PID and Fuzzy Logic Control of Ball and Beam System Using Particle Swarm Optimization

In this research, we carried out the modeling of the ball and beam system (BBS) within the MATLAB/Simulink framework by applying both proportional-integral-derivative (PID) and fuzzy logic control strategies to govern the dynamics of this constructed model. The underlying non-linear dynamic equations adjusting the behavior of the BBS system are based on Newton’s second law of motion. The physical installation of the BBS, designed for potential real-time application, comprises a lengthy beam subject to movement through the action of a DC servomotor, with a ball traversing the beam in a reciprocating manner. A distance sensor is strategically placed in front of the beam to determine the exact position of the ball. In this system, an electrical control signal applied to the DC servomotor causes the beam to pivot about its horizontal axis, thereby enabling the ball to move freely along the beam's length. To avoid the risk of losing the ball equilibrium on the beam and to achieve precise system control, a mathematical model was devised and implemented within the MATLAB/Simulink environment. The use of the particle swarm optimization (PSO) algorithm was aimed at tackling the task of refining and optimizing the PID controller specifically designed for the linearized ball and beam control system. The presented system is controlled using both PID and fuzzy logic, and the use of the PSO algorithm enhances the system’s responsiveness efficiency.

Active control and experiment study of a flexible hub-beam system

The first-order approximation coupling （FOAC） model was proposed recently for dynamics and control of flexible hub-beam systems. This model may deal with system dynamics for both low and high rotation speed, while the classical zeroth-order approximation coupling （ZOAC） model is only available for low rotation speed. This paper assumes the FOAC model to present experimental study of active positioning control of a flexible hub-beam system. Linearization and nonlinear control strategies are both considered. An experiment system based on a DSP TMS320F2812 board is introduced. The difference between linearization and nonlinear control strategies are studied both numerically and experimentally. Simulation and experimental results indicate that, linearized controller can make the system reach an expected position with suppressed vibration of flexible beam, but the time taken to position is longer than expected, whereas nonlinear controller works well with precise positioning, suppression of vibration and time control.

Intelligent Dynamic Inversion Controller Design for Ball and Beam System

The Ball and beam system(BBS)is an attractive laboratory experimental tool because of its inherent nonlinear and open-loop unstable properties.Designing an effective ball and beam system controller is a real challenge for researchers and engineers.In this paper,the control design technique is investigated by using Intelligent Dynamic Inversion(IDI)method for this nonlinear and unstable system.The proposed control law is an enhanced version of conventional Dynamic Inversion control incorporating an intelligent control element in it.The Moore-PenroseGeneralized Inverse(MPGI)is used to invert the prescribed constraint dynamics to realize the baseline control law.A sliding mode-based intelligent control element is further augmented with the baseline control to enhance the robustness against uncertainties,nonlinearities,and external disturbances.The semi-global asymptotic stability of IDI control is guaranteed in the sense of Lyapunov.Numerical simulations and laboratory experiments are carried out on this ball and beam physical system to analyze the effectiveness of the controller.In addition to that,comparative analysis of RGDI control with classical Linear Quadratic Regulator and Fractional Order Controller are also presented on the experimental test bench.

Dynamic Analysis of Kineto-Elastic Beam System with Second-order Effect

Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-Bernoulli beam elements were used. Because accuracy is higher in non-linear structural analysis,three-node beam elements are used to deduce shape functions and stiffness matrices in dynamic equations of flexible elements. Static condensation method was used to obtain the finial dynamic equations of three-node beam elements. According to geometrical relations of nodal displacements in concomitant and global coordinate system,dynamic equations of elements can be transformed to global coordinate system by concomitant coordinate method in order to build the global dynamic equations. Analyzed amplitude condition of flexible arm support of a port crane,the results show that second-order effect should be considered in kinetic-elastic analysis for heavy load machinery of big flexibility.

Three-to-one internal resonance in multiple stepped beam systems

In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales （a perturbation technique）. The modulation equations of the amplitudes and the phases are derived for two modes. These equations are utilized to determine steady state solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and .frequency- response curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots.

Dynamic Calculation Method of Beam System Under Low Velocity Impact

The bearing beams and the supporting beams under low velocity impact may be in four different strain stages of deformation depending on the impact intensity and beam structure strength.Based on the different judging conditions of deformation stages,the corresponding calculation models are proposed,the calculation formulae for the determination of the impact force and the beam's lateral displacement are obtained.Calculation shows that the beam's total deflection is small when the flexibility of the supporting component is high and the effect of diminishing deflection disappears almost when the stiffness of the supporting component is high.

EIGENFREQUENCIES OF THE THREE DIMENSIONAL EULER－BERNOULLI BEAM SYSTEM WITH DISSIPATIVE JOJNTS

In this paper, we will compute the transfer matrices to find the eigenfrequenciesfor the vibrations of the general non-collinear Euler-Bernoulli or Timoshenko beamstructure with dissipative joints. We will allow the structure to be three dimensional,and thus we must consider all types of vibrations simulaneously, including longitudinaland torsional vibrations. The general structure considered will consist of any number ofbeams joined end to end to form a chain. Many, different kinds of dampers areallowed, even within the same structure. We also will allow different materials withinthe structure as well as different beam widths. We then will show. that asymptotic estimates can be used to find the eigenfrequencies approximately.

