DOI: https://doi.org/10.21203/rs.3.rs-2361698/v1
To determine how the anti-lock braking system is implemented, it is necessary to examine how the wheels can be prevented from locking. Depending on how the car's transmission system is designed in braking conditions, if one of the car's wheels has a higher or lower rotational speed than the other wheels, that wheel may be locked. So the first step is to check the condition of each wheel in braking mode. For this purpose, automotive engineers turn to electronics and study the conditions of each wheel using sensors mounted on each wheel. In the next step, the engineers take the wheel out of the critical state by changing the force from the brake. That is, if a wheel spins at a slower speed than other car wheels in braking mode, by reducing the braking force on this wheel, its rotational speed will increase, and the wheel will exit the critical state. In the other case, if a wheel spins faster than other car wheels in braking mode, the rotational speed can be reduced by increasing the braking force on that wheel to get the wheel out of the critical state. The anti-lock braking system (ABS) improves vehicle control during abrupt braking, especially on slippery road surfaces. The purpose of such control is to increase the tensile force of the wheel in the desired direction and, at the same time, the appropriate stability and strength of the vehicle and also to reduce the stopping distance of the vehicle. In this paper, an optimal fuzzy controller is presented. The functional purpose of the anti-lock braking system is to optimally maintain the wheel slip to achieve maximum wheel traction and maximum vehicle deceleration.
Control theory commonly uses an explicit mathematical (analytical) model. It uses a process controlled by a closed-loop controller This approach will suffer if the model is difficult to obtain or (section of it) is unknown or highly nonlinear[1, 2].
This paper presents the design of a fuzzy logic controller (4 inputs _4 outputs _11 fuzzy rule) for ABS brakes. The system is nonlinear, and a quarter of the car is modeled. The simulations showed that a fuzzy controller in combination with fuzzy decision logic for estimating road conditions is a fast and effective means of providing brake torque control over operating conditions ranging from dry road to icy road. It turned out that this controller is quite resistant and is not very sensitive to internal and external noise signals (rough road). The least-squares do the first optimization on the controller. The response time of the fuzzy controller to sudden changes in road conditions is compared with model-based adaptive control programs. This paper presents a fuzzy logic controller for an anti-lock braking system [3].
The controller discussed in this paper is genetic neural fuzzy. The proposed controller has two components: a) Irrational neural optimizer (uses vehicle acceleration as input and detects wheel slippage based on the road surface). B) Genetically tuned fuzzy logic (to generate braking torque so that natural wheel slip detects reference slip). This paper optimized the adjustment by fuzzy logic controller genetic algorithm, and the anti-lock braking system was significantly improved [4].
This paper, aims to keep the wheels from slipping to obtain the maximum tensile force of the wheel and the maximum vehicle speed reduction. This paper presents an optimized fuzzy controller. All components of the fuzzy system are optimized using a genetic algorithm, and this controller has fast convergence and good performance. The input variable controls the wheel speed and acceleration of the vehicle. Fuzzy controller rules are of TSK type, and the controller is optimized using genetic algorithm and error-based optimization technique. In order to obtain the optimal value in a shorter time and a much wider area, the error-based optimization method is used and shows a much faster response than the genetic algorithm. However, in this paper, the values of the main parameters of the system dynamics were not present [5].
There are many studies on the car braking system that depend on the mathematical modeling of the system, but the overall behavior of the drivers is more influential than the exact mathematical model. The vehicle is a nonlinear system, so it is not easy to find a mathematical model. Thus, fuzzy logic has been used to develop automation control because fuzzy mimics the performance of a skilled human operator in language tulips that do not require the use of a mathematical model. The fuzzy system is potent and effective for controlling uncertainties and nonlinear systems such as the braking system [6]. Due to the fact that braking systems are used in various vehicles, for example, the automatic braking system of a train must have a precise and fast response. In the semi-automatic system that controls the train system in human hands, there is a possibility of error in applying the right amount of brake power. In order to deal with this concern, an automatic braking system based on fuzzy logic is designed to stop the alignment of the train. According to this paper, an attempt has been made to implement the subway train braking system based on fuzzy logic. Mamdani (Min-Max) type fuzzy logic based controller is developed using MATLAB simulation in fuzzy logic toolbox [7].
In paper, an anti-lock braking system based on fuzzy logic is developed and optimized to deal with changes in road conditions. Conventional control systems must be adjusted by performing simulations and testing on different surfaces before using them. As such, large amounts of computational and experimental time are required which is one of the main challenges of this paper [8].
