A Fuzzy Adaptive PID Coordination Control Strategy Based on Particle Swarm Optimization for Auxiliary Power Unit

Abstract

Range extender hybrid vehicles have the advantages of better dynamics and longer driving range while reducing pollution and fuel consumption. This work focuses on the control strategy of an Auxiliary Power Unit (APU) operating in power generation mode for a range-extender mixer truck. When an operating point is switched, the engine speed and generator torque of the APU will switch accordingly. In order to ensure APU fast and stable adjustment to meet the power demand of the vehicle as well as operate at the lowest fuel consumption, a fuzzy adaptive PID coordination control strategy based on particle swarm optimization (PSO) is proposed to control the APU. The optimal operating curve of APU is calculated by coupling the engine and generator first. Then, the adaptive PID algorithm is used to control the speed and torque of the APU in a dual closed loop. The PSO is used to optimize the PID control parameter. Through hardware-in-the-loop tests under different working conditions, the control strategy is verified to be effective and real-time. The results show that the proposed control strategy can coordinate the operating of engine and generator and control the APU to track target power stably and quickly under minimum fuel consumption. Compared with traditional PID control strategy, the overshoot, regulation time and steady-state error are reduced by 55.1%, 11.1% and 77.3%, respectively.

1. Introduction

With the rapid development of the automobile industry, the problems of energy shortage and environmental pollution become increasingly prominent [1]. Nowadays, the green revolution in the automobile industry has become a major trend. As a heavy construction vehicle, concrete mixer trucks have high fuel consumption and emissions, which is a pressing problem. An extended-range concrete mixer truck is a good solution. The extended-range concrete mixer truck has two power sources: an auxiliary power unit (APU) and battery pack [2]. The APU is composed of an engine and generator, and the engine drives the generator to generate electricity for the vehicle [3]. Since the engine operates independently of the driving conditions, it can operate stably in the optimal working area, which can save fuel while extending the range. The extended-range vehicles are widely recognized as the ideal vehicles for the transition from traditional engineering vehicles to pure engineering electric vehicles.

When the APU is in power generation mode, the improvement in fuel economy and efficiency mainly relies on the control strategy of APU [4,5]. The auxiliary power control unit (APCU) decouples the target power sent by the VCU into target speed and target torque. The engine speed is controlled by adjusting the throttle opening and the generator torque is controlled by vector control method to adjust the generator current. However, due to the highly nonlinear and strong coupling between the engine and generator in the APU [6], in actual conditions, it is usually difficult for the APU to adjust quickly and stably to meet the power demand of the vehicle and output target power under minimum fuel consumption. The phenomena of long regulation time, large overshoot and steady-state error often occur. The dynamic response of the engine and generator are very different; therefore, the coordination control of the engine and generator to improve the dynamic performance, stability and efficiency of APU is of crucial importance.

In terms of the coordination control of APU, researchers have proposed many control strategies [7,8]. Nowadays, there are mainly two control strategies. One is to control the engine speed and the generator torque. The generator torque is the load of the engine [9,10,11]. The other is to control the generator speed and engine torque. The engine torque is the load of the generator. Although the second strategy outputs power faster, when the engine torque changes suddenly, the APU speed will change, which can easily cause speed fluctuation in the generator. In addition, since the current of the generator is more stable and the output torque is more accurate than that of the engine, the first strategy can reduce the vibration between engine and generator during the APU start-up phase. Therefore, we control the engine speed and the generator torque for a better control effect.

With the development and application of global optimization algorithms, some researchers have applied them to the coordination control of the APU for optimization, which has further improved the dynamic property and stability of the APU. Specifically, this has included particle swarm optimization (PSO) [12], a genetic algorithm (GA) [13,14], dynamic programming (DP) [15,16], model predictive control (MPC) [17,18], sliding mode control (SMC) [19,20] and neural network (NN) [21].

In [22], a cascade PID-based controller was established to control the speed and torque of the powertrain; the results show that the method has a high control accuracy. Taking the minimum fuel consumption as the control goal, Barsali et al. [23] used a fuzzy prediction algorithm to control the engine speed to make it operate at the optimal operating curve. Darwich et al. [24] used a PSO algorithm to solve the optimal problem of nonlinear system; the engine speed and generator torque are optimized through the global exploration ability of particle swarms to achieve efficient control of the APU.

