Electric cars have emerged as a pivotal solution to the global energy crisis and environmental degradation. As a core component of the powertrain, the transmission plays a critical role in determining the overall performance of electric cars. While fixed-speed reducers are widely adopted due to their simplicity, they fail to fully exploit the potential of traction motors. The two-speed Automated Manual Transmission (AMT), on the other hand, enables traction motors to operate nearer to their optimal efficiency zones by switching between two distinct gear ratios. This configuration provides high torque at low speeds and improves high-speed efficiency. Research on such gearshift strategies is crucial to balancing the often conflicting demands of dynamic performance, energy economy, and ride comfort in electric cars. However, many existing gearshift strategies largely overlook real-time variations in driver behavior and vehicle speed trajectories, which frequently gives rise to gear hunting, suboptimal shift timing, and a mismatch with the driver’s demands. To address these shortfalls, I focus my research on a two-speed AMT tailored for heavy-duty electric cars. I construct a gearshift control model within the MATLAB/Simulink® simulation environment, devise a novel gearshift control strategy that accounts for the driver’s style and predicted future vehicle speed, and analyze its operational behavior under diverse driving cycles. The focal point of this work, for both theoretical development and practical validation, is to strengthen the dynamic response, energy economy, and ride comfort of heavy-duty electric cars.
Before detailing the methodology, it is instructive to review recent developments in this area. Globally, researchers have extensively investigated gearshift strategies, powertrain matching, energy management, and hardware-in-the-loop testing. Many studies use dynamic programming, model predictive control, fuzzy logic, and neural networks. In particular, the international community has made progress in high-precision simulation and adaptive control strategies, while the local research community has focused on rule-based strategies, intelligent optimization algorithms, and low-cost practical implementations. In this body of work, performance objectives are often optimized in a multi-objective fashion, where fuel or energy consumption, shift quality, and dynamic performance are considered simultaneously. Nonetheless, a systematic method to weave driving styles and future vehicle speed information into an adaptive gearshift decision framework remains highly desirable. The development presented here aims at contributing to that direction. The rationale is as follows: if the control system can perceive whether the driver has an aggressive or cautious style, and also anticipates the upcoming speed trend, shifts can be planned in a more informed fashion, reducing unnecessary gear changes and improving shift discipline. Furthermore, once a shift decision is made, precise control of the synchronization process is essential to minimize transient shock and power interruption. My approach is thereby decomposed into two interrelated subproblems: a gear decision layer that benefits from driving-style recognition and vehicle-speed prediction, and an execution layer that combines fuzzy logic with classical PID control for synchronization of the shift actuator. This integrated framework is systematically validated through numerical simulations and laboratory tests of the shift motor without load.
Powertrain Modelling and Synchronizer Dynamics
For this research, I first carried out a comprehensive dynamic analysis of the shift mechanism of a heavy-duty two-speed AMT. The shift execution system is built around a synchronizer, selected because of its superior capacity to equalize the speed between the input and output shafts before gear engagement. During the gear changing process, the synchronizer friction elements dissipate kinetic energy into heat, thus enabling the mesh of the gear teeth without undue wear and shock. To make this analysis rigorous, I investigated the working principle of the locking-ring synchronizer and established the corresponding dynamic equations. The inertia parameters of the driveline were identified with precision. Equations (1)–(4) list several important moments of inertia that I calculated for the driveline system.
$$J_2′ = J_3\left(\frac{Z_6}{Z_8}\right)^2 = 8.555 \times 10^{-3} \, \mathrm{kg \cdot m^2} \tag{1}$$
$$J_1′ = (J_4 + J_1)\left(\frac{Z_2}{Z_3}\right)^2 = 0.3783 \, \mathrm{kg \cdot m^2} \tag{2}$$
$$J_{\text{low}} = J_1′ + J_3′ + J_2 = 0.4276 \, \mathrm{kg \cdot m^2} \tag{3}$$
$$J_{\text{high}} = J_1′ + J_3′ + J_2 = 0.4663 \, \mathrm{kg \cdot m^2} \tag{4}$$
where \(J_1\), \(J_2\), \(J_3\), and \(J_4\) correspond to the moments of inertia of the input shaft, synchronizer shaft, output shaft, and motor shaft, respectively, while \(Z_i\) denotes the number of teeth on gear \(i\). These parameters were critical for predicting the shift force and frictional work during synchronization. Additionally, I defined several metrics to evaluate shift quality: shift force, shift impulse, vehicle jerk, frictional work, and the duration of power interruption. Figure 2 below shows some typical engagement phases of a locking-ring synchronizer, i.e., pre-synchronization, synchronization, unlocking, and final engagement.
