined, and their corresponding calculation expression is given by:

$$L_p = (f_{r1}^{ 2}- f_{r2}^{ 2})/(4 {\pi }^2 C_{test} f_{r1}^{ 2}{f}_{r2}^{ 2}),$$

(21)

$$C_p=C_{test} f_{r2}^{ 2}/(f_{r1}^{ 2}-f_{r2}^{ 2}),$$

(22)

In this study, an RC–TVS (Transient voltage suppression) snubber circuit was connected in parallel with the power MOSFET, where R_snub denotes the snubber resistor, and C_snub denotes the snubber capacitor, as shown in Figure 5c. Their corresponding calculation expression is given by [25,26]:

$$R_{snub} = 0.5 \sqrt{L_p/C_p}$$

(23)

C_snub = 2/(π f_r1 R_sub),

(24)

3. Design Consideration

The specifications of the buck–boost converter, single inverter and motor, and battery pack [27] employed in the developed UGV of this study are listed in

Table 2. The part specifications used in the developed UGV of this study.

Description and Notation	Value
Buck–boost converter
Input voltage, Vi	20 to 29 V
Output voltage, Vo	24 V
Output current, Io	0 to 10 A
Maximum output power, Po	240 W
Maximum duty cycle ratio, don(max)	0.75
Operating frequency, fs	105 kHz
Conversion efficiency, η	>0.7
Single inverter (motor driver)
Rated input voltage	24 V
Rated output power	150 W
Single motor
Rated power	120 W
Rated torque	3.9 kg-cm
Rated maximum speed	3000 rpm
Battery pack
Number of series cell	8
Voltage at SOC 30%	26.92 V (charging at 0.5 C)
Voltage at SOC 50%	27.05 V (charging at 0.5 C)
Voltage at SOC 70%	27.23 V (charging at 0.5 C)
Capacity	35 Ah

.

The PWM controller LM5118 was used for the buck–boost converter in this study. The design considerations and calculated values for each component are presented as follows.

• Inductance value calculation

From Table 2, substituting P_o = 240 W, η = 0.7, and the minimum input voltage V_i(min) = 20 V into (13) can yield the input current I_i = 17.14 A. Substituting V_o = 24 V, f_s = 105 kHz, and α = 10% into (14) can obtain L_bb = 63.64 μH.

• Specifications of power MOSFET and diode

According to (15), the voltage stress that the power MOSFET M₁ and diode D₁ must withstand corresponds to the maximum input voltage V_i(max). Based on Table 2, v_ds1(max) = v_d1(max) = V_i(max) = 29 V.

According to (16), the voltage stress that the M₂ and diode D₂ must withstand corresponds to the output voltage V_o. Based on Table 2, v_ds2(max) = v_d2(max) = V_o = 24 V.

Based on Equation (17), the current that the power MOSFETs and diodes must withstand originates from the input current I_i, under the minimum input voltage. According to Equation (13), I_i = 17.14 A; therefore, i_ds1 = i_ds2 = i_d1 = i_d2 = I_i = 17.14 A.

In summary, the power MOSFET used in this study was the DMTH8012LK3Q (Diodes Inc., Plano, TX, USA), and the selected power diode was the DF20SC9M (Shindengen Corp., Tokyo, Japan). Their specifications are listed in

Table 3. Specifications of the power MOSFET and diode.

Power MOSFET
Parameter description	Value
Drain-source stress voltage	80 V
Continue drain current	35 A
Power diode
Forward current	20 A
Forward-bias voltage	0.75 V
Maximum reversed withstand voltage	90 V

.

• Output capacitance value calculation

Substitution of I_o = 10 A, d_M1 = d_on(max) = 0.75, β = 1%, V_o = 24 V, and f_s = 105 kHz into Equation (18), can obtain the output capacitor C_o = 312.5 μF.

