INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
Overview of Use of PID, Fuzzy Logic, and Model Predictive Control  
in Autonomous Vehicle Systems  
H.G.E.M.R.S.J. Ekanayake1, P.A.I.S. Abejeewa2, W.A.L. Priyankara1,2, Ashan Induranga 1,2  
1 Department of Engineering Technology, Faculty of Technology, Sabaragamuwa University of Sri  
Lanka  
2 Center for Nano Device Fabrication and Characterization (CNFC), Faculty of Technology,  
Sabaragamuwa University of Sri Lanka, Belihuloya 70140, Sri Lanka  
DOI: https://dx.doi.org/10.51244/IJRSI.2025.1210000318  
Received: 02 October 2025; Accepted: 08 October 2025; Published: 21 November 2025  
ABSTRACT  
This review article provides a brief overview of the applications of Proportional – Integral – Derivative (PID),  
Fuzzy Logic, and Model Predictive Control (MPC) technologies in the autonomous vehicles industry. PID is a  
popular control method used in various industries because of its simplicity and tuning methods. PID control  
serves as a fundamental building block for many control systems due to its simplicity. Fuzzy Logic control offers  
flexibility and robustness to handle uncertainties. MPC provides advanced predictive control while working as  
a cutting-edge control strategy. This paper tried to develop an overview of the use of the above-mentioned  
technologies in autonomous vehicle speed control, steering control, path following, stability control, and energy  
management in the recent past, while providing a brief introduction to the controlling mechanisms along with  
their history.  
Keywords: Autonomous, Fuzzy logic, MPC, PID, Process control, Robot control  
INTRODUCTION  
Stabilog  
Pre-act and Hyper-reset  
Fulscope  
Proportional and reset controls  
Proportional – Integral (PI) controller  
PID Controller  
Self and Auto tuning Proportional-  
Integral-Derivative Controller (PID)  
Figure 1: The development of PID controlling technology in the past decades  
Page 3685  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
A brief history of PID technology  
PID technology has a very long history. N. Minorsky first introduced the concept of PID controlling technology  
by analyzing the ship steering problem and proposing a mathematical model for automatic control [1]. Taylor  
layered a great foundation on PID technology with their “Fulscope” pneumatic controller in 1939 [2]. In the next  
decades, this controller developed its function according to the following Figure 1.  
Introduction to PID technology  
Figure 2 : Closed loop control system with an PID controller  
A PID controller operates in a closed-loop control system, as given in Figure 2.  
According to Figure 2, the PID controller observes the error between the process variable and the set point. Then,  
it generates the controlling signal and provides it to the process to minimize the error. The controller's output is  
derived from the sum of three distinct components called proportional, integral, and derivative modes [3], [4].  
The controlling signal can be expressed as “Equation (1)”.  
( )  
u(t) = K e(t) + K  
( )  
+ Kd  
(1)  
∫
i
p
0
Where Kp is the proportional gain. Ki is the integral gain. Kd is the derivative gain, where e(t) and u(t) are errors.  
The proportional term is directly proportional to the present error of the system. It takes necessary actions to  
correct the real-time error. However, the only use of proportional terms can’t remove the steady state error that  
can occur in the process.  
The integral controller has the ability to correct the error that occurred past by integrating. This eliminates the  
steady-state error and reduces the system’s error by considering its average error over the past time. However,  
the use of integral mode along with proportional mode can lead to overshoots and oscillations. A derivative  
controller can be employed to reduce overshoots and unnecessary oscillations. The derivative mode is responsive  
to the rate of change of the error, which predicts future errors and corrects them.  
Fuzzy logic controlling  
1). A brief history of fuzzy technology:  
Fuzzy logic was first introduced in 1965 by Prof. Lotti Zadeh, who is a mathematician, computer scientist, and  
electrical engineer [5]. Later, he published works such as ‘ARationale for Fuzzy Control’ in 1972 and ‘Linguistic  
Approach’ in 1973, which layered a strong foundation for other researchers in this field [6]. In the next decades,  
this topic improved very well, and hardware was also developed as fuzzy logic controllers beyond the  
mathematical concept developments [7].  
2). Introduction to Fuzzy Logic:  
Fuzzy logic is a popular controlling mechanism used in different fields, such as automotive systems, robotics,  
and industrial process systems. Fuzzy logic can be identified as an extended version of Boolean logic. In the  
Boolean systems, it only represents two states called 0 and 1, or OFF and ON, or LOW and HIGH. However,  
the main drawback of the Boolean system is that it cannot be used to represent states such as VERY LOW,  
Page 3686  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
PARTIALLY LOW, MEDIUM, PARTIALLY HIGH, and VERY HIGH states that are between the LOW to HIGH  
(0 to 1) states. As a solution, these system variables are presented as a value between 0 and 1 [8], [9].  
Fuzzy  
controller  
Rule base  
Interference  
Fuzzifier  
Engine  
Defuzzifier  
Crisp control  
signal  
Process  
output  
Controlled  
Process  
Figure 3 : Fuzzy logic system architecture  
In fuzzy logic control, there are four major components to follow, as given below.  
i) Fuzzification: The system variable is converted into a fuzzy variable.  
ii) Rule-based: This component involves the rule setting. The rule settings are mostly followed by the IF-THEN  
function.  
iii) Inference engine: This component applies the fuzzy rules to the fuzzy input values to produce fuzzy outputs.  
iv) Defuzzification: The fuzzified values are converted again to the system variable values.  
