A new control study for a pure electric vehicle equipped with a two-speed automated mechanical transmission has proposed an integrated shift strategy that combines driving-style recognition with real-time vehicle-speed prediction. The research targets three persistent challenges in electric vehicle drivetrains: shift timing that does not match driver demand, shift speed that is poorly coordinated with pedal input, and excessive shift frequency under dynamic operating conditions. The work focuses on a heavy-duty electric vehicle platform and evaluates the strategy across multiple drive cycles, including LA92, Ftp72, and Japan_urban, while also examining a lock-ring synchronizer as the shift actuator and a permanent magnet synchronous motor as the traction source.
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Research Context: Two-Speed AMT as a Key Enabler for the Electric Vehicle
The electric vehicle market has expanded rapidly as governments and manufacturers pursue lower emissions and higher energy efficiency. For heavy-duty electric vehicle applications, a single-speed reduction gear can limit the motor’s efficient operating range and may not provide the best compromise between low-speed torque and high-speed energy consumption. A two-speed automated mechanical transmission allows the electric vehicle to use a larger ratio for low-speed torque and gradeability and a smaller ratio for high-speed cruising and efficiency. This flexibility is particularly relevant for heavy-duty electric vehicle platforms that must handle varied loads, routes, and driver demands.
The research examined a pure electric heavy-duty vehicle with a two-speed AMT, a lock-ring synchronizer, a permanent magnet synchronous motor, and a lithium-ion battery. The electric vehicle powertrain model included the drive motor, battery, transmission system, and longitudinal vehicle dynamics. The control study was built in MATLAB/Simulink and validated under the INRETS cycle before being extended to the LA92, Ftp72, and Japan_urban cycles. The central proposition is that an electric vehicle can achieve better power delivery, energy efficiency, and ride comfort when shift decisions are based not only on current vehicle speed but also on recognized driving style and predicted future speed.
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Powertrain Modeling and Synchronizer Dynamics for the Electric Vehicle
The research selected a lock-ring synchronizer as the shift execution mechanism. The synchronizer is responsible for matching the speed of the driving and driven plates before gear engagement, reducing shock and wear during shifting. The study analyzed the synchronizer’s working process, including pre-synchronization, synchronization, lock release, and engagement. It also established the dynamic relationships for the shift force, shift impulse, jerk, friction work, and power interruption time. These five indicators were used as smoothness evaluation metrics for the electric vehicle shift process.
The electric vehicle model included a permanent magnet synchronous motor model, a lithium-ion battery model, a transmission model, and a vehicle longitudinal dynamics model. The motor model used d-q axis voltage equations, electromagnetic torque equations, and mechanical motion equations. The battery model represented the state of charge and internal resistance behavior. The transmission model defined the relationships among motor speed, synchronizer gear speed, wheel speed, and vehicle speed. The vehicle dynamics model accounted for rolling resistance, aerodynamic drag, acceleration resistance, and grade resistance.
The synchronizer analysis distinguished among the self-locking pre-synchronization stage, the neutral pre-synchronization stage, the synchronization stage, and the engagement stage. Each stage has different force conditions and shift-force requirements. The research calculated the rotational inertia of the input shaft, synchronizer shaft, output shaft, and motor output shaft, and then converted those values to the synchronizer shaft for low-speed and high-speed gear cases. These calculations provided the basis for the later fuzzy PID shift execution model and for the evaluation of shift quality in the electric vehicle.
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Driving-Style Recognition and Markov-Chain Speed Prediction for the Electric Vehicle
The proposed electric vehicle strategy uses driving-style recognition to adapt shift behavior to the driver. The research selected a 200-second recognition period and extracted vehicle speed information to calculate jerk. Because average jerk alone does not fully capture fluctuations, the study introduced a driving-style analysis coefficient based on the standard deviation of jerk and the mean absolute value of jerk. The coefficient was compared with two thresholds: 0.3 and 0.8. A value below 0.3 indicated a mild driving style, a value between 0.3 and 0.8 indicated a standard driving style, and a value above 0.8 indicated an aggressive driving style.
