PID Controller Research Articles

Hover Flight Improvement of a Quadrotor Unmanned Aerial Vehicle Using PID Controllers with an Integral Effect Based on the Riemann–Liouville Fractional-Order Operator: A Deterministic Approach

The hovering flight of a quadrotor Unmanned Aerial Vehicle (UAV) refers to maintaining the aircraft in a fixed position in the air, without lateral, vertical, or rotational movements, using only the vehicle’s control systems to maintain proper balance in all spatial dimensions. Algorithms and control systems have been developed to continuously adjust motor speeds to counteract deviations from the desired position and achieve effective hovering flight. This paper proposes a set of PID controllers with an integral effect based on the Riemann–Liouville fractional-order approach to improve the hovering flight of a quadrotor UAV. This research innovates by introducing a set of fractional-order PID controllers for UAV hover stability, which offer better adaptability to non-linear dynamics and robustness than traditional PID controllers. Also presented is the development of new performance metrics (MSE, BQC-LR), which allow for more comprehensive control system evaluations. A thorough comparative analysis with conventional control methods demonstrates the superior performance of fractional-order control in real-world simulations. The numerical simulation results show the effectiveness of the proposed Fractional Integral Action PID Controller in the control of UAV hovering flight, while comparative analyses against a classical controller emphasize the benefits of the fractional-order approach in terms of control accuracy.

Transition flight of a concept of lifting-wing quadcopter

Abstract This paper presents the concept of a lifting-wing quadcopter unmanned aerial vehicle (UAV), a vertical take-off and landing vehicle (VTOL) with a rear wing, a canard at its front and four propellers. The aerodynamic surfaces are designed so that their mounting angle can be adjusted and fixed before flight, so its performance in transition flight can be studied for a combination of wing and canard mounting angles. A dynamic model using rigid-body equations of motion is presented, which is used to compute the transition flight trajectory from hover to cruise in horizontal flight. The trim conditions were computed for a range of fixed wing and canard mounting angles to study the effects of these variables on transition trajectory parameters such as required power, body pitch angle and propeller rotation speeds as a function of flight speed. Furthermore, a transition flight control algorithm is presented, which has a cascaded PID controller and a reference scheduler to switch between the proper reference states, controls and control allocation matrix. Finally, the transition control algorithm of the conceptual UAV is numerically simulated. Results show that this configuration can perform a fast and smooth transition from hover to cruise flight using the proposed flight control algorithm, substantially reducing required propulsive power in cruise of up to 64%. The application of the control algorithm made notable a transition manoeuver that consists of negatively inclining the aircraft at a negative pitch angle, initially at high intensity, and as the final cruising speed approaches, the inclination is attenuated until the equilibrium pitch angle is reached. Simultaneously with the negative inclination of the pitch angle, there is a slight drop in altitude, which is quickly resumed as the trajectory develops until the final cruising speed. Lastly, this aircraft configuration can be widely used in applications where performance gains in operations currently carried out by multicopters, which cover large distances and need long flight time, would bring great operational advantages.

Investigation into the Yaw Control of a Twin-Rotor 10 MW Wind Turbine

Multi-rotor system (MRS) wind turbines can provide a competitive alternative to large-scale wind turbines due to their significant advantages in reducing capital, transportation, and operating costs. The main challenges of MRS wind turbines include the complexity of the supporting structure, mathematical modeling of the aerodynamic interaction between the rotors, and the yaw control mechanism. In this work, MATLAB 2018b/Simulink® software was used to model and simulate a twin-rotor wind turbine (TRWT), and an NREL 5 MW wind turbine was used to verify the model outputs. Different random signals of wind velocities and directions were used as inputs to each rotor to generate different thrust loads, inducing twisting moments on the main tower. A yaw controller system was adapted to ensure that the turbine constantly faced the wind to maximize the power output. A DC motor was used as the mechanism’s actuator. The goal was to achieve a compromise between aligning the rotors with the wind direction and reducing the torque induced on the main tower. A comparison between linear and nonlinear controllers was performed to test the yaw system actuator’s response at different wind speeds and directions. Sliding mode control (SMC) was chosen, as it was suitable for the nonlinearity of the system, and its performance showed a faster response compared with the PID controller, with a settling time of 0.17 sec and a very low overshoot. The controller used the transfer function of the motor to generate a sliding surface. The dynamic responses of the controlled angle are shown and discussed. The controller showed promising results, with a suitable response and low chattering signals.

