Basic Study on Operation Control Systems of Internal Combustion Engines in Hybrid Small Race Cars to Improve Dynamic Performance

Abstract

Hybrid vehicles utilize multiple power sources, making them energy-efficient and enhancing both fuel efficiency and dynamic performance. As a result, hybrid vehicles have recently been adopted as race cars, which demand high powertrain performance. The hybrid vehicle system comprises two power sources: an internal combustion engine (ICE) and an electric motor, both of which require precise control. Controlling the output of the internal combustion engine is particularly challenging. This study investigated the dynamic response of an actuator in an electronic throttle system. The experimental results demonstrated that optimized parameters significantly improved the dynamic response. As a result, we propose a mechanism for hybrid vehicle performance and report the characteristics of an electronic throttle. The improvement in throttle opening can be verified by adjusting the P term.

1. Introduction

Reportedly, global warming has led to a rise in sea levels, primarily due to the melting of Arctic ice, and has increased the frequency of extreme weather events associated with climate change. Petroleum reserves in oil wells, which began to be widely used in the early 20th century, are expected to be depleted by the middle of this century. To ensure the sustainable development of a mobile society centered around automobiles—an evolution intertwined with petroleum-based civilization—groundbreaking innovations in engine and powertrain technologies are essential. Efforts to reduce CO₂ emissions and produce cleaner exhaust gases, particularly through advancements in powertrain systems, are being aggressively pursued. Hybrid systems, which combine engines and electric motors, present a practical solution to address these challenges.

A hybrid vehicle shuts off its engine when the vehicle stops, thereby eliminating fuel waste. At low speeds, the engine remains off, and the vehicle operates on an efficient electric motor. During acceleration, the motor supplies the necessary power, conserving fuel in the process. Any excess energy, beyond what is required for driving, is stored in the battery and later used to power the motor [1].

Hybrid vehicles rely on multiple power sources. Recently, numerous automakers have introduced vehicles powered by these dual systems. An internal combustion engine (ICE) delivers high torque at high speeds, while one or more electric motors generate high torque at low speeds. These vehicles are also highly energy-efficient. The powertrain is managed using control unit algorithms, which, in the case of hybrid systems, can enhance both fuel efficiency and dynamic performance. This capability has encouraged various companies to integrate hybrid systems into competitive vehicles.

For small race cars, the primary goals are to enhance performance and reduce lap times. Prior research has concentrated on optimal battery control methods for hybrid vehicles, systems designed to minimize lap times, and comparative studies on acceleration performance. In our laboratory, we have analyzed motor reduction ratios and final reduction ratios to optimize vehicle performance [2]. Additionally, we have modeled vehicles and verified the theory and utility of a quasi-steady lap-time simulation, which provides simplified performance predictions.

Figure 1 illustrates both conventional and proposed hybrid systems. Conventional hybrid systems are available in various layouts, typically combining the power of the ICE and the electric motor using gears or planetary gears. However, these designs often have drawbacks, such as increased system weight and limited flexibility in component placement. Furthermore, most existing systems combine the torque of the electric motor with the ICE torque before passing through the transmission, resulting in low torque at low speeds.

To harness the electric motor’s high torque at low speeds, we propose a hybrid system that synthesizes the torque from the ICE (converted through the transmission) and the electric motor’s torque without routing the motor’s output through the transmission. The proposed system reduces the transmission of the electric motor’s torque, improving efficiency. While various power system layouts have been reported in the past [3,4], hybrid systems specifically tailored for small race cars remain underexplored. To demonstrate the proposed system’s performance, precise control of the electric motor and ICE outputs is required. This is achieved through a command signal from the accelerator pedal to the control unit. Motor current is easily controlled by the motor driver, while ICE output is managed by adjusting the airflow through the throttle valve and modifying the fuel flow rate accordingly. However, achieving responsiveness and precise output control is challenging due to the high inertia of the pistons and crankshaft. This makes responsiveness and output control challenging. As a result, throttle-by-wire technology, where the throttle valve is operated by an actuator, becomes essential for controlling an ICE using a command signal. However, the responsiveness of this technology has not been fully investigated. This study focused on the performance of a small hybrid racing car, the Formula Hybrid [5], and examined the characteristics of the power system under small-race-car conditions. It also evaluated the driving performance of the hybrid system and the feasibility of implementing an electronic throttle controlled by an ICE [6].

