Vehicle ACC Control Based on Fuzzy PID

: ACC (Adaptive Cruise Control) is a crucial technology to control the automatic driving of a vehicle, which can automatically adjust the driving status of the vehicle according to the driving status of the vehicle in front so that the vehicle always keeps a safe distance from the vehicle in front, which can primarily relieve the driver's driving pressure and avoid tailgating. The research is of great significance to the realization of intelligent driving of vehicles. In this paper, the fuzzy PID control method is used to study the vehicle ACC system. Firstly, the basic concept and key components of the ACC system are explained, the vehicle longitudinal dynamics model is established, and the primary ranges of kp , ki and kd parameters are determined through simulation; based on this, the fuzzy PID control algorithm of vehicle ACC is designed considering three different driving conditions of fixed speed and following cruise mode. The fuzzy PID control algorithm of the vehicle ACC system is designed and established. The joint simulation model of MATLAB is used to simulate the vehicle ACC system under three different driving conditions. The simulation results show that the vehicle ACC system designed in this paper ensures the safety and stability of following the vehicle while providing the vehicle's ride's comfort.

and points out the future development trend. Literature designed different control algorithms for the ACC system, using predictive model control to optimize multi-objective control, using adaptive cruise control algorithm to achieve multi-objective control, comprehensively considering the driver's expected output, vehicle following Factors such as safety and the physical limitations of the vehicle itself achieve the best matching of the ACC controller's working modes and a smooth transition between different ways. Considering the vehicle driving situation on the road with a low adhesion coefficient, the road adhesion coefficient is estimated by the least square method to determine the limit constraint conditions when the model predictive control is solved. The nonlinear model predictive control algorithm considering the fuel consumption rate of the engine and the efficiency of the motor is comprehensively considered, and the nonlinear longitudinal dynamics model of the hybrid electric vehicle is established. Reference designed a vehicle ACC platform based on fuzzy control and compared it with the PID control scheme; the simulation results show that the fuzzy control effect is better. In addition, there are strategies such as hierarchical control, parameterization of key characteristics, and fuzzy control algorithms for adaptive cost functions. The above solutions generally have good feedback under specific operating conditions. Still, when faced with complex road conditions in real situations, the road conditions faced by the vehicle are summarized into seven categories, and the fuzzy PID control method is used to study the problem. First, the PID method is robust and suitable for various control fields (Chamraz & Balogh, 2018). Second, the fuzzy control summarizes the driver's rich driving experience and can adjust the PID control parameters (Anand & Ohol,

ACC System Working Mode
The road conditions the car is driving are usually complex and diverse. To cope with different driving conditions, the ACC system is generally divided into two working modes: cruise control and the following cruise mentioned above. It can be divided into acceleration control, deceleration control, start control and stop control.
(1) Cruise control When there are no vehicles or other obstacles in front of the vehicle, the vehicle will drive at a constant speed at a speed pre-set by the driver.
(2) The following control mode is divided into four cases: acceleration control, deceleration control, start control and stop control.

Vehicle Modelling Based on Cars
Based on the above-mentioned adaptive cruise, there are mainly two working modes: constant speed and the following cruise. Cruise control is to control the speed of the longitudinal movement of the vehicle to reach a pre-set cruising speed. In contrast, the next cruise means that the vehicle needs to control the vehicle's direction according to the vehicle's motion state in front and maintain a stable and safe distance between the vehicle and the vehicle in front.
To avoid rear-end collisions, cruise control and follow cruise control the longitudinal movement of the vehicle. The mechanisms that control the longitudinal motion of the vehicle are the vehicle's power system and braking system. Vehicle power system mainly includes an engine, torque converter and automatic transmission. Vehicle braking system control precisely controls the pressure of the brake cylinder to generate braking force and act on the wheels for braking. The adaptive cruise control system designed in this paper adopts layered control. The upper layer controller calculates the desired acceleration required by the vehicle according to the motion state of the vehicle, and the lower layer control converts the expected acceleration into the throttle valve that the actuator of the model vehicle should apply. This paper uses Carsim software to establish longitudinal vehicle dynamics. The vehicle inverse dynamics model needs to control the driving and braking actuators of the vehicle according to the expected acceleration calculated by the upper controller. It is a calculation module.