Frequency stabilization of interconnected diverse power systems with integration of renewable energies and energy storage systems

Recent improvements in renewable energy sources (RESs) and their extensive use in the power industry have created significant issues for their operation, security, and management. Due to the ongoing reduction of power system inertia, maintaining operational frequency at its nominal value and minimizing tie-line power variations constitute essential variables for these improvements. A novel improved frequency stabilization approach based on modified fractional order tilt controller is presented for interconnected diverse power systems with integration of sea wave energy, photovoltaic, wind, energy storage system and biodiesel generator. The fractional order tilt integral double derivative (FOTIDD2) is a novel controller that is developed to address the frequency stabilization problems of a hybrid power structure that is integrated with sources of clean energy and devices for storing energy. A recent optimization algorithm inspired by human behavior called mother optimization algorithm (MOA) is applied to adjust the coefficient of the proposed cascaded controller. The FOTIDD2 controller was compared with other control methods in terms of its transient performance, in order to determine its effectiveness. Further, the mother optimization algorithm results are compared with those of sine cosine algorithm (SCA), fox optimization algorithm (FOA), and grey wolf optimization (GWO). FOTIDD2 controller was found to be more effective than PID controller in respect of reducing overshoot (Osh) by 79.31%, 83.78% and 67.99%, improving time settlement by 33.22%, 29.87%, and 22.45% and reducing undershoot (Ush) by 79.13%, 89.34%, and 86.90% for the (∆F1), (∆F2), and (∆Ptie), respectively.

Fuzzy Logic-Based Smart Control of Wind Energy Conversion System Using Cascaded Doubly Fed Induction Generator

This paper introduces a robust system designed to effectively manage and enhance the electrical output of a Wind Energy Conversion System (WECS) using a Cascaded Doubly Fed Induction Generator (CDFIG) connected to a power grid. The solution that was investigated is the use of a CDFIG that is based on a variable-speed wind power conversion chain. It comprises the electrical and mechanical connection of two DFIGs through their rotors. The originality of this paper lies in the innovative application of a fuzzy logic controller (FLC) in combination with a CDFIG for a WECS. To demonstrate that this novel configuration enhances control precision and performance in WECSs, we conducted a comparison of three different controllers: a proportional–integral (PI) controller, a fractional PID (FPID) controller, and a fuzzy logic controller (FLC). The results highlight the potential of the proposed system in optimizing power generation and improving overall system stability. It turns out that, according to the first results, the FLC performed optimally in terms of tracking and rejecting disturbances. In terms of peak overshoot for power and torque, the findings indicate that the proposed FLC-based technique (3.8639% and 6.9401%) outperforms that of the FOPID (11.2458% and 10.9654%) and PI controllers (11.4219% and 11.0712%), respectively. These results demonstrate the superior performance of the FLC in reducing overshoot, providing better control stability for both power and torque. In terms of rise time, the findings show that all controllers perform similarly for both power and torque. However, the FLC demonstrates superior performance with a rise time of 0.0016 s for both power and torque, compared to the FOPID (1.9999 s and 1.9999 s) and PI (0.0250 s and 0.0247 s) controllers. This highlights the FLC’s enhanced responsiveness in controlling power and torque. In terms of settling time, all three controllers have almost the same performance of 1.9999. An examination of total harmonic distortion (THD) was also employed to validate the superiority of the FLC. In terms of power quality, the findings prove that a WECS based on an FLC (0.93%) has a smaller total harmonic distortion (THD) compared to that of the FOPID (1.21%) and PI (1.51%) controllers. This system solves the problem by removing the requirement for sliding ring–brush contact. Through the utilization of the MATLAB/Simulink environment, the effectiveness of this control and energy management approach was evaluated, thereby demonstrating its capacity to fulfill the objectives that were set.