Shift forces are important to perceive the load experienced by the actuator over different phases. Under the condition of self-locking in the pre-synchronization phase, the required shift force is expressed by equations (5) and (6). During the neutral pre-synchronization phase, equations (7) and (8) represent the forces under the influence of the chamfer angle \(\alpha_1\), while during the synchronization stage, the axial force is related to the synchronizer torque \(T_C\) and the angular acceleration mismatch. Equations (9)–(12) summarize these relationships for the synchronization phase.
$$F_{\text{self}} = f_k\left(2\sin\alpha\cos\alpha \mu_k \cos^2\alpha\right) \tag{5}$$
$$F_H = F_{\text{self}} \tag{6}$$
$$F_{\text{disengage}} = \frac{f_{n1}\left( \sin\alpha_1 + \mu_n\cos\alpha_1 \right)}{\cos\varphi} \tag{7}$$
$$F_H = \frac{F_{\text{disengage}}}{\cos\varphi} \tag{8}$$
$$T_C = F \cdot R_C \frac{\sin\phi}{\mu_c} \tag{9}$$
$$T_C = J_R \frac{\Delta\omega}{t} \tag{10}$$
$$t = \frac{J_R \Delta\omega \sin\phi}{F \cdot R_C \mu_c} \tag{11}$$
$$F_H = \frac{F}{\cos\varphi} \tag{12}$$
Here, \(\mu_c\) is the dynamic friction coefficient of the synchronizer cone, \(R_C\) is the average radius of the cone friction surface, \(\phi\) is the cone angle, and \(\Delta\omega\) denotes the angular velocity difference between the cone surfaces. At the engagement phase, the relation is expressed by equations (13) and (14).
$$f_{t0} = f_{n0}\left( \sin\alpha_2 + \mu_0\cos\alpha_2 \right), \quad F_H = \frac{f_{t0}}{\cos\varphi} \tag{13}$$
$$F_H = f_{t0} / \cos\varphi \tag{14}$$
The shift impulse and the sliding frictional work are also defined in Eqs. (15) and (16), while Eq. (17) defines the vehicle jerk as the derivative of the acceleration, which is one of the most direct indicators of ride comfort.
$$I = \int_0^t F_H \, dt \tag{15}$$
$$W = \int_{t_0}^{t_1} T_C \cdot \Delta\omega \, dt \tag{16}$$
$$J = \frac{da}{dt} = \frac{d^2v}{dt^2} \tag{17}$$
To analyze the gearshift control loop, I modeled several subsystems in MATLAB/Simulink® environment. The traction motor is a permanent magnet synchronous motor (PMSM). The motor is rated at 165 kW with a peak power of 230 kW, a maximum torque of 1100 N·m, and a maximum speed of 8000 rpm. Its voltage equations in the d-q reference frame are expressed in Eqs. (18) and (19), while the electromagnetic torque and mechanical dynamics are described by Eqs. (20) and (21). I list the motor parameters in Table 1.
$$u_d = R_s i_d + L_d \frac{di_d}{dt} – \omega_e L_q i_q \tag{18}$$
$$u_q = R_s i_q + L_q \frac{di_q}{dt} + \omega_e (L_d i_d + \psi_f) \tag{19}$$
$$T_e = \frac{3}{2} p\left[ \psi_f i_q + (L_d – L_q)i_d i_q \right] \tag{20}$$
$$T_e – T_L = J \frac{d\omega_m}{dt} + B\omega_m \tag{21}$$
| Parameter | Value |
| Maximum speed (rpm) | 8000 |
| Peak power (kW) | 230 |
| Rated power (kW) | 165 |
| Peak torque (N·m) | 1100 |
Moreover, I built a lithium-ion battery model because the battery state-of-charge (SOC) is a crucial variable for assessing economic efficiency in electric cars. The battery voltage and internal resistance are represented as polynomial functions of the SOC by Eqs. (22) and (23). The SOC update is governed by the current integral in Eq. (24). This battery model was integrated into the whole vehicle model to capture the effect of gearshift decision on the global energy consumption.
