Optimal Trajectory Tracking Control for a Wheeled Mobile Robot Using Fractional Order PID Controller

In this study, a nonlinear Archimedes wave swing (AWS) energy conversion system was employed to enable the use of irregular sea waves to provide useful electricity. Instead of the conventional PI controllers used in prior research, this study employed fractional-order PID (FOPID) controllers to control the back-to-back configuration of AWS. The aim was to maximize the energy yield from waves and maintain the grid voltage and the capacitor DC link voltage at predetermined values. In this study, six FOPID controllers were used to accomplish the control goals, leading to an array of thirty parameters required to be fine-tuned. In this regard, a hybrid jellyfish search optimizer and particle swarm optimization (HJSPSO) algorithm was adopted to select the optimal control gains. Verification of the performance of the proposed FOPID control system was achieved by comparing the system results to two conventional PID controllers and one FOPID controller. The conventional PID controllers were tuned using a recently presented metaheuristic algorithm called the Coot optimization algorithm (COOT) and the classical particle swarm optimization algorithm (PSO). Moreover, the FOPID was also tuned using the well-known genetic algorithm (GA). The system investigated in this study was subjected to various unsymmetrical and symmetrical fault disturbances. When compared with the standard COOT-PID, PSO-PID, and GA-FOPID controllers, the HJSPSO-FOPID results show a significant improvement in terms of performance and preserving control goals during system instability

A fractional-order proportional integral derivative (FOPID)controller has replaced the classical PID controller used in industries for process control application. FOPID is less sensitive to the change of control parameters than PID Controller, due to which better results are obtained. The FOPID provides a robust and stable system for a higher-order system as of iso- damping property. This study aims to find a stable and controlled structure by tuning the FOPID controller with the Particle Swarm Optimization (PSO) algorithm, fuzzy-based logic approach, and Adaptive Neuro-fuzzy inference system (ANFIS). The tuning of FOPID is done to overcome deficits of PID controller using the different types of optimization method to overcome large overshoot and large settling time. This paper presented useful techniques based on PSO, fuzzy logic, and ANFIS to optimize FOPID controlled high-performance drilling machines. On the analysis and comparisons of simulation findings, it is observed that the FOPID-PSO approach provides better performance over the Ziegler-Nichols (ZN)-FOPID and the above-mentioned intelligent techniques in terms of less settling time (ts=0.823sec.) & optimized peak overshoot (Mp=2.44%) for the mentioned target.

A robust control technique is proposed to address the problem of trajectory tracking of an autonomous ground vehicle (AGV). This technique utilizes a fractional-order proportional integral derivative (FOPID) controller to control a non-holonomic autonomous ground vehicle to track the behaviour of the predefined reference path. Two FOPID controllers are designed to control the AGV’s inputs. These inputs represent the torques that are used in order to manipulate the implemented model of the vehicle to obtain the actual path. The implemented model of the non-holonomic autonomous ground vehicle takes into consideration both of the kinematic and dynamic models. In additional, a particle swarm optimization (PSO) algorithm is used to optimize the FOPID controllers’ parameters. These optimal tuned parameters of FOPID controllers minimize the cost function used in the algorithm. The effectiveness and validation of the proposed method have been verified through different patterns of reference paths using MATLAB–Simulink software package. The stability of fractional-order system is analysed. Also, the robustness of the system is conducted by adding disturbances due to friction of wheels during the vehicle motion. The obtained results of FOPID controller show the advantage and the performance of the technique in terms of minimizing path tracking error and the complement of the path following.

Direct Current (DC) motors are extensively used in various applications due to their versatile and precise control capabilities. However, they face operational challenges such as speed instability and sensitivity to load variations and external disturbances. This study compares the performance of several advanced control methods—Proportional Integral Derivative (PID), Fractional Order PID (FOPID), Integral State Feedback (ISF), Sliding Mode Control (SMC), and Fuzzy Logic Controller (FLC) for DC motor control. Particle Swarm Optimization (PSO) is employed to optimize the tuning parameters of PID, FOPID, ISF, and SMC controllers, while FLC is implemented without optimization. The simulation results indicate that the PSO-FOPID controller exhibits the best overall performance, characterized by the fastest rise and settling times and the lowest ITSE, despite a minor overshoot. The PSO-PID controller also performs well, with fast response times, although it is less efficient in terms of settling time and ITSE compared to PSO-FOPID. The OBL/HGSO-PID controller, while stable and overshoot-free, has a slower response. The PSO-ISF controller shows the highest stability with the lowest SSE values, making it suitable for applications requiring high stability. The PSO-SMC controller demonstrates good stability but is slightly slower than PSO-ISF. The FLC controller, however, performs the worst, with significant overshoot and long recovery times, making it unsuitable for fast and precise control applications. The robustness analysis under varying motor parameters further confirms the superiority of the PSO-FOPID controller, which outperforms OBL/HGSO and OBL-MRFO-SA optimizations across both PID and FOPID controllers, making it the most effective solution for applications requiring high precision and rapid response.