2. Hybrid System for Small Race Cars

2.1. Proposed Hybrid System for Small Race Cars

Figure 2 and Figure 3a,b illustrate various components of a small race car and a schematic of the proposed hybrid system during acceleration and deceleration. As shown in Figure 3a, during acceleration in the proposed hybrid system, the shaft torque generated by the ICE is transferred through the transmission, reduced in speed, and conveyed from the ICE sprocket to the drive-shaft-side sprocket via a chain. Consequently, the torque is transmitted to the axle through a one-way clutch and the final gear. Similarly, the shaft torque generated by the electric motor is reduced in speed, transferred to the drive-shaft-side sprocket via a chain, and transmitted to the axle through the final gear. The total drive torque generated at the tires is the sum of the torques transmitted to the axle shaft by the ICE and the electric motor. This system has a simple structure using lightweight chains and sprockets, which can also be expected to reduce the weight of the vehicle.

Conversely, during deceleration, as shown in Figure 3b, no driving force is supplied by the ICE. The one-way clutch prevents the driving force of the electric motor from being transmitted back to the ICE, rendering the ICE sprockets on the drive-shaft side idle. The braking force exerted at the tire–ground interface generates torque on the axle shaft in the opposite direction of acceleration. This torque is transmitted to the electric motor shaft via the final gear and sprocket, enabling the electric motor to generate electricity and regenerate energy [2].

In the future, we plan to explore the installation of a regenerative braking system to enhance energy recovery during deceleration.

2.2. Driving-Force Simulation of the Proposed Hybrid System

The driving force of the hybrid system was simulated using an ICE (model G363E, installed in a YAMAHA WR250R) and an electric motor, as illustrated in Figure 4.

Table 1. Specifications of the ICE [2].

Engine model number	G363E
Engine type	250 cc liquid-cooled DOHC 4-stroke, 4-valve
Bore × stroke	77.0 mm × 53.6 mm
Compression ratio	11.8:1
Fuel delivery	Fuel injection
Ignition	TCI (transistor-controlled ignition)
Transmission	Constant-mesh, 6-speed, multiplate wet clutch
Max power	23 kW/10,000 rpm
Max torque	24 Nm/8000 rpm
Gear 1	2.642
Gear 2	1.812
Gear 3	1.318
Gear 4	1.04
Gear 5	0.888
Gear 6	0.785
Final drive ratio	3.145

lists the ICE specifications. The output data for the engine and electric motor were cited from the results of the respective power tests conducted at our university.

An air-cooled Motenergy ME0913 brushless motor (Figure 5) with a maximum output of less than 30 kW was used as the electric motor.

Table 2. Specifications of the electric motor [2].

Drive voltage	DC 24–96 V
Maximum current	550 A
Maximum rotation speed	5000 rpm (no load)
Maximum output	30 kW (DC 96 V)
Maximum torque	90 Nm
Continuous output	12 kW (DC 96 V)
Continuous current	180 A
Continuous efficiency	92%
Continuous rotation speed	3000 rpm
Mass	15.9 kg
Poles	4 (magnet 8)
Cooling method	Air-cooling forced-fan system

lists the specifications of the electric motor. Figure 6 shows the driving force and speed for each gear and electric motor, and Figure 7 shows the total driving force and speed.

The combination of the ICE and the electric motor increased the total driving force by approximately 500 N. Figure 6 and Figure 7 demonstrate that the electric motor could efficiently accelerate the small race car up to a speed of 20 m/s. However, its contribution to acceleration performance is expected to diminish at speeds exceeding 30 m/s. Based on these findings, we conclude that a high-performance powertrain can be achieved by utilizing the electric motor in the low-speed range and relying on the ICE in the high-speed range.