Figure 5 Vehicle Dynamics Model Structure
The simulation experiment in this paper uses the C-Class Hatchback2017 model of Carsim software, and the relevant parameters are shown in the following table.

Concrete Model Engine Model
The selected engine model parameters refer to Audi A6L 2.0T automobile engine; select the 125KW engine in the software, and the parameter settings are shown in the following figure:

Automatic Transmission Model
The model vehicle automatic transmission used in this paper is a 6-speed transmission, of which the direct gear is 4. Figure 8 shows the automatic transmission parameters.

Research Method
The drive-brake switching algorithm is designed, and the simulation model of the drive-brake control switching and safety clearance strategy is built (Li et al., 2022). The fuzzy PID control method is used to design the vehicle adaptive cruise control algorithm based on the vehicle longitudinal dynamics model (Ambroziak & Chojecki, 2023). Two cruise control algorithms are designed for different working conditions: cruise control algorithm at fixed speed and cruise control algorithm following and two algorithms are built-simulation model Suwoyo et al., 2021).
In the formula, ( ) is the proportional control term, is called the proportional coefficient; is the integral control term, is the integral time constant; is the Derivative control term, is the derivative time constant (Shi, 2020). The PID control block diagram is shown in Figure 10.

Figure 10 PID Control Block Diagram
The PID controller is mainly used in the series correction link. The function of the PID controller is as follows: (1) The proportional link can speed up the system's response speed, and increasing can reduce the steady-state error of the system. Still, an excessively large will worsen the system's dynamic quality, cause system oscillation, and deteriorate the dynamic performance and stability of the system.
(2) The function of the integral coefficient ; reduces the system's steady-state error. The larger ; precision. The proportional control term plus the integral control term can eliminate the system's steady-state error, but the system's dynamic process will slow down. If the integral control is too strong, the overshoot of the system will increase, making the system unstable.
(3) The function of the differential coefficient is to predict the deviation change in advance, suppress the overshoot caused by and in advance, speed up the response speed of the system, reduce the overshoot and oscillation, and help to improve the dynamic performance of the system. But too large will make the system control process break in advance, thus prolonging the time of system adjustment. Fuzzy PID control is a control method that combines fuzzy control and PID control. In PID control, because the three PID parameters selected by different designers are different, and the three parameters are obtained mainly by field heuristics, PID control is often not optimal, but a "sub-optimal" controller that meets specific index requirements, and the fixation of three parameters also limits the all-around performance of PID control. To make up for this deficiency, it has been found that better control effects can be obtained by designing the three PID parameters to be variable and able to change following the response adaptively. The basic principle of fuzzy PID control is to use the theory and method of fuzzy mathematics to formulate fuzzy control rules and store these rules, control effect evaluation indicators, and PID control initial parameters in the computer knowledge base, adjust the parameters of PID control to achieve the best control effect (Suwoyo et al., 2018). Therefore, this paper adopts the fuzzy PID control method to study the problem of vehicle adaptive cruise, the principle of fuzzy PID control is shown in Figure 11.

Algorithm Design of Cruise Control
The primary purpose of cruise control is to control the vehicle to maintain its speed. The set speed does not change. In the fuzzy PID control algorithm, the input of the fuzzy controller is the difference between the target speed and the actual speed and the rate of change of the speed difference, the output is the three parameters 1, 1, and 1 of the PID controller, and the input of the PID controller is the target speed and the actual speed. The difference in speed, the output is the desired acceleration of the vehicle (Rout et al., 2016;Suwoyo et al., 2020).