A neural network algorithm is used to optimize the PID tuning to realize the real-time adjustment of the engine speed [25]. In order to improve the robustness and stability of the system, a sliding mode optimum control algorithm is used in the coordination control of the APU [26]. In [27], a control strategy combining fuzzy logic and adaptive optimal control was proposed to optimize the transient response of the hybrid powertrain. In [28], a strategy combining SMC technology with first-order low pass filter and adaptive PID controller was proposed, which can optimize the control parameters K_P, K_I and K_D of PID controller online in a short time. Kang et al. [29] used the MPC strategy to optimize the engine speed and generator torque online, which greatly improves the power response speed of the APU.

At present, PID controllers are mostly used in the coordinated control of the APU, but due to the strong coupling characteristics of the APU, it is difficult for a single PID control to ensure that the range extender system achieves good dynamics, stability and fuel economy. The fuzzy PID can adjust the control parameters of the PID in real time but relies excessively on the fuzzy rules. The parameters of the fuzzy controller remain unchanged and optimal control cannot be achieved. Therefore, we adaptively optimize fuzzy control parameters by PSO to improve the stability and robustness of the system. According to the working status of the APU, the PID control parameters are adjusted in real time to improve the system adjustment speed and steady-state accuracy, and reduce the amount of overshoot. In this work, the APU power tracking control strategy is proposed. The strategy uses a fuzzy PID algorithm for dual closed-loop control of engine speed and generator torque, and the PSO algorithm is utilized to correct the PID tuning parameters. To minimize fuel consumption, the APU fuel consumption characteristics map is obtained through coupling, and the engine fuel consumption map and generator efficiency map are calculated. Further, the optimal operating curve is also obtained. The target power is decoupled into target engine speed and target generator torque according to the optimal operating curve of APU. The strategy controls APU tracking target power by adjusting the engine speed and generator torque to a certain target value in a dual closed loop. Through the fuzzy adaptive PID algorithm based on PSO, the engine speed and generator torque are adjusted to the target values. As a result, the APU responds to the target power more quickly, accurately and stably. Finally, a hardware in the loop (HIL) test platform is built to verify the effectiveness and reliability of the control strategy. The proposed control strategy has good application prospects in efficient and stable control of the APU.

2. Models and Methods

2.1. Powertrain and System Configuration

The powertrain model of the extended-range concrete mixer truck is shown in Figure 1. The extended-range concrete mixer truck is mainly composed of the power battery pack, APU, drive motor, gearbox, hydraulic transmission system, reducer and mixing drum. Compared to hybrid vehicles, extended-range concrete mixer trucks have two power consumption units—drive motor and mixing drum [30,31]—which makes the powertrain more complex. There are two power sources in the extended-range concrete mixer truck: the battery pack as the main power source and the APU as the auxiliary power source. When the vehicle is operating, the battery pack and the APU together provide the energy required by the drive motor and the mixing drum. The APU is composed of engine, integrated starter and generator (ISG) and clutch. The engine is a diesel engine with good power and reliability and the ISG is a three-phase permanent magnet synchronous motor (PMSM). The configuration of the engine and ISG is shown in

Table 1. Configuration of engine.

Engine	ISF 3.8 Four-Stroke High-Speed Diesel Engine
Number of cylinders	4
Engine displacement (L)	3.76
Rated speed (rpm)	2600
Maximum torque speed	1200–1900
Maximum output power (kW)	125
Maximum output torque (Nm)	450–600

and

Table 2. Configuration of ISG.

Generator	YQW3-225Z-18A-RA2
Rated power (kW)	80
Rated torque (N·m)	425
Rated speed (rpm)	1800
Peak power (kW)	130
Maximum speed (rpm)	3000
Rated current (A)	119
Number of pole pairs of the motor	6

.