3. Electronic Throttle

3.1. Throttle Control of ICE

An overview of the KTM 390 Duke electronic throttle is shown in Figure 8. Figure 9 illustrates the relationship between throttle opening and intake air volume. The throttle position sensor (TPS) is a variable resistor comprising a resistive element and sliding components. The motor moves the butterfly valve, altering the resistance values of two resistors. By changing these resistance values, the opening and closing actions of the butterfly valve, indicated by the arrows, are adjusted to control the intake air volume.

Figure 10 depicts the proposed driving-force control system, which manages the intake air volume and can artificially vary the energy generated by combustion. In conventional experimental models, the throttle and accelerator pedal are mechanically connected, allowing throttle opening to be controlled by adjusting the pressure on the accelerator pedal. While this system is straightforward, controlling the throttle in a small race car is challenging and entirely dependent on the driver.

A hybrid system that combines two power sources—an ICE and an electric motor—requires precise control of each source. Motor current can be easily controlled using a motor driver; however, controlling the output of an ICE is more complex. To address this challenge, this study explored the implementation of an electronic throttle, enabling inputs from both the driver and the small race car.

In this study, the throttle-opening degree in response to input was controlled using an Arduino, as shown in Figure 11. Controlling the ICE is critical for realizing the proposed hybrid system. To achieve this, we conducted experiments to investigate the characteristics of an electronic throttle.

3.2. Experimental Procedure

The calculation algorithm for the Arduino Due employs the proportional–integral–derivative (PID) control method. This method was chosen because it can be easily tuned by adjusting the gain of each term and implemented using cost-effective computational hardware, as it does not rely on complex control theories. The PID control can be expressed as follows [7]. In the future, we aim to explore various other control methods to enhance system performance [8,9,10,11,12,13].

$$u\left(t\right)=-K_{P}y\left(t\right)-K_D\dot{y}\left(t\right)-K_I{\int }_0^{t}y\left(\mathcal{T}\right)d\mathcal{T}\left(\dot{r}=0\right)$$

(1)

The electronic throttle was evaluated using four criteria, as shown in Figure 12: rise time, settling time, overshoot, and throttle opening. Rise time refers to the time required for the instantaneous value of the pulse to first reach a specified lower limit and then reach a specified upper limit, defined as 10% and 90% of the final value, respectively. Settling time is the duration required for the throttle position to stabilize within 2% of its steady-state value. Overshoot is the extent to which the maximum response exceeds the final steady-state value. Throttle opening represents the steady-state value of the throttle position. Efforts were focused on reducing rise time, settling time, and overshoot. Additionally, the closer the actual throttle opening is to the target value for each opening position, the more ideal the performance. And we believe that improving the responsiveness of the electronic throttle will result in immediate drive torque, allowing the vehicle to accelerate instantly and contribute to a reduction in lap times.

Figure 13 shows the experimental setup for the electronic throttle system. In this experiment, an Arduino Due was used as the controller for the electronic throttle, along with a regulated power supply. A toggle switch, positioned between the potentiometer and the Arduino Due, was used for input control. The experimental conditions for when the P term and I term were changed are shown in

Table 3. Experimental conditions.

	−50%	−40%	−30%	−20%	−10%	0%	+10%	+20%	+30%	+40%	+50%
P term	0.25	0.3	0.35	0.4	0.45	0.5	0.55	0.6	0.65	0.7	0.75
I term	0.45	0.54	0.63	0.72	0.81	0.9	0.99	1.08	1.17	1.26	1.35
D term	/	/	/	/	/	0.01	/	/	/	/	/

.

The P term of the PID control was varied from 0.25 (−50%) to 0.75 (+50%), and the I term was adjusted from 0.45 (−50%) to 1.35 (+50%). The D term was fixed at 0.01. When one term was modified, the other two terms remained at their initial (0%) values. The P, I, and D terms were determined based on previous experimental results. The target input volume was set at 80%, representing the maximum pressure expected on the accelerator pedal during a race.

3.3. Experimental Results

Figure 14 shows the experimental results when the P term was changed. Figure 14a, 14b, 14c, and 14d show the rise time, settling time, overshoot, and throttle opening, respectively. Figure 15 shows a comparison of the experimental results for the TPS when the P term was changed.