Technical considerations in Fuzzy logic control  
When applying fuzzy logic to autonomous vehicle control, the design of membership functions, rule base,  
inference mechanism, and defuzzification method critically affects performance.  
i) Membership function design: It defines how continuous inputs, such as steering error, lateral deviation, or  
speed error, map to fuzzy sets [10].  
ii) Rule-based construction: The rule base dictates how the controller responds to different conditions using  
linguistic IF-THEN statements. Increasing the number of rules generally improves control precision but also  
increases computational burden [11].  
iii) Inference mechanism: The Mamdani inference method is commonly used in automotive fuzzy control due  
to its intuitive reasoning and continuous implementation. It combines rules using fuzzy AND/OR operations and  
aggregates the outputs.  
iv) Defuzzification strategy: After inference, fuzzy outputs must be converted to crisp actuator signals. There  
are different methods, including Centroid and Mean of Maximum Bisector.  
In centroid, it provides smooth output but is computationally heavier. The mean of the maximum method is  
simpler but potentially less precise. In many vehicle control applications, the centroid method is used because  
of its accuracy, even at the cost of some computation [12].  
Model predictive control (MPC)  
1). A brief history of MPC:  
The controlling methods, such as PID and Fuzzy logic, are not self-tuning; instead of incorporating them are  
incorporated with some developments for self-tuning. The foundation for MPC was first laid in the 1970s and  
Page 3687  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
1980s by several research studies. The survey conducted by Garica et al. analyzed several MPC techniques  
available in the 1980s. This study has analyzed the MPC relation to linear quadratic control as well [13]. Keyser  
et al. also conducted similar research by comparing the available long-range MPC techniques by comparing  
them with each other [14].  
In the next decades, several researchers introduced and developed the MPC to the present level by introducing  
features such as Constrained receding-horizon predictive control [15]and the use of long-range (LR), long-range  
quadratic programming (LRQP), and quadratic programming (QP) methods along with MPC to handle input and  
output constraint controlling [16].  
2). Introduction to MPC  
MPC is the complex and precise control method used in feedback control systems. The main advantage of this  
method is that it can be used with multi-input output systems while maintaining constraints. MPC is different  
from PID and Fuzzy logic in future predictive behavior.  
MPC uses a mathematical model to make several predictions to reach the reference value. These predictions are  
made to predict the future behavior of the system over a time horizon in a systematic way. During these  
predictions, the MPC model satisfies the given constraints for both inputs and outputs. This model optimizes the  
mathematical model in order to reduce the cost function of the system.  
MPC functions in accordance with mainly two parameters called the prediction horizon and the control horizon.  
Prediction horizon: The future window that predicts the behavior of the system. A longer prediction horizon  
allows the system to better long-term planning, but it requires higher computational power.  
Control horizon: The control horizon is smaller than the prediction horizon. The control variables are optimized  
within this window to follow a pre-defined path.  
Control function: The cost function represents the amount of errors produced by the system with weighted values.  
In order to improve the performance of the system, MPC always tries to minimize the cost function [17].  
Control  
inputs  
Output  
Process  
MPC  
Model  
Optimization  
Figure 4: MPC system architecture  
A brief history of autonomous technology  
With the developments of electrical and electronic engineering, computing technology, and network systems,  
vehicles have been developed into very advanced systems over the past few decades. The first implication of the  
concept of autonomous technology was introduced in the 1920s with radio-controlled vehicles by the Houdini  
Radio Control Company, which was called the “American Wonder” [18]. This vehicle was operated by radio  
signals from another pilot vehicle. After several attempts and research, the 21st century marked the evaluation  
of autonomous vehicles with many commercially available products. Most of the major vehicle manufacturing  
companies started to spend a considerable amount of money on the R&D activities of autonomous car  
development. The development of autonomous cars was highly contributed to by the development of electrical  
Page 3688  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
and electronic engineering, computing technology, sensing technology, image processing, and artificial  
intelligence, along with its subfields such as machine learning and deep learning. The Google company took a  
good initiative by developing the Google car, which achieved a significant number of miles in 2010 in urban  
areas. After that, there were commercial productions such as Mercedes-Benz S-Class S500 and Tesla Model S.  
Along with these commercial products, Uber and General Motors have developed AV taxi services [19], [20].  
The development of autonomous vehicle technology helps to reduce accidents since there is no possibility of  
conditions such as drunk driving or distractions. However, this reduction can only be successful if this vehicle  
fulfills all the safety requirements along with the advanced controlling techniques with minimum or zero errors  
[21].  
As mentioned in the previous paragraphs, PID is a popular and well-established control method in control  
systems. It has been well developed in autonomous vehicle technology as well, with the integration of techniques  
such as fuzzy logic and artificial intelligence [22]. In the 21st century, these controlling mechanisms have been  
well developed with the introduction of mechanisms such as MPC, Artificial Neural Networks, and Genetic  
Algorithms in autonomous vehicle controlling [23].  
Comparative Evaluation of PID, Fuzzy Logic, and MPC in Autonomous Vehicle Control  
Autonomous vehicle control requires robust, efficient, and adaptive algorithms to handle dynamic environments,  
nonlinear vehicle dynamics, and real-time constraints. PID, Fuzzy Logic, and MPC method offers distinct  
strengths and limitations. The comparative table provides an analysis of each of the methods in comparing of  
complexity, real-time feasibility, nonlinear handling, and predictive ability.  
Table 1: Comparative summary table  
Feature  
Complexity  
PID  
Fuzzy Logic  
Medium  
MPC  
High  
Low  
High  
Real-time feasibility  
Nonlinear handling  
Predictive ability  
Best for  
Medium  
Limited  
Strong  
Strong  
Weak  
Strong  
None  
None  
Basic control, Speed  
Uncertain environments  
Steering, stability,  
optimization  
Hybrid and AI Augmented Control for Autonomous Vehicles  
Recent research increasingly focuses on hybrid and AI-enhanced control strategies that combine the strength of  
classical control methods, such as PID and MPC, with intelligent methods. Hybrid and AI-enhanced methods  
are:  
Fuzzy-PID hybrid controllers: Fuzzy logic can dynamically adjust the gains Kp, Ki, and Kd of a PID controller  
based on driving conditions, improving adaptability and performance under varying vehicle conditions and  
uncertainties. Studies have shown that fuzzy-PID controllers achieve reliable, superior response time and  
stability in lane-keeping tasks [11].  