As Figure 2 shows, the architecture of the whole vehicle’s control system is multi-layer and distributed. The top layer is the VCU, which is the core of the control system. The middle layer includes a battery management system (BMS), APCU and others, and receives the command signals from the VCU, coordinates the internal operation of each subsystem, and feeds back the status signals of each subsystem in real time. The bottom layer is the control units of actuators, which are also the controllers closest to the mechanical components, mainly including the engine control unit (ECU), ISG control unit (GCU) and clutch control unit (CCU). The function of the bottom layer is to receive the signals from the middle layer controllers and control the operating states of the actuators. Data are transmitted via CAN bus.

This study mainly focuses on the control strategy of the APU. After receiving the commands from the VCU, the APCU controls the start and stop of the engine, clutch and ISG. The APCU decouples the target power into target engine speed and target ISG torque along the optimal operating curve. The signals of target engine speed and target ISG torque are transferred to the ECU and GCU, then the engine and ISG respond to the control commands from the APCU and provide feedback on the state signals in real time. The dual closed-loop control strategy controls the engine and ISG through the fuzzy adaptive PID algorithm based on PSO to adjust the actual output power to be closer to the target power.

2.2. Selection of APU Operating Point

The operating point of the APU affects the dynamics and economy property, which should not only satisfy the power demand of the whole vehicle, but also ensure the APU operates at the lowest fuel consumption. Since the APU is composed of an engine and ISG, we can get APU fuel consumption characteristics map based on engine fuel consumption map and ISG efficiency map.

• Engine Model

According to the experimental data of the engine, the engine fuel consumption map is expressed as shown in Figure 3. The full load speed characteristics curve indicates the maximum torque corresponding to different engine speeds at maximum power.

2.

ISG Model

According to the experimental data of ISG, the ISG efficiency map is expressed as shown in Figure 4. Figure 4 is divided into two parts according to the positive and negative torque. In the upper part, ISG operates at the electric mode and in the lower part it operates at the power generation mode. The full load speed characteristics curve indicates the maximum torque corresponding to different ISG speeds at maximum power.

3.

APU Model

During the steady-state power generation mode, the clutch is fully engaged, and the engine and the ISG share the same speed. At that speed, the corresponding operating efficiency and actual torque of the ISG can be calculated. The APU output power can be calculated by (1).

$$P_{APU}=P_e\times {\eta }_{ISG}$$

(1)

where ${\eta }_{ISG}$ is the operating efficiency of ISG, $P_{APU}$ is the output power of APU and $P_e$ is the output power of engine.

The APU fuel consumption characteristics map can be coupled with the engine and ISG characteristics, as shown in Figure 5. By using the ergodic optimization algorithm, the optimal operating point which ensures engine operating at the minimum fuel consumption for each power can be found. Connect these points to form the optimal operating curve of the APU. When the target power is known, we decouple the target power into target engine speed and target ISG torque along the optimal operating curve. The signals of target speed and torque are transferred to ECU and GCU, respectively, for tracking control. The actual output power of the APU can be expressed as (2).

$$P_{APU}=N_e\times T_{ISG}/9550$$

(2)

3. Power Control Strategy for APU

3.1. Fuzzy PID Control Strategy

The coordinated control strategy of APU is shown in Figure 6. Firstly, the target generation power is determined, and then the target power is decoupled into target speed and target torque according to the optimal fuel consumption curve of the APU. The engine and ISG are controlled by control algorithm in a dual closed loop, respectively. This strategy provides dual closed-loop control of the engine and ISG to achieve a fast and stable response of speed and torque to target values. For the dual closed-loop algorithm, the difference between engine target and actual speed and ISG target and actual torque are the inputs and the actual speed and torque are the outputs.

4.

Incremental PID

Dual closed-loop control for speed and torque is the basis of coordinated control strategy. Control of speed and torque can be tracked using a PID algorithm.

The discrete expression of the PID algorithm is as (3).

$$u(k)=K_{P}e(k)+K_I{\displaystyle \sum _{j=0}^{k}e(k)T}+K_D\left[e(k)-e(k-1)\right]/T$$

(3)

where $e(k)$ is the difference between the target and actual value at moment k. $u(k)$ is the output control quantity. T is the sampling period. $K_P$ is the proportional gain. $K_I$ is the integral gain and $K_D$ is the derivative gain.