$$E_{SOC} = E_0 + \sum_{i=1}^5 E_i SOC^i \tag{22}$$
$$R_{SOC} = \delta_0 R_0 + \sum_{i=1}^6 \lambda_i SOC^i \tag{23}$$
$$SOC(t+1) = SOC(t) – \frac{I(t)}{Q_{bat}} \tag{24}$$
On the mechanical side, the powertrain comprises a two-speed gearbox with the parameters in Table 2. The relationship between synchronous-shaft speed, motor speed, and vehicle velocity was derived through Eqs. (25)–(29). By carefully placing the gear pairs, it is possible to calculate the gear ratio between the motor output speed and the synchronizer speed. The key ratios are \(n_{QG} = Z_2/Z_1\) for high gear and \(n_{QD} = Z_4/Z_3\) for low gear. In these expressions, \(\i_1\), \(\i_2\), \(\i_0\), and \(\i_3\) denote the first gear ratio, second gear ratio, final drive ratio, and side-reducer ratio, respectively; \(r\) denotes the wheel radius; and \(n_Q\) stands for motor output speed. The vehicle longitudinal dynamics model, given by Eq. (37), incorporates rolling resistance, aerodynamic drag, grade resistance, and acceleration resistance, which is essential for accurate simulation of vehicle response during gear shifting.
$$n_0 v = n_0 \cdot i_1\cdot i_0\cdot i_3 \tag{27}$$
$$v = \frac{3.6 \cdot 2\pi r n_0 \cdot i_1}{i_1 i_0 i_3} \tag{29}$$
$$n_Q = n_{sync} \cdot i_Q \tag{30}$$
$$F_t = F_f + F_w + F_j + F_i \tag{31}$$
$$F_t = \frac{T_e \cdot i \cdot \eta}{r} \tag{32}$$
$$F_j = m\delta \frac{dv}{dt} \tag{35}$$
$$m\frac{dv}{dt} = F_t – F_f – F_w – F_i \tag{37}$$
| Parameter | Value |
| Wheel radius (m) | 0.31 |
| First gear ratio | 2.05 |
| Second gear ratio | 1.03 |
| Final drive ratio | 2.45 |
| Side reducer ratio | 5.05 |
With these model blocks, I built a simulation model based on a conventional speed-based gearshift rule. The model was evaluated in the INRETS driving cycle to check whether the fundamental components work. The results proved that the vehicle followed the target speed properly and the gear choice was just as expected, which gives sound assurance of the model credibility for further investigations.
Gearshift Strategy Incorporating Driving Style and Vehicle Speed Prediction
After verifying the full vehicle simulation model, I went one step further to incorporate information on the driver’s intent as well as predicted future driving conditions into the gearshift decision. Figure 4 shows the logic flow of my proposed strategy: first the driving style is identified via the vehicle jerk, second the future vehicle speed is predicted based on historical speed samples, and finally a fuzzy logic controller and an adaptive gear coefficient selection logic determine the target gear. Then, in the shift execution phase, I built a fuzzy PID controller that takes the speed difference at the synchronizer and its changing rate as inputs, so as to output a modulated speed command to the shift motor.