Fuzzy-MPC for adaptive cruise control: In adaptive cruise control systems, a fuzzy-MPC framework has been  
proposed that adapts weighting factors in the MPC objectives based on driving conditions. This enables real-  
time interchange between safety, comfort, and energy efficiency [24].  
Page 3689  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
Neural- Fuzzy and Learning based controllers: These types of controllers have been designed for steering control  
in vision-based unmanned vehicles, improving robustness under parametric uncertainty and external  
disturbances [25].  
PID for Speed Control of Autonomous Vehicles  
PID controllers play a crucial role in maintaining precise speed control for autonomous vehicles. Research by  
Tagor Hossain et al. [26]demonstrates their application in adjusting the throttle pedal position based on the  
calculated velocity error. This ensures the vehicle adheres to the desired speed profile, contributing to overall  
trajectory tracking performance, especially when navigating sharp curves.  
The design of a speed controller within the path-tracking system highlights how the controller utilizes vehicle  
dynamics and trajectory data to regulate the vehicle's speed while following a predefined path. Another study  
[27] explores optimizing PID controller performance for speed control. This research investigates the use of  
metaheuristics like genetic algorithms to achieve this. Optimizing PID parameters minimizes factors like  
overshoot, settling time, and steady-state error, leading to a high level of control accuracy and stability for  
autonomous vehicles.  
The speed control is based on the integration of vehicle dynamics into the control system, where the dynamic  
model of the vehicle influences the speed adjustments to ensure accurate path tracking. Lu et al. [28] discuss the  
development of a Personalized Behavior Learning System (PBLS) for Human-Like longitudinal speed control  
in autonomous vehicles, focusing on improving motion planning in complex traffic environments. The study  
highlights the importance of personalized adaptation in motion planning to enhance driving smoothness,  
comfort, and human-like behavior in autonomous vehicles, aiming to increase their acceptance by considering  
human personalities. The process of reproducing observed real driving scenes in PreScan using collected real  
driving data emphasizes the integration of real-world driving behaviors into the simulation environment for  
training purposes.  
The PID controller is utilized to generate control commands for throttle and brake systems based on the output  
of the controller. The PID controller output is converted into throttle and brake control commands through a  
conversion block embedded in PreScan, known as the 'Path follower' module. Real driving data is collected and  
used to train the PBLS in PreScan for speed control applications. The PID controller is tested in a simulation  
platform built by PreScan and MATLAB /Simulink for evaluating the performance of the proposed learning  
system in speed control applications.  
The paper proposes a novel coupled lateral and longitudinal controller based on MPC for autonomous vehicles.  
An 8-degree-of-freedom (DOF) vehicle model is used as the prediction model, while a 14-DOF vehicle model  
is employed as the plant model. The MPC controller determines the optimal road-wheel steering angle for lateral  
control, and a PID controller is embedded in the solution to regulate the total driving or braking wheel torque  
for longitudinal control. The PID controller is utilized for longitudinal dynamics control in the proposed system.  
In the suggested system, longitudinal dynamics are controlled using a PID controller. It regulates the overall  
driving or braking wheel torque based on the difference between the target and the actual speed of the vehicle.  
The PID controller assists in keeping the vehicle's speed near to the intended speed by changing the acceleration  
and braking input signals as needed. The research accomplishes effective speed control by incorporating the PID  
controller within the MPC framework and considering time-varying speed profiles in the path-tracking process  
[29].  
Tiwari et al. [30] implement a PID controller for both lateral and longitudinal control of the autonomous vehicle.  
The longitudinal control module focuses on maintaining the speed profile of the vehicle, integrating both lateral  
and longitudinal controllers for improved performance in various terrains and speeds. The PID controller in the  
longitudinal control system generates acceleration commands for the upper-level controller, which then  
translates these commands into throttle and brake inputs for precise vehicle tracking and utilizes feedback control  
mechanisms to adjust the vehicle's acceleration based on deviations from the desired speed profile, thus aiding  
in achieving accurate speed tracking.  
Page 3690  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
PID For Steering and Stability Control of Autonomous Vehicles  
PID control is a valuable tool for steering control in autonomous vehicles. One study [31] emphasizes its role in  
maintaining stability and smoothness during maneuvers, ensuring the vehicle stays centered within the lane  
boundaries. This control mechanism is crucial for both software simulations and hardware testing of autonomous  
vehicles.  
Beyond basic steering control, advanced techniques utilizing PID controllers have also been explored.  
Furthermore, research by Chunjiang Bao et al. [32] discusses the use of adaptive PID control algorithms for path  
tracking in unknown environments. This approach demonstrates the adaptability of PID control for various  
steering control scenarios in autonomous driving.  
A PID controller that enables track maneuvering for self-driving cars is proposed by Farag et al. [33]. Three  
distinct design approaches are employed to identify and optimize the controller hyperparameters. One of these  
is "WAF- Tune," an ad hoc trial-and-error technique proposed in this research for this particular application. The  
suggested controller accepts only the cross-track error as an input and outputs the steering command. Extensive  
simulation studies on complex tracks with many sharp curves were conducted to assess the performance of the  
proposed controller at various speeds. The analysis demonstrates that the proposed strategy outperforms the  
others. The utility and limitations of the suggested tuning mechanism are also examined in detail.  