In order to obtain better control stability, we use the incremental PID control algorithm with the calculation (4). The differences between the target speed/torque and actual speed/torque values are used as inputs, and the incremental PID algorithm regulates the engine throttle opening and the current of the ISG to control speed/torque.

$$\Delta u(k)=K_P\left[e(k)-e(k-1)\right]+K_{I}e(k)+K_D\left[e(k)-2e(k-1)+e(k-2)\right]$$

(4)

where $\Delta u(k)$ denotes the rate of change of the control quantity.

5.

Fuzzy PID

The traditional incremental PID control algorithm can achieve power tracking, but its steady-state and transient performance is still poor. Fuzzy PID is the combination of fuzzy control and PID control, which has the advantage of strong stability. To achieve a fast and stable tracking to the target power and improve APU efficiency, we utilize fuzzy PID algorithm for dual closed-loop control of speed and torque. As Figure 7 shows, the error E and the differential error $dE/dt$ of the engine speed and ISG torque are inputs, and through inference and calculation of the fuzzy logic controller (FLC), the correction coefficients $\Delta K_P$, $\Delta K_I$ and $\Delta K_D$ are outputs to the PID controller for adjustment of PID parameters. In Figure 7, $K_E$ and $K_{Ec}$ are quantification factors of the error and differential error, respectively. $K_U$ is the scale factor.

The inputs of the FLC are E and $dE/dt$ of speed/torque and the outputs are correction coefficients $\Delta K_P$, $\Delta K_I$ and $\Delta K_D$. Considering that the fuzzy PID controller has 2 inputs, the two-dimensional FLC is used. The continuous variables of inputs are converted to fuzzy variables in the discrete universe by (5):

$${\epsilon }_a=[\epsilon -(a+b)/2]\times 2n/(b-a)$$

(5)

where $\epsilon$ is the input variables in continuous interval, $\epsilon \in [a,b]$; ${\epsilon }_a$ is the corresponding fuzzy value of $\epsilon$ in the discrete universe of discourse, ${\epsilon }_a\in [-n,n]$.

Variables are divided into seven linguistic labels: negative big (NB), negative medium (NM), negative small (NS), zero (ZE), positive small (PS), positive medium (PM) and positive big (PB). In order to achieve a fast response time, while taking into account a large range of variations in engine speed and ISG motor torque, membership functions (MFs) are a combination of triangles and bilateral Gaussian functions. The MFs of inputs and outputs are shown in Figure 8.

Fuzzy rules are the core of FLC. According to the role of control parameters in the system, we designed the fuzzy rules for $\Delta K_P$, $\Delta K_I$ and $\Delta K_D$, as shown in

Table 3. Fuzzy rule for $\Delta K_P$.

	${\mathit{E}}_{\mathit{c}}$	NB	NM	NS	ZE	PS	PM	PB
$\mathit{E}$
NB		PB	PB	PM	PM	PM	PS	ZE
NM		PB	PB	PB	NM	PM	ZE	ZE
NS		PM	PM	PM	PS	ZE	NB	NM
ZE		PM	PS	PS	ZE	NS	NS	NM
PS		NM	NB	NB	NB	PS	PM	PM
PM		NB	NM	NM	PM	PM	PM	PB
PB		NB	NB	NM	NM	PM	PB	PB

,

Table 4. Fuzzy rule for $\Delta K_I$.

	${\mathit{E}}_{\mathit{c}}$	NB	NM	NS	ZE	PS	PM	PB
$\mathit{E}$
NB		NB	NB	NB	NM	NM	ZE	ZE
NM		NB	NB	NM	NM	NS	ZE	ZE
NS		NM	NM	NS	NS	ZE	PS	PS
ZE		NM	NS	NS	ZE	PS	PS	PM
PS		NS	NS	ZE	PS	PS	PM	PM
PM		ZE	ZE	PM	PM	PM	PM	PB
PB		ZE	NS	PS	PM	PB	PB	PB

and

Table 5. Fuzzy rule for $\Delta K_D$.

