Research on Coordinated Control Strategy of DHT Mode Switching Based on Multiple Power Sources

Abstract

To suppress the severe output torque fluctuations caused by clutch engagement when a hybrid electric vehicle equipped with a dedicated hybrid transmission (DHT) switches from pure electric (E) drive mode to hybrid (H) drive mode, a coordinated control method for power source switching is proposed. First, an adaptive fuzzy proportional-integral (PI) controller regulates the engine speed based on the speed difference between the engine and the P2 motor. Second, an active disturbance rejection control (ADRC) controller is employed for trajectory tracking to eliminate the speed difference across the synchronizer’s friction surfaces. This compensates for clutch torque variations during engine startup and ensures rapid synchronizer engagement. Finally, the torque interruption caused by the decoupling of the engine and P2 motor from the driveline is compensated via feedforward control from the P3 motor. The proposed strategy was validated through MATLAB Simulink simulations and CANape calibration tests. The results indicate that applying the proposed method to E-H mode switching slightly extended the total duration by 0.02 s. However, compared with uncoordinated control, the maximum longitudinal jerk was reduced by 73.8%, and the clutch sliding work decreased by 38.6%. This significantly enhances switching smoothness and prolongs the clutch’s service life.

1. Introduction

As the automobile industry advances rapidly, increasingly stringent environmental protection policies are being enforced [1,2,3]. With the ongoing implementation of vehicle fuel consumption restrictions in various countries, traditional energy-saving methods are becoming less viable, making it essential to fully explore new energy alternatives [4,5,6]. The dedicated hybrid transmission (DHT) that deeply couples the power of the engine and motor has received much attention because it saves some mechanical parts, making the overall transmission lighter in weight and smaller in overall size [7,8,9]. At the moment, most related research focuses on add-on hybrid transmissions, with only a few studies on special hybrid transmissions integrated with motors and motor controllers [10,11].

Different configuration schemes have great differences in the direction of energy flow, the coordination strategy that can be realized, and the applicability of working conditions. In recent years, hybrid power system configurations have often been related to the location of the electric machine in the driveline. As shown in Figure 1, hybrid power system configurations are widely classified based on the electric machine’s location within the driveline, commonly known as P0–P4 architectures. Building upon these standard topologies, this study focuses on a highly integrated P2 + P3 DHT system.

Because there is no traditional starter in the P2 configuration, the DHT can only be started through the clutch slip, and if the starting process is not coordinated, then it will not only affect the clutch life but also cause an impact on the vehicle [12,13]. Therefore, the ride comfort and driving comfort of a P2 configuration during mode switching have become important research focuses.

Moreover, to improve the comfort of the hybrid electric vehicle, it is necessary to coordinate the control design by matching the dynamic coupling configuration. Lin [14] proposed a fuzzy control strategy and coordinated torque control strategy based on the P2 configuration to reduce torque fluctuation and vehicle impact. However, it only considered the control clutch and did not coordinate the control of other key components. Wang [15] proposed a new mode switching control method based on a model predictive control (MPC) algorithm to adjust the speed or torque of the engine, motor, or clutch, but the MPC algorithm is still difficult to apply to real-time control. Xu [16] further reduced the impact vibration during mode switching by disconnecting the clutch at the moment of engine ignition, but the control strategy they proposed only considered the engine start time under different engine start conditions without considering the impact on the vehicle. Zhao [17] and Dong [18] proposed a similar multi-phase engine start control strategy to make the engine start smoothly by using the slipping status of the separating clutch and shifting clutch, respectively, but this was also only for the process of starting the engine. Li [19] proposed a control strategy that combines shift control and energy management, which can smooth engine torque through motor torque compensation and effectively reduce shifting frequency, thus improving driving comfort. Some scholars [20,21,22] proposed the control method of collaborative control mode switching and shifting, and they simulated the three modes of mode switching and shifting, which greatly shortened the duration of mode switching and shifting, lowered the number of mode switches, and improved the smoothness of mode switching to some extent. The control strategy proposed by some scholars [23,24,25] can reduce the torque ripple and swing of the vehicle and fully meet the domestic requirements. However, it only considers the coordinated control of the clutch and fails to coordinate the power source. Li C. et al. [26]. investigated an engine startup torque coordinated control strategy for multimode hybrid electric vehicles equipped with a two-speed dedicated hybrid transmission. Furthermore, Huang C. et al. [27] proposed a multiple model predictive control (mMPC) approach to suppress torsional vibrations and vehicle jerk during the mode transition process in parallel hybrid electric vehicles. However, these advanced model-based methods heavily rely on highly accurate mathematical models of the powertrain and demand substantial computational resources, making their real-time implementation in actual vehicle controllers challenging.

