Search Results (10)

Seismic-induced vibration mitigation in multi-degree-of-freedom (MDOF) building structures calls for efficient and adaptive control strategies. Fractional-order PI^λD^μ controllers allow increased flexibility in tuning when compared with the conventional proportional integral derivative (PID) controllers. However, considering highly dynamic seismic conditions, selecting their optimal parameters remains challenging. A Particle Swarm Optimization (PSO)-based fractional order controller approach is presented in this paper for the optimal tuning of five key parameters of the PI^λD^μ controller using a two-story building model subjected to the 1940 El Centro earthquake. The controller structure is formulated using fractional-order calculus, while PSO is utilized to determine optimal gains and fractional orders without prior knowledge about the model. Simulation results indicate that the proposed fractional order proportional integral derivative (FOPID) controller is effective in suppressing structural vibrations, outperforming both classical PID control and the uncontrolled case. It is demonstrated that incorporating intelligent optimization techniques along with fractional-order control can be a promising approach toward enhancing seismic resilience in civil structures. Full article

Continuous decrease in inertia and sensitivity to load/generation fluctuation are significant challenges for present-day power networks. The primary reason for these issues is the increased penetration capabilities of renewable energy sources. An imbalanced load with significant power output has a substantial impact on the frequency and voltage characteristics of electrical networks. Various load frequency control (LFC) technologies are widely used to address these issues. Existing LFC approaches in the literature are inadequate in addressing system uncertainty, parameter fluctuation, structural changes, and disturbance rejection. As a result, the purpose of this work is to suggest a better LFC approach that makes use of a combination of a one plus tilt fractional filtered derivative (1+TDF^λ) cascaded controller and a fractional order proportional–integral–derivative (PI^λD^μ) controller, which is referred to as the recommended 1+TDF^λ/PI^λD^μ controller. Drawing inspiration from the dynamics of religious societies, including the roles of followers, missionaries, and leaders, and the organization into religious and political schools, this paper proposes a new application of the efficient divine religions algorithm (DRA) to improve the design of the 1+TDF^λ/PI^λD^μ controller. A triple-area test system is constructed to analyze a realistic power system, taking into account certain physical restrictions such as nonlinearities as well as the impact of PV and wind energy integration. The effectiveness of the presented 1+TDF^λ/PI^λD^μ controller is evaluated by comparing their frequency responses to those of other current controllers like PID, FOPID, 2DOF-PID, and 2DOF-TID^μ. The integral time absolute error (ITAE) criterion was employed as the objective function in the optimization process. Comparative simulation studies were conducted using the proposed controller, which was fine-tuned by three recent metaheuristic algorithms: the divine religions algorithm (DRA), the artificial rabbits optimizer (ARO), and the wild horse optimizer (WHO). Among these, the DRA demonstrated superior performance, yielding an ITAE value nearly twice as optimal as those obtained by the ARO and WHO. Notably, the implementation of the advanced 1+TDF^λ/PI^λD^μ controller, optimized via the DRA, significantly minimized the objective function to $0.4704\times {10}^{-4}$. This reflects an approximate enhancement of $99.5\%$ over conventional PID, FOPID, and 2DOF-TID^μ controllers, and a $99\%$ improvement relative to the 2DOF-PID controller. The suggested case study takes into account performance comparisons, system modifications, parameter uncertainties, and variations in load/generation profiles. Through the combination of the suggested 1+TDF^λ/PI^λD^μ controller and DRA optimization capabilities, outcomes demonstrated that frequency stability has been significantly improved. Full article

This paper presents a comprehensive vehicle model featuring an active suspension system integrated with semi-active seat and engine mounting controls. The time-domain stochastic excitation of the four tires was modeled using the filtered white noise method, and the required road excitation was simulated using MATLAB software R2022b. Four comprehensive performance indices, including engine dynamic displacement, vehicle body acceleration, suspension dynamic deflection, and tire dynamic displacement, were selected and made dimensionless by the performance indices of a passive suspension under the same working conditions to construct the fitness function. A fractional-order PI^λD^μ (FOPID) controller was proposed, and its structural parameters were optimized using a gray wolf optimization algorithm. Furthermore, the optimized FOPID controller was evaluated under five road conditions, and its performance was compared with integer-order PID control and passive suspensions. The results demonstrate that the FOPID controller effectively improves the smoothness of the vehicle by reducing engine mounting deflection, vehicle body acceleration, suspension deflection, and tire displacement. Moreover, the simulation results indicate that, compared to the passive suspension, the FOPID-controlled suspension achieves an average optimization of over 42% in the root mean square (RMS) of body acceleration under random road conditions, with an average optimization of more than 38% for suspension deflection, 4.3% for engine mounting deflection, and 2.5% for tire displacement. In comparison to the integer-order PID-controlled suspension, the FOPID-controlled suspension demonstrates an average improvement of 28% in the RMS of acceleration and a 2.1% improvement in suspension deflection under random road conditions. However, the engine mounting deflection and tire displacement are reduced by 0.05% and 0.3%, respectively. FOPID control has better performance in vehicle acceleration control but shows asymmetrical effects on tire dynamic deflection. Full article