	${\mathit{E}}_{\mathit{c}}$	NB	NM	NS	ZE	PS	PM	PB
$\mathit{E}$
NB		NB	NB	NB	ZE	ZE	PS	PS
NM		NB	NB	NB	ZE	ZE	PS	PS
NS		NB	ZE	ZE	ZE	ZE	PS	PS
ZE		ZE	ZE	ZE	ZE	ZE	ZE	ZE
PS		NB	NB	ZE	ZE	ZE	PS	PS
PM		NB	NB	NB	ZE	ZE	PS	PS
PB		NB	NB	NB	ZE	ZE	PS	PS

. The fuzzy rules surfaces are shown in Figure 9.

Finally, defuzzification is carried out by the weighted average method to convert the fuzzy quantities obtained by the fuzzy rules into the corresponding numerical data. The formula is

$$Y={\displaystyle \sum _{i=1}^n{w}_i{Y}_i/{\displaystyle \sum _{i=1}^n{w}_i}}$$

(6)

where $Y$ refers to the final output; $Y_i$ is the output elements; $w_i$ is the membership function value of $Y_i$.

3.2. Fuzzy Adaptive PID Coordination Control Strategy Based on PSO

The fuzzy PID can adjust the control parameters of the PID in real time, but relies excessively on the fuzzy rules. The parameters of the fuzzy controller remain unchanged and optimal control cannot be achieved. Therefore, we adaptively optimize fuzzy control parameters by PSO to improve the stability and robustness of the system. Based on the analysis above, we propose a fuzzy adaptive PID coordination control strategy based on PSO.

• Particle Swarm Optimization Algorithm

PSO is a swarm intelligent optimization algorithm developed by Eberhart and Kennedy based on the foraging behavior of animals. First, the velocity and position of particles are randomly initialized. Then, through an iterative search, the motion state of each particle is updated and the search range is continuously converged. At the end of the iterative search, the optimal value is obtained [32]. The velocity and position of each particle in the PSO algorithm can be expressed as

$$\left\{\begin{array}{l}{v}_{k+1}=w{v}_k+c_1{r}_1(p{b}_k-x_k)+c_2{r}_2(g{b}_k-x_k)\\ x_{k+1}=x_k+v_{k+1}\end{array}\right.$$

(7)

where w is the inertia weight, which determines the inheritance degree of the current velocity to the previous velocity of the particle; $v_k$ is the current velocity vector of the particle; $x_k$ is the current position of the particle; $c_1$ and $c_2$ are both learning rates, which represent the attraction intensity of the individual optimal solution and group optimal solution to the particle, respectively. $p{b}_k$ represents the best historical position of the particle and $g{b}_k$ represents the global best position of the particle swarm by current iteration. $r_1$ and $r_2$ are random numbers between [0,1].

In order to solve the disadvantage that the parameters of fuzzy control cannot be adjusted adaptively, this paper uses the PSO algorithm to optimize the quantization factors $K_E$, $K_{Ec}$ and scale factor $K_U$ of the fuzzy PID controller. Taking Integral of Time and Absolute Error (ITAE) as the evaluation index, the fitness function is as follows [33,34]:

$$J={\displaystyle {\int }_0^{\infty }t\left|e\right|dt}$$

(8)

where $J$ is evaluation index, $t$ represents time and $e$ is error.

Figure 10 shows the schematic of fuzzy PID control based on PSO. Using E and E_c of speed/torque as the inputs, $K_E$, $K_{Ec}$ and $K_U$ are optimized through the PSO algorithm. Find the factor with the highest level fitness and optimize E, E_c and correction coefficients $\Delta K_P$, $\Delta K_I$ and $\Delta K_D$ of PID parameters to realize the adaptive control of speed and torque.

Writing PSO algorithm in MATLAB (R2021a) and joint simulation with fuzzy PID controller model in Matlab/Simulink (R2021a). The number of particles is set to 20. w = 0.6. The maximum number of iterations is 100, and the learning rates $c_1=c_2=2$. The fitness function curves of the controller for speed and torque are shown in Figure 11. From Figure 11, we know that the fitness function value of the speed obtains the optimal solution at the 39th iteration, with the value of 1.293. The optimized parameters are as follows: E = 3.5, E_c = 0.75, ∆K_P = 11.8103, ∆K_I = 0.1833, ∆K_D = 0.0558; the fitness function value of the torque obtains the optimal solution at the 35th iteration, with the value of 1.162. The optimized parameters are as follows: E = 1.5, E_c = 0.2, ∆K_P = 2.0225, ∆K_I = 0.2334, ∆K_D = 0.1065.