Formulation of Fuzzy Rules for Cruise Control
Cruise control is divided into two situations: acceleration to cruise speed and deceleration to cruise speed. The input of the fuzzy control in the cruise control fuzzy PID controller is the deviation E1 between the cruise speed and the actual speed and the change rate E of the deviation; the output is the three parameters 1, 1, 1 of PID control. The strength of proportional, integral and differential effects in each control stage is determined according to different deviations and deviation change rates. In formulating fuzzy rules, the dynamic error When the absolute value of the speed deviation E1 is significant, it is necessary to quickly reduce the deviation to make the vehicle reach cruising speed as soon as possible. At this time, the adjustment range should be increased to increase the vehicle speed, and the values of 1 and Ki1 should be increased. The adjustment will affect the driving stability and ride comfort of the vehicle. The increase of the parameters 1 and 1 should be determined according to the deviation change rate Ec. Value.
When the absolute value of the speed deviation E1 is generally significant, to reduce the steadystate error of the control system to reach the set cruise speed as soon as possible, in the case that the output does not oscillate, increase 1, according to the deviation change rate E. To suppress the control strength of 1 and reduce the overshoot of the system at the same time, to ensure the comfort of riding, Ka1 should be appropriately increased.
If the absolute value of the speed deviation E1 is small, the actual speed of the vehicle is not much different from the cruising speed. At this time, it is necessary to continue to reduce the steady-state error while avoiding a significant overshoot that affects ride comfort and vehicle stability. To improve the sex, the size of 1 and ;1 should be kept moderate, and Ka1 should be appropriately increased. When the absolute value of the speed deviation E1 and the deviation change rate Ec tend to 0, the vehicle should drive at a constant speed. For a certain steady-state error, 1, 1 should be appropriately reduced, and 1 should be increased.

Cruise Control Fuzzy PID Controller
The fuzzy PID control module for cruise control is built in MATLAB/Simulink, as shown in Figure 12. The input of the fuzzy controller is the speed deviation and the rate of change of the variation, and the output is the parameters 1, 1, 1 of the PID controller. The PID controller the input is the deviation between the actual speed and the target speed. The variation and the controller's three parameters 1. 1 and 1 are summed through proportional, integral and differential operations, and the output is the expected acceleration of the vehicle.  Suppose the absolute value of the deviation E2 is small. This situation usually occurs when starting to follow, following the acceleration and deceleration of the preceding vehicle, and stopping to observe. The distance between the two vehicles is close to the safety distance. To control the overshoot and improve the anti-interference ability of the control system, 2 should be appropriately reduced according to the relative speed V of the two vehicles, and 2 and 2 should be increased.
Suppose the absolute value of the deviation E tends to be 0. In that case, this situation may occur when starting to follow, following the acceleration and deceleration of the preceding vehicle, when the prior vehicle cuts into the vehicle's lane and stops and follows. The distance between the two vehicles is approximately equal to the safety distance. The distance from the vehicle in front should be kept constant. To suppress the overshoot in advance to ensure the comfort of riding, 2 should be appropriately increased, and 2 and 2 should be appropriately increased according to the relative speed Vr of the two vehicles to achieve stability following the vehicle in front the goal .
In the condition that the preceding vehicle cuts out of the own vehicle's lane when the primary vehicle has not cut out of the own vehicle's route, the own vehicle is in the following mode of following the preceding vehicle's acceleration and deceleration conditions, the three parameters of PID control and the absolute value of the deviation E2 and the two The  Drive/Brake module. The opening degree or desired brake pressure is output to the vehicle model to control the vehicle to realize the cruise control function. When the vehicle is in the following cruise mode, the expected safe distance calculated by the safe distance calculation module Safe Distance and the actual distance between the two vehicles are calculated and then input to the FC Fuzzy PID control module. The deviation between the deviation and the relative speed of the vehicle and the vehicle in front, calculate the expected acceleration of the output vehicle, convert the expected acceleration into the vehicle's expected throttle opening or expected brake pressure through the Drive/Brake module to the vehicle model, and control the vehicle to achieve follow cruise Function.

Research on Cruise Control
The cruise control simulation is divided into two working conditions, namely acceleration and deceleration of the vehicle to the specified cruising speed. The specific simulation conditions are as follows.

Simulation of Acceleration Conditions
Set the vehicle's initial speed to 50Km/h and the target cruising speed to 100km/h. Carry out a cruise simulation of the vehicle at a constant rate. The obtained speed and acceleration curves are shown in Figure 16.