Because the mode switching process of the hybrid electric vehicle involves the working characteristics of different power sources and the power transmission of nonlinear components, if the characteristics are not controlled separately, then smooth mode switching cannot be achieved. Based on the above problems, and in accordance with the configuration of the P2 + P3 DHT, a multi-power source coordinated control strategy is proposed in this paper. The specific technical innovations of this strategy are threefold. Firstly, to overcome the nonlinearities during engine startup, an adaptive fuzzy PI controller is designed for independent engine speed regulation by taking the speed difference between the engine and the P2 motor as input. Secondly, to proactively handle the unmodeled dynamics and sudden load changes during clutch engagement, an active disturbance rejection control (ADRC) is innovatively applied to the ISG motor. It takes the elimination of the speed difference across the synchronizer’s friction surfaces as the tracking target, treating the clutch torque variations as a total disturbance for real-time compensation, thereby accelerating synchronizer engagement. Finally, to prevent vehicle longitudinal jerk, a feedforward control is implemented, using the P3 motor to seamlessly compensate for the torque interruption caused by the decoupling of the engine and the ISG motor from the driveline.

The remainder of this paper is organized as follows. Section 2 introduces the model of the DHT system. Section 3 provides a DHT mode switching coordination control policy, and analyzes the simulation and test results. Finally, Section 4 provides the conclusions.

2. DHT Transmission System Structure

In this article, a dual-motor, two-speed DHT system from an automobile company is taken as the research object. The rear transmission system on the vehicle is composed of the engine, the dual motor at P2 + P3, the two-speed automatic mechanical transmission (AMT), and the differential, as shown in Figure 2. The engine is connected to the input shaft of the AMT by a clutch, the ISG motor is connected to the input shaft of the AMT by a reduction gear, the traction motor (TM) is connected to the output shaft of the AMT by a reduction gear, and finally, the wheels are driven by the differential. At low speeds, the TM motor drives the vehicle alone or in conjunction with the ISG motor, with the engine turned off to reduce fuel consumption and emissions [28,29,30]. In order to avoid the effects of engine drag torque, the clutch is separated. When the speed exceeds a certain value, the mode is switched to hybrid drive mode through clutch engagement. Since the TM motor has the shortest power transmission chain from the wheel, it can recover energy during braking to ensure high efficiency of energy recovery [31,32,33]. The parameters for each component are shown in

Table 1. Parameters of each component.

Item
ENG	Max. torque ($T_{emax}$)	210 N·m
ISG	Max. torque ($T_{m1max}$)	150 N·m
	Rated speed (${\omega }_{m1max}$)	12,000 r/min
	Gear ratio ($I_{m1}$)	1.644
TM	Max. torque ($T_{m2max}$)	225 N·m
	Rated speed (${\omega }_{m2max}$)	12,000 r/min
	Gear ratio ($I_{m2}$)	2.024
AMT	Gear ratios ($I_{amt}$)	1.553/0.873

.

The dynamic system model is shown in Figure 3. Based on the dynamic model of a hybrid power system, Newton’s second law is adopted to analyze the dynamics of each component of the power system. The damping properties between components were not considered, except for the right and left half shafts, and the components were considered to be rigid bodies.

In Figure 3, $J_e$ is the combined inertia of the accessory and the engine; $J_{m1}$ is the combined inertia of the ISG motor and its input end gear; and $J_{cl}$ is the moment of inertia of the clutch driving disc.

Meanwhile, $J_{cr}$ is the moment of inertia of the clutch driven disk; $J_{si}$ is the moment of inertia of the input shaft, including the moment of inertia of the gear at the output end of the ISG motor; $J_{ti}$ is the moment of inertia at the transmission input; $J_{to}$ is the moment of inertia at the output end of the transmission; $J_{so}$ is the moment of inertia of the output shaft, including the input gear of the main reducer and the output gear of the TM motor; $J_{m2}$ is the combined inertia of the TM motor and its input gear; $J_{ra}$ is the moment of inertia of the rear axle; and $J_w$ is the inertia of the wheel assembly. In addition, $T_e$ is the output torque of the engine; $T_c$ is the clutch torque when the clutch is engaged; $T_{ml}$ is the output torque of the ISG motor; $T_s$ is the transmission torque; $T_{m2}$ is the output torque of the TM motor; $T_L$ is the equivalent resistance moment of the wheel side; ${\omega }_e$ is the speed of the engine; ${\omega }_{m1}$ is the speed of the ISG motor; ${\omega }_{m2}$ is the speed of the TM motor; ${\omega }_w$ is the speed of the wheel side; $k_0$ and $c_0$ are the equivalent stiffness and equivalent damping of the wheel side, respectively; ${\mu }_s$ is the dynamic friction factor of the clutch friction plate; $F_c\left(t\right)$ is the normal pressure of the contact area of the friction disk; $R_c$ is the equivalent friction radius of the clutch friction plate; N is the number of clutch friction pairs; A is the piston pressure area; and $\Delta \omega$ is the angular velocity difference between the driving disc and the driven disc of the clutch.