Design and Implementation of Small Modular Amphibious Robot System

Various marine engineering facilities have been eroded by marine organisms and wind waves for a long time, resulting in different types of damage to the surface of marine engineering facilities, such as the pile legs of offshore platforms. Therefore, in order to carry out safety inspections and other work on marine engineering facilities, a small amphibious robot structure system and a set of control systems adapted to it are independently developed. Various problems such as the modular design of the structure, composite motion mode, adsorption stability, wall adaptability of the crawling mode, and flaw localization have been solved by means of three-dimensional modeling, mechanical analysis, simulation, and electronic design. At the same time, a set of control systems including hardware and software is developed for the amphibious robot. In order to improve the stability and efficiency of the amphibious robot working underwater, a sliding mode control algorithm based on the exponential reaching law and saturation function is designed. For the fixed depth and fixed heading control functions, the sliding mode control algorithm and the PID control algorithm are simulated and compared. Finally, several types of experiments are carried out for the amphibious robot. The simulation and experimental results show that all the functions of the amphibious robot meet work requirements, such as the motion performance of the composite motion mode. Compared with the PID control algorithm, the sliding mode control algorithm has a faster response speed and better stability, which is conducive to the efficient and stable work of the amphibious robot underwater.

Defining and Mitigating Flow Instabilities in Open Channels Subjected to Hydropower Operation: Formulations and Experiments

A thorough literature review was conducted on the effects of free surface oscillation in open channels, highlighting the risks of the occurrence of positive and negative surge waves that can lead to overtopping. Experimental analyses were developed to focus on the instability of the flow due to constrictions, gate blockages, and the start-up and shutdown of hydropower plants. A forebay at the downstream end of a tunnel or canal provides the right conditions for the penstock inlet and regulates the temporary demand of the turbines. In tests with a flow of 60 to 100 m3/h, the effects of a gradually and rapidly varying flow in the free surface profile were analyzed. The specific energy and total momentum are used in the mathematical characterization of the boundaries along the free surface water profile. A sudden turbine stoppage or a sudden gate or valve closure can lead to hydraulic drilling and overtopping of the infrastructure wall. At the same time, a PID controller, if programmed appropriately, can reduce flooding by 20–40%. Flooding is limited to 0.8 m from an initial amplitude of 2 m, with a dissipation wave time of between 25 and 5 s, depending on the flow conditions and the parameters of the PID characteristics.

Non-linear cascade control with gain-scheduling and startup control strategy study for thermionic space reactor TOPAZ-II

The TOPAZ-II thermionic space reactor system, which was designed by the Soviet Union, is characterized by its high degree of nonlinearity and positive temperature reactivity feedback. The thermionic space reactor exhibits characteristics of high inertia and significant delay in controlling its electrical power and outlet temperature. The simple PID controller is difficult to achieve good performance. To carry out controller design for thermionic space reactor, the simulation platform for thermionic space reactor is developed based on coupling between reactor system thermal-hydraulic code RESYS and control system simulator in this study. After that, based on the cascade control strategy and gain-scheduling, the reactor thermal controller, electric power controller, outlet temperature controller applicable for the full power range is designed with transfer function model and frequency domain analysis method. To validate the nonlinear electric power controller performance, the continuous minor step disturbances, major step disturbances, and ramp variation of electric power setpoint is simulated. The performance of outlet temperature controller is verified with the simulation result of step and ramp variation of outlet temperature setpoint. Thereafter, the start-up process of the thermionic space reactor TOPAZ-II is simulated and analyzed. The simulation result reveals that the controller designed in this paper can overcome the nonlinearity of the thermionic space reactor system and has good performance throughout the entire power range. Compared to traditional simple PID controller, the cascade controller has better performance and can achieve good control performance even in situations where simple PID controllers cannot function properly.

