Search Results (16)

To address the issues of poor stability and susceptibility to external disturbances in traditional model reference adaptive systems (MRASs) for permanent magnet synchronous motors (PMSMs), this paper proposes a sliding mode control strategy based on an improved model reference adaptive observer. First, the dynamic equations of the PMSM are used as the reference model, while the stator current equations incorporating speed variables are constructed as the adjustable model. Subsequently, a novel adaptive law is designed using Popov’s hyperstability theory to enhance the estimation accuracy of rotor position. A fractional-order system was introduced to construct both a fractional-order sliding surface and reaching law. Subsequently, a comparative study was conducted between the conventional integral terminal sliding surface and the proposed novel sliding mode reaching law. The results demonstrate that the new reaching law can adaptively adjust the switching gain based on system state variables. Under sudden load increases, the improved system achieves a 25% reduction in settling time compared to conventional sliding mode control (SMC), along with a 44% decrease in maximum speed fluctuation and a 42% reduction in maximum torque ripple, significantly enhancing dynamic response performance. Furthermore, a variable-gain terminal sliding mode controller is derived, and the stability of the closed-loop control system is rigorously proven using Lyapunov theory. Finally, simulations verify the effectiveness and feasibility of the proposed control strategy in improving system robustness and disturbance rejection capability. Full article

This study introduces an enhanced Adaptive Fuzzy Sliding-Mode Control (AFSMC) approach based on the fuzzy logic systems (FLSs) to achieve trajectory tracking of multiple-input and multiple-output (MIMO) fractional-order nonlinear systems in the presence of uncertain nonlinear terms and disturbances. An integral SMC approach is proposed for achieving state trajectory tracking control. However, uncertainties in real systems are complex and diverse, not only uncertain bounded disturbances but unknown nonlinear functions. Therefore, in this paper, the FLSs are used not only to approximate unknown functions but also to improve the switching function of the SMC. The stability of the system with designed input control laws is demonstrated through the fractional-order Lyapunov function stability criterion. Subsequently, the simulation results are displayed and serve to validate the efficacy and resilience of the proposed control methodology. These results underscore the ability of the proposed method to perform reliably under various conditions, thereby confirming its robustness as a viable solution. Full article

Switched adaptive laws for parameter estimation have been proposed in recent years to improve the balance between control energy and system performance in adaptive schemes, which is often a big issue when using traditional integer-order or fractional-order adaptive laws in adaptive identification and control. These switched adaptive laws are represented as fractional-order differential equations whose order can switch between a number within the range $(0,1)$ and 1. However, a general analytical framework that allows proving the boundedness of the solutions and convergence of the estimation/tracking error is not yet available, with only particular analyses for specific schemes being accessible. This paper address this issue, presenting the analysis of four error models that can appear in the field of adaptive systems when these adaptive laws are chosen. The boundedness of the solutions is proved for all cases, together with the convergence to zero of the estimation/tracking error. Additionally, sufficient conditions for parameter convergence are presented, showing that the excitation condition required for parameter convergence in the vector case is also sufficient for parameter estimation in the matrix case. A numerical example is included to show the possible advantages of using switched adaptive laws in a Model Reference Adaptive Control application. Results show that controller parameters can be found for the switched controller, enabling us to obtain an overall improvement of 7.75% with respect to the non-switched integer-order controller and 34.6% with respect to the non-switched fractional-order controller. Full article

Taking a Vienna rectifier as the research object, the power mathematical model based on a switching function is established according to its working principle. A sliding mode variable structure control algorithm based on the reaching law is examined in order to address the issues of the slow response speed and inadequate anti-interference of classical PI control in the face of abrupt changes in the DC-side load. In response to the sluggish convergence rate and inadequate chattering suppression of classical integer order sliding mode control, a fractional order exponential reaching law sliding mode, direct power control approach with rapid convergence is developed. The fractional calculus is introduced into the sliding mode control, and the dynamic performance and convergence speed of the control system are improved by increasing the degree of freedom of the fractional calculus operator. The method of including a balance factor in the zero-sequence component is employed to address the issue of the midpoint potential equilibrium in the Vienna rectifier. Ultimately, the suggested control is evaluated against classical PI control through simulation analysis and experimental validation. The findings indicate that the proposed technique exhibits rapid convergence, reduced control duration, and enhanced robustness, hence augmenting its resistance to interference. Full article