By summing the moments of inertia of the parts with the same speed all the time, the whole vehicle drivetrain is divided into six segments, and their moments of inertia are calculated by the following formulae:

$$I_1=J_e+J_{cl}$$

(1)

$$I_2=J_{cr}+J_{m1}·i_1+J_{si}+J_{ti}$$

(2)

$$I_3=J_{to}+J_{so}+J_{m2}·i_2$$

(3)

$$I_4=J_{ra}+J_w$$

(4)

Here, $i_1$ and $i_2$ represent the transmission ratios of the ISG and TM motor reduction, respectively. The equivalent moments of inertia of $I_1$, $I_2$, $I_3$, and $I_4$ to the rear axle are $I_1{i}_g{i}_0$, $I_2{i}_g{i}_0$, $I_3{i}_0$, and $I_4$, respectively. Thus, the dynamic equations of the mode switching process of the hybrid power skid starting can be obtained:

$$I_1·{\dot{\omega }}_e=T_e+T_c$$

(5)

$$I_2·{\dot{\omega }}_{m1}=T_{m1}·i_1-T_c-T_s$$

(6)

$$I_3·{\dot{\omega }}_{m2}=T_{m2}·i_2+T_s·i_g-{\displaystyle \frac{1}{i_0}}\left[k_0{\theta }_0+c_0({\displaystyle \frac{{\omega }_{m2}}{i_0{i}_2}}-{\omega }_w)\right]$$

(7)

$$I_4·{\dot{\omega }}_w=k_0{\theta }_0+c_0({\displaystyle \frac{{\omega }_{m2}}{i_0{i}_2}}-{\omega }_w)-T_L$$

(8)

$$T_c\left(t\right)={\mu }_s·F_c\left(t\right)·R_c·N·A·sign\left(\Delta \omega \right)$$

(9)

3. DHT Mode Switching Coordination Control Policy

3.1. Engine Automatic Speed Control

In the engine speed regulation stage of the process of switching from pure electric drive mode to hybrid drive mode, although the engine has reached its idle speed and has been ignited and started to work, the engine speed has not reached the ISG motor speed, so there is still a speed difference between the two sides of the clutch [34]. After the engine starts, the engine must be speed-controlled to avoid the clutch producing large sliding forces and thus reducing the service life of the clutch [35]. And the speed regulation process should be completed as soon as possible; otherwise, it will increase the time of mode switching, affecting the power [36].

The speed control of the engine is realized by controlling the throttle opening. When the speed difference between the engine and the ISG motor is reduced to 20 r/min, the clutch can be engaged quickly. The engine starting and synchronizing process involves strong nonlinearities, combustion instability, and time-varying frictional resistance. A conventional PI controller with fixed parameters struggles to balance rapid dynamic response with stability (such as avoiding overshoot) under these highly fluctuating conditions. Therefore, to ensure robust and fast speed synchronization, an adaptive fuzzy PI controller is adopted to dynamically tune the control parameters in real time. Fuzzy logic models and expert systems are extensively utilized to manage highly nonlinear and uncertain dynamic systems robustly, making them highly suitable for coordinating engine speed tracking during mode switching [37]. The method of adaptive fuzzy PI control is used to carry out the automatic speed regulation of the engine, and the principle is shown in Figure 4. The speed error $\Delta {\omega }_1$ and the difference d$\Delta {\omega }_1$/dt of the speed error were taken as inputs, and the scale variation was processed by quantization factors. The adjustment of the two scale coefficients of the PI controller was taken as the output control variable, and the unified theory domain was set as [−6, 6]. Figure 5 is the logical block diagram of the automatic speed control of the engine. The membership function and fuzzy control rules are shown in Figure 6. Here, the fuzzy language set is NB, NM, NS, Z, PS, PM, PB. The input is the speed difference between the wheel speed converted to the input shaft speed and the engine speed, the controller output is the engine target torque with the engine speed as the target, the control object is the engine, and the output is the engine speed.