Design, Simulation, and Implementation of MRAC Controller with PMAC Target Hardware for Controlling 7.5 m Antenna

The article presents the design of an adaptive controller, simulation, code generation, and porting of the algorithm into target hardware, movement of the 7.5 m antenna, testing, verification, and validation of theoretical and experimental results of the antenna system. The conventional servo control methods based on PID controllers are being used for tracking X-band missions. As the need for higher data rates is increasing, missions are switching to the Ka band, as a result the satellite ground stations will have to track the satellite in the Ka band where the antenna band beam width is narrowed by a factor of 3 when compared to the X-band antenna beamwidth. These challenges had driven the designer to design and implement a Model Reference Adaptive Controller over PID to improve and achieve the tracking accuracy of less than 25m° from the present 30 m°. Thus, consistent and constant performance is achieved throughout the trajectory tracking of the mission using PID + MRAC (Model Reference Adaptive Control). MRAC uses a reference model that specifies the desired response of the antenna system and adjusts the controller parameters such that the plant follows the reference to achieve the desired performance. The entire drive chain modules and their parameters are considered in the design of the plant, namely MRAC controller, PID controller, Power Drive electronic (Rectifier and Inverter), Servo Motor, mechanical torque coupling, Gear reducer, Slew Ring Bearing (SRB), and absolute encoder modules of each axis for position feedback from the antenna. Model Order Reduction of higher-order actual Plant model to the standard second-order system is optimized. The modelled and analysed outcomes of the MRAC scheme using the Modified MIT are demonstrated. The developed model is tested against step, ramp, parabolic, satellite trajectory, velocity and acceleration inputs in MATLAB/Simulink and validated with practical/ experimental test results with antenna load at the satellite ground Station. The achieved results indicate that the PID + MRAC controller has significant and consistent performance improvements when compared to the PID controller alone.

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

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.

Research on anti-swing control system of slewing crane based on fuzzy PID.

The slewing crane is easily affected by the wind and the manipulation level of the operator when it is working, which in turn impacts its swing angle, affects the working efficiency and safety of the crane. Toimprove the operation safety andreduce the swing angle, this study design and research the anti-swing control system for the slewing crane. Firstly, based on the Lagrange equation, the dynamic model of the crane hoisting system is established. Then, the mechanical anti-swing mechanism driven by a four-motor rope is established. Finally, based on fuzzy PID control, an anti-swing platform is established, and the performance of anti-swing control is verified. Compared to no anti-swing control, the in-plane swing angle θ1 and out-of-plane swing angle θ2 of the lifting arm are reduced by 88% and 75% respectively. The results show that the four-motor rope-driven anti-swing mechanism can achieve better anti-swing effect, which provides an effective swing suppression method for the slewing crane in the actual operation.

Load Frequency PID Controller Design Based on Pole Placement Method of an Islanded Microgrid

Load Frequency PID Controller Design Based on Pole Placement Method of an Islanded Microgrid

Model Reference Adaptive Control (MRAC) for dual-axis solar tracker applied in CPV

In this work, the simulation of the behavior of an MRAC assisted solar tracker in solar trajectory tracking tasks has been developed for a prototype of a two-axis solar tracker that presents structural and performance characteristics capable of supporting PV, CPV, and HCPV-type technology. The proposal is numerically validated by developing an experimental methodology consisting of two stages. The first stage is associated with developing tests of the MRAC-assisted solar tracker to reproduce a solar trajectory (obtained offline by a numerical method) with and without the injection of disturbances (with dynamics equivalent to wind loads in reality), respectively. On the other hand, in the second stage, after replicating the conditions of the tests of stage one but with the assistance of a simple PID type controller, the analysis and comparison of the performance of each alternative is carried out, the above, in terms of tracking error or pointing accuracy. The results show that both alternatives are functional in the development of tests under favorable conditions. However, under conditions with disturbances, it can be noted that the MRAC reduces the tracking error by around 87% compared to PID control.

Modeling and Regulation of Dynamic Temperature for Layer Houses Under Combined Positive- and Negative-Pressure Ventilation.

The environmental control of layer houses with multi-tiered cage systems is influenced by factors such as the structure of the henhouses and the heat dissipation of the flock, leading to low precision and large fluctuations in temperature control. Based on a new combined positive- and negative-pressure ventilation (CPNPV) mode, a dynamic temperature model is constructed. Additionally, a temperature control method for a layer house is designed using a variable universe fuzzy PID control algorithm (VFPID). First, based on the principles of energy and mass balance, and by decoupling the relationship between positive- and negative-pressure ventilation volumes, a dynamic temperature model for layer houses under CPNPV was established. Then, the PID parameters and the proportional relationship between positive- and negative-pressure ventilation were optimized through fuzzy rules, and a proportional exponential function was introduced to adjust the scaling of the universe, enabling fine-tuned control. Finally, a temperature control model for the layer house was built using Simulink. The results show that the coefficients of determination (R2) of the constructed dynamic temperature models are between 0.79 and 0.88, respectively, indicating high accuracy. The designed VFPID method outperformed traditional on-off control and improved control precision by 20-23.53% and 10.34-22.22% compared with PID control and fuzzy PID(FPID) control methods, respectively. This study provides new insights for the development of environmental control equipment and precise environmental regulation of layer houses.