For a class of fractional-order singular multi-agent systems (FOSMASs) with local Lipschitz nonlinearity, this paper proposes a closed-loop ${\mathcal{D}}^{\alpha }$-type iterative learning formation control law via input sharing to achieve the stable formation of FOSMASs in a finite time. Firstly, the formation control issue of FOSMASs with local Lipschitz nonlinearity under the fixed communication topology (FCT) is transformed into the consensus tracking control scenario. Secondly, by virtue of utilizing the characteristics of fractional calculus and the generalized Gronwall inequality, sufficient conditions for the convergence of formation error are given. Then, drawing upon the FCT, the iteration-varying switching communication topology is considered and examined. Ultimately, the validity of the ${\mathcal{D}}^{\alpha }$-type learning method is showcased through two numerical cases. Full article

This paper presents the design and analysis of Switched Fractional Order Model Reference Adaptive Controllers (SFOMRAC) for Multiple Input Multiple Output (MIMO) linear systems with unknown parameters. The proposed controller uses adaptive laws whose derivation order switches between a fractional order and the integer order, according to a certain level of control error. The switching aims to use fractional orders when the control error is larger to improve transient response and system performance during large disturbed states, and to obtain smoother control signals, leading to a better control energy usage. Then, it switches to the integer order when the control error is smaller to improve steady state. Boundedness of all the signals in the scheme is analytically proved, as well as convergence of the control error to zero. Moreover, these properties are extended to the case when system states are affected by a bounded non-parametric disturbance. Simulation studies are carried out using different representative plants to be controlled, showing that fractional orders and switching error levels can be found in most of the cases, such as when SFOMRAC achieves a better balance among control energy and system performance than the non-switched equivalent strategies. Full article

The present paper investigates a fixed-time tracking control with fractional-order dynamics for a quadrotor subjected to external disturbances. After giving the formulation problem of a quadrotor system with six subsystems like a second-order system, a fractional-order sliding manifold is then designed to achieve a fixed-time convergence of the state variables. In order to cope with the upper bound of the disturbances, a switching fixed-time controller is added to the equivalent control law. Based on the switching law, fixed-time stability is ensured. All analysis and stability are proved using the Lyapunov approach. Finally, the higher performance of the proposed controller fixed-time fractional-order sliding mode control (FTFOSMC) is successfully compared to the two existing techniques through numerical simulations. Full article

In this study, the state consensus problem is investigated for a class of nonlinear fractional-order multi-agent systems (FOMASs) by using a dynamics event-triggered sliding mode control approach. The main objective is to steer all agents to some bounded position based on their own information and the information of neighbor agent. Different from the existing results, both asymptotic consensus problem and Zeno-free behavior are ensured simultaneously. To reach this objective, a novel event-triggered sliding mode control approach is proposed, composed of distributed dynamic event-triggered schemes, event-triggered sliding mode controllers, and auxiliary switching functions. Moreover, to implement the distributed control scheme, the fractional-order adaptive law is also developed to tuning the coupling weight, which is addressed in distributed protocol. With the improved distributed control scheme, all signals in the fractional-order closed-loop systems are guaranteed to be consensus and bounded, and a novel approach is developed to avoid the Zeno behavior. Finally, the availability and the effectiveness of the above-mentioned approach are demonstrated by means of a numerical example. Full article

To obtain new solitary wave solutions for non-linear directional couplers using optical meta-materials, a new extended direct algebraic technique (EDAT) is used. This model investigates solitary wave propagation inside a fiber. As a result, twin couplers are the subject of this study. Kerr law is the sort of non-linearity addressed there. Because it offers solutions to problems with large tails or infinite fluctuations, the resulting solution set is more generalized than the current solution because it is turned into a fractional-order derivative. Furthermore, the found solutions are fractional solitons with spatial–temporal fractional beta derivative evolution. In intensity-dependent switches, these nonlinear directional couplers also serve as limiters. Non-linearity alters the transmission constants of a system’s modes. The significance of the beta derivative parameter and mathematical approach is demonstrated graphically, with a few of the extracted solutions. A parametric analysis revealed that the fractional beta derivative parameter has a significant impact on the soliton amplitudes. With the aid of the advanced software tools for numerical computations, the categories of semi-dark solitons, singular dark-pitch solitons, single solitons of Type-1 along with 2, intermingled hyperbolically, trigonometric, and rational solitons were established and evaluated. We also discussed sensitivity analysis, which is an inquiry that determines how sensitive our system is. A comparative investigation via different fractional derivatives was also studied in this paper so that one can easily understand the correlation with other fractional derivatives. The findings demonstrate that the approach is simple and efficient and that it yields generalized analytical results. The findings will be extremely beneficial in examining and comprehending physical issues in nonlinear optics, specifically in twin-core couplers with optical metamaterials. Full article