Considering the shape of the fuzzy membership function comprehensively, the centroid method can obtain smoother outputs, and thus the centroid calculation method was used to defuzzize the output control quantity of fuzzy rules:

$$d_0={\displaystyle \frac{{\sum }_{k=1}^m{d}_k{\mu }_d\left(d_k\right)}{{\sum }_{k=1}^m{\mu }_d\left(d_k\right)}},d_k\in D$$

(10)

The final control parameters of the fuzzy PI speed controller are

$$k_p=k_p^{\prime }+{\beta }_p\Delta k_p$$

(11)

$$k_i=k_i^{\prime }+{\beta }_i\Delta k_i$$

(12)

where $k_p^{\prime }$ and $k_i^{\prime }$ are the initial control parameters of the PI controller and ${\beta }_p$ and ${\beta }_i$ are the proportional factors of the parameter adjustment value.

3.2. ISG Motor Assisted Speed Control

During the transition from pure electric drive mode to hybrid drive mode, the friction surfaces of the synchronizer rotate at the speeds of the ISG and TM motors, respectively, due to disengagement of the synchronizer gear.

When the TM motor needs to complete mode switching on one side of the synchronizer, the output torque of the ISG motor will drive the speed on the other side of the synchronizer to increase rapidly and narrow the speed difference between the two friction surfaces of the synchronizer. When the speed difference is reduced to 20 r/min, the synchronizer will engage quickly by controlling the fork. During the instantaneous engagement of the clutch, the system experiences severe inertia mutations and sudden frictional torque spikes, which act as strong external disturbances. Conventional controllers purely relying on error feedback generally exhibit phase lag and poor disturbance rejection capabilities. To address this, active disturbance rejection control (ADRC) is employed. Its core motivation lies in utilizing an extended state observer (ESO) to actively estimate and immediately compensate for these unmodeled total disturbances in real time, effectively suppressing secondary speed drops.

The motor ISG speed regulation process is controlled by ADRC. By taking ${\omega }_0$ = 0 as the control goal, and with the speed difference $\Delta$${\omega }_2$ between the wheel and the motor converted to the same shaft as the controller input state variable, the ISG motor speed regulating controller based on ADRC is designed, and the ADRC controller compensates the torque according to the change in the clutch’s transmission torque. Then, we make the $\Delta$${\omega }_2$ track a given control target. Figure 7 is an active control block diagram based on the following ADRC speed, where $\Delta$${\omega }_0$ is the control target of ADRC, $\Delta$${\omega }_2$ is the speed difference between the wheel and motor converted to the same shaft, and $T_{m1}$ is the output control quantity of the ADRC controller.

According to the torque and motion equation of the ISG motor, the differential equation of the input and output speed of ADRC is of the first order. However, in first-order active disturbance rejection control, only the error effect of the tracking quantity and observed quantity is considered, and the error effect of the tracking quantity and observed quantity differential is not considered. In order to fully consider various influencing factors and improve the control effect, the classical second-order active disturbance rejection controller is used to deal with the first-order controlled object. Figure 8 shows a structure diagram of the ISG motor speed-regulating ADRC controller.

The working principle of the ISG motor speed self-disturbance rejection controller is as follows. Firstly, through the tracker differential (TD), the system tracks and filters signals to obtain the state variables and their differential signals. Subsequently, an extended state observer (ESO) is employed to observe disturbances in real time, treating the total disturbance as an additional state variable to cancel out interference. Based on the system’s input and output, the ESO estimates the original state of the system, thereby optimizing the dynamic response speed of the control system. Finally, the error between the outputs of the TD and the ESO is processed using nonlinear state error feedback (NLSEF) to derive the error feedback control quantity. This process calculates the initial compensation torque $T_0$, which after feedforward compensation generates the final torque $T_m$. Specifically, the total disturbances affecting the ISG motor in this system primarily include internal unmodeled dynamics (such as mechanical backlash and inertia parameter variations) and strong external physical interferences (such as the highly nonlinear friction torque fluctuations during clutch engagement and the torque ripples from the engine ignition process). The main contribution of employing the ADRC method here is its ability to actively estimate these complex, hard-to-model physical disturbances via the ESO and compensate for them in real time, thereby decoupling the ISG motor control from the complex clutch–engine dynamics and ensuring robust, fast speed synchronization without relying on an exact mathematical model.