The electric vehicle speed prediction module used a fourth-order Markov chain. Ten representative drive cycles were used as sample data: INDIA_URBAN_SAMPLE, UDDS, WVUSUB, MANHATTAN, NurembergR36, NYCC, WVUCITY, HWFET, NREL2VAIL, and US06_HWY. The speed and acceleration data were discretized into 30 speed intervals and 30 acceleration intervals. Four probability output matrices were built for successive 0.5-second prediction steps, producing a 2-second prediction horizon. The predicted acceleration with the highest probability was used to calculate the next speed point, and the process was repeated to generate future electric vehicle speed.
Prediction Element Reported Configuration Prediction model Fourth-order Markov chain Sample drive cycles INDIA_URBAN_SAMPLE, UDDS, WVUSUB, MANHATTAN, NurembergR36, NYCC, WVUCITY, HWFET, NREL2VAIL, US06_HWY Speed states 30 intervals Acceleration states 30 intervals Prediction step 0.5 seconds Prediction horizon 2 seconds The speed prediction results were checked in two ways. When the ten sample cycles were fed back into the model, the reported error between actual and predicted speed was below 3 percent, and the acceleration prediction error was also below 3 percent. The model was then tested on LA92, Ftp72, and Japan_urban, which were not part of the sample set. During stable electric vehicle operation, the reported prediction error remained below 5 percent. Larger deviations appeared during sharp speed fluctuations, which is consistent with the difficulty of predicting rapid changes in real electric vehicle operation.
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Fuzzy Decision-Making and Adaptive Gear Selection for the Electric Vehicle
The gear decision system used driving style and predicted speed as inputs to a fuzzy controller. The output was a gear coefficient representing the driver’s demand for the target gear. The predicted speed input covered a range from 0 to 100 meters per second. The driving-style input used three values: 1 for mild, 2 for standard, and 3 for aggressive. Because the electric vehicle transmission has two gears, the gear coefficient ranged from 1 to 2. The fuzzy rules were designed so that higher predicted speed and more aggressive driving style would push the coefficient toward the second gear, while lower predicted speed and milder driving style would keep the coefficient closer to the first gear.
To avoid frequent shifting in the electric vehicle, the research added an adaptive adjustment layer after the fuzzy controller. The system recorded the interval between shifts, collected vehicle speed, and calculated motor speed from the current gear ratio. The target gear was then determined by the gear coefficient, motor speed, and shift interval. The reported logic included the following conditions: when the gear coefficient was greater than 1.8 and motor speed approached the maximum speed, the target gear moved to second gear; when the gear coefficient was greater than 1.8 and the shift interval exceeded 60 seconds, the target gear moved to second gear; when the gear coefficient was between 1.2 and 1.8, the target gear remained unchanged; and when the gear coefficient was below 1.2 and the shift interval exceeded 60 seconds, the target gear moved to first gear.
This adaptive layer is important for the electric vehicle because frequent shifting can interrupt torque delivery and reduce comfort even when each individual shift is acceptable. By combining driving style, predicted speed, motor speed, and shift interval, the strategy seeks to preserve responsive power delivery while preventing unnecessary gear hunting. The research reported that this decision structure reduced shift frequency across different driving styles and different drive cycles, which is a direct benefit for electric vehicle drivability and powertrain durability.
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Synchronizer Shift Execution and Fuzzy PID Control for the Electric Vehicle
The shift execution model used a fuzzy PID structure to control the shift motor and synchronizer displacement. The research set the low-speed gear target displacement at -12.5 millimeters and the high-speed gear target displacement at 12.5 millimeters. The PID controller calculated the error between the target displacement and the actual displacement. The shift motor speed was converted into shift displacement through motor angle, transmission ratio, fork arm length, and fork angle relationships. The model also used a speed-torque lookup table and limited the shift motor speed to a maximum of 3000 revolutions per minute.
The fuzzy controller for the shift execution process used the speed difference between the driving and driven plates and the rate of change of that speed difference as inputs. The output was a shift-motor speed demand coefficient ranging from 0.5 to 1. The speed difference range was set from 0 to 10000 revolutions per minute, and the speed-difference rate was based on a 0.002-second interval. The fuzzy rules were designed so that a larger speed difference would encourage more conservative synchronization, while a smaller speed difference would allow smoother engagement. A larger rate of change indicated a more urgent driver demand and could support a higher shift-motor speed to shorten the shift, whereas a smaller rate of change supported a gentler shift for better comfort in the electric vehicle.