• Characteristic Curve of Input Voltage–to–Duty Cycle Ratio

As listed in Table 2, the input voltage V_i ranges from 20 V to 29 V, while the output voltage is fixed at V_o = 24 V. Based on the derivation in Section 2.2, the gain factor was calculated as k = V_o/12 = 24/12 = 2, substituting these parameters into (5)–(10), the resulting characteristic curve of input voltage versus duty cycle ratio, applicable to this study, is shown in Figure 6 and detailed as follows:

(1)

Substituting V_i = 32.8 V to 36 V and k = 2 into (7), the line segment w₁ was obtained.

(2)

When V_o = 24 V and V_i = 32.8 V to 36 V, the buck–boost converter operated in buck mode.

(3)

Therefore, when d_M1 ≤ 0.75 and d_M2 = 0, the corresponding region was represented by line segment w₂.

(4)

Substituting V_i = 26.4 V to 32.8 V and k = 2 into (8), the line segment w₃ was obtained.

(5)

Substituting V_i = 26.4 V to 32.8 V and k = 2 into (9), the line segment w₄ was obtained.

(6)

When V_i = 24 V to 26.4 V, the buck–boost converter was operated in the buck–boost mode. In this voltage range, the duty cycle ratios of d_M1 and d_M2 both vary around 0.5, corresponding to line segment w₅.

The characteristic curve plotted using MATLAB is shown in Figure 6. The ranges of d_M1 and d_M2 ranges for V_o = 24 V are listed in

Table 4. Characteristic curve for V_o = 24 V.

Input Voltage (V)	dM1 Range	dM2 Range
32.8 to 36	0.67 to 0.75	0
26.4 to 32.8	0.75 to 0.5	0 to 0.5
24 to 26.4	0.5	0.5

.

A summary of related studies on buck–boost converter technologies and applications, including comparisons of characteristic curve types and the adoption of linear equation analysis, is provided in

Table 5. A summary of related studies on buck–boost converter technologies and applications.

Literature	Technology Description	Topology of Switching-Mode Power Supply	Characteristic Curve Type	Linear Equation Analysis for Characteristic Curve	Snubber Design for Power Switch
[28]	Buck-boost DC–DC converters are useful as DC grid interfaces for renewable energy resources. Buck-boost DC-DC converter privileges the buck region through the extension of the duty-cycle range, enabling buck operation.	Buck-boost converter	Non-linear	Not mentioned	Not mentioned
[29]	Operating procedure analysis. Mathematical model derivation.	Buck-boost converter	Non-linear	Not mentioned	Not mentioned
[30]	To attain additional mitigation of output transients and a linear input/output voltage characteristic in buck and boost modes, the linearization of dc gain of the large-signal model in boost operation is analyzed. To improve the output voltage ripple in the applications based on noninverting buck–boost converter topologies.	Buck-boost converter	Linear	Not mentioned	Not mentioned
[31]	A continuous-conduction mode noninverting buck–boost converter with a fast duty-cycle calculation control and duty-cycle locking strategy. The input voltage changes, the FDCC control adopts auxiliary slopes and variable slope of the modulation signal to rapidly determine an accurate duty cycle and effectively keep the compensator output in the buck and the boost modes.	Buck-boost converter	Linear	Not mentioned	Not mentioned
[32]	Line commutated converter based high-voltage direct current transmission is characterized by long-distance power transfer, a complex and harsh corridor environment, and the rapid fault evolution of DC lines. An extended single and double-ended measurement-based relaying for LCC-HVDC transmission lines, utilizing the transient current measurement at the boundary of positive and negative polarity transmission lines.	Not mentioned	Not mentioned	Not mentioned	Not mentioned
[33]	By modelling various cyber-physical contingencies as reformulations of simulation boundaries, a variable-coefficient analytical method is devised to address scenarios characterized by discontinuity and abrupt changes. Case studies reveal several key insights. An N-1 contingency evaluation method for cyber-physical integrated electricity and gas systems.	Not mentioned	Not mentioned	Not mentioned	Not mentioned
This study	The relationship between voltage gain and duty cycle ratio was analytically derived. A linear equation, based on the characteristic curve provided in the original datasheet, was formulated and subsequently extended to cover the required input voltage range for this design. A buck–boost converter was developed to supply a stable DC voltage as the input power source for inverters. This design allowed the inverters to drive the motors of a UGV without being affected by fluctuations in the input voltage.	Buck-boost converter	Linear	It has been performed	It has been performed

.