Adaptive control of airway pressure during the expectoration process in a cough assist system.

Existing Mechanical Insufflation-Exsufflation (MI-E) devices often overlook the impact of cough airflow pressure on mucus clearance, particularly lacking in control over airway pressure during the expiratory phase, which can lead to airway collapse and other types of airway damage. This study optimizes the design of cough assist system and explores the effectiveness of PID and adaptive control methods in regulating airway pressure. The adaptive control method compensates for hose pressure drop by online estimation of the ventilatory hose characteristics. It achieves precise tracking of target pressure and ensures the generation of peak flow rates effective for mucus clearance, even in the absence of known patient lung physiological states and unknown hose leakage parameters. Through a series of comparative experiments, this paper confirms the significant advantages of adaptive control in reducing oscillations and overshoot, capable of more stable and precise airway pressure adjustments. This improved control strategy not only enhances clinical safety but also significantly improves therapeutic outcomes and reduces the risk of complications. The findings indicate that the revamped cough assist system, employing an adaptive control strategy, can effectively prevent airway damage during assisted coughing, offering a safer and more effective sputum clearance solution for critically ill patients with expectoration disorders.

An Intermittent Fertilization Control System for Fruit Tree Crown Detection

In light of the current dearth of strip intermittent fertilization devices in standardized orchards, this study presents the design of an intermittent fertilization control system based on fruit tree crown detection, developed with the objective of meeting the agronomic requirements of strip furrow fertilization in standardized orchards. The initial stage of the process entails the design of the essential components of the fertilization apparatus, followed by the construction of the intermittent fertilization control system. The ultrasonic sensor was employed as the fruit tree crown detection module, and a mathematical model of fertilization speed was constructed to achieve uniform intermittent fertilization. Furthermore, in order to enhance the responsiveness and reliability of the fertilization servo motor, MATLAB Simulink was employed to assess the dynamic performance of the system under disparate control strategies. Ultimately, to validate the simulation outcomes, a field trial was conducted to assess the precision and uniformity of intermittent fertilization. The results demonstrate that the dynamic performance of the system under the fuzzy PID control strategy is optimal, and the coefficient of variation of the fertilizer uniformity of the intermittent fertilization device is less than 7%. The mean effective fertilization rate exceeded 85%, with the primary indices satisfying the agronomic criteria.

Wireless PID-Based Control for a Single-Legged Rehabilitation Exoskeleton

The demand for remote rehabilitation is increasing, opening up convenient and effective home-based therapy for the sick and elderly. In this study, we use AnyBody simulations to analyze muscle activity and determine key parameters for designing a rehabilitation exoskeleton, as well as selecting the appropriate motor torque to assist patients during rehabilitation sessions. The exoskeleton was designed with a PID control mechanism for the precise management of motor positions and joint torques, and it operates in both automated and teleoperation modes. Hip and knee movements are monitored via smartphone-based IMU sensors, enabling real-time feedback. Bluetooth communication ensures seamless control during various training scenarios. Our study demonstrates that remotely controlled rehabilitation systems can be implemented effectively, offering vital support not only during global health crises such as pandemics but also in improving the accessibility of rehabilitation services in remote or underserved areas. This approach has the potential to transform the way physical therapy can be delivered, making it more accessible and adaptable to the needs of a larger patient population.