Aiming at the uncertainty problem caused by the time-varying modeling parameters associated with ship speed in the course tracking control of underactuated surface vessels (USVs), this paper proposes a control algorithm based on the dynamic neural fuzzy model (DNFM). The DNFM simultaneously adjusts the structure and parameters during learning and fully approximates the inverse dynamics of ships. Online identification and modeling lays the model foundation for ship motion control. The trained DNFM, serving as an inverse controller, is connected in parallel with the fractional-order PI^λD^μ controller to be used for the tracking control of the ship’s course. Moreover, the weights of the model can be further adjusted during the course tracking. Taking the actual ship data of a 5446 TEU large container ship, simulation experiments are conducted, respectively, for course tracking, course tracking under wind and wave interferences, and comparison with five different controllers. This proposed controller can overcome the influence of the uncertainty of modeling parameters, tracking the desired course quickly and effectively. Full article

The suspension system is a crucial part of an electric vehicle, which directly affects its handling performance, driving comfort, and driving safety. The dynamics of the 8-DoF full-vehicle suspension with seat active control are established based on rigid-body dynamics, and the time-domain stochastic excitation model of four tires is constructed by the filtered white noise method. The suspension dynamics model and road surface model are constructed on the Matlab/Simulink simulation software platform, and the simulation study of the dynamic characteristics of active suspension based on the fractional-order PI^λD^μ control strategy is carried out. The three performance indicators of acceleration, suspension dynamic deflection, and tire dynamic displacement are selected to construct the fitness function of the genetic algorithm, and the structural parameters of the fractional-order PI^λD^μ controller are optimized using the genetic algorithm. The control effect of the optimized fractional-order PI^λD^μ controller based on the genetic algorithm is analyzed by comparing the integer-order PID control suspension and passive suspension. The simulation results show that for optimized fractional-order PID control suspension, compared with passive suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions reaches over 25%, the average optimization of suspension dynamic deflection exceeds 30%, and the average optimization of tire dynamic displacement is 5%. However, compared to the integer-order PID control suspension, the average optimization of the root mean square (RMS) of acceleration under random road conditions decreased by 5%, the average optimization of suspension dynamic deflection increased by 3%, and the average optimization of tire dynamic displacement increased by 2%. Full article

In order to further improve the control effect of proportion integral differential (PID) control and linear quadratic regulator (LQC) control, and improve vehicle ride comfort and enhance body stability, the 7 DOF semi-active suspension model was established, and the fractional order PI^λD^μ-LQR controller was designed by combining fractional order PI^λD^μ control theory and LQR control theory. The semi-active suspension model in this paper is more complex, and there are many parameters in the controller. The optimal weighting coefficient of 12 vehicle smoothness evaluation indicators and parameters K_p, K_i, K_d, λ and μ in the controller were founded by NSGA-II algorithm. After optimization, the optimized parameters were brought into the controller for random pavement simulation. Compared to the traditional passive suspension, fractional order PI^λD^μ individual control and LQR separate control, the simulation results show that the effect of fractional order PI^λD^μ-LQR control is very significant. The evaluation index of vehicle smoothness has been significantly improved, and the use of fractional order PI^λD^μ-LQR control has significantly improved the working performance of the suspension and improved the smoothness of the vehicle. At the same time, the adjusting force output of the actuator is very balanced, which inhibits the roll of the body and improves the anti-roll performance. After simulation, the excellent performance of the designed fractional PI^λD^μ-LQR controller was verified, and the introduced NSGA-II algorithm played an important role in the controller parameter tuning work, which shows that the fractional order PI^λD^μ-LQR controller and NSGA-II algorithm cooperate with each other to achieve good control effects. Full article