4. Experimental Result

A DC power supply served as the input source for the buck–boost converter, while an electronic load was connected to its output. When the input voltage V_i is set to 20 V, 24 V, and 29 V, and the output current I_o is maintained at 10 A by the electronic load, the corresponding experimental waveforms of input current I_i and output voltage V_o = 24 V are as shown in Figure 7. This experiment demonstrates that V_o remains consistently regulated at 24 V, unaffected by variations in the input voltage.

A lithium iron phosphate battery pack was used as the input power source for a buck-boost converter, whose output side was connected to an inverter that derived a motor. Figure 8 shows the experimental waveforms of input voltage V_i, input current I_i, output voltage V_o, and output current I_o of the buck-boost converter, measured at a battery voltage V_i = 24.2 V and motor speeds of 1000 rpm, 2000 rpm, 3000 rpm, and 3500 rpm. In Figure 8, V_o remained stable at 24 V regardless of changes in motor speed. Specifically, I_o increases as the motor speed increases: at 1000 rpm, I_o = 0.81 A, as shown in Figure 8a; at 2000 rpm, I_o = 0.86 A, as shown in Figure 8b; at 3000 rpm, I_o = 2.25 A, as shown in Figure 8c; and at 3500 rpm, I_o = 2.3 A, as shown in Figure 8d.

• Transition from buck operation mode to buck–boost operation mode

Figure 9 presents the experimental waveforms of the gate-source voltage (v_gs1 and v_gs2) and inductor current (i_Lbb) of the power MOSFETs M₁ and M₂, with an input voltage of V_i = 29 V and I_o = 10 A. The duty cycle ratio of d_M1 was 5.86 μs/9.52 μs = 0.61 (estimated in Figure 6: 0.6), while that of d_M2 is 2.93 μs/9.52 μs = 0.31 (estimated in Figure 6: 0.3). These results are consistent with the characteristic curve shown in Figure 6.

According to the notations in Figure 3, substituting d_M1 = 0.61 and d_M2 = 0.31 into (4) can yield an experimental voltage gain (V_o/V_i) of 0.87, which closely approximates the estimated voltage gain of 0.83. The corresponding experimental results are summarized in

Table 6. Corresponding voltage gain results based on Equation (4) and experimental verification.

dM1	dM2	don = dM1	don2 = dM1 − dM2	Vo/Vi = don/(1 − don + don2)	Vi	Vo	Vo/Vi
0.61	0.31	0.61	0.3	0.87	29 V	24 V	0.83
0.54	0.54	0.54	0	1.17	24 V	24 V	1

.

Figure 10 presents the experimental waveforms of the gate-source voltages (v_gs1 and v_gs2) and inductor current (i_Lbb) of M₁ and M₂, with an input voltage of V_i = 24 V and I_o = 10 A. The duty cycle ratio of d_M1 is 5.21 μs/9.52 μs = 0.54 (estimated in Figure 6: 0.5), while that of d_M2 is 5.21 μs/9.52 μs = 0.54 (estimated in Figure 6: 0.5). These results are consistent with the characteristic curve shown in Figure 6.

According to the notations in Figure 3, substituting d_M1 = 0.54 and d_M2 = 0.54 into (4) can yield an experimental voltage gain (V_o/V_i) of 1.17, which closely approximates the estimated voltage gain of 1. The corresponding experimental results are summarized in Table 6.