Driving-Style Recognition Based on Jerk
Driving style is often considered the main reason behind the variation of acceleration usage in electric cars. Since aggressive drivers usually press the acceleration pedal faster, the rate of change of drive torque can be used as an indirect indicator of the driver’s style. In the vehicle longitudinal dynamics, the jerk \(J\) is directly related to the motor torque derivative as shown in Eq. (38), which illustrates that the jerk calculation provides the necessary signal for style classification.
$$\frac{dT_e}{dt} = \frac{(I_{out} \cdot i_0 \cdot i_g + I_{in})}{i_0 \cdot i_g} \cdot J \cdot r \tag{38}$$
I selected a fixed observation window of \(T=200\) s. Within each time window, the jerk samples \(J_i\) are recorded. The standard deviation \(SD_J\) and the mean absolute jerk \(\bar{J}\) are then calculated according to Eq. (39-40). A coefficient \(R_{driver}\) is then defined by Eq. (41), which essentially quantifies whether the spread of jerk values is significant relative to the absolute jerk magnitude. I considered three driver categories: “cautious” for \(R_{driver} R_{agg}\). The thresholds \(R_{norm}=0.3\) and \(R_{agg}=0.8\) were calibrated based on heavy-vehicle driving experience. When I ran this recognition algorithm on the LA92 driving cycle over an interval of 200 s, the indicator classified the style as “cautious”, which is plausible because the speed profile of that particular segment is not severe.
$$SD_J = \sqrt{\frac{1}{T}\sum_{i=1}^{T}(J_i – \bar{J})^2} \tag{39}$$
$$\bar{J} = \frac{1}{T}\sum_{i=1}^{T}|J_i| \tag{40}$$
$$R_{driver} = \frac{SD_J}{\bar{J}} \tag{41}$$
Vehicle Speed Prediction Based on Markov Chain
Vehicle speed prediction is beneficial because it anticipates the future driving condition so that gear decisions can be made proactively rather than reactively. I constructed a four-step Markov chain model. The future vehicle speed is predicted for a horizon of 2 s using the current speed and the acceleration probability matrices. Specifically, I discretized speed into 30 bins and acceleration into 30 bins. The transition probability for each stage was computed from ten standard driving cycles: INDIA_URBAN_SAMPLE, UDDS, WVUSUB, MANHATTAN, NurembergR36, NYCC, WVUCITY, HWFET, NREL2VAIL, and US06_HWY. For the first prediction step, the current speed \(v_t\) is used to identify the most probable acceleration \(a_{t\to t+0.5}\). The estimated speed after 0.5 s is given by Eq. (42). In a recursive fashion, the estimated speed is used to predict the next acceleration, yielding the speed for the following time steps. This is the so-called 4th-order Markov chain, since four sequential stages are used: from \(t\) to \(t+0.5s\), to \(t+1s\), \(t+1.5s\), and finally \(t+2s\). The selection principle is given in Eq. (43) and is based on the maximum probability criterion.
$$v_{t+\Delta t} = v_t + a_{t\to t+\Delta t} \cdot \Delta t \tag{42}$$
$$\hat{x}_t(j) = \max_i \hat{P}_t(i,j) \tag{43}$$
where \(\hat{P}_t\) denotes the Markov transition matrix at time \(t\), and \(\hat{x}_t\) is the most probable index of acceleration. The prediction output was compared with the ten sample cycles used for training. The maximum error remained under 3%, indicating that the Markov model captures the main statistical behavior of the speed profiles. Later, I also tested the model under new cycles that were not part of the training data. For stable vehicle operation, the prediction error was less than 5%, which is acceptable for gear planning. This speed prediction is essential for minimizing unnecessary shifts and for choosing the gear that will be suitable in the immediate future.
Fuzzy Gear Decision and Adaptive Gear Selection
The predicted vehicle speed and the recognized driver style are fed into a fuzzy controller to determine the gear coefficient. The gear coefficient is a value between 1 and 2 that expresses the driver’s demand for the target gear. In the fuzzy inference system, I designed membership functions with the ranges: predicted vehicle speed from 0 to 100 km/h, driver style from 1 to 3, and gear coefficient from 1 to 2. The linguistic variables of driving style are “cautious”, “typical”, and “aggressive”. At the same time, the predicted vehicle speed is described by sets such as “very low”, “low”, “medium”, “high”, “very high”. The central output gear coefficient values may be “low gear”, “tend to low”, “neutral”, “tend to high”, “high gear”. A representative set of rules is described in Table 3.