Figure 16 Vehicle Speed Change Curve (Left) and Vehicle Acceleration Variation Curve (Right)
It can be seen from Figures 22 and 23 that the speed of the vehicle is 50km/h at 0s, and it starts to accelerate from 0s, and after 10s, the speed increases from 50km/h to 100.6km/h, and then quickly falls back to 100km/h. The acceleration process After completion, the vehicle continues to drive at a speed of 100 km/h. The vehicle's acceleration increases from 0 to 1.69 m/s2 at the moment of acceleration. After experiencing a small fluctuation, the acceleration remains unchanged at 1.39 m/s2 until the end of the acceleration process, and the acceleration quickly drops to -0.1 m/s2, and then returns to 0 m /s2 and remains unchanged, the acceleration change corresponds to the speed change trend, and is consistent with the expected acceleration curve. During the whole process, the speed change is relatively stable.
Although the acceleration fluctuates, the amplitude is small. The maximum peak value of the acceleration is 1.69 m/s2, and the minimum peak value is -0.1m/s2, so the driver's driving comfort is also guaranteed.

Simulation of Deceleration Conditions
Set the initial speed of the vehicle as 100km/h and the target cruising speed as 80km/h, and simulate and analyse the vehicle. The curve of vehicle speed and acceleration obtained under this condition is shown in Figure 17.

Figure 17 Vehicle Speed Change Curve (Left) and Vehicle Acceleration Variation Curve (Right)
It can be seen from Figures 24 and 25 that the vehicle starts to decelerate from 0s, the deceleration process lasts for 6.7s, and the vehicle speed decreases from 100km/h to a minimum of 79.6km/h, after which the vehicle speed slightly recovers to 80km/h and remains stable at 80km/h. h Do a uniform linear motion. The vehicle's acceleration decreased from 0 to -0.88m/s2 at the moment of deceleration and then slightly recovered to -0.86 m/s2 and remained unchanged to 6.7s. During this process, the vehicle continued to decelerate. After 6.7s, the acceleration began to pick up, and at 7s, the acceleration rose to the highest point of 0.15m/s2, and then gradually decreased to 0m/s2, and remained unchanged. The acceleration variation trend corresponds to the velocity variation trend and fits well with the expected acceleration variation. During the whole process, the vehicle's acceleration is not lower than -1m/s2, which ensures the vehicle's comfort.

Follow-Up Cruise Research
The following cruise simulation mainly considers the acceleration and deceleration of the following target vehicle. At this time, the vehicle's initial speed is set to be 30km/h. From 0s, the vehicle follows the motion state of the target vehicle and automatically adjusts the motion state of the vehicle to follow the target vehicle. The simulation time is in the 70s, and the simulation conditions are shown in Figure 18. Figure 19 shows the motion of the target vehicle in the Carsim software.    It can be seen from Figure 20 that there is no vehicle in front of the vehicle at the beginning, and the value returned by the ranging radar is -1. After the vehicle travels at a speed of 80 /ℎ for 5 , the vehicle radar detects that the front vehicle cuts into the lane at 30 ahead, and the vehicle immediately decelerates. The speed decreases to 70 /ℎ at 11.3 . After driving at a constant rate of 9.6 , the vehicle accelerates. At 30.06 , the vehicle accelerates to 80 /ℎ. The car's speed is the same, and finally, the two vehicles move together at a constant speed in a straight line at the same speed. During this process, the distance between the car and the car in front increases. When the rate of the two vehicles is the same, the distance between the car and the car in front is 79.19 ; keep this spacing the same. The positive and negative acceleration of the vehicle reflects the changing trend of the speed. The acceleration is consistent with the expected acceleration curve. Although there are fluctuations in the middle, it is small, and the duration is short. The acceleration and expected acceleration curves indicate that the controller has good followability. The maximum peak value of acceleration is 0.31 / , and the minimum peak value is -0.5 / , so the driver's riding experience will be more comfortable.

Conclusions
In this paper, the fuzzy PID control theory is used to study the longitudinal driving ACC system of the vehicle, mainly including the research on domestic and foreign adaptive cruise technology research and the explanation and analysis of its advantages and disadvantages.
Models of vehicle engine, torque converter and automatic transmission are established in Carsim software to participate in the simulation. A fuzzy PID control algorithm is designed and tested under three working conditions, and good feedback is obtained.