The nonlinear function serves as a core component of active disturbance rejection control (ADRC). The quality of its design significantly impacts the control performance. When designing the nonlinear function, it is essential to ensure that the function is continuous and convergent at the origin, with a value of zero at this point. The traditional nonlinear function, denoted as $fal(\cdot )$, is expressed as follows:

$$fal\left(e,{\alpha }_i,\delta \right)=\left\{\begin{array}{cc}e{\delta }^{{\alpha }_i-1}\hfill & \mathrm{if}\left|e\right|\le \delta \hfill \\ \left|e\right|sgn\left(e\right)\hfill & \mathrm{if}\left|e\right|\ge \delta \hfill \end{array}\right.$$

(13)

where $\alpha$ is the parameter of the $fal(\cdot )$ function and e is the variable of the $fal(\cdot )$ function.

The observation equation of the ESO is established as follows:

$$\left\{\begin{array}{c}e\left(k\right)=z_1\left(k\right)-\Delta {\omega }_2\hfill \\ z_1(k+1)=z_1\left(k\right)+h\left[z_2\left(k\right)-{\beta }_1\mathrm{fal}(e\left(k\right),a_1,\delta )\right]\hfill \\ z_2(k+1)=z_2\left(k\right)+h\left[z_3\left(k\right)-{\beta }_2\mathrm{fal}(e\left(k\right),a_2,\delta )+b_0{T}_0\left(k\right)\right]\hfill \\ z_3(k+1)=z_3\left(k\right)-h{\beta }_3\mathrm{fal}(e\left(k\right),a_3,\delta )\hfill \end{array}\right.$$

(14)

where h is the sampling step; $\delta$ is the length of the linear segment; $e\left(k\right)$ is the observation error; $a_1,a_2,a_3$ are the nonlinear factors; and $b_1,b_2,b_3$ are the observer gains.

The mathematical model of the TD is

$$\left\{\begin{array}{c}{\omega }_1(k+1)={\omega }_1\left(k\right)+h{\omega }_2\left(k\right)\hfill \\ {\omega }_2(k+1)={\omega }_2\left(k\right)+hfhan\left({\omega }_1\left(k\right)-\Delta {\omega }_2,{\omega }_2\left(k\right),r,h_0\right)\hfill \end{array}\right.$$

(15)

where $\Delta {\omega }_2$ is the controller reference signal; ${\omega }_1$ is the tracking signal of the TD to the reference signal; ${\omega }_2$ is the differential signal of the TD with respect to ${\omega }_1$; h is the controller step size; and r is the parameter used to adjust the TD tracking speed, while $fhan(\cdot )$ is the piecewise nonlinear function selected by the TD, and its expression is as follows:

$$fhan({\omega }_1,{\omega }_2,r,h_0)=\left\{\begin{array}{cc}-r{\displaystyle \frac{a}{d}}\hfill & \mathrm{if}\left|a\right|\le d\hfill \\ -rsgn\left(a\right)\hfill & \mathrm{if}\left|a\right|\ge d\hfill \end{array}\right.$$

(16)

Compared with the linear models, the nonlinear state estimation feedback (NLSEF) exhibits superior control performance. To achieve more precise regulation of the motor torque, the specific formulation is as follows:

$$\left\{\begin{array}{c}{e}_1\left(k\right)={\omega }_1\left(k\right)-z_1\left(k\right)\hfill \\ e_2\left(k\right)={\omega }_2\left(k\right)-z_2\left(k\right)\hfill \\ T_0={\beta }_4\mathrm{fal}(e_1\left(t\right),a_4,\delta )+{\beta }_5\mathrm{fal}(e_2\left(t\right),a_5,\delta )\hfill \\ T_m=T_0-{\displaystyle \frac{1}{b_0}}{z}_3\hfill \end{array}\right.$$

(17)

where $e_{1}k$ is the error between the output value of the tracking differentiator and the estimated value of the improved state observer, $e_{2}k$ is the error between the integral of the output value of the tracking differentiator and the estimated value of the improved state observer, ${\beta }_4$ and ${\beta }_5$ are the gain coefficients of the observer, ${\alpha }_4$ and ${\alpha }_5$ are the nonlinear factors, and $T_m$ is the nonlinear control output.

Since there are many parameters in the ADRC controller, T, $h_0$, ${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$, ${\alpha }_4$, ${\alpha }_5$, $\delta$, and other parameters can be determined first when the parameters are set. Therefore, T and $\delta$ were determined according to the requirements of data acquisition accuracy and control accuracy, respectively. The filtering factor $h_0$ was set at about six times the sampling interval length, and the exponential power parameter ${\alpha }_i$ (i = 1, 2, 3, 4, 5) was usually set as a fixed value. The parameters ${\beta }_1$, ${\beta }_2$, and ${\beta }_3$ of the ESO and ${\beta }_4$, ${\beta }_5$ of the NLSEF in the transmission system dynamic load ADRC controller were optimized step by step, using the adaptive genetic algorithm to determine the parameters ${\beta }_1$, ${\beta }_2$, ${\beta }_3$, ${\beta }_4$, and ${\beta }_5$. Advanced meta-heuristic optimization algorithms have been widely proven to effectively solve complex multi-parameter tuning problems and enhance control accuracy across various industrial applications [38].

