Search Results (71)

Piezoelectric flexure micro-positioning stages are essential micromotion actuators for micro-assembly, atomic force microscopy and nano-manufacturing, but intrinsic hysteresis nonlinearity of piezoelectric stacks distorts the linear voltage-to-displacement mapping and induces significant micro-positioning errors. Conventional hysteresis compensation based on offline-calibrated Krasnosel’skii-Pokrovskii (KP) models cannot adapt to time-varying excitation, whereas state-of-the-art adaptive KP control requires auxiliary dynamic equations and imposes high computational overhead on miniature real-time controllers. To address these limitations, this paper develops a single-degree-of-freedom micromotion positioning device equipped with symmetric two-stage displacement amplification mechanisms and straight circular flexure hinges. ANSYS finite element simulations validate the mechanical stiffness, structural safety and linear amplification characteristic of the micro-positioning stage, achieving a maximum output stroke of 95.95 μm. A discretized KP hysteresis model is constructed to accurately capture the asymmetric rate-dependent hysteresis of piezoelectric stacks. On this basis, a lightweight adaptive inverse control framework is proposed, which realizes online tuning of KP weights through gradient descent iteration only relying on real-time position feedback, eliminating static pre-calibration and extra dynamic correction links. Tracking experiments under 0.1–2 Hz sinusoidal waveforms and 3–7 V variable-amplitude sinusoidal waveforms are implemented. Experimental results show that the proposed approach reduces the root-mean-square error (RMSE) by 7.41–85.65% and the mean absolute percentage error (MAPE) by 7.56–87.81% compared with uncompensated open-loop micromotion control. The combined micro-flexure mechanical design and adaptive hysteresis compensation strategy greatly improves positioning accuracy and anti-interference capacity, offering a low-computation technical route for high-performance micro-positioning systems. Full article

Space-time adaptive processing (STAP) is regarded as a highly effective approach for clutter mitigation in airborne radar applications. However, in practical range-ambiguous scenarios, the clutter suppression performance of traditional STAP algorithms can be severely degraded. Element-pulse coding (EPC) radar introduces extra controllable freedoms by assigning frequency offsets among array elements, which provides a promising means to cope with the influence of range ambiguity. On this basis, EPC-assisted STAP techniques have attracted increasing attention. Even so, the large number of adaptive degrees of freedom (DoFs) required by EPC-STAP makes its performance highly dependent on sufficient training snapshots, and a noticeable degradation may occur when only limited snapshots are available. To overcome this limitation, this study focuses on reduced-dimension (RD) STAP for airborne EPC radar under range-ambiguous conditions and develops an efficient reduced-dimension EPC-STAP scheme. Specifically, the received signal model of the airborne EPC-STAP system is first formulated to characterize the data structure. Subsequently, a tailored linear mapping matrix is constructed to compress the original high-dimensional observation space. The resulting RD-EPC-STAP processor is then obtained according to the minimum variance distortionless response principle using the transformed lower-dimensional data. Numerical experiments verify that the proposed algorithm provides improved clutter rejection capability while retaining strong tolerance to array gain and phase errors. Full article

An optical lens focuses light and a similar device can be developed to focus surface water waves. A detailed description of such hydrodynamic lenses is given, for which the focusing is induced by shaping the bathymetry of the bottom. Classically, the Luneburg lens uses a specific radial variation of the refractive index. The modified Luneburg lens (MLL) introduces an extra degree of freedom, permitting the focal point to be tuned. It is shown how to design the MLL for water waves, and then its performance is evaluated. Compared with a simple parabolic-shaped mount, the MLL is shown to be free of spherical aberration, resulting in a focus with larger intensity and smaller size of the focal point. Moreover, the focusing properties can be tuned and enhanced thanks to the possibility of changing the position of the focal point. The focusing quality of the MLL is described in all water-depth regimes (covering dispersive and non-dispersive waves) and the focusing of linear and nonlinear waves is revealed experimentally. The option of moving the focal point outside the lens, where the water depth is constant, may be useful when locating devices for harvesting wave energy. Full article

The frequency diverse array (FDA) radar can provide an increased degree of freedom (DOF) in the range domain and offer benefits in range-dependent interference suppression. This paper proposes a vertical frequency diverse array (VFDA)-based approach to suppress deceptive jamming for forward-looking array radar under diving motion. Specifically, the effects of diving motion and frequency increment on the beampattern and clutter spectrum are analyzed. Diving motion introduces azimuth information into the elevation dimension echo, and VFDA offers extra DOF in the elevation dimension to distinguish the false-target jamming from the true target. On this basis, an elevation filter is designed using the linearly constrained minimum variance (LCMV) criterion to mitigate deceptive jamming. Then, the space–time adaptive processing (STAP) processor with clutter compensation is applied to suppress the remaining clutter. In addition, the design criterion for the frequency increment and computational complexity analysis are provided. Numerical simulations verify the effectiveness of the proposed method. The signal model is developed for the diving forward-looking array radar based on the VFDA. The effects of the diving motion and frequency increment on the beampattern and clutter spectrum are analyzed. A novel VFDA STAP approach is proposed to mitigate clutter and deceptive jamming. The design criterion for the frequency increment is provided and the computational complexities are analyzed. MSC: 94A12 Full article