The PID controller in one of the research [34] showed varying performance compared to other controllers like  
PD and MPC. In the closed-loop steering performance evaluation with jacked front wheels, the PID controller  
had a steady state error exceeding 2%. This indicated that the PID controller struggled more with maintaining  
the setpoint accurately. During on-road testing at 1 km/h, the PID controller performed with an error below 2%,  
showing a relatively higher error compared to the PD controller. At higher speeds, such as 2 km/h, the PID  
controller outperformed the PD controller, which initially experienced instability but eventually recovered.  
However, the PID controller still exhibited some unstable responses. The PID controller's power consumption  
was noted to be the lowest in a specific scenario compared to the PD and MPC controllers. As the sampling time  
of the controller decreased to -0.002 seconds, the PID controller's performance degraded compared to PD and  
MPC controllers, indicating that lower sampling times impacted its performance significantly. It is important to  
note that while the PID controller showed lower power consumption in certain scenarios, it struggled with  
achieving precise setpoint control in comparison to the other controllers tested in the research.  
PID control contributes significantly to stability control in autonomous vehicles. A study conducted by Lin et al.  
[35] explores the application of PID controllers in maintaining roll stability using a fuzzy PID algorithm.  
The PID controller is integrated into the fuzzy PID control framework to regulate the lateral transfer ratio (LTR)  
and ensure vehicle roll stability by controlling the braking cylinder pressure of each tire. This approach combines  
the strengths of fuzzy control and PID control to provide robustness, fast response, and the ability to handle  
nonlinearities, all crucial for maintaining vehicle stability. This application emphasizes the role of PID  
controllers in enhancing safety for autonomous vehicles. The study by Tingting Wang et al. [36] investigates the  
use of PID controllers within an adaptive fuzzy control algorithm to ensure the stable operation of AGVs. This  
approach utilizes dynamic modeling and parameter analysis to design the steering control system for AGVs,  
achieving stable operation after optimization. This demonstrates the effectiveness of PID control in enhancing  
in-situ steering stability for specific types of autonomous vehicles. The PID controller is embedded into the  
system to analyze and enhance the stability of the AGV during steering operations by regulating the steering  
dynamics and minimizing deviations in the rotation center.  
Motion sickness (MS) is caused by inappropriate wheel turning, causing significant lateral acceleration and  
increased head movement. Passengers tilt their heads toward the direction of lateral acceleration, causing an  
increment in MS. The study proposes a fuzzy-proportional integral derivative (PID) controller for an MS  
minimization control structure, focusing on lateral acceleration and head tilt to reduce lateral acceleration. The  
control uses head movement as a controlled variable for corrective wheel angle computation. An experiment  
using a driving simulator confirmed the system's performance, reducing motion sickness incidence by 3.95% for  
single laps and 11.49% for ten laps [37].  
Page 3691  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
The paper employs a multi-objective digital PID controller design method using the parameter space approach  
of robust control. It starts by focusing on absolute stability, ensuring that the closed-loop poles remain inside the  
unit circle in the digital PID controller parameter space. Additionally, the design considers phase margin, gain  
margin, and a mixed sensitivity bound as frequency domain constraints to enhance controller performance and  
robustness. An example illustrating the application of this method in path following controller design for an  
automated driving vehicle is provided, showcasing the practical utility of the proposed approach [38].  
The paper proposed a novel method for steering control in autonomous vehicles, utilizing type-2 fuzzy logic  
control combined with PI control. This primary control system had inputs of distance, navigation, and speed,  
with the output being the steering angle value. This output was then used as input for the secondary control, PI  
control, which adjusted the motor's position based on the steering angle. The study results demonstrated that  
type-2 fuzzy logic control and PI control provided better and smoother control compared to type-1 fuzzy logic  
control and PI. Type-2 fuzzy logic control showed more robustness to disturbances, resulting in smoother turning  
angle control and shorter response times. The secondary control, PI control, played a crucial role in adjusting  
the motor's position to manifest the steering angle. It ensured that the motor response closely followed the output  
of the fuzzy logic control system, leading to fast and precise control responses. Additionally, the paper explored  
the use of PD and PID controls in conjunction with type-2 fuzzy logic control. The results showed that while  
PID control responded faster initially, PD control was better at maintaining the expected values over time [39].  
The research uses a Proportional-Integral-Derivative (PID) controller paradigm to provide longitudinal trajectory  
tracking in autonomous electric vehicles using the CARLA simulation environment. A three-level iterative  
testing approach is used to assess the performance of the developed controller. This method involves modifying  
the controller's error definition and proportional gain to determine its stability and accuracy. To assess the  
controller's performance, a sequence of ten increasingly oscillating trajectories is employed to disturb the control  
process. This testing method aids in determining how well the controller can handle various tough conditions.  
The study undertakes an investigation of several error ratio definitions to examine their impact on the controller's  
effectiveness [40].  
PID for Path Following of Autonomous Vehicles  
PID controllers are instrumental in achieving accurate path following for autonomous vehicles. Acore study [41]  
investigates the use of a PID controller with three different tuning approaches for steering an autonomous car  
along a pre-defined track. The controller utilizes Cross-Track Error (CTE) as input and generates steering  
commands as output, enabling the car to navigate complex tracks with sharp turns. The Path Tracking Controller  
(PTC) of autonomous vehicles also utilizes PID control. As highlighted in another research [42], the PTC acts  
as an interface between the vehicle's dynamic behavior and the path planner, using sensory feedback to  
implement accurate path tracking. Additionally, research by Chunjiang Bao et al.[32] discusses the use of a  
nested PID steering control algorithm for path-tracking experiments on roads with uncertain curvature. This  
showcases the effectiveness of PID control in various path-following scenarios for autonomous vehicles. PID  
controllers are extensively applied in autonomous vehicles, particularly in Automated Guided Vehicles (AGVs)  
[43]. The study utilized Particle Swarm Optimization (PSO) to optimize the PID controller parameters for each  
motor of the AGV, enhancing route-tracking performance. By adjusting 12 parameters based on the error  
between reference and actual motions, the PSO algorithm determined optimal PID coefficients for each motor,  
ensuring efficient control input generation. This optimization process facilitated the adjustment of AGV motion  
by correlating wheel angular velocities with motor control input voltages, resulting in successful route tracking  
with fast response and strong stability.  