| Driving Style | Predicted Speed | Gear Coefficient |
| Cautious | Low | 1.0 |
| Cautious | Medium | 1.8 |
| Cautious | High | 2.0 |
| Typical | Low | 1.4 |
| Typical | Medium | 2.0 |
| Typical | High | 2.0 |
| Aggressive | Low | 1.6 |
| Aggressive | Medium | 1.8 |
| Aggressive | High | 2.0 |
To avoid gear hunting, I applied an adaptive gear-selection scheme after the fuzzy inference. The adaptive scheme uses not only the fuzzy gear coefficient but also the time elapsed since the last shift and the motor speed. It computes the motor speed for the currently engaged gear using Eq. (44). The target gear is only changed when one of the following conditions is satisfied:
$$n_{motor} = \frac{v \cdot i_{gear}}{\pi \cdot r / 30} \tag{44}$$
where \(i_{gear}\) is the active gear ratio. The final gear decision logic is as follows:
(a) If the gear coefficient is greater than 1.8, and the motor speed approaches the maximum allowed value, or the elapsed time since the last shift exceeds 60 s, then upshift to the second gear is allowed. (b) If the gear coefficient lies between 1.2 and 1.8, the current gear is held. (c) If the gear coefficient is below 1.2, the elapsed time since the last shift is greater than 60 s, and the motor speed is not high, then downshift to first gear is allowed.
This method, together with the fuzzy inference and the predictive speed signal, effectively suppresses redundant shift actions under highly dynamic cycles. Figure 5 shows the overall architecture of the gear decision layer.
Fuzzy PID Control for the Shift Execution Process
Once the target gear is determined, the synchronizer must be moved precisely so that the engagement is completed quickly yet smoothly. I developed a fuzzy PID elevator control architecture for the shift actuator motor. Classic PID control is used to follow the target shift position, while a fuzzy module varies the speed demand coefficient according to the real-time relative speed between the two sides of the synchronizer and its rate of change. The concept is that a large engaging speed difference means a higher risk of impact; therefore, the system should modulate the speed of the shift motor accordingly. If the difference is small, the shift motor may move fast to reduce the total interruption time. The driving demand from the accelerator pedal is indirectly captured by the change rate of the speed difference. In Eq. (45), I give the general form of the PID controller:
$$u(t) = K_p e(t) + K_i \int_0^t e(\tau) \, d\tau + K_d \frac{de(t)}{dt} \tag{45}$$
where \(e(t)\) is the error between the target and actual shift displacement.
In the fuzzy PID structure, the fuzzy controller takes the speed difference \(\Delta n\) and its derivative \(\dot{\Delta n}\) as inputs and outputs a gain factor \(K_{shift}\) in the range of 0.5 to 1.0. Let me define the speed difference at the synchronizer as \( \Delta n = n_{active} – n_{target} \). If \( \Delta n\) is small and varies slowly, then the gear meshing can proceed quickly, so the fuzzy output \(K_{shift}\) approaches 1.0. In contrast, a high \( \Delta n\) with rapid variation makes the fuzzy module lower the coefficient to achieve a safer mesh. Table 4 lists the second fuzzy rule set with linguistic values for \( \Delta n\) and \( \dot{\Delta n}\).
| \(K_{shift}\) | \(\Delta n\): VS | S | MS | JS | M | JB | MB | B | VB |
| \(\dot{\Delta n}\): NB | VS | S | MS | JS | M | JB | MB | VB | VB |
| NM | VS | S | JS | M | JB | MB | B | VB | VB |
| Z | S | MS | JS | M | JB | MB | VB | VB | VB |
| PM | VS | S | JS | M | JB | MB | B | VB | VB |
| PB | VS | S | MS | JS | M | JB | MB | VB | VB |
The shift motor speed command is obtained by multiplying the base motor speed by \(K_{shift}\). The base motor speed corresponds to a nominal synchronization speed calibrated for a comfortable shift, around 3000 rpm. This modulated speed is then integrated to obtain the angular movement of the shift motor, which is converted into the axial displacement of the shift fork through the gear ratio of the actuator and the geometry of the fork, as described by Eqs. (46)–(48):
$$\theta_D = \int_0^t \omega_D \, dt \tag{46}$$
$$\theta_B = \frac{\theta_D}{n_H} \tag{47}$$
$$x_D = l_B \sin(\theta_B) \tag{48}$$
Here, \(\theta_D\) is the motor angle, \(n_H\) is the actuator gear ratio, \(\theta_B\) is the angular displacement of the fork, and \(x_D\) is the axial displacement of the synchronizer sleeve. In this way, the fuzzy PID strategy of Fig. 6 was built in MATLAB/Simulink, enabling direct integration of the proposed gear-decision logic and the actuator regulation. In practice, the shift displacement for first gear is -12.5 mm, while that for second gear is +12.5 mm. The control system monitors the difference between the target displacement and the actual one to determine when the gearshift is complete.