The approximation of a fractional order PI^λD^μ-controller transfer function using a chain fraction theory is considered. Analytical expressions for the approximation of $s^{\pm \alpha }$ components of the transfer functions of PI^λD^μ-controllers were obtained through the application of the chain fraction theory. Graphs of transition functions and frequency characteristics of D^μ (α = μ = 0.5) and I^λ (α = λ = −0.5) parts for five different decomposition orders were obtained and analyzed. The results showed the possibility of applying the approximation of the PI^λD^μ-controller transfer function by the method of chain fractions with different valuesof λ and μ. For comparison, the transfer functions with the same order polynomials, obtained by the methods of Oustaloup transformation and chain fractions, were approximated for α = ±0.5. The analysis proved the advantages of using the chain fraction method to approximate the transfer function of the PI^λD^μ-controller. The performed approximation opens up the possibility of developing engineering methods for the technical implementation of PI^λD^μ-controllers. The accuracy of the same order transfer function approximation is higher when the method of chain fractions is used. It has been established that the adequacy of the frequency characteristics of the transfer functions obtained by the chain fraction method also depends on the approximation order. Full article

For the uncertainty caused by the time-varying modeling parameters with the sailing speed in the course control of underactuated ships, a novel identification method based on an adaptive neural fuzzy model (ANFM) is proposed to approximate the inverse dynamic characteristics of the ship in this paper. This model adjusts both its own structure and parameters as it learns, and is able to automatically partition the input space, determine the number of membership functions and the number of fuzzy rules. The trained ANFM is used as an inverse controller, in parallel with a fractional-order PI^λD^μ controller for the course control of underactuated ships. Meanwhile, the sine wave curve and the sawtooth wave curve are considered as the input learning samples of ANFM, respectively, and the inverse dynamics simulation experiments of the ship are carried out. Two different ANFM structures are obtained, which are connected in parallel with the fractional-order PI^λD^μ controller respectively to control the course of ship. The simulation results show that the proposed method can effectively overcome the influence of uncertainty of ship modeling parameters, track the desired course quickly and effectively, and has a good control effect. Finally, comparative experiments of four different controllers are carried out, and the results show that the FO PI^λD^μ controller using ANFM has the advantages of small overshoot, short adjustment time, and precise control. Full article

Thermoelectric generators (TEGs) are equipment for transforming thermal power into electricity via the Seebeck effect. These modules have gained increasing interest in research fields related to sustainable energy. The harvested energy is mostly reliant on the differential temperature between the hot and cold areas of the TEGs. Hence, a reliable maximum power point tracker is necessary to operate TEGs too close to their maximum power point (MPP) under an operational and climate variation. In this paper, an optimized fractional incremental resistance tracker (OF-INRT) is suggested to enhance the output performance of a TEG. The introduced tracker is based on the fractional-order PI^λD^μ control concepts. The optimal parameters of the OF-INRT are determined using a population-based sine cosine algorithm (SCA). To confirm the optimality of the introduced SCA, experiments were conducted and the results compared with those of particle swarm optimization (PSO) and whale optimization algorithm (WOA) based techniques. The key goal of the suggested OF-INRT is to overcome the two main issues in conventional trackers, i.e., the slow dynamics of traditional incremental resistance trackers (INRT) and the high steady-state fluctuation around the MPP in the prevalent perturb and observe trackers (POTs). The main findings prove the superiority of the OF-INRT in comparison with the INRT and POT, for both dynamic and steady-state responses. Full article

Fractional Calculus is usually applied to control systems by means of the well-known PI^λD^μ scheme, which adopts integral and derivative components of non-integer orders λ and µ. An alternative approach is to add equally distributed fractional-order terms to the PID scheme instead of replacing the integer-order terms (Distributed Order PID, DOPID). This work analyzes the properties of the DOPID scheme with five terms, that is the PII^1/2DD^1/2 (the half-integral and the half-derivative components are added to the classical PID). The frequency domain responses of the PID, PI^λD^μ and PII^1/2DD^1/2 controllers are compared, then stability features of the PII^1/2DD^1/2 controller are discussed. A Bode plot-based tuning method for the PII^1/2DD^1/2 controller is proposed and then applied to the position control of a mechatronic axis. The closed-loop behaviours of PID and PII^1/2DD^1/2 are compared by simulation and by experimental tests. The results show that the PII^1/2DD^1/2 scheme with the proposed tuning criterium allows remarkable reduction in the position error with respect to the PID, with a similar control effort and maximum torque. For the considered mechatronic axis and trapezoidal speed law, the reduction in maximum tracking error is −71% and the reduction in mean tracking error is −77%, in correspondence to a limited increase in maximum torque (+5%) and in control effort (+4%). Full article