Optimal Control of FSBB Converter with Aquila Optimizer-Based PID Controller

This paper presents a new methodology for determining the optimal coefficients of a PID controller for a four-switch buck–boost (FSBB) converter. The main objective of this research is to improve the performance of FSBB converters by fine-tuning the parameters of the PID controller using the newly developed Aquila Optimizer (AO). PID controllers are widely recognized for their simple yet effective control in FSBB converters. However, to further improve the efficiency and reliability of the control system, the PID control parameters must be optimized. In this context, the application of the AO algorithm proves to be a significant advance. By optimizing the PID coefficients, the dynamic responsiveness of the system can be improved, thus reducing the response time. In addition, the robustness of the control system is enhanced, which is essential to ensure stable and reliable operation under varying conditions. The use of AOs plays a key role in maintaining system stability and ensuring the proper operation of the control system even under challenging conditions. In order to demonstrate the effectiveness and potential of the proposed method, the performance of the AO-optimized PID controller was compared with that of PID controllers tuned by other optimization algorithms in the same test environment. The results show that the AO outperforms the other optimization algorithms in terms of dynamic response and robustness, thus validating the efficiency and correctness of the proposed method. This work highlights the advantages of using the Aquila Optimizer in the PID tuning of FSBB converters, providing a promising solution for improving system performance.

Advanced Study: Improving the Quality of Cooling Water Towers’ Conductivity Using a Fuzzy PID Control Model

Cooling water towers are commonly used in industrial and commercial applications. Industrial sites frequently have harsh environments, with certain characteristics such as poor air quality, close proximity to the ocean, large quantities of dust, or water supplies with a high mineral content. In such environments, the quality of electrical conductivity in the cooling water towers can be significantly negatively affected. Once minerals (e.g., calcium and magnesium) form in the water, conductivity becomes too high, and cooling water towers can become easily clogged in a short time; this leads to a situation in which the cooling water host cannot be cooled, causing it to crash. This is a serious situation because manufacturing processes are then completely shut down, and production yield is thus severely reduced. To solve these problems, in this study, we develop a practical designation for a photovoltaic industry company called Company-L. Three control methods are proposed: the motor control method, the PID control method, and the fuzzy PID control method. These approaches are proposed as solutions for successfully controlling the forced replenishment and drainage of cooling water towers and controlling the opening of proportional control valves for water release; this will further dilute the electrical conductivity and control it, bringing it to 300 µS/cm. In the experimental processes, we first used practical data from Company-L for our case study. Second, from the experimental results of the proposed model for the motor control method, we can see that if electrical conductivity is out of control and the conductivity value exceeds 1000 µS/cm, the communication software LINE v8.5.0 (accessible via smartphone) displays a notification that the water quality of the cooling water towers requires attention. Third, although the PID control method is shown to have errors within an acceptable range, the proportional (P) controller must be precisely controlled; this control method has not yet reached this precise control in the present study. Finally, the fuzzy PID control method was found to have the greatest effect, with the lowest level of errors and the most accurate control. In conclusion, the present study proposes solutions to reduce the risk of ice-water host machines crashing; the solutions use fuzzy logic and can be used to ensure the smooth operation of manufacturing processes in industries. Practically, this study contributes an applicable technical innovation: the use of the fuzzy PID control model to control cooling water towers in industrial applications. Concurrently, we present a three-tier monitoring checkpoint that contributes to the PID control method.

PID Controller with an Override Mode for a Wall-Following Robot with a Rotating Sensor Compartment

This paper presents the design of a wall-following robot (WFR) with a rotating sensor compartment to reduce the number of distance sensors used. Two infrared (IR) sensors were fitted in the compartment that rotates back and forth at 45°, producing four measurement values at each rotation cycle. The WFR was regulated using a novel control scheme of PID controller with an override mode. A discrete PID controller in position form was used to run the WFR to follow straight wall segments or walls turning left, while an override mode governed the WFR to follow walls turning right. The sampling time was set to 300 ms. The parameters of the PID controller were tuned using a trial-and-error method. The Mean Absolute Errors (MAE) was selected as the cost function. The WFR conducted twelve trial runs along a trial track with a length of 200 cm, consisting of one right turn and one left turn. The parameters that yielded the lowest MAE of 0.90 cm were used for further tests. Subsequently, a closed track for testing was constructed with a length of 845 cm, consisting of 7 right turns and 2 left turns. The WFR completed five test runs successfully, each elapsing the test track twice. The lowest MAE during the tests was 1.06 cm. The favorable performance of the proposed WFR strengthens future development efforts to equip the robot with more hardware to fulfill specific tasks and to put the completion time into optimization consideration.