The study used Gaussian membership functions for the fuzzy variables. The shift-motor speed demand coefficient was multiplied by the PID-generated speed command to produce the final shift-motor speed demand. This structure allowed the electric vehicle to coordinate shift speed with the synchronizer’s speed state and with the driver’s implied urgency. The research evaluated the resulting shift process through shift displacement, speed difference between the driving and driven plates, and synchronizer fork angle. The reported shift displacement response showed distinct first-gear, second-gear, and downshift phases, with synchronization times depending on the speed difference at the moment of shifting.
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Simulation Validation and Speed Prediction Accuracy for the Electric Vehicle
The electric vehicle shift control model was first validated under the INRETS cycle. The simulated vehicle speed matched the cycle speed, and the gear distribution followed the expected speed thresholds: second gear was engaged above 20 kilometers per hour, and first gear was engaged below 19 kilometers per hour. The motor power output responded to the cycle, and the battery state of charge changed consistently with the power demand and regenerative braking. These checks supported the feasibility of the electric vehicle model before the optimized strategy was applied.
The optimized model then combined the gear decision system and the synchronizer shift system with the drive motor, battery, transmission, and performance analysis modules. The speed prediction module was tested with the ten sample cycles and with LA92, Ftp72, and Japan_urban. The reported prediction error was below 3 percent for the sample data and below 5 percent during stable operation in the non-sample cycles. This level of accuracy is significant for an electric vehicle because a 2-second prediction horizon can provide enough lead time to adjust gear selection before a speed change becomes fully established.
The simulation also examined the shift process in detail. The speed difference between the driving and driven plates, the shift displacement, and the synchronizer fork angle were recorded. In one reported sequence, the first-gear start could synchronize directly because the speed difference was below the 1500 revolutions per minute engagement threshold. The upshift to second gear required waiting for speed synchronization, and the downshift showed a different synchronization duration as vehicle speed fell. These results illustrate how the electric vehicle shift controller responds to the actual synchronizer state rather than applying a fixed shift force or fixed shift time.
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Shift-Frequency Control Across Driving Styles and Drive Cycles
The research compared the optimized electric vehicle strategy with a conventional vehicle-speed-based shift strategy. In LA92, the conventional strategy produced 42 shifts. Under the optimized strategy, the mild driving style produced 18 shifts, the standard driving style produced 16 shifts, and the aggressive driving style produced 22 shifts. Relative to the conventional strategy, the shift-frequency reductions were 57.14 percent for mild, 61.90 percent for standard, and 47.62 percent for aggressive driving styles. These results show that the electric vehicle strategy can reduce shift activity while still adapting to different driver profiles.
Driving Style in LA92 Conventional Shift Count Optimized Shift Count Reported Shift-Frequency Reduction Mild 42 18 57.14 percent Standard 42 16 61.90 percent Aggressive 42 22 47.62 percent The study also varied the drive cycle while keeping a mild driving style. In LA92, the optimized strategy reduced shift frequency by 57.14 percent. In Ftp72, the conventional strategy produced 36 shifts and the optimized strategy produced 23 shifts, a reduction of 36.11 percent. In Japan_urban, the conventional strategy produced 36 shifts and the optimized strategy produced 22 shifts, a reduction of 38.89 percent. These findings indicate that the electric vehicle strategy is not limited to a single cycle and can suppress unnecessary shifting across different speed profiles.
Drive Cycle with Mild Driving Style Conventional Shift Count Optimized Shift Count Reported Shift-Frequency Reduction LA92 42 18 57.14 percent Ftp72 36 23 36.11 percent Japan_urban 36 22 38.89 percent -
Power, Economy, and Comfort Outcomes for the Electric Vehicle
The research evaluated power performance using the integral of motor torque over time. In LA92, the conventional strategy produced 14.46 kilonewton-meter-hours, while the optimized strategy produced 17.55 kilonewton-meter-hours, a reported power-performance improvement of 21.36 percent. In Ftp72, the values were 20.51 and 21.97 kilonewton-meter-hours, an improvement of 7.18 percent. In Japan_urban, the values were 15.67 and 16.10 kilonewton-meter-hours, an improvement of 2.74 percent. These results suggest that the optimized electric vehicle strategy can deliver more torque-time output under the same speed cycle, which can support better gradeability and responsiveness.