Simulation Results and Bench Test Verification
In this section, I verify the proposed strategy by comparing its numerical predictions with those of the conventional speed-based shift strategy under several driving cycles, namely LA92, Ftp72, and Japan_urban. First, I verify the vehicle-speed prediction on its own. For the training cycles, the error stays within 3% for both speed and acceleration predictions. For the test cycles not used in the training data, the prediction error is less than 5%, but mainly during very dynamic transitions. This is acceptable for gear planning. Figure 7 shows, for example, the prediction results under the LA92 driving cycle.
Evaluation of Shift Frequency
I next evaluated the impact of the proposed gear-decision scheme on the number of gear shifts. The conventional speed-based model was run as a control group. In the LA92 cycle, the control group performed 42 gearshift operations, while the proposed strategy produced only 18 shifts for a cautious driver, 16 shifts for a typical driver, and 22 shifts for an aggressive driver. These numbers correspond to reductions of 57.14%, 61.90%, and 47.62%, respectively. The large decrease in shift activity confirms that the strategy suppresses unnecessary gear changes and, in so doing, contributes to more stable driving behavior. A similar trend was also observed in the Ftp72 and Japan_urban cycles. In Ftp72, the control group shifted 36 times, while my strategy shifted 23 times, a reduction of 36.11%. In Japan_urban, the control group shifted 36 times, while the proposed strategy shifted 22 times, a reduction of 38.89%. Table 5 summarizes these comparisons.
| Driving Cycle | Control Strategy (# shifts) | Proposed Strategy (# shifts) | Reduction (%) |
| LA92 (cautious) | 42 | 18 | 57.14 |
| LA92 (typical) | 42 | 16 | 61.90 |
| LA92 (aggressive) | 42 | 22 | 47.62 |
| Ftp72 (cautious) | 36 | 23 | 36.11 |
| Japan_urban (cautious) | 36 | 22 | 38.89 |
Evaluation of Dynamic Performance
To assess the dynamic performance, I integrated the product of motor torque and time. Since the proposed strategy tends to keep the vehicle in a lower gear more often during acceleration and predicts impending needs, the powertrain is more willing to deliver high torque under the same vehicle speed. For the LA92 cycle, the integral value of the control group was 14.46 kN·m·h, whereas the proposed strategy achieved 17.55 kN·m·h, indicating an improvement of 21.36%. For Ftp72, the dynamic metric increased by 7.18%, from 20.51 kN·m·h to 21.97 kN·m·h. For Japan_urban, the increase was 2.74% (15.67 kN·m·h to 16.10 kN·m·h). Table 6 provides the details.
| Driving Cycle | Control (\(kN\cdot m\cdot h\)) | Proposed (\(kN\cdot m\cdot h\)) | Improvement (%) |
| LA92 | 14.46 | 17.55 | 21.36 |
| Ftp72 | 20.51 | 21.97 | 7.18 |
| Japan_urban | 15.67 | 16.10 | 2.74 |
These results demonstrate that the gearshift strategy that uses speed prediction can seize opportunities to downshift and upshift at moments that favor the dynamic reserve of electric cars. In practice, heavy-duty electric cars often climb slopes or carry varying loads, so this improvement in dynamic capability is meaningful.