Holovatenko et al. [44] implemented PID controllers for each wheel of a two-wheel AGV, with parameters such  
as an overshoot of 0% and fast settling time. The PID controllers were constructed with specific P, I, and D  
constants for both the left and right wheels. By utilizing PID controllers in AGVs, the system can effectively  
regulate the movement of the vehicle, ensuring precise trajectory tracking with minimal energy consumption.  
The PID controller is used for comparison with the SDC-NMPC controller to evaluate performance, showing  
that the SDC-MPC outperforms the PID controller in handling complex tracks with sharp turns. The PID  
Page 3692  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
controller is employed in the SDC system for offline training of the neural network before adaptive nonlinear  
MPC approach testing, where data is collected from the system running under PID control.  
The PID control strategy is applied to calculate the lateral deviation between the expected and actual path,  
enabling the vehicle to track the desired trajectory effectively [45]. By simplifying the vehicle's structure into a  
two-degree-of-freedom kinematic and dynamic model, the PID feedback control law is utilized to enhance path-  
tracking performance, ensuring safety and stability during operation. This approach improves the speed and  
accuracy of path tracking control, making it suitable for intelligent vehicles operating under safe conditions. The  
simulation results demonstrate that the designed PID control system offers excellent tracking accuracy, real-time  
performance, and driving stability across different speeds, validating its effectiveness in autonomous vehicle  
path-tracking applications.  
Yao et al. [46] propose a trajectory optimization method for autonomous vehicles, focusing on driving efficiency,  
safety, comfort, and handling stability. It addresses issues like vehicle handling stability, model simplification,  
and lack of objective evaluation of comfort. The paper also presents a hierarchical control framework based on  
SMC for enhancing control strategies for autonomous vehicle path tracking. Additionally, the Hamilton  
algorithm-based vehicle yaw rate follow control method is discussed for improving path tracking. In this  
approach, the model parameters are identified through the forgetting factor least squares algorithm, and PID  
control parameters are adjusted using a BP neural network.  
A novel path-tracking approach for autonomous driving addresses the limitations of traditional methods like PID  
controllers and pure pursuit (PP) in another research conducted by Shan et al. [44]. It uses a reinforcement  
learning (RL) model to integrate PID with PP, improving tracking performance and ride quality. The RL model  
includes an actor model trained for smoothness and accuracy in path-tracking tasks. PID directly adjusts to  
tracking errors, reducing lateral errors in path tracking. By adjusting the weight of PID, tracking accuracy can  
be significantly enhanced while maintaining system stability. However, improper weights may amplify jerks and  
oscillate, highlighting the challenge of finding a balance between tracking error and ride quality. The RL model  
effectively addresses the weight-adjustment problem of PID and PP, surpassing traditional manual adjustments  
for optimal performance in path tracking.  
The research paper proposes a comprehensive control method that combines MPC and Fuzzy PID control. MPC  
is utilized to ensure the vehicle's yaw stability during path tracking by considering various factors such as front  
wheel angle, sideslip angle, tire slip angles, and yaw rate. The PID control aspect, specifically the Fuzzy PID  
algorithm, contributes to maintaining the vehicle's roll stability by regulating the braking force applied to each  
tire. The combination of MPC for yaw stability and Fuzzy PID control for roll stability creates a robust and  
effective control system that significantly improves the autonomous vehicle's path-tracking performance [35].  
Two-layer controllers also can be used for accurate lateral path tracking control of autonomous vehicles [47].  
The upper-layer controller consists of a Linear Time-Varying MPC (LTV-MPC) optimized offline with PSO,  
implementing front wheel steering angle control. A constraint on the slip angle is imposed to maintain vehicle  
stability by preventing lateral forces from saturating. The lower layer employs a radial basis function neural  
network proportion-integral-derivative (RBFNN-PID) controller to generate electric current control signals for  
steering motor operation. The nonlinear characteristics of the steering system are modeled and adapted online  
using RBFNN (Radial Basis Function) to adjust PID control parameters. The PID controller outputs the steering  
angle while ensuring accurate lateral path tracking control in autonomous vehicles. By using an RBFNN-PID  
setup, the system can rapidly track the target steering angle by adjusting the electric current signals sent to the  
steering motor.  
The RBFNN helps in identifying the nonlinear characteristics of the steering system so that the PID controller  
can effectively adapt and maintain stability during the path tracking process.  
The paper simplifies the vehicle structure into a two-degree-of-freedom kinematic and dynamic vehicle model  
to design the path-tracking controller based on PID control. This controller calculates the lateral deviation  
between expected and actual paths and outputs the front wheel rotation angle for the vehicle to travel along the  
expected path. The developed PID path tracking controller is used to follow a circular reference path at a speed  
Page 3693  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
of 30 km/h. The results reveal that the front wheel angle changes smoothly, allowing for regular vehicle operation  
and stability during the tracking procedure [48].  
PID For Energy Management of Autonomous Vehicles  
Autonomous vehicles use PID control to optimize energy. Another research article on energy management in  
autonomous vehicles discusses the application of a PID controller in reducing fuel consumption [49]. The PID  
controller is utilized to control the air/fuel ratio by adjusting the throttle angle based on the road power demand  
model, which considers environmental conditions, driver behavior, and vehicle specifications. The intelligent  
energy management system, incorporating a Fuzzy Logic System and the PID controller, aims to optimize engine  
torque generation and air/fuel ratio control to enhance energy efficiency in conventional autonomous vehicles.  