For economy, the study compared motor energy consumption and battery state of charge. In LA92, the conventional strategy used 5.97 kilowatt-hours and the optimized strategy used 5.73 kilowatt-hours, a reported motor-power reduction of 4.02 percent. The state-of-charge comparison showed a reported range-equivalent improvement of 3.94 percent. In Ftp72, the conventional strategy used 8.94 kilowatt-hours and the optimized strategy used 8.61 kilowatt-hours, a reduction of 3.69 percent, with a reported range-equivalent improvement of 3.7 percent. In Japan_urban, the conventional strategy used 7.18 kilowatt-hours and the optimized strategy used 6.97 kilowatt-hours, a reduction of 2.92 percent, with a reported range-equivalent improvement of 2.94 percent.
For comfort, the study used shift impulse over time as a proxy for power impact. In LA92, the reported reduction was 31.81 percent. In Ftp72, the reported change was 0.00 percent. In Japan_urban, the reported reduction was 4.62 percent. The LA92 cycle showed the strongest overall optimization effect for the electric vehicle, combining the largest power improvement, the largest economy improvement, the largest power-impact reduction, and the largest reduction in total power-interruption time.
Drive Cycle Reported Power Improvement Reported Motor-Power Reduction Reported Range-Equivalent Improvement Reported Power-Impact Reduction Reported Power-Interruption Reduction LA92 21.36 percent 4.02 percent 3.94 percent 31.81 percent 55.43 percent Ftp72 7.18 percent 3.69 percent 3.7 percent 0.00 percent 33.64 percent Japan_urban 2.74 percent 2.92 percent 2.94 percent 4.62 percent 37.24 percent -
Power-Interruption and Shift-Quality Analysis for the Electric Vehicle
Power interruption is a critical issue for an electric vehicle with an AMT because torque delivery is interrupted during synchronization and engagement. The research compared the total power-interruption time before and after optimization. In LA92, the conventional strategy had a total interruption time of 47.66 seconds, while the optimized strategy had 21.24 seconds, a reduction of 55.43 percent. In Ftp72, the total interruption time fell from 41.02 seconds to 27.22 seconds, a reduction of 33.64 percent. In Japan_urban, the total interruption time fell from 40.98 seconds to 25.72 seconds, a reduction of 37.24 percent.
The study also reported that the average single-shift time of the optimized model was 1.18 seconds, compared with 1.14 seconds for the conventional model. Although the single-shift duration increased slightly, the optimized electric vehicle strategy shifted far less often, so the total interruption time was substantially lower. This is an important trade-off for electric vehicle control: a slightly more controlled single shift can be preferable when it prevents repeated interruptions and reduces driver disturbance over a complete drive cycle.
The LA92 case provided a detailed interruption comparison. The conventional model had repeated shifts with target and actual gear signals separated by response delay and shift execution time. The optimized model also showed response delay and shift execution time, but the number of shift events was much lower. The combined effect was a large reduction in total interruption time. For an electric vehicle, lower total interruption time supports smoother acceleration, less driveline shock, and better driver confidence in the two-speed AMT.
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Shift-Motor Bench Validation for the Electric Vehicle Control Approach
The research included a bench-level functional test of the shift motor. The test setup used a PC-based host, a TODE driver, CAN communication, and a 200-watt, 24-volt direct-current permanent magnet synchronous shift motor with a rated speed of 3000 revolutions per minute. The objective was to verify that the shift motor could follow commanded speed values and that speed control could be used to optimize the shift execution process in the electric vehicle.
With a commanded speed of 200 revolutions per minute, the reported average speed was 200.00 revolutions per minute, the fluctuation amplitude was 0.51 revolutions per minute, and the error was below 1 percent. With a commanded speed of -30 revolutions per minute, the reported speed magnitude was 30.00 revolutions per minute, the fluctuation amplitude was 0.25 revolutions per minute, and the error was below 1 percent. These results indicate that the shift motor responded accurately to the PC command and that the functional behavior was stable under the tested conditions.