The fuzzy system is quite powerful and effective for controlling the braking system, and the Mamdani method is acceptable due to its extensive expert knowledge. Mamdani is one of the types of fuzzy inference methods. In Mamdani inference, if and then are defined as law [9].
A fuzzy inference system is a computing framework based on fuzzy set theory concepts. It can be applied in many fields such as control, decision support, system identification, prediction, etc. It is mainly due to the closeness to human perception and reasoning and their intuitive handling and simplicity, which are important factors for the acceptance and usability of the systems [10].
One of the innovations of this paper is a large number of belonging functions, despite which more situations are under control, and because the optimal braking force is used, then the braking system is one of the essential Car safety systems that are less prone to breakdowns, including overheating of the pads.
Generally, the car brake system operates manually because the driver needs to press the brake pedal. If the brake fails, the result can also be destructive. In recent years, research has been done to develop the brake system. Brake improvements have led to more excellent driving safety
The car braking system is essential. Generally, the car brake system operates manually because the driver needs to press the brake pedal. If the brake fails, the result can also be destructive. In recent years, research has been done to develop the brake system. Brake improvements have led to more excellent driving safety.
The car brake system is the most important safety system installed in vehicles. This paper presents an automatic braking system using Mamdani fuzzy logic control. This car braking system consists of two inputs and one output. Inputs are vehicle position and vehicle speed. The vehicle's position indicates the vehicle's distance from the detected obstacle, and the speed indicates the speed of the vehicle towards the obstacle. The output of the brake system indicates the force of the vehicle to stop the vehicle. Inputs use five belonging functions, and outputs use three belonging functions. The designed car braking system uses twenty-five fuzzy rules. The brake function can be checked in terms of distance and speed of obstruction to prevent an accident.
Due to the dynamics of the engine, the slip of the wheels and the friction of the car are ignored, and only Newton's second law is used, and the acceleration that causes the force is calculated based on it [11].
|
\(v={F}_{x}∕m\) |
(1) |
|---|---|
|
\(K\omega =(R{F}_{x}-Tb)/J\) |
(2) |
|
\({F}_{x}= \mu \lambda {F}_{z}\) |
(3) |
|
\({\lambda }=\text{v}-{\omega }\text{R}∕\text{v}\) |
(4) |
|
\(F=m.a=m.\ddot{y}\) |
(5) |
|
\(Ke=\frac{1}{2} .m.{v}^{2}\) |
(6) |
|
\(W=F.y\) |
(7) |
|
\(\frac{1}{2} .m.{v}^{2}=F.y \to F=\frac{m.{\dot{y}}^{2}}{2.y}\) |
(8) |
In the equations, \(Ke\)(Newton) is the kinetic energy, and \(W\)(Joule) is the amount of work.
The values of the car brake system parameters are as follows:
Car mass: 2000 kg
Position of the car to start the brake: -30 meters
Initial car speed: 10 km / h (2.7 m / s)
Car braking force: 9263 Newtons
According to the system's dynamics, the maximum braking force is limited to 9263 Nm, and the maximum speed is 100 km/h, and the maximum distance of the vehicle to the obstacle is 60 meters.
Many studies on the car brake system depend on mathematical modeling, but the actual behaviors of drivers depend more on experience than on exact mathematical modeling. The vehicle is a nonlinear system, so it is not easy to find a mathematical model. Thus, fuzzy logic has been used to develop automation control because fuzzy logic follows the performance of a skilled human operator in linguistic terms that do not require a mathematical model.
The fuzzy system is quite powerful and effective for controlling the braking system, and the Mamdani method is acceptable due to its extensive expert knowledge. Mamdani is one of the types of fuzzy inference methods. In Mamdani inference, if and then is defined as the law. The fuzzy output set of each rule is reshaped with a matching number, and after aggregation of all these fuzzy sets is deformed, it is necessary to resize. The fuzzy inference system is a computational framework based on the concepts of fuzzy set theory.
The way it works is that to design the fuzzy controller of this system, two parameters of car position and speed are considered as input, and the output will be equal to the braking force. Now we start designing the controller using MATLAB fuzzy toolbox. First, we start from the car's position, and according to the paper, we consider five attribution functions for it, the information of which is in the table below. The position's value is from zero to sixty meters, and the range of changes of the affiliation functions is from zero to one. In order to improve the fuzzy speed, the Gaussian function (gauss 2mf, gauss mf) has been selected as the affiliation function. Value periods are obtained based on system dynamics and coding in MATLAB Simulink and fuzzy rules.