Through simulations, it was demonstrated that implementing this intelligent energy management system led to  
a 6.8% improvement in energy efficiency, showcasing the effectiveness of PID controllers in optimizing energy  
consumption in autonomous vehicles. Phan et al. [50] discuss the application of a PID controller in energy  
management systems for conventional autonomous vehicles, aiming to enhance powertrain efficiency. The PID  
controller is utilized to regulate the throttle of the engine, adjusting the air-to-fuel ratio to produce the desired  
torque based on the optimal torque generated by a neuro-fuzzy system. This system dynamically considers the  
road power demand of the vehicle, leading to improved fuel efficiency. Another great application of the PID  
controller can be identified as being utilized specifically for managing the state of charge (SoC) of the battery in  
the hybrid electric vehicle, ensuring efficient energy utilization and optimal performance [51]. The PID controller  
in this application helps regulate the charging and discharging of the battery to maintain the SoC within desired  
levels, contributing to improved fuel economy and overall system efficiency. By effectively controlling the SoC  
of the battery, the PID application ensures that the energy management system operates optimally, leading to  
enhanced performance and reduced energy consumption in the vehicle.  
Ye et al. introduce a new PID energy management structure optimized using the Particle Swarm Optimization  
(PSO) algorithm, resulting in the PSO-PID energy management strategy [52]. The PID controller is utilized to  
optimize the battery working mode by controlling the power system, aiming to reduce energy consumption while  
maintaining battery operation. Results show that the PSO-PID strategy effectively optimizes battery output  
current, compensates for high-frequency power output with a supercapacitor, and minimizes the total energy  
consumption of the HESS (hybrid energy storage system).  
The PID control strategy optimized by the PSO algorithm effectively reduces the peak current of the battery by  
17.9350 A and 2.1906 A under different simulation conditions, showcasing improved energy efficiency and  
battery protection.  
CONCLUSION AND FUTURE DIRECTIONS  
In this review, the principal control strategies were discussed including PID, Fuzzy logic, and MPC. Each method  
has unique advantages. PID for simplicity and real time implementation, Fuzzy logic for handling uncertainty  
and nonlinearity and MPC for prediction, optimization and constraint management.  
However, no single control methodology enough for all autonomous driving tasks. Hybrid controllers such as  
Fuzzy-PID and Fuzzy-MPC give reliable performance by leveraging the strengths of each underlying controller.  
Based on the studies the future research should focus on developing real time computationally efficient MPC  
solvers for embedded automotive platforms, integrating reinforcement learning with MPC to enable online  
adaption and applying these control strategies to energy efficient autonomous vehicle, where control decisions  
directly impact energy consumption.  
REFERENCES  
1. S. Bennett, “The Past of PID Controllers,” IFAC Proc. Vol., vol. 33, no. 4, pp. 1–11, 2018, doi:  
10.1016/S1474-6670(17)38214-9.  
2. S. Bennett and S. Bennett, “Development of the PID Controller,” no. January 1994, 2017, doi:  
Page 3694  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
10.1109/37.248006.  
3. “PID control system analysis, design, and technology | IEEE Journals & Magazine | IEEE Xplore.”  
Accessed: Nov. 06, 2025. [Online]. Available: https://ieeexplore.ieee.org/document/1453566  
4. L. Objectives, “1 PID Control Technology,” pp. 1–2.  
5. C. W. Liu and S. C. Kang, “A video-enabled dynamic site planner,” Comput. Civ. Build. Eng. - Proc.  
2014 Int. Conf. Comput. Civ. Build. Eng., vol. 353, pp. 1562–1569, 2014, doi:  
10.1061/9780784413616.194.  
6. Y. Dote, “Introduction to fuzzy logic,” IECON Proc. (Industrial Electron. Conf., vol. 1, no. June, pp. 50–  
56, 1995, doi: 10.2298/fuee0502319m.  
7. M. J. Patyra, J. L. Grantner, and K. Koster, “Digital fuzzy logic controller: design and implementation,”  
IEEE Trans. Fuzzy Syst., vol. 4, no. 4, pp. 439–459, 1996, doi: 10.1109/91.544304.  
8. J. M. Mendel, “Fuzzy Logic Systems for Engineering: A Tutorial,” Proc. IEEE, vol. 83, no. 3, pp. 345–  
377, 1995, doi: 10.1109/5.364485.  
9. J. M.ꢀ; Rodríguez-Valderrama et al., “AReview onApplications of Fuzzy Logic Control for Refrigeration  
Systems,” Appl. Sci. 2022, Vol. 12, Page 1302, vol. 12, no. 3, p. 1302, Jan. 2022, doi:  
10.3390/APP12031302.  
10. L. Li, J. Li, and S. Zhang, “Review article: State-of-The-Art trajectory tracking of autonomous vehicles,”  
Mech. Sci., vol. 12, no. 1, pp. 419–432, Apr. 2021, doi: 10.5194/MS-12-419-2021.  
11. M. Samuel, K. Yahya, H. Attar, A. Amer, M. Mohamed, and T. A. Badmos, “Evaluating the Performance  
of Fuzzy-PID Control for Lane Recognition and Lane-Keeping in Vehicle Simulations,” Electron. 2023,  
Vol. 12, Page 724, vol. 12, no. 3, p. 724, Feb. 2023, doi: 10.3390/ELECTRONICS12030724.  
12. R. Saran and S. Praveen, “Steering Control in Electric Power Steering Autonomous Vehicle Using Fuzzy  
Logic Control and Pi Control,” Int. J. Eng. Res. Technol., vol. 12, no. 2, May 2024, doi:  
10.17577/IJERTCONV12IS02054.  