Commanded Shift-Motor Speed Reported Mean Speed Reported Fluctuation Reported Error 200 revolutions per minute 200.00 revolutions per minute 0.51 revolutions per minute Below 1 percent -30 revolutions per minute 30.00 revolutions per minute in magnitude 0.25 revolutions per minute Below 1 percent The bench test supports the feasibility of controlling shift-motor speed to optimize the shift execution process in the electric vehicle. The test did not represent a full vehicle validation, but it provided evidence that the actuator layer can track the command with high accuracy. For an electric vehicle two-speed AMT, this actuator accuracy is a foundation for coordinating synchronizer speed, shift force, and shift time.
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Industry Implications for Electric Vehicle Shift Control
The research indicates that an electric vehicle with a two-speed AMT can benefit from a control strategy that looks ahead and adapts to the driver. The combination of driving-style recognition and Markov-chain speed prediction gives the electric vehicle controller a short preview of future speed, while the fuzzy gear decision layer converts that preview into a target gear coefficient. The adaptive anti-hunting layer then prevents unnecessary shifting by considering motor speed and shift interval. The synchronizer fuzzy PID layer coordinates the shift motor with the speed difference and its rate of change, allowing the electric vehicle to balance shift speed and shift smoothness.
The reported simulation results show that the strategy reduced shift frequency, improved power output, lowered motor energy consumption, reduced power impact in the LA92 cycle, and shortened total power-interruption time across LA92, Ftp72, and Japan_urban. The strongest results appeared in LA92, where the electric vehicle strategy improved power performance by 21.36 percent, reduced motor power by 4.02 percent, improved range-equivalent performance by 3.94 percent, reduced power impact by 31.81 percent, and reduced total power-interruption time by 55.43 percent. These findings are relevant to electric vehicle manufacturers seeking to improve drivability and energy efficiency without adding a large number of hardware components.
For the electric vehicle industry, the study also highlights a practical control architecture. The strategy can be implemented through a gear decision module, an adaptive adjustment module, and a synchronizer shift execution module. The gear decision module uses driving style and predicted speed. The adaptive module uses gear coefficient, motor speed, and shift interval. The execution module uses speed difference, speed-difference rate, fuzzy rules, and PID control. This layered structure is suitable for electric vehicle controllers that must manage real-time sensor signals, actuator commands, and safety constraints.
The research further suggests that speed prediction and driving-style recognition can be integrated without abandoning conventional shift logic. The conventional vehicle-speed-based strategy remains a baseline, while the new electric vehicle strategy adds preview and driver adaptation. This approach can help electric vehicle developers reduce calibration effort because the fuzzy rules and adaptive thresholds provide a structured way to tune shift behavior for different drivers and cycles. The reported shift-frequency reductions of 57.14 percent, 61.90 percent, and 47.62 percent across mild, standard, and aggressive styles in LA92 demonstrate that the electric vehicle controller can respond to driver variation while avoiding excessive gear hunting.
In heavy-duty electric vehicle applications, the benefits of reduced power interruption and improved torque delivery can be especially important. Heavy electric vehicle platforms often operate with high loads and frequent speed changes, so a two-speed AMT must deliver torque reliably while protecting the synchronizer and driveline. The research’s focus on shift force, shift impulse, jerk, friction work, and power interruption time provides a balanced evaluation framework. The reported improvements in power, economy, and comfort indicate that the proposed electric vehicle shift strategy can support the broader adoption of two-speed AMTs in electric vehicle platforms that require both gradeability and highway efficiency.
The shift-motor bench validation adds an actuator-level check to the electric vehicle control study. The reported tracking error below 1 percent for both the 200 revolutions per minute and -30 revolutions per minute commands shows that the shift motor can follow demand signals with high accuracy. This result supports the view that the synchronizer fuzzy PID layer can be translated into real actuator commands. The electric vehicle strategy therefore connects high-level driving-style and speed-prediction information with low-level shift-motor control in a coherent control chain.
Overall, the research presents a data-driven and rule-based framework for electric vehicle two-speed AMT control. It does not rely on a single fixed shift map. Instead, it uses driving style, predicted speed, gear coefficient adaptation, and synchronizer speed feedback to decide when and how to shift. The reported results across LA92, Ftp72, and Japan_urban show that the electric vehicle strategy can reduce shift frequency, improve power and economy, and shorten total power-interruption time. These outcomes are directly relevant to electric vehicle powertrain engineers working on multi-speed transmissions, driver-adaptive control, and energy-efficient driveline operation.