Precise and stable trajectory tracking in mobile robotics is challenging due to dynamic disturbances and uncertain conditions. Traditional controllers like P-D and PID often underperform in non-linear, unpredictable environments. They also lack the adaptability needed for real-time, vision-based control systems. To address these issues, this paper explores and compares the effectiveness of three control approaches: P-D, PID, and a Fractional Order PID (FOPID) controller optimized using the World Cup Optimization Algorithm (WCOA). The control system is driven by inputs from a computer vision setup, and the controllers are evaluated on their ability to maintain accurate setpoint tracking under simulated dynamic disturbances. The FOPID controller’s parameters are tuned using WCOA, enhancing its adaptability and precision. The robustness of WCOA is also validated using standard benchmark functions including Sphere, Rastrigin, Ackley, Rosenbrock, and Griewank. Simulation results show that the WCOA-tuned FOPID controller significantly outperforms both P-D and PID controllers in minimizing error, maintaining control stability, and ensuring accurate trajectory tracking. Its superiority is also demonstrated through real-time tests on a mobile robot. Furthermore, feasibility evaluations reveal high levels of usability, operability, and learnability. These results highlight the strong potential of WCOA as a robust optimization method for advanced control systems and provide a foundation for future research in dynamic environments, hybrid optimization techniques, and broader engineering applications.

Trajectory tracking control is indispensable for a wheeled mobile robot to achieve successful navigation. The classical tracking control systems that are used in wheeled mobile robots do not compensate for the parameter uncertainties and external disturbances. For control strategy, this paper presents a novel hybrid approach, combining a neural network-based kinematic controller and a model reference adaptive control. The controller parameters are adaptively determined online using neural networks. The adaptively tuned kinematic controller ensures a fast convergence to the desired trajectory. The model reference adaptive controller retains the desired tracking performance when parameter and model uncertainties occur. The Lyapunov stability method is used to obtain the adaptive gains which guarantee the asymptotic stability of the error dynamics, where the error is the difference between the outputs of the reference model and the actual plant. The performance of the proposed controller is compared with that of the PID controller, kinematic controller, and adaptive dynamic controller using different performance analysis indices such as integral absolute error, integral squared error, and mean absolute error. Simulation studies demonstrate that the proposed controller achieves high tracking accuracy and fast convergence as compared to the PID, kinematic, and adaptive dynamic controllers considering parameter uncertainties and slip disturbances. The outcomes of the simulation studies also illustrate that the proposed controller achieves the best transient performance. Experiments using real-world tests based on a two-wheeled differential drive robot architecture have elucidated the feasibility of the developed controller regarding tracking accuracy, total control effort, and robustness against uncertainties.

A GBMO-based PI λ D μ controller for vibration mitigation of seismic-excited structures

The paper proposes a comparative study of the performance of the fractional-order PID(FOPID) controller with the conventional controllers. The parameters of the FOPID controller is estimated using particle swarm optimization (PSO) algorithm, and the values are compared with the values obtained through conventional optimization techniques. This paper aims to find out optimal settings for a fractional PIαDβ controller in order to achieve five different design specification for a closed system and also presents identification of fractional-order system using PSO. By obtaining optimal settings, fractional-order PID controller can enhance system control performance and robustness.

<span>This paper proposes the fractional-order proportional integral derivative (FOPID) controller, as a speed controller for permanent magnet direct current (PMDC) motor, instead of the traditional integer-order PID controller. The FOPID controller is the general form of the integer-order PID controllers, which found wide applications in all engineering fields. In this work a hybrid M-file and SIMULINK program is developed to simulate the overall system, the FOPID controller has five associated parameters. The optimum values of those parameters are found out by using particle swarm optimization technique. Simulation results show excellent command speeds tracking and superior dynamic response in conjunction with that of the integer-order PID controller. The proposed controller shows a high ability to overcome any external disturbance the system may be exposed; also, it performs a high degree of robustness to control the system in motoring and regenerative operating modes.</span>

An optimal control technique is proposed to address the problem of path tracking of an autonomous ground vehicle. This technique utilizes a Fractional Order Proportional Integral Derivative (FOPID) controller to control a non-holonomic autonomous ground vehicle to track the behaviour of the predefined reference path. Two FOPID controllers are designed to control the vehicle's inputs. These inputs represent the torques that are used in order to manipulate the implemented model of the vehicle to obtain the actual path. The implemented model of the non-holonomic autonomous ground vehicle takes into consideration both of the kinematic and dynamic models. In additional, a Particle Swarm Optimization (PSO) algorithm is used to optimize the FOPID controllers' parameters. These optimal tuned parameters of FOPID controllers minimize the cost function used in the algorithm. The effectiveness and validation of the proposed method have been verified through different patterns of reference paths using MATLABSIMULINK software package. The newly obtained results of FOPID controller show the advantage and the performance of the technique in terms of minimizing path tracking error and the complement of the path following.