13. C. E. García, D. M. Prett, and M. Morari, “Model predictive control: Theory and practice—A survey,”  
Automatica, vol. 25, no. 3, pp. 335–348, May 1989, doi: 10.1016/0005-1098(89)90002-2.  
14. R. M. C. De Keyser, P. G. A. Van de Velde, and F. A. G. Dumortier, “Acomparative study of self-adaptive  
long-range predictive control methods,” Automatica, vol. 24, no. 2, pp. 149–163, Mar. 1988, doi:  
10.1016/0005-1098(88)90024-6.  
15. “6 Constrained Receding Horizon Controls 6.1,” Constraints, pp. 4–5.  
16. “Algorithms for industrial model predictive control | Request PDF.” Accessed: Nov. 06, 2025. [Online].  
Available:  
https://www.researchgate.net/publication/3363634_Algorithms_for_industrial_model_predictive_contr  
ol  
17. R. Zhang, F. Rossi, and M. Pavone, “Model predictive control of autonomous mobility-on-demand  
systems,” Proc. - IEEE Int. Conf. Robot. Autom., vol. 2016-June, pp. 1382–1389, Jun. 2016, doi:  
10.1109/ICRA.2016.7487272.  
18. G. Heinzelman, “Autonomous Vehicles , Ethics of Progress Autonomous Vehicles , Ethics of Progress  
April , 2019 TMC 592 - Research , Ethical Issues in Technology Prof . Jason Bronowitz Arizona State  
University,” no. April, 2019, doi: 10.13140/RG.2.2.28046.31048.  
19. S. A. Bagloee, M. Tavana, M. Asadi, and T. Oliver, “Autonomous vehicles: challenges, opportunities,  
and future implications for transportation policies,” J. Mod. Transp., vol. 24, no. 4, pp. 284–303, 2016,  
doi: 10.1007/s40534-016-0117-3.  
20. N. Sousa, A. Almeida, J. Coutinho-Rodrigues, and E. Natividade-Jesus, “Dawn of autonomous vehicles:  
Review and challenges ahead,” Proc. Inst. Civ. Eng. Munic. Eng., vol. 171, no. 1, pp. 3–14, 2018, doi:  
10.1680/jmuen.16.00063.  
21. D. J. Fagnant and K. Kockelman, “Preparing a nation for autonomous vehicles: opportunities, barriers  
and policy recommendations,” Transp. Res. Part A Policy Pract., vol. 77, pp. 167–181, Jul. 2015, doi:  
10.1016/J.TRA.2015.04.003.  
22. V. Vartika, S. Singh, S. Das, S. K. Mishra, and S. S. Sahu, “A Review on Intelligent PID Controllers in  
Autonomous Vehicle,” Lect. Notes Electr. Eng., vol. 693 LNEE, no. April, pp. 391–399, 2021, doi:  
10.1007/978-981-15-7675-1_39.  
23. H. Etezadi and S. Eshkabilov, “A Comprehensive Overview of Control Algorithms, Sensors, Actuators,  
and Communication Tools of Autonomous All-Terrain Vehicles in Agriculture,” Agric., vol. 14, no. 2,  
Page 3695  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
2024, doi: 10.3390/agriculture14020163.  
24. J. Mao, L. Yang, Y. Hu, K. Liu, and J. Du, “Research on Vehicle Adaptive Cruise Control Method Based  
on Fuzzy Model Predictive Control,” Mach. 2021, Vol. 9, Page 160, vol. 9, no. 8, p. 160, Aug. 2021, doi:  
10.3390/MACHINES9080160.  
25. J. Guo, K. Li, J. Fan, Y. Luo, and J. Wang, “Neural-Fuzzy-Based Adaptive Sliding Mode Automatic  
Steering Control of Vision-based Unmanned Electric Vehicles,” Chinese J. Mech. Eng. 2021 341, vol.  
34, no. 1, pp. 88-, Sep. 2021, doi: 10.1186/S10033-021-00597-W.  
26. T. Hossain, H. Habibullah, and R. Islam, “Steering and Speed Control System Design for Autonomous  
Vehicles by Developing an Optimal Hybrid Controller to Track Reference Trajectory,” Machines, vol.  
10, no. 6, 2022, doi: 10.3390/machines10060420.  
27. J. E. Naranjo, F. Serradilla, and F. Nashashibi, “Speed control optimization for autonomous vehicles with  
metaheuristics,” Electron., vol. 9, no. 4, pp. 1–15, 2020, doi: 10.3390/electronics9040551.  
28. H. L. Speed, “A Personalized Behavior Learning System for Autonomous Vehicles,” 2区Q1Sensors,  
2019.  
29. G. H. Salih, “Controlling a Longitudinal Autonomous Vehicle Using Modified Particle Swarm  
Optimization,”  
2023,  
[Online].  
Available:  
https://doi.org/10.21203/rs.3.rs-  
3655040/v1%0Ahttps://www.researchsquare.com/article/rs-3655040/v1  
30. M. Rasib, M. A. Butt, F. Riaz, A. Sulaiman, and M. Akram, “Pixel Level Segmentation Based Drivable  
Road Region Detection and Steering Angle Estimation Method for Autonomous Driving on Unstructured  
Roads,” IEEE Access, vol. 9, no. December, pp. 167855–167867, 2021, doi:  
10.1109/ACCESS.2021.3134889.  
31. M. E. Abed, M. Aly, H. H. Ammar, and R. Shalaby, “Steering Control for Autonomous Vehicles Using  
PID Control with Gradient Descent Tuning and Behavioral Cloning,” 2nd Nov. Intell. Lead. Emerg. Sci.  
Conf. NILES 2020, pp. 583–587, 2020, doi: 10.1109/NILES50944.2020.9257946.  