Evaluation of Energy Economy
Energy economy is a major selling point for electric cars. I compared the electrical energy consumption of the traction motor and the final SOC. Under the LA92 cycle, the control strategy consumed 5.97 kW·h of traction motor energy, whereas the proposed strategy consumed 5.73 kW·h. This corresponds to a 4.02% reduction in energy consumption. Under the Ftp72 cycle, the energy demand dropped from 8.94 kW·h to 8.61 kW·h, a reduction of 3.69%. Under the Japan_urban cycle, the energy demand decreased from 7.18 kW·h to 6.97 kW·h, a reduction of 2.92%. In terms of battery SOC, with the initial SOC set at 90%, the conventional strategy finished the LA92 cycle with 89.8756%, whereas my strategy finished with 89.8805%, corresponding to a 3.94% increase in driving range. Ftp72 yielded around 3.7% range improvement, and Japan_urban yielded around 2.94% improvement. I give the main economic comparison in Table 7.
| Driving Cycle | Energy Consumption Reduction (%) | Driving Range Improvement (%) |
| LA92 | 4.02 | 3.94 |
| Ftp72 | 3.69 | 3.7 |
| Japan_urban | 2.92 | 2.94 |
The reason for the improved economy is partly the reduction of gear hunting, which avoids unnecessary interruptions and transient losses. In addition, the low gear in the two-speed AMT expands the high-efficiency region for acceleration, whereas the high gear is used during cruising. The predictive nature of the algorithm prevents too-early or too-late upshifts, thereby keeping the motor operating in an efficient window for longer periods.
Evaluation of Ride Comfort and Shift Shock
Ride comfort is described by several indices, including shift force, shift impulse, and jerk. Here, I mainly discuss shift impulse and the aggregated impulse-time integral. I compare the proposed strategy and the conventional strategy in the three cycles. In LA92, the proposed strategy showed only 18 peaks of shift impulse versus 42 peaks for the conventional one. The cumulative impulse-time value for the proposed strategy was 45,475 N·s² compared with 66,687 N·s² for the conventional strategy, i.e., a 31.81% reduction. In Ftp72, the proposed strategy produced 23 shift-force peaks against 35 for the conventional method, so the shift frequency is lower by 34.29%. The cumulative impulse-time metric remained almost the same, around 0% difference. In Japan_urban, the proposed strategy had 22 peaks versus 36 for the conventional strategy and the cumulative impulse-time value dropped by 4.62%. Table 8 summarizes these results.
| Driving Cycle | Control cumulative impulse (\(N\cdot s^2\)) | Proposed cumulative impulse (\(N\cdot s^2\)) | Impact decrease (%) |
| LA92 | 66687 | 45475 | 31.81 |
| Ftp72 | 57346 | 57499 | -0.00 |
| Japan_urban | 57517 | 54858 | 4.62 |
For LA92, the proposed method dramatically reduces the total power interruption time. The conventional model has an average shift time of about 1.14 s per event; the proposed model gives about 1.18 s per event on average. However, because the shift events are much fewer, the total power interruption duration decreased significantly. In LA92, the conventional strategy accumulated 47.66 s of total interruption, while the proposed strategy accumulated only 21.24 s, which is a reduction of 55.43%. In Ftp72, the total interruption time decreased from 41.02 s to 27.22 s, corresponding to a reduction of 33.64%. In Japan_urban, the figures were 40.98 s for the control and 25.72 s for the proposed, a reduction of 37.24%. Table 9 lists the data.
| Driving Cycle | Control interruption time (s) | Proposed interruption time (s) | Reduction (%) |
| LA92 | 47.66 | 21.24 | 55.43 |
| Ftp72 | 41.02 | 27.22 | 33.64 |
| Japan_urban | 40.98 | 25.72 | 37.24 |
Detailed Shift-Process Behavior
The simulation yields detailed curves of the shift displacement, speed difference, and synchronizer fork angle. In the launch scenario from standstill, the vehicle starts in first gear; the speed difference at the synchronizer is below 1500 rpm, so the gear can mesh directly after about 0.8 s. Later, when an upshift to second gear is initiated, the controller waits for the motor speed to be reduced appropriately. The actual synchronization process lasts about 0.22 s, while the entire shift event lasts about 1.76 s. The fork angle range is between -7° and +7°, which corresponds to the displacement range of -12.5 mm to +12.5 mm. These dynamic responses are consistent with the expected mechanical behavior.