A pressurized heavy water reactor (PHWR) is a nuclear power reactor,that commonly uses unenriched natural uranium as its fuel and heavy water as its coolant and moderator. The PHWR has become an important component of the present day power generation industry. Working of a PHWR may often require reduction of nuclear power within a small finite time interval in accordance to the varying load conditions. This phenomenon is referred to as step back condition. Therefore, for the efficient working of the PHWR it is very important to have a control algorithm that has the capability to handle the step back condition very precisely. The fractional order control strategy has emerged as one of the very versatile and accurate control strategies in the recent times. The fractional order PID (FOPID) controllers are known to give very robust performance both in nominal as well as varying operating conditions. However, most of the design techniques available for the FOPID controllers are mathematically very lengthy and complex. Therefore, in this paper an FOPID controller design technique has been suggested using the concept of internal model control (IMCFOPID) for the PHWR under step back conditions. Further, the performance of the proposed controller has been compared with the conventional FOPID controller using the various integral error criterions. The proposed IMC-FOPID controller is found to give an improved performance as compared to the conventional FOPID controller.

In this paper, fractional order PID (FOPID) controller is implemented to stabilize x-z inverted pendulum (vertical inverted pendulum). Three FOPID controllers are used to control the angle and position (horizontal and vertical) of inverted pendulum. Mathematical model of the pendulum is used for designing the Simulink model and various parameters of the FOPID are obtained using the Whale optimization algorithm (WOA) technique. Simulation results obtained from FOPID is compared with PID controller. From the simulation results it is noticed that overall performance of the proposed controller is satisfactory with and without disturbances.

As a position servo system to isolate disturbance from its carrier, stabilized platform requires high-precision and high-adaptability control. However, conventional integer-order PID (IOPID) control fails to meet that requirement. In this paper, a new controller design scheme is proposed for stabilized platform based on fractional calculus. The designed controller is called fractional-order PID (FOPID) controller, which has two extra parameters compared to conventional PID controller. On one hand, it provides more degrees of freedom to design FOPID controller. On the other hand, its differential order and integral order provides more flexibility to tune the controller performance. Therefore, a design method of FOPID controller based on dynamic software modeling is presented. To obtain the ideal controller's parameters, the particle swarm optimization (PSO) bionic algorithm is used to optimize an objective function. In addition, software simulation platform and hardware experiment system are built to design and test the FOPID controller. Finally, the results of simulation and experiment are included to show the effectiveness of the new control method.

In this article, an attempt is made to design the fractional order proportional integral derivative (FO-PID) controller for multi-input multi-output (MIMO) system using teaching learning-based optimization (TLBO) algorithm. The control of MIMO system always offers a complicated control paradigm due to its structure. It is realized that dynamic systems can be effectively represented by fractional order dynamics which is based on fractional calculus. The PID controller is still the most reliable controller due to its uncomplicated structure, and the FO-PID controller is predicted to have better performance as compared to conventional PID controller due to increment of two more parameters. The performance of non-integer PID controller depends upon the five constants; hence, the tuning of these five constants is most important for the optimum performance. In the presented work, TLBO technique is adopted for the tuning of the non-integer PID controller. The designed controller is implemented on the four tank MIMO system in MATLAB. The performance of the designed controller is also compared from the previous results available in literature.KeywordsFour tank MIMO systemFO-PIDTLBO

The main objective of this paper is to implement the Fractional Order Proportional Integral Derivative (FOPID) controller for output voltage control of DC - DC Zeta converter. Implementing a distinct control technique for DC-DC converters has also been introduced with the commercial availability of integrated circuits (ICs) to carry out this task. The simulation of Classical Proportional Integral Derivative (PID) and Fractional Order PID (FOPID) control techniques for the control of Zeta converter and its characteristics of a dc-dc converter, where aspects such as the output voltage, required peak overshoot and rise time specifications are investigated using MATLAB/ Simulink model. Through simulation it is confirmed that the propounded FOPID controller gives better the transient response of the feedback system by using a significantly smaller control effort (i.e., less on-off switches), the Internal Absolute Error (IAE) of the variations of the output voltage is minimized and improves the strength of the DC - DC ZETA converter to variations in the input voltage. Artificial Bee Colony (ABC) algorithm offers fine tuning the factors of the FOPID controller.