3.3. TM Motor Direct Torque Control and Clutch Engagement Oil Pressure Control

The frame diagram of the TM motor direct torque control and clutch engagement oil pressure control are shown in Figure 9. During the mode switching process, the mechanical decoupling and engine torque response lag inevitably cause a temporary torque interruption in the driveline. Because the TM motor is directly coupled to the wheels, it possesses the fastest dynamic response capability. Therefore, a direct torque feedforward control strategy was adopted for the TM motor to immediately fill this torque hole, maintaining a smooth output torque profile and minimizing longitudinal vehicle jerk. Due to the hard connection between the TM motor and wheel, its speed cannot be controlled. The hybrid power control unit (HCU) directly sends torque instructions to the motor control unit (MCU), which are converted by the MCU into a current or voltage signal to control the motor after analysis, thus controlling the motor torque.

The clutch engagement oil pressure is dynamically regulated based on the engine’s starting state. During the initial engine startup phase, a lower engagement oil pressure is applied. This limits the rate of frictional torque transfer, thereby effectively mitigating sudden driveline shocks and minimizing longitudinal vehicle jerk. Once the engine is dragged to its target ignition speed (${\omega }_s$ is 751 rpm), the coordinated speed regulation takes over. Finally, the overall hierarchical control structure for mode switching is illustrated in Figure 10. In this architecture, the management layer outputs the power demand, the coordination layer executes the mode-switching logic, and the execution layer at the bottom provides feedback signals to form a comprehensive closed-loop system.

3.4. Simulation Verification

With Stateflow in MATLAB and Simulink (version R2010b), the DHT hybrid power system simulation model was set up as shown in Figure 11 and contained the driver model, engine, transmission, drive motor, power battery module, etc. Recently, simulated environments have been increasingly recognized as essential tools for optimizing validation protocols and improving testing efficiency in the automotive industry [39].

Table 2. Vehicle parameters.

Item	Parameter
Total mass (m)	1889 kg
Wheel rolling radius (r)	371 mm
Coefficient of air resistance ($C_D$)	0.395
Windward area (A)	2.705 m2
Coefficient of rolling resistance (f)	0.014
Main reducer transmission ratio ($i_0$)	3.941

shows the main set parameters for simulation.

The World Light Vehicle Test Cycle (WLTC) was selected as the driving cycle condition to verify the effectiveness of the model, and the simulation interval size was 0.01 s. To ensure reproducibility of the numerical simulations, the detailed configuration was specified as follows. The 19 dynamic and control equations presented in Section 2 and Section 3 were modeled utilizing MATLAB and Simulink foundational blocks and S-functions. The numerical integration was executed using a fixed-step solver (ode4 Runge–Kutta) with a fundamental sample time of 0.01 s, which strictly matched the signal transmission frequency of the actual vehicle’s CAN bus. The initial states of the numerical model were initialized to the steady-state conditions of the pure electric drive mode. The simulated speed can be observed in Figure 12. Throughout the entire cycle, the simulation speed closely followed the target speed, with the maximum error remaining below 5%. The model met the requirements of WLTC dynamic performance, and it can be used to verify the mode switching coordination control method of hybrid electric vehicles.

At present, the impact degree of drive mode switching on vehicle driving performance is still mainly evaluated by the rate of change in acceleration. The jerk (J) and grinding work (W) in particular can be used to quantitatively analyze and evaluate the quality of the mode switching process. These indexes are expressed as shown in Equations (18) and (19):

$$J={\displaystyle \frac{da}{dt}}={\displaystyle \frac{d^{2}v}{d{t}^2}}$$

(18)

$$W_f={\int }_{t_1}^{t_2}{T}_c({\omega }_2-{\omega }_1)dt$$

(19)

where $t_2$ and $t_1$ are the duration of clutch slippage; v is vehicle speed; and a is the vehicle acceleration.