32. C. Bao, J. Feng, J. Wu, S. Liu, G. Xu, and H. Xu, “Model predictive control of steering torque in shared  
driving of autonomous vehicles,” Sci. Prog., vol. 103, no. 3, pp. 1–22, 2020, doi:  
10.1177/0036850420950138.  
33. W. Farag, “Complex Trajectory Tracking Using PID Control for Autonomous Driving,” Int. J. Intell.  
Transp. Syst. Res., vol. 18, no. 2, pp. 356–366, 2020, doi: 10.1007/s13177-019-00204-2.  
34. S. Gokul Krishnan, P. Suresh Kumar, N. Nassar Matara, and Y. Wang, “Real-Time Experimental  
Evaluation and Analysis of PID and MPC Controllers Using HIL Setup for Robust Steering System of  
Autonomous Vehicles,” IEEE Access, vol. 12, no. May, pp. 74711–74723, 2024, doi:  
10.1109/ACCESS.2024.3406219.  
35. “Research on autonomous vehicle path tracking control considering roll stability - Fen Lin, Shaobo  
Wang, Youqun Zhao, Yizhang Cai, 2021.” Accessed: Nov. 06, 2025. [Online]. Available:  
https://journals.sagepub.com/doi/abs/10.1177/0954407020942006  
36. F. A. G. V Based, “Research on Stability Design of Di ff erential Drive,” 2020.  
37. S. A. Saruchi et al., “applied sciences Novel Motion Sickness Minimization Control via Fuzzy-PID  
Controller for Autonomous Vehicle,” Appl. Sci., 2020.  
38. H. Wang, S. Y. Gelbal, and L. Guvenc, “Multi-Objective Digital PID Controller Design in Parameter  
Space and its Application to Automated Path following,” IEEE Access, vol. 9, pp. 46874–46885, 2021,  
doi: 10.1109/ACCESS.2021.3066925.  
39. B. Arifin, B. Y. Suprapto, S. A. D. Prasetyowati, and Z. Nawawi, “Steering Control in Electric Power  
Steering Autonomous Vehicle Using Type-2 Fuzzy Logic Control and PI Control,” World Electr. Veh. J.,  
vol. 13, no. 3, 2022, doi: 10.3390/wevj13030053.  
40. D. Chu, H. Li, C. Zhao, and T. Zhou, “Trajectory Tracking of Autonomous Vehicle Based on Model  
Predictive Control with PID Feedback,” IEEE Trans. Intell. Transp. Syst., vol. 24, no. 2, pp. 2239–2250,  
Feb. 2023, doi: 10.1109/TITS.2022.3150365.  
41. Y. Lv et al., “Hybrid Supervised and Reinforcement Learning for Motion-Sickness-Aware Path Tracking  
in Autonomous Vehicles,” Sensors, vol. 25, no. 12, pp. 1–21, 2025, doi: 10.3390/s25123695.  
42. M. Rokonuzzaman, N. Mohajer, S. Nahavandi, and S. Mohamed, “Review and performance evaluation  
of path tracking controllers of autonomous vehicles,” IET Intell. Transp. Syst., vol. 15, no. 5, pp. 646–  
670, 2021, doi: 10.1049/itr2.12051.  
43. M. H. Demir and M. Demirok, “Designs of Particle-Swarm-Optimization-Based Intelligent PID  
Page 3696  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
Controllers and DC/DC Buck Converters for PEM Fuel-Cell-Powered Four-Wheeled Automated Guided  
Vehicle,” Appl. Sci., vol. 13, no. 5, 2023, doi: 10.3390/app13052919.  
44. I. Holovatenko and A. Pysarenko, “Energy-Efficient Path-Following Control System of Automated  
Guided Vehicles,” J. Control. Autom. Electr. Syst., vol. 32, no. 2, pp. 390–403, 2021, doi:  
10.1007/s40313-020-00668-8.  
45. Z. Wang et al., “Driverless simulation of path tracking based on PID control,” IOP Conf. Ser. Mater. Sci.  
Eng., vol. 892, no. 1, 2020, doi: 10.1088/1757-899X/892/1/012050.  
46. Q. Yao, Y. Tian, Q. Wang, and S. Wang, “Control Strategies on Path Tracking for Autonomous Vehicle:  
State of the Art and Future Challenges,” IEEE Access, vol. 8, pp. 161211–161222, 2020, doi:  
10.1109/ACCESS.2020.3020075.  
47. Z. He, L. Nie, Z. Yin, and S. Huang, “A two-layer controller for lateral path tracking control of  
autonomous vehicles,” Sensors (Switzerland), vol. 20, no. 13, pp. 1–20, 2020, doi: 10.3390/s20133689.  
48. J. Ma, H. Xie, K. Song, and H. Liu, “Self-optimizing path tracking controller for intelligent vehicles  
based on reinforcement learning,” Symmetry (Basel)., vol. 14, no. 1, 2022, doi: 10.3390/sym14010031.  
49. D. Phan et al., “Intelligent energy management system for conventional autonomous vehicles,” Energy,  
vol. 191, p. 116476, Jan. 2020, doi: 10.1016/J.ENERGY.2019.116476.  
50. D. Phan et al., “Neuro-fuzzy system for energy management of conventional autonomous vehicles,”  
Energies, vol. 13, no. 7, 2020, doi: 10.3390/en13071745.  
51. Z. Al-Saadi et al., “Intelligent Driver Assistance and Energy Management Systems of Hybrid Electric  
Autonomous Vehicles,” Sustain., vol. 14, no. 15, 2022, doi: 10.3390/su14159378.  
52. K. Ye and P. Li, “A new adaptive PSO-PID control strategy of hybrid energy storage system for electric  
vehicles,” Adv. Mech. Eng., vol. 12, no. 9, pp. 1–15, 2020, doi: 10.1177/1687814020958574.  
Page 3697