We investigate the Kaluza–Klein modes of a bulk $U(1)$ gauge field coupled to a dilaton in six-dimensional brane-world scenarios. We demonstrate that four-dimensional gauge invariance is preserved via a Stueckelberg-like mechanism driven by scalar KK modes arising from the extra-dimensional components. By introducing a bulk gauge-fixing constraint to determine the scalar dynamics and mapping the equations of motion into Schrödinger-like forms, we numerically analyze the mass spectra for two distinct brane solutions. Crucially, we clarify that the physical scalar degree of freedom arises from a gauge-invariant coupling between two underlying scalar modes. Our numerical results reveal that this mixing effect lifts the spectral degeneracy, establishing a distinct mass hierarchy where the massive vector modes are consistently heavier than the physical scalar modes. Full article

We develop a fully gauge-invariant analysis of gravitational-wave polarizations in metric $f\left(R\right)$ gravity with a particular focus on the modified Starobinsky model $f\left(R\right)=R+\alpha R^2-2\mathsf{\Lambda }$, whose constant-curvature solution $R_d=4\mathsf{\Lambda }$ provides a natural de Sitter background for both early- and late-time cosmology. Linearizing the field equations around this background, we derive the Klein–Gordon equation for the curvature perturbation $\delta R$ and show that the scalar propagating mode acquires a mass $m_{\psi }^2=1/\left(6\alpha \right)$, highlighting how the same scalar degree of freedom governs inflationary dynamics at high curvature and the propagation of gravitational waves in the current accelerating Universe. Using the scalar–vector–tensor decomposition and a decomposition of the perturbed Ricci tensor, we obtain a set of fully gauge-invariant propagation equations that isolate the contributions of the scalar, vector, and tensor modes in the presence of matter. We find that the tensor sector retains the two transverse–traceless polarizations of General Relativity, while the scalar sector contains an additional massive scalar propagating degree of freedom, which manifests through breathing and longitudinal tidal responses depending on the wave regime and detector frame. Through the geodesic deviation equation—computed both in a local Minkowski patch and in fully covariant de Sitter form—we independently recover the same polarization content and identify its tidal signatures. The resulting framework connects the extra scalar polarization to cosmological observables: the massive scalar propagating mode sets the range of the fifth force, influences the time evolution of gravitational potentials, and affects the propagation and dispersion of gravitational waves on cosmological scales. This provides a unified, gauge-invariant link between gravitational-wave phenomenology and the cosmological implications of metric $f\left(R\right)$ gravity. Full article

Although parallel mechanisms are used in various fields, their application is often limited by singularities and a restricted workspace. Kinematic redundancy is a promising approach for mitigating these issues while also extending the functionality of the mechanisms. This article contributes to this field by introducing two novel Delta-type kinematically redundant parallel mechanisms with linear actuators. The moving platform in these mechanisms has three translational degrees of freedom and consists of two parts connected by a prismatic joint, providing an extra translation between the parts. First, we present closed-form solutions to the inverse and forward kinematic problems, accompanied by numerical examples that validate the theoretical derivations. Next, we analyze singular configurations of the mechanisms with a symmetrical design, focusing on parallel singularities. Using an iterative approach, we identify points within the workspace corresponding to these configurations, including finite-motion singularities. Based on this analysis, we changed the geometrical parameters of one mechanism and presented the design where the singularity-free region of the workspace occupies 95% of the total workspace. This study forms the basis for future research on the proposed mechanisms and their prototyping. Full article