The simulation process of switching from pure electric mode to hybrid drive mode was carried out. The traditional control method and the proposed control method in this paper were used, and their performances were compared. Here, the “traditional control method” refers to an uncoordinated baseline strategy that relies solely on a conventional fixed-parameter PI controller for engine speed regulation without incorporating active disturbance rejection control (ADRC) for the ISG motor or direct torque feedforward compensation for the TM motor. Figure 13 shows the simulation results of switching from pure electric drive mode to hybrid drive mode under the traditional control method. The switchover lasted about 1.14 s. The vehicle ran in pure electric mode until 606.84 s, and the mode switching began at 606.84 s, after which the clutch alone slid the engine from stationary to synchronous with the drive shaft speed, and then the clutch locked at 607.26 s. After 607.68 s, the power source output torque gradually converged to the target torque, signifying the completion of engine intervention and the transition to hybrid drive mode. During this mode-switching process, the substantial speed difference across the clutch resulted in a significant frictional torque transfer from the engine, leading to a sudden reduction in speed and causing a notable reverse impact on the vehicle. As shown in Figure 13, the maximum reverse impact was about 20.61 m/s³, and the clutch slip produced a slip work of 2185.2 J.

Figure 14 shows the simulation results of the coordinated control method designed in this paper. It can be concluded from Figure 14 that the whole switching process lasted about 1.16 s, which was 0.02 s longer than the traditional control method. The vehicle was running in pure electric mode until 606.85 s. The vehicle triggered the threshold condition of drive mode switching at 606.85 s, when the synchronizer was in neutral and the ISG motor speed dropped rapidly. Before 607.16 s, the clutch was controlled to apply 10% of the maximum engagement oil pressure to the skid engine, causing it to transition from static to an ignition speed of 751 r/min and completing the first stage of the engine starting process. Between 607.16 s and 607.23 s, the engine speed was adjusted to 1034 r/min, and at 607.26 s, the clutch fully engaged, and the second stage of the engine speed regulation process was over. After 608.01 s, the power source output torque gradually followed the target torque to complete the engine power intervention stage. This completed the whole mode-switching process. When the engine was not cut into the transmission system, the ISG motor compensated for the dragging torque disturbance generated by the engine and carried out auxiliary speed regulation. After the motor started, it carried out automatic speed regulation control so as to promote fast synchronization of the clutch’s follower plate. As shown in Figure 14, this strategy can suppress the impact during the mode switching process, and its variation range was controlled between −2.65 and 5.39 m/s³, with the clutch sliding process generating 1340.7 J of grinding work.

Compared with the traditional control method, although the proposed control algorithm slightly extended the duration of mode switching, the maximum impact on the vehicle was reduced by 73.8%, and the grinding work in the clutch engagement process was reduced by 38.6%, which improves the smoothness of mode switching and greatly prolonging the service life of the clutch.

The effectiveness of this proposed strategy will be further verified by the experimental test results shown later in Figure 15. Figure 16 shows the status of each component in the mode switching coordination control process:

• In phase 1, the hybrid electric vehicle was in pure electric drive mode. At this time, the clutch $C_0$ was separated, the synchronizer $S_0$ was in gear, and the ISG motor and TM motor drove the wheel together.
• When the speed reached about 20 km/h, the mode switched into the second stage. At this time, the synchronizer $S_0$ was placed in neutral, the clutch $C_0$ entered the slippery state, and the torque distributed by the engine and ISG motor was gradually replaced by the TM motor.
• In phase 3, when the engine speed reached 750 r/min through the sliding of the clutch $C_0$, the engine started its ignition and carried out automatic speed regulation, assisted by the ISG motor. Other components were in the same state as in phase 2.
• At the fourth stage, when the speed difference between the two sides of the clutch $C_0$ was less than 20 r/min, the clutch $C_0$ would be locked, the ISG motor would speed up, and the synchronizer $S_0$ would start to enter a gear.
• When the synchronizer was placed in gear, the speed of each power source was synchronized, but the output torque was still in a state of delayed response.
• When each power source increased gradually to meet the demand torque, torque redistribution was complete, and the hybrid electric vehicle entered hybrid drive mode. Here, stage 6 ends.

3.5. Experimental Verification

In order to verify the effectiveness and feasibility of the proposed mode switching coordinated control strategy in this paper, a hybrid electric vehicle produced by an automobile company was taken as a sample vehicle, and a P2 + P3 dual-motor DHT was installed to carry out the whole vehicle test. Figure 17 shows the control system architecture, including the experimental vehicle, experimental runway, DHT, and HCU placement. The control strategy developed in MATLAB and Simulink was converted into a C language program using the Real-Time Workshop (RTW) toolbox under the XPC Target operating environment to generate executable binary files and download them to the HCU. The torque request generated by processing each boundary condition through the HCU was sent to the engine control unit (ECU), transmission control unit (TCU), and MCU through the CAN network. The angular speed of the wheel rotation could be obtained by detecting the pulse frequency with the speed sensor installed at the half shaft, and the speed could be obtained by combining the wheel radii. Through the CANape monitoring and calibration system, the HCU uploaded the obtained original acceleration signal, which was saved by the upper computer. The sampling interval of the signal was 0.01 s.