2.

Fuzzy adaptive PID coordination control strategy based on PSO

The strategy structure is presented in Figure 12. The VCU allocates the energy reasonably and calculates the generating power required by the APU according to the actual driving conditions. The APCU decouples the target power into engine target speed and ISG target torque based on the optimal operating curve. The control module receives the target and actual values of engine speed and ISG torque and calculates the error and differential error. The PSO algorithm takes E and the $dE/dt$ as inputs. $K_E$, $K_{Ec}$ and $K_U$ are iterative-optimized by PSO. Taking ITAE as the judgment standard, the factor with the highest level of fitness is found and the optimal combination of $K_E$, $K_{Ec}$ and $K_U$ are obtained. At the same time, the FLC infers and outputs factors according to the knowledge base. $K_U$ is used to optimize the factors to obtain the correction coefficients $\Delta K_P$, $\Delta K_I$ and $\Delta K_D$. Then, the control parameters $K_P$, $K_I$ and $K_D$ of the PID controller with optimal performance under this operating condition are obtained. The PID controller with optimized control parameters can control the engine speed and ISG torque in real time and adaptively.

4. Experiment and Analysis

In this section, the effectiveness and real-time performance of the control strategy are verified through an HIL test. The power response characteristic test of the coordination control strategy is completed at various working conditions. The PID control strategy, fuzzy PID control strategy and fuzzy adaptive PID coordination control strategy based on PSO are all tested and compared, and the test results are statistically analyzed.

4.1. HIL Test Platform

The HIL test platform is shown in Figure 13. It mainly consists of the real-time system, upper computer software and APU controller. The chip of APU controller is XC2267M, manufactured by Infineon in Munich, Germany. Connect the actual controller to the simulation platform. The real-time system simulates the operation state of the APU and the signals are transferred among the upper computer, controller and real-time system through a CAN bus. The HIL system runtime is synchronized with real time, so it can accurately reflect the control effect of the control strategy.

We build a real-time system based on xPC-Target environment, which operates in “dual-computer mode”. The real time system is composed of the target computer and the host computer. The target computer is composed of a processor, CAN communication board, analog resistance board, etc., which is used to carry the powertrain model of the APU and drive the program code. The host computer is responsible for building the model and monitoring the status of the target computer. The function configuration of the main ports of the real-time system is shown in

Table 6. Main ports configuration of real time system.

Name	Number	Range
Bidirectional PWM	4	0–5 V/0–24 V
PWM signal output	10	0–5 V/0–24 V
Hall signal acquisition	10	0–5 V/0–24 V
High effective digital signal output	32	5–24 V
Low effective digital signal output	32
Analog signal output	12	0–5 V
Analog signal acquisition	32	0–5 V/0–12 V/0–24 V Configurable
CAN communication node	12
High-side driven load	10
Low-side driven load	20
Fault injection port	100

.

4.2. HIL Test

The HIL system adopts a real controller, which can restore real computing environment and sampling time. In order to verify the feasibility and real-time performance of the proposed fuzzy adaptive PID coordination control strategy based on PSO, power response tests under different working conditions are carried out on the HIL test system.

The target power variation for simulation testing is set as 0–1–3–6–10–15–21–28–36–45–55 kW to study the power response at power transitional conditions. The target power increments of this working condition are 1–2–3–4–5–6–7–8–9–10 kW per second. As Figure 14 shows, when the target power is small, the APU responds quickly and it can control the engine and ISG to execute the corresponding commands in time. With the increase in the amount of power change per unit time, the power regulation time gradually increases, but the overshoot and steady-state error are both within 1 kW. During the test, when the regulation time is less than 1 s, the power tracking effect can be achieved.