Figure 16 presents the experimental results for when the I term was adjusted. Figure 16a, 16b, 16c, and 16d show the rise time, settling time, overshoot, and throttle opening, respectively. Figure 17 provides a comparison of the experimental results for the TPS when the I term was changed.

4. Discussion

For each result, the maximum rise time was 0.1371 s when the P term was adjusted to −30%, and the minimum rise time was 0.073 s when the P term was set to −10%. The maximum settling time was 0.1552 s at a P term of −30%, while the minimum settling time was 0.0408 s when the P term was set to +30%. The maximum overshoot was 71.3533% when the P term was increased by +40%, and the minimum overshoot was 6.9733% when the P term was decreased by −40%. The throttle opening was at its minimum when the P term was set to −20%, settling at 63% of the target input volume (80%), and was at its maximum when the P term was adjusted to +50%, settling at 74% of the target input volume. In Figure 15, as the P term was increased from −20% to +50%, the throttle opening increased by 11%. This change is highlighted in the area indicated by the red square in the figure. The throttle opening reached its highest value when the P term was set to +50%. The rise and settling times showed a decreasing trend as the value of the P term increased. In contrast, the overshoot and throttle opening rates tended to increase. Because the P term is proportional, increasing the gain also enhances the proportionality. As a result, the time required to reach the target input volume was reduced, leading to shorter rise and settling times. However, because the target value was exceeded, both the overshoot and throttle opening were observed to increase. When the I term was increased from −50%, the rise time remained relatively steady, while the settling time showed some variability. However, the overshoot tended to decrease, and the throttle opening remained stable. For the rise time, when the I term was decreased from the initial value to −30%, it decreased by about 24%. Under other conditions, the experimental results fluctuated without capturing a clear trend. In the case of settling time, when the I term was decreased from the initial value to −30%, it decreased by about 52%. However, the experimental results remained scattered, and no consistent trend could be identified. For overshoot, when the I term was increased from −20% to +30%, it decreased by 94%, improving control performance. A further increase in the I term did not result in significant changes. Conversely, when the I term was decreased, the overshoot increased, and at −20%, it was roughly twice the initial value. In terms of throttle opening, when the I term was increased, it reached a maximum of 75% at +10%. However, under other experimental conditions, the throttle opening remained nearly constant, and no clear trend was observed. Figure 17 illustrates that the overshoot decreased by 94% when the I term was increased from −20% to +30%, as highlighted in the red box. When the I term was −20%, the overshoot was highest, reaching approximately 105% of the throttle opening. Based on these results, the optimal P term was determined to be 0.75 (+50%), and the optimal I term was found to be 1.17 (+30%), considering the response of the electronic throttle.

5. Conclusions

In this paper, we propose a mechanism for hybrid vehicle performance and the characteristics of an electronic throttle. The combination of an ICE and an electric motor increased the total driving force by approximately 500 N. Based on these results, we believe that a high-performance powertrain can be achieved by utilizing an electric motor in the low-speed range and an ICE in the high-speed range. An experiment was conducted to verify the required follow-up time when the accelerator pedal was operated to implement an electronic throttle. As the P term was increased, the rise and settling times decreased, while the overshoot and throttle opening increased. Therefore, the improvement in throttle opening can be verified by adjusting the P term. Furthermore, by increasing the P term, the startup time is reduced, and with the throttle butterfly opening instantly, instantaneous drive torque is generated, which improves the vehicle’s acceleration performance while also enhancing its control performance. We intend to implement this hybrid mechanism and install an electronic throttle in the engine for verification in the future [14,15,16,17,18,19,20,21,22,23,24]. Additionally, we plan to measure horsepower, torque, and fuel consumption using a dynamometer. To further investigate the usefulness of the variable intake air volume system and the characteristics of the flow inside the intake pipe, we aim to create a model simulating the ICE intake system and validate it using 3D CFD analysis [25,26,27,28,29,30]. Therefore, in the future, we aim to improve the output performance of the ICE through intake air control, and we would like to verify the behavior of the intake around the throttle butterfly considering the engine speed using three-dimensional CFD analysis. We would also like to produce small racing vehicles and conduct circuit runs and lap-time measurements.