Moreover, to avoid the step change caused by the step point, which in turn leads to the maximum value of the signal after the quadratic difference, this paper used MATLAB and Simulink to design a low-pass filter with a cutoff frequency of 10 Hz for the collected speed signals. The impact value of a certain test was obtained by the quadratic difference of the filtered velocity signal. After multiple vehicle calibration tests, the test results in Figure 15 were obtained. The coordinated control time of the mode switching was 1.26 s (from 48.32 to 49.58 s), which was different by 0.14 s compared with the simulation switching result. According to Figure 15, when the speed of the input shaft reached 2600 r/min—that is, when the speed reached 24.2 km/h—mode switching occurred.

The engine was first accelerated to the starting state by the clutch slip, and the torque output was unstable during engine ignition. In the first stage, the torque increased sharply. In order to prevent racing, the ISG motor adjusted the torque stability of the engine. In the second stage, the torque surge of the engine decreased with the regulation of the motor. Due to the existence of automatic speed regulation control, the speed of the three-stage engine was accelerated, and the speeds of the clutch and synchronizer at both sides of the last four stages were almost synchronized. Then, the control system sent the engagement command. Given that the strategy was out of gear, and the dynamic response of the engine torque lagged, the TM drive motor compensated for the disturbance of the system via feedforward compensation to ensure smooth power output and meet the driver’s torque requirements. In the whole mode switching process, the speed changed gently and did not appear to drop suddenly, and the maximum impact of the vehicle did not exceed 7.54 m/s³. The specific indicators of mode switching are listed in

Table 3. Specific indicators of pattern transformation.

Item	Result
Switching coordination time	1.26 s
Slipping friction work of clutch	1.54 kJ
Maximum acceleration of vehicle	2.59 m/s2
Maximum jerk of vehicle	7.54 m/s3

. To explicitly validate the numerical model, a quantitative comparison between the simulation predictions (Figure 14) and experimental measurements (Figure 15) was conducted. As noted, the experimental switching time was 1.26 s, which was merely 0.10 s longer than the simulation prediction of 1.16 s. Furthermore, the maximum longitudinal jerk observed in the experiment was 7.54 m/s³, compared with 5.39 m/s³ in the simulation. These minor numerical deviations were practically acceptable and primarily attributed to unmodeled real-world dynamics, such as hydraulic valve response delays and sensor measurement noise. Nevertheless, the experimental curves and overall trends were highly consistent with the model predictions, which robustly validates both the accuracy of the established numerical model and the practical effectiveness of the proposed methodology. The experimental findings align closely with the simulation outcomes, further validating the effectiveness of the proposed coordinated control strategy. This strategy successfully mitigated the fluctuations in the coupling torque on the drive shaft, reducing the longitudinal impacts on the vehicle, better satisfied the torque demands of the driver, and significantly improved the quality of mode switching.

4. Conclusions

This paper took a P2 + P3 two-speed hybrid transmission as its research object. Based on the starting state of the engine, the switching process from pure electric drive mode to hybrid drive mode was divided into six stages. The corresponding controllers were designed for the three power sources, and a multi-power source mode switching coordination control method was proposed.

Established in the Stateflow simulation model of MATLAB’s Simulink, carrying two P2 + P3 two-motor block DHT hybrid power systems, simulation of the designed control strategy showed that compared with the traditional control method, this control strategy slightly prolonged the duration of mode switching, but the impact on the vehicle during the switching process was reduced by 29.7%, and the grinding work during clutch engagement was reduced by 38.6%, which improved the smoothness of mode switching and greatly prolonged the service life of the clutch.

The control strategy was verified by using CANape to carry out a real vehicle calibration test. The test results show that the total control time of the proposed strategy in the process of mode switching was 1.23 s, during which the clutch slip loss was about 1.54 kJ, and the maximum impact on the vehicle was only 7.54 m/s³. the experimental and simulation results showed consistent trends, which verifies the effectiveness of the proposed strategy.

In conclusion, the dynamic performance and comfort of vehicles with this control strategy were significantly improved. At the same time, it expands the theoretical knowledge of DHT hybrid electric vehicles with P2 + P3 and promotes the application of special transmissions in hybrid electric vehicles.