Brushless DC (BLDC) motors are commonly used in electric vehicles (EVs) because of their efficiency, small size and great torque-speed performance. These motors have a few benefits such as low maintenance, increased reliability and power density. Nevertheless, BLDC motors are highly nonlinear and their dynamics are very complicated, in particular, under changing load and supply conditions. The above features require the design of strong and adaptable control methods that can ensure performance over a broad spectrum of disturbances and uncertainties. In order to overcome these issues, this paper uses a Fractional-Order Proportional-Integral-Derivative (FOPID) controller that offers better control precision, better frequency response, and an extra degree of freedom in tuning by using non-integer order terms. Although it has the benefits, there are three primary drawbacks: (i) it is not real-time adaptable, (ii) it is hard to choose appropriate initial gain values, and (iii) it is sensitive to big disturbances and parameter changes. A new control framework is suggested to address these problems. First, a Reinforcement Learning (RL) approach based on Deep Deterministic Policy Gradient (DDPG) is presented to optimize the FOPID gains online so that the controller can adjust itself continuously to the variations in the system. Second, Snake Optimization (SO) algorithm is used in fine-tuning of the FOPID parameters at the initial stages to guarantee stable convergence. Lastly, cascade control structure is adopted, where FOPID controllers are used in the inner (current) and outer (speed) loops. This construction adds robustness to the system as a whole and minimizes the effect of disturbances on the performance. In addition, the cascade design also allows more coordinated and smooth control actions thus reducing stress on the power electronic switches, which reduces switching losses and the overall efficiency of the drive system. The suggested RL-enhanced cascade FOPID controller is verified by Hardware-in-the-Loop (HIL) testing, which shows better performance in the aspects of speed regulation, robustness, and adaptability to realistic conditions of operation in EV applications. Full article

This paper presents the development of a novel aerodynamic model tailored for the Bio-Inspired Rotating Empennage (BIRE), a non-traditional fixed-wing aircraft empennage inspired by avian flight. The BIRE replaces the conventional vertical stabilizer with an extra degree of freedom for the horizontal stabilizer, which is allowed to rotate about the body-fixed x axis. This empennage is similar to the tail of a bird, and allows control of both longitudinal and lateral moments. However, such a design introduces complex nonlinear longitudinal and lateral aerodynamic interactions, not typically accounted for in most fixed-wing aircraft aerodynamic models below stall. This work presents a nonlinear sinusoidal aerodynamic model that can be used for fixed-wing aircraft with this type of empennage. Although the aerodynamic model is constructed to accurately capture the degrees of freedom of this particular empennage design, similar methods could be used to develop other aerodynamic models for non-traditional control effectors. A large dataset of low-fidelity aerodynamic data was generated using a modern numerical lifting-line algorithm, and these data were fit to the nonlinear sinusoidal aerodynamic model. A method for fitting the data is demonstrated, and the results show that the nonlinear sinusoidal aerodynamic model can be fit to the data with an accuracy of less than 10% of the maximum deviation of the aerodynamic coefficients in root-mean-square error. The underlying physics of many of the longitudinal and lateral nonlinear sinusoidal aerodynamic properties of the aircraft are discussed in detail. The methodology presented here can be extended to other non-traditional control effectors, encouraging innovative approaches in aerodynamic modeling and aircraft design. In contrast, choosing to model control effectors using the traditional, linear approach can obscure key aerodynamic behaviors key for trim and control analyses. The study’s findings underscore the importance of developing adaptable aerodynamic models to support the advancement of next-generation aircraft designs and control systems. Full article

The output processer of interval type-2 fuzzy logic systems (IT2FLSs) is a complex operator which performs type-reduction plus defuzzification (TR+D) tasks. In this paper, a complexity-reduced yet high-performance TR+D for IT2FLSs based on Maclaurin series approximation is utilized within a feedback-error-learning (FEL) control structure for controlling linear move stages. IT2FLSs are widely used for control purposes, as they provide extra degrees of freedom to increase control accuracies. FEL benefits from a classical controller, which is responsible for providing overall system stability, as well as a guideline for the training mechanism for IT2FLSs. The Kalman filter approach is utilized to tune IT2FLS parameters in this FEL structure. The proposed control method is applied to a linear stage in real time. Using an identification process, a model of the real-time linear stage is developed. Simulation results indicate that the proposed FEL approach using the Kalman filter as an estimator is an effective approach that outperforms the gradient descent-based FEL method and the proportional derivative (PD) classical controller. Motivated by the performance of the proposed Kalman filter-based FEL approach, it is used to control a linear move stage in real time. The position feedback of the move stage is provided by a precision laser interferometer capable of performing measurements with an accuracy of less than $1\mathsf{\mu }\mathrm{m}$. Using this measurement system in a feedback loop with the proposed control algorithm, the overall steady state of the system is less than $20\mathsf{\mu }\mathrm{m}$. The results illustrate the high-precision control capability of the proposed controller in real-time. Full article