Shift Motor Functional Bench Test
Since bench conditions do not yet allow full powertrain testing, I validated the control command of the shift motor under no-load conditions. The test bench consists of a 200 W/24 V DC permanent-magnet synchronous motor, a matching servo driver, a DC power supply, a CAN communication interface, and a PC-based host controller. I selected the motor to operate in speed control mode, then sent speed commands from the host computer. Two representative commands, +200 rpm and -30 rpm, are shown to assess whether the motor could track the desired speed faithfully. At +200 rpm, the average measured speed was 200.00 rpm with a fluctuation of 0.51 rpm, i.e., the error is below 1%. At -30 rpm, the average speed was -30.00 rpm with a fluctuation of 0.25 rpm, again an error lower than 1%. The results demonstrate that the shift motor can accurately execute discrete speed commands, so it can faithfully execute the fuzzy PID-modulated speed demand. This provides confidence that the proposed control structure can be physically implemented in a real actuator system. Table 10 indicates the bench test data.
| Command speed (rpm) | Average actual speed (rpm) | Fluctuation (rpm) | Relative error (%) |
| 200 | 200.00 | 0.51 | <1 |
| -30 | -30.00 | 0.25 | <1 |
Conclusion and Future Outlook
In this work, I have explored a gearshift control strategy that takes into account driver style and predicted vehicle speed for a two-speed AMT installed in heavy-duty electric cars. The whole framework consists of a gear decision layer and an execution layer.
At the decision layer, I proposed a combined structure of a jerk-based driving-style identification module and a Markov-chain-based future speed prediction module. A fuzzy inference system maps the predicted speed and the driver style to a gear coefficient, after which an adaptive gear-selection logic uses the time since the last shift and the motor speed to make the final gear decision. This effectively suppresses unnecessary gear changes. At the execution layer, a customized fuzzy PID controller modulates the actuator motor speed to improve the engagement process, taking into account the synchronizer speed difference and its rate of change. Therefore, the shifting process is more gentle yet still sufficiently rapid.
From the simulations performed in the LA92, Ftp72, and Japan_urban driving cycles, the main findings are:
(1) Frequent gear changing is substantially decreased. The number of shifts decreases by 47–62% depending on driving style, and by 36–39% depending on the cycle. (2) The proposed prediction-based gear decision strategy improves dynamic performance. Under LA92, the dynamic torque-time integral increases by 21.36%, while the changes under Ftp72 and Japan_urban are +7.18% and +2.74%, respectively. (3) Energy economy is also improved: the motor energy consumption is reduced by 2.92% to 4.02%, and the equivalent driving range improves by roughly 3–4%. (4) In the LA92 cycle, the new strategy cuts the cumulative impulse-time value by 31.81%, demonstrating less shift shock. In Japan_urban the improvement is 4.62%, while in Ftp72 the cumulative impulse is essentially unchanged. (5) The total power interruption time is meaningfully reduced: 55.43% in LA92, 33.64% in Ftp72, and 37.24% in Japan_urban, primarily due to the large reduction in the number of shifts.
The experimental study of the shift motor shows excellent speed tracking errors below 1%. It indicates that the proposed strategy is practically implementable for gearshift control in electric cars.
Despite the promising results, there are limitations. First, the vehicle dynamics model neglects the temperature variation and complex friction phenomena in the synchronizer. Second, the Markov chain prediction uses a limited set of driving cycles, so the robustness under unseen road and traffic conditions may still be insufficient. Third, the test bench only validates the shift motor without load. Therefore, future work should aim at building full powertrain test rigs or conducting vehicle-level experiments. Furthermore, the integration of connected vehicle technologies, such as traffic light information and cloud-based route prediction, may improve the prediction horizon from 2 s to 5 s or even longer. With extended prediction, the gearshift decision could be made even more forward-looking.
Finally, this research underlines the importance of combining human factors with predictive control in electric cars. The connection between driving style, future vehicle speed prediction, and gearshift execution is not only a key to improving energy economy and ride comfort but also a step toward intelligent and personalized electric mobility.