Table I. Functions belonging to vehicle position and periods
|
state |
symbol |
period |
|---|---|---|
|
Very near |
VN |
[3.14 -9.28 3.14 4.72] |
|
Near |
N |
[3.4 17.4] |
|
Medium |
M |
[3.9 27.4] |
|
Far |
F |
[2.95 37.25] |
|
Very far |
VF |
[4.17 50.95 10.2 63.29] |
The next input is the vehicle speed, which is from zero to one hundred kilometers per hour, and for that, we consider five belonging functions, which are as follows with the periods.
Table II. Functions of vehicle speed and periods
|
state |
symbol |
period |
|---|---|---|
|
Very slow |
VS |
[17 -18.13 2.96 8.7] |
|
Slow |
S |
[6.5 27.7] |
|
Medium |
M |
[10 42] |
|
Fast |
F |
[6.6 53] |
|
Very fast |
VF |
[6.11 69.07 0.812 112.2] |
Finally, the control system's output, which is the braking force and its maximum value is based on the system dynamics, is 9263 N, and three attribution functions are considered for it.
Table III. Functions of vehicle speed and periods
|
state |
symbol |
period |
|---|---|---|
|
Small |
S |
[660 2520] |
|
Medium |
M |
[1250 4630] |
|
Big |
B |
[999 5999] |
Now, use the MATLAB fuzzy toolbox and set it to Mamdani inference, with input and output defined according to its attribution functions. 25 rewrites fuzzy rules for it, and because there were only 10 rules for this system, you had to act on all the rules.
(9)\(\text{I}\text{f} \left(\text{c}\text{a}\text{r} \text{p}\text{o}\text{s}\text{i}\text{t}\text{i}\text{o}\text{n} \text{i}\text{s}\dots \right) \text{A}\text{n}\text{d} \left(\text{c}\text{a}\text{r} \text{s}\text{p}\text{e}\text{e}\text{d} \text{i}\text{s}\dots \right)\dots\)\(\text{t}\text{h}\text{e}\text{n} \left( \text{b}\text{r}\text{a}\text{k}\text{e} \text{f}\text{o}\text{r}\text{c}\text{e}\right)\)
Figure 3 is part of the fuzzy rules view in the fuzzy Toolbox of MATLAB software.
Figure 4 shows the values of the vehicle position and its speed and braking force using Mamdani fuzzy logic. According to the results obtained from MATLAB, if the car's position is 44.31 meters and its speed is 71.36 kilometers per hour, the amount of braking force will be 6000 N.
This section aims to simulate the car braking system using Mamdani fuzzy logic control. Figure 6 shows a three-dimensional display of fuzzy logic with inputs and outputs. The braking force varies according to the speed and distance of the vehicle to the obstacle. This system can be created with higher safety by further increasing the number of belonging functions at the input and output.
Designing a reliable and efficient control system for the car braking system is one of the most challenging issues for the car. This paper presents the efficient and reliable design of the car braking system using Mamdani fuzzy logic control. The result is an entirely soft braking system, which means that according to the distance of the car to the obstacle ahead and the speed of the car, the amount of force. The brakes are adjusted and applied to prevent sudden braking that disturbs the comfort of the driver and other occupants of the car, which is why the brakes are said to work safely and smoothly.
Competing Interests
The author(s) declared no potential conflict of interests with respect to the research, authorship and/or publication of this article.
Funding
No funding was received.
Authors’ contribution
M. R. Vazifeh Ardalani was born in Tehran, Iran. He received an M.S. degree in Mechanical Engineering from the Iran university of science and technology, Iran, in 2021; his research interests include machine learning, deep learning, mechatronics, and Robotics.
H. R. Adriani was born in Isfahan Iran on March 10, 1997. He received his B.Sc. in Mechanical Engineering from the Isfahan University of Technology in 2019 and a master of mechanical engineering from the Iran University of Science and Technology in 2022. His current research and interests include: robotics, intelligent control, machine learning, manufacturing, and mechatronics systems.
A. P. Kia was born in Ahwaz, Iran, on April 1, 1997. He received his B.Sc. in Mechanical Engineering from the Shahid Chamran university in 2019 and a master of mechanical engineering from the Iran University of Science and Technology in 2022. His current research and interests include: robotics, intelligent control, machine learning, optimization, and cooperative robots.
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