Search Results (5)

Chaotic behavior and memory-dependent dynamics in fractional-order brushless DC motors (FOBLDCMs) pose significant challenges for robust and stable control design, particularly when physical constraints such as actuator saturation and rate limitations are present. Existing control frameworks often neglect these nonlinear limitations, resulting in performance degradation and potential instability in practical applications. Motivated by these challenges, this paper presents a comprehensive Lyapunov-based stability and control synthesis framework for FOBLDCMs within the fractional-order (FO) range $0<v<1$. The proposed methodology employs indirect, direct, and composite Lyapunov functions to derive sufficient stability conditions under four scenarios: unconstrained input, saturation-only, rate-limited-only, and combined constraints. For each case, a family of stabilizing controllers is designed to explicitly handle the respective limitations. To the best of our knowledge, this is the first study to rigorously address both saturation and rate limitations in the control design of FO chaotic systems. Numerical simulations confirm that the proposed controllers significantly improve performance over existing methods. Specifically, the unconstrained controller achieves a notable reduction in control energy (from $2.72\times {10}^5$ to $1.83\times {10}^5$), a 26.3% decrease in maximum control effort, and enhanced or comparable tracking accuracy, as indicated by lower ISE and RMSE values. These results highlight the robustness and practical applicability of the proposed control framework for real-world FO electromechanical systems. Full article

Renewable energy sources play a pivotal role in the pursuit of sustainable and eco-friendly power solutions. While offering environmental benefits, they present inherent challenges. Photovoltaic systems rely on surrounding conditions, wind systems contend with variable wind speeds, and fuel cells are both costly and inefficient. Furthermore, the energy injected by renewable energy sources (RES) exhibits unpredictable behavior. To tackle these problems, researchers employ diverse power electronic devices and converters like inverters, power quality filters, and DC–DC choppers. Among these, DC–DC converters stand out for effectively regulating DC voltage and enhancing the efficiency of RESs. The meticulous selection of a suitable DC–DC converter, coupled with the integration of an efficient control technique, significantly influences overall power system performance. This paper introduces a novel approach to the design of switching controllers for DC–DC converters, specifically tailored for application in renewable energy systems. The proposed controller leverages the power of composite switched Lyapunov functions (CSLF) to enhance the efficiency and performance of DC–DC converters, addressing the unique challenges posed by renewable energy sources. Through comprehensive analysis and simulation, this study demonstrates the efficacy of the controller in optimizing power transfer, improving stability, and ensuring reliable operation in diverse renewable energy environments. Moreover, the small-scale DC–DC converter experiment’s findings are presented to confirm and validate the proposed scheme’s practical applicability. Full article

In practice, various factors such as friction, unmodeled dynamics and uncertain external disturbances often affect overhead cranes. The existing crane control methods often neglect these factors or address these factors by robust techniques. Moreover, most of them do not take input saturation into account and require full-state feedback. In this paper, taking the practical issues of uncertain disturbances, input saturation and output feedback into account, we propose an input-saturated output feedback control strategy for the underactuated two-dimensional (2-D) overhead crane systems with uncertain disturbances. Specifically, we first design a disturbance observer that can accurately estimate the external disturbance. Then, the virtual horizontal location signal is introduced and the new energy storage function is constructed. A novel composite control method for overhead crane systems is proposed based on the developed disturbance observer and the new energy storage function. The stability and convergence analysis are given through Lyapunov techniques and LaSalle’s invariance theorem. In order to verify the performance of the proposed controller, we perform a series of simulation tests and compare the proposed method with some existing control methods. Full article

In this paper, an adaptive iterative learning control (AILC) law is developed for two-link rigid-flexible coupled manipulator system in three-dimensional (3D) space with time-varying disturbances and input constraints. Based on the Hamilton’s principle, a dynamic model of a manipulator system is established. The conditional equation that is coupled by ordinary differential equations and partial differential equations is derived. In order to achieve high-precision tracking of the revolving angles and vibration suppression of the elastic part, the iterative learning control law based on the disturbance observer is considered in the process of the design controller. The composite Lyapunov energy function is proposed to prove that the angle errors and elastic deformation can eventually converge to zero with the increase of the number of iterations. Ultimately, the simulation results to rigid-flexible coupled manipulator system are given to prove the convergence of the control objectives under the adaptive iterative learning control law. Full article

Background: Pneumatic muscle actuator (PMA) actuated multisection continuum arms are widely applied in various fields with high flexibility and bionic properties. Nonetheless, their kinematic modeling and control strategy proves to be extremely challenging tasks. Methods: The relationship expression between the deformation parameters and the length of PMA with the geometric method is obtained under the assumption of piecewise constant curvature. Then, the kinematic model is established based on the improved D-H method. Considering the limitation of PMA telescopic length, an impedance iterative learning backstepping control strategy is investigated. For one thing, the impedance control is utilized to ensure that the ideal static balance force is maintained constant in the Cartesian space. For another, the iterative learning backstepping control is applied to guarantee that the desired trajectory of each PMA can be accurately tracked with the output-constrained requirement. Moreover, iterative learning control (ILC) is implemented to dynamically estimate the unknown model parameters and the precondition of zero initial error in ILC is released by the trajectory reconstruction. To further ensure the constraint requirement of the PMA tracking error, a log-type barrier Lyapunov function is employed in the backstepping control, whose convergence is demonstrated by the composite energy function. Results: The tracking error of PMA converges to 0.004 m and does not exceed the time-varying constraint function through cosimulation. Conclusion: From the cosimulation results, the superiority and validity of the proposed theory are verified. Full article