Referring to Figure 2 and Figure 5a, when the buck–boost converter was operated without a parallel test capacitor or snubber circuit across the drain-source terminals of the power MOSFETs, the drain-source voltages (v_ds1 and v_ds2) of M₁ and M₁ were measured, as shown in Figure 11. Upon turn-off of M₁ and M₂, v_ds1 and v_ds2 transitioned from a low to a high voltage level. During this transition, when V_i was 20 V and 24 V, the surge voltages at v_ds1 and v_ds2 exhibited the oscillation frequencies f_r1 of 50 MHz and 58.8 MHz, respectively, as shown in Figure 11a,b.

Referring to Figure 2 and Figure 5b, the test capacitor C_test = 1000 pF was connected in parallel across the drain-source terminals of the power MOSFETs in the buck–boost converter. During this transition, when V_i was 20 V and 24 V, the surge voltages at v_ds1 and v_ds2 exhibited the oscillation frequencies f_r1 of 23.53 MHz and 25 MHz, respectively, as shown in Figure 11c,d.

Substituting the minimum f_r1 = 50 MHz and f_r2 = 23.53 MHz into (19) to (24), the equivalent parasitic inductance L_p was calculated to be 35.62 nH, and the equivalent parasitic capacitance C_p was 284.46 pF. Additionally, the snubber resistor value R_snub was determined to be 5.94 Ω (practically 6.2 Ω), and the snubber capacitor C_snub was 2.28 nF (practically 2.2 nF), as shown in Figure 5c.

• With RC snubber circuit

When the buck-boost converter operates at input voltages of 20 V, 24 V, and 29 V with an output current of 10 A, the drain-source voltages v_ds1 and v_ds2 without snubber resistors and capacitors are as shown in Figure 12.

The designed snubber resistor and capacitor were connected across the source-drain terminals of M₁ and M₂. When the buck–boost converter is operated at input voltages of 20 V, 24 V, and 29 V with an output current of 10 A, the waveforms of v_ds1 and v_ds2 are as illustrated in Figure 13. The experimental results confirmed that the incorporation of the snubber circuit effectively suppresses the resonant voltage amplitude of v_ds.

The dynamic performance of the proposed buck–boost converter on the UGV is shown in Figure 14. The figure presents the experimental waveforms at an input voltage of V_i = 20 V; when the motor toque increased from 500 to 3500 rpms, the output current I_o of the buck–boost converter rose accordingly, while the output voltage V_o was maintained at 24 V.

Therefore, as shown in Figure 8, the developed buck–boost converter was able to provide a stable output voltage to the inverter regardless of variations in the battery voltage. Furthermore, as shown in Figure 14, the inverter can also operate with a stable input voltage at different speeds.

The developed UGV chassis prototype in this study is shown in Figure 15. The figure illustrates the installation positions of the lithium-ion battery pack, inverter, motorized wheels, and buck–boost converter on the underside of the UGV chassis. The chassis dimensions are 40 cm in length, 45 cm in width, and 18.3 cm in height.

5. Conclusions

In this study, a buck–boost converter was developed to supply a stable DC voltage as the input power source for inverters. This design allowed the inverters to drive the motors of a UGV without being affected by fluctuations in the input voltage. Experimental results demonstrated that the converter maintained a constant output voltage at the rated output current under varying input voltage conditions, confirming the effectiveness of the proposed approach. The PWM controller employed in this study operated in both buck–boost and buck modes, resulting in the simultaneous turn-on of the two power MOSFETs. Under this operating condition, the relationship between voltage gain and duty cycle ratio was analytically derived. A linear equation, based on the characteristic curve provided in the original datasheet, was formulated and subsequently extended to cover the required input voltage range for this design. Using an adding test capacitor method, the equivalent parasitic inductance and capacitance of the circuit were identified. Based on these values, an RC–TVS snubber circuit was designed and connected across the drain-source terminals of the power MOSFETs. Experimental results confirmed that the proposed snubber effectively suppressed the drain-source voltage surge. In addition to validating the design considerations, the buck–boost converter prototype was successfully integrated into a UGV, where it converted the lithium iron phosphate battery power into the operating voltage required by inverters to drive motors.