In order to further verify the power tracking effect of the control strategy when the operating point is switched, we use three working conditions for the HIL test, as

Table 7. Working conditions for HIL test.

Working Conditions	Target Power (kW)	Power Increment Change (kW/s)
1	0–1–3–6–10–15–21–28–36–45–55	1–2–3–4–5–6–7–8–9–10
2	0–2–6–12–20–30–38–44–48–50	2–4–6–8–10–8–6–4–2
3	0–10–20–30–40–50–60–70–80–90	10–10–10–10–10–10–10–10–10

shows.

For the APCU, the response effect of target power is mainly evaluated by the performance index such as overshoot, regulation time and steady-state error at transitional conditions. In this paper, taking power transition from 45 kW to 55 kW in working condition 1, power transition from 20 kW to 30 kW in working condition 2 and power transition from 50 kW to 60 kW in working condition 3 as transitional conditions, the control strategy is validated. The target power for all these three transition conditions is 10 kW per second, and these three transition conditions cover multiple typical power variation intervals, so the control strategy can be validated comprehensively.

Figure 15 is the HIL test results. From Figure 15, we can see that in the early adjustment stage, the PID control strategy has the phenomenon of oscillation and the largest steady-state error, but it can still meet the power demand. Combined with the test data in

Table 8. HIL test results of different control strategies.

Condition	Control Algorithm	Overshoot (kW)	Regulation Time (s)	Steady-State Error (kW)
45–55 kW	PID	0.34	0.86	0.76
	FUZZY_PID	0.20	0.94	0.33
	PSO_FUZZY_PID	0.15	0.80	0.18
20–30 kW	PID	0.42	0.84	0.70
	FUZZY_PID	0.27	0.93	0.41
	PSO_FUZZY_PID	0.19	0.75	0.12
50–60 kW	PID	0.46	0.90	0.79
	FUZZY_PID	0.31	0.99	0.36
	PSO_FUZZY_PID	0.21	0.85	0.21

, we know that the fuzzy PID control strategy has obvious improvement in terms of overshoot and steady-state error compared with traditional PID control strategy, but the regulation time is relatively increased. The fuzzy adaptive PID coordination control strategy based on PSO has the steady-state power closest to the target power as well as the minimal adjustment time and overshoot. The fuzzy adaptive PID coordination control strategy based on PSO has the best control effect. Compared with the PID control strategy, the overshoot, regulation time and steady-state error of the fuzzy adaptive PID coordination control strategy based on PSO are reduced by 55.1%, 11.1% and 77.3%, respectively, which has the best control effect.

The HIL test results indicate that the fuzzy adaptive PID coordination control strategy based on PSO has the best power response effect and control performance, which can effectively reduce the overshoot, regulation time and steady-state error. The proposed control strategy can not only coordinate the control engine and ISG, but also improve the power response speed and stability of APU on the basis of operating at minimum fuel consumption. Regular methods require frequent parameter adjustments to adapt to environmental variations, which is cumbersome. Meanwhile, the proposed PSO_FUZZY_PID can adaptively regulate the parameters, which enables it to be better applied in various operation scenarios.

5. Conclusions

In this paper, three speed-torque adjustment modes are proposed for the control of engine speed and ISG motor torque, and the control performance of simultaneous speed and torque adjustment is proved to be the best through simulation verification. On this basis, the FUZZY_PID and PSO_FUZZY_PID control algorithms are designed to optimize and adjust the control parameters of the system in real time, which have good simulation results. A fuzzy adaptive PID coordination control strategy based on PSO was proposed. HIL test results show that the proposed control strategy can coordinate the operation of the engine and ISG. The strategy can make the APU output the target power quickly and accurately by controlling the engine speed and ISG torque in a dual closed loop. Moreover, it can control the APU to generate power efficiently and stably on the basis of operating at minimum fuel consumption. Compared with PID control strategy, the fuzzy adaptive PID coordination control strategy based on PSO has a 55.1% decrease in power overshoot, 11.1% decrease in regulation time and 77.3% decrease in steady-state error.

The developed range extender control system and control strategy are carried out on the simulation platform, and the follow-up work will be tested on the bench and the real vehicle to further verify its effectiveness and feasibility.