In this paper, a novel flow tracking control scheme for particleboard glue system with complex disturbance and unmeasurable system state is investigated. The method is based on hyperbolic tangent extended state observer and adaptive fuzzy fractional order global sliding mode control with exponential reaching law. The novel compound control scheme has the following advantages: Firstly, the extended state observer with hyperbolic tangent function can improve the estimation ability for the system state and complex disturbance without detailed knowledge of the controlled plant and disturbance model. Secondly, the global sliding mode control method based on fractional calculus can improve the response speed and robustness of the system, and provide a more flexible controller structure than the traditional sliding mode controller. Thirdly, the adaptive fuzzy controller is introduced to approximate the sliding mode switching term, so as to reduce the chattering phenomenon of the system. In addition, the convergence of the proposed observer and asymptotic stability of the control system are verified based on strict Lyapunov analysis. Finally, the numerical simulation results show the effectiveness of the proposed compound control scheme for particleboard glue system. Full article

In this paper, robust $H_{\infty }$ control for fractional-order switched systems (FOSSs) with uncertainty is studied. Firstly, the fractional-order switching law for FOSSs is proposed. Then, $H_{\infty }$ control for FOSSs is proven based on the switching law and linear matrix inequalities (LMIs). Moreover, $H_{\infty }$ control for FOSSs with a state feedback controller is extended. Furthermore, the LMI-based condition of robust $H_{\infty }$ control for FOSSs with uncertainty is proven. Furthermore, the condition of robust $H_{\infty }$ control is proposed to design the state feedback controller. Finally, four simulation examples verified the effectiveness of the proposed methods. Full article

This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the multi-switching synchronization method. The stochastic disturbances are considered as nonlinear uncertainties and external disturbances. Our theoretical part considers that the drive-response systems have the same or different dimensions. Firstly, a FO sliding surface is established in terms of the fractional calculus. Secondly, depending on the FO Lyapunov stability theory and the sliding mode control technique, the multi-switching adaptive controllers (MSAC) and some suitable multi-switching adaptive updating laws (MSAUL) are designed. They can ensure that the state variables of the drive systems are synchronized with the different state variables of the response systems. Simultaneously, the unknown parameters are assessed, and the upper bound values of stochastic disturbances are examined. Selecting the suitable scale matrices, the multi-switching projection synchronization, multi-switching complete synchronization, and multi-switching anti-synchronization will become special cases of MSSMCS. Finally, examples are displayed to certify the usefulness and validity of the scheme via MATLAB. Full article

This research paper deals with the passivity and synchronization problem of fractional-order memristor-based competitive neural networks (FOMBCNNs) for the first time. Since the FOMBCNNs’ parameters are state-dependent, FOMBCNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, the conventional robust control scheme cannot guarantee the synchronization of FOMBCNNs. Under the framework of the Filippov solution, the drive and response FOMBCNNs are first transformed into systems with interval parameters. Then, the new sufficient criteria are obtained by linear matrix inequalities (LMIs) to ensure the passivity in finite-time criteria for FOMBCNNs with mismatched switching jumps. Further, a feedback control law is designed to ensure the finite-time synchronization of FOMBCNNs. Finally, three numerical cases are given to illustrate the usefulness of our passivity and synchronization results. Full article

In this paper, an adaptive double feedback fuzzy neural fractional order sliding control approach is presented to solve the problem that lumped parameter uncertainties cannot be measured and the parameters are unknown in a micro gyroscope system. Firstly, a fractional order sliding surface is designed, and the fractional order terms can provide additional freedom and improve the control accuracy. Then, the upper bound of lumped nonlinearities is estimated online using a double feedback fuzzy neural network. Accordingly, the gain of switching law is replaced by the estimated value. Meanwhile, the parameters of the double feedback fuzzy network, including base widths, centers, output layer weights, inner gains, and outer gains, can be adjusted in real time in order to improve the stability and identification efficiency. Finally, the simulation results display the performance of the proposed approach in terms of convergence speed and track speed. Full article

Topology structure and system parameters have a great influence on the dynamical behavior of dynamical networks. However, they are sometimes unknown or uncertain in advance. How to effectively identify them has been investigated in various network models, from integer-order networks to fractional-order networks with the same order. In the real world, many systems consist of subsystems with different fractional orders. Therefore, the structure identification of a dynamical network with different fractional orders is investigated in this paper. Through designing proper adaptive controllers and parameter updating laws, two network estimators are well constructed. One is for identifying only the unknown topology structure. The other is for identifying both the unknown topology structure and system parameters. Based on the Lyapunov function method and the stability theory of fractional-order dynamical systems, the theoretical results are analytically proved. The effectiveness is verified by three numerical examples as well. In addition, the designed estimators have a good performance in monitoring switching topology. From the practical viewpoint, the designed estimators can be used to monitor the change of current and voltage in the fractional-order circuit systems. Full article