Wavelength selective switches (WSSs) are essential elements for wavelength division multiplexing (WDM) optical networks, as they offer cost-effective, high port-count and flexible spectral channel switching. This work proposes a new hybrid WSS architecture that leverages the beam shaping and steering features of uniform silicon nitride-based end-fire optical phased arrays (OPAs). By introducing beamforming to a WSS system, the spectral channels on the liquid crystal on silicon (LCoS) panel can be tailored and arranged properly, depending on the optical configuration, using the beam control capabilities of OPAs. Combining 3D-FDTD and ray tracing simulations, the study shows that, by reducing the input beam dimensions with proper sizing of the OPAs, the WSS design with a null-steering OPA layout and 4 × N_o switch size features increased spectral resolution. This extensive beamforming study on the steering-enabled layout reveals the acquirement of an even higher input channel number, matching the 8 × N_o WSS scheme, with flexible channel routing on the LCoS panel. Such implementation of beamsteerers can unlock an extra degree of freedom for the switching capabilities of hybrid WSS devices. The results show great promise for the introduction of OPAs in WSS systems and provide valuable insight for the design of future wireless communication links and WDM systems. Full article

Silicon nitride (Si₃N₄) is an ideal candidate for the development of low-loss photonic integrated circuits. However, efficient light coupling between standard optical fibers and Si₃N₄ chips remains a significant challenge. For vertical grating couplers, the lower index contrast yields a weak grating strength, which translates to long diffractive structures, limiting the coupling performance. In response to the rise of hybrid photonic platforms, the adoption of multi-layer grating arrangements has emerged as a promising strategy to enhance the performance of Si₃N₄ couplers. In this work, we present the design of high-efficiency surface grating couplers for the Si₃N₄ platform with an amorphous silicon (α-Si) overlay. The surface grating, fully formed in an α-Si waveguide layer, utilizes subwavelength grating (SWG)-engineered metamaterials, enabling simple realization through single-step patterning. This not only provides an extra degree of freedom for controlling the fiber–chip coupling but also facilitates portability to existing foundry fabrication processes. Using rigorous three-dimensional (3D) finite-difference time-domain (FDTD) simulations, a metamaterial-engineered grating coupler is designed with a coupling efficiency of −1.7 dB at an operating wavelength of 1.31 µm, with a 1 dB bandwidth of 31 nm. Our proposed design presents a novel approach to developing high-efficiency fiber–chip interfaces for the silicon nitride integration platform for a wide range of applications, including datacom and quantum photonics. Full article

In this article, we study the form of the deviation of geodesics (tidal forces) and the Raychaudhuri equation in a Schwarzschild–Finsler–Randers (SFR) spacetime which has been investigated in previous papers. This model is obtained by considering the structure of a Lorentz tangent bundle of spacetime and, in particular, the kind of the curvatures in generalized metric spaces where there is more than one curvature tensor, such as Finsler-like spacetimes. In these cases, the concept of the Raychaudhuri equation is extended with extra terms and degrees of freedom from the dependence on internal variables such as the velocity or an anisotropic vector field. Additionally, we investigate some consequences of the weak-field limit on the spacetime under consideration and study the Newtonian limit equations which include a generalization of the Poisson equation. Full article

Bimetallic nanoparticles expand the possibilities of catalyst design, providing an extra degree of freedom for tailoring the catalyst structure in comparison to purely monometallic systems. The distribution mode of two metal species defines the structure of surface catalytic sites, and current research efforts are focused on the development of methods for their controlled tuning. In light of this, a comprehensive investigation of the factors which influence the changes in the morphology of bimetallic nanoparticles, including the elemental redistribution, are mandatory for each particular bimetallic system. Here we present the combined XPS/STM study of the surface structure and morphology of bimetallic Pt-Au/HOPG nanoparticles prepared by thermal vacuum deposition and show that thermal annealing up to 350 °C induces the alloying process between the two bulk-immiscible metal components. Increasing the treatment temperature enhances the extent of Pt-Au alloying. However, the sintering of nanoparticles starts to occur above 500 °C. The approach implemented in this work includes the theoretical simulation of XPS signal intensities for a more meticulous analysis of the compositional distribution and can be helpful from a methodological perspective for other XPS/STM studies of bimetallic nanoparticles on planar supports. Full article

The mobile platform of the parallel robot designed for picking and placing operations is usually equipped with one or two extra degree(s) of freedom to enable flexible grasping orientations. However, additional motors indicate extra loads for the moving platform, and the total payload performance shrinks. This paper proposes a spatial picking-and-placing manipulator, in which one actuator that is supposed to be installed on the mobile platform is placed far away from the mobile platform. The platform has a large workspace along one direction. The comprehensive analytical inverse and forward kinematic solutions of this robot are derived. The reachable workspace of the parallel manipulator module is then explored. The novel performance level index is designed to normalize the performance index and demonstrate the performance rank for any pose. A mathematical proof is provided for this novel index. The manipulability index is taken as an example to examine the level indicator. A multi-objective optimization is implemented to pursue optimal performance; then, the initial design and optimized results are compared in detail. A sample trajectory is provided to verify the correctness of the kinematic mathematical model of the parallel mechanism. Full article