Visual Feedback Balance Control of a Robot Manipulator and Ball-Beam System

In this paper, we present a vision guided robotic ball-beam balancing control system, consisting of a robot manipulator (actuator), a ball-beam system (plant) and a machine vision system (feedback). The machine vision system feedbacks real-time beam angle and ball position data at a speed of 50 frames per second. Based on feedback data, the end-effector of a robot manipulator is driven to control the ball position by maneuvering of the inclination angle of the ball-beam system. The overall control system is implemented with two FPGA chips, one for machine vision processing, and one for robot joints servo PID controllers as well as ball position PD controller. Experiments are performed on a 5-axes robot manipulator to validate the proposed ball beam balancing control system.

Two-dimensional precise figuring of 500 mm-long X-ray mirror using one-dimensional ion beam system

In this study,a new method was developed to realize two-dimensional(2D)figure correction of grazing-incidence X-ray mirrors using a one-dimensional(1D)ion-beam figuring system.A mask of holes was specifically designed to generate removal functions at different widths and extend the figuring capability over a wide area.Accordingly,a long mirror could be manufactured.Using this method,the surface height root-mean-square(RMS)error of the center area of 484 mm×16 mm was reduced from 11.49 nm to 2.01 nm,and the 1D meridional RMS error reached 1.0 nm.The proposed method exhibits high precision and cost effectiveness for production of long X-ray mirrors.

Seismic performance evaluation of hybrid coupled shear wall system with shear and flexural fuse-type steel coupling beams

Replaceable flexural and shear fuse-type coupling beams are used in hybrid coupled shear wall(HCSW)systems,enabling concrete buildings to be promptly recovered after severe earthquakes.This study aimed to analytically evaluate the seismic behavior of flexural and shear fuse beams situated in short-,medium-and high-rise RC buildings that have HCSWs.Three building groups hypothetically located in a high seismic hazard zone were studied.A series of 2D nonlinear time history analyses was accomplished in OpenSees,using the ground motion records scaled at the design basis earthquake level.It was found that the effectiveness of fuses in HCSWs depends on various factors such as size and scale of the building,allowable rotation value,inter-story drift ratio,residual drift quantity,energy dissipation value of the fuses,etc.The results show that shear fuses better meet the requirements of rotations and drifts.In contrast,flexural fuses dissipate more energy,but their sectional stiffness should increase to meet other requirements.It was concluded that adoption of proper fuses depends on the overall scale of the building and on how associated factors are considered.

Method for active spatial alignment and stabilization of laser beams in multi-beam systems

We propose a new method for the development of multi-beam systems for the spatial alignment and stability of beams based on the error separation technique.This method avoids alignment errors caused by coupling effect of piezoelectric devices,inaccurate correction calculations,and detection mode of the angular deviation.According to the results by external detectors,the error value of spatial alignment and the root mean square[RMS]of deviations under control during 1 h can be equivalent to approximately 0.87 and 1.06 nm at the sample plane under an oil immersion lens[focal length f=2 mm].The RMS of deviations is less than one-third of those currently reported for multi-beam systems;therefore,higher alignment and stability accuracy can be achieved with our proposed method.

Miniature tunable Airy beam optical meta-device

Tunable Airy beams with controllable propagation trajectories have sparked interest in various fields,such as optical manipulation and laser fabrication.Existing research approaches encounter challenges related to insufficient compactness and integration feasibility,or they require enhanced tunability to enable real-time dynamic manipulation of the propagation trajectory.In this work,we present a novel method that utilizes a dual metasurface system to surpass these limitations,significantly enhancing the practical potential of the Airy beam.Our approach involves encoding a cubic phase profile and two off-axis Fresnel lens phase profiles across the two metasurfaces.The validity of the proposed strategy has been confirmed through simulation and experimental results.The proposed meta-device addresses the existing limitations and lays the foundation for broadening the applicability of Airy beams across diverse domains,encompassing light-sheet microscopy,laser fabrication,optical tweezers,etc.

NOMA-Based Collaborative Beam Hopping Frequency Allocation Mechanism for Future LEO Satellite Systems

Low Earth orbit(LEO) satellite systems provide terrestrial users with services that are not limited by geographical location. However, the conflict between existing allocation schemes and the business variability between beams is becoming increasingly prominent. Beam hopping technology allows for a more flexible and versatile approach to satellite resource allocation. This paper proposes a beam hopping pattern optimization scheme that jointly considers the interference threshold distance and beam service priority, reducing the inter-beam co-channel interference(CCI). In the cluster area, a non-orthogonal multiple access(NOMA)-based collaborative beam hopping(NCBH) scheme is proposed to minimize the cell-edge user(CEU) interference. Since there is a difference in channel gain between the CEU and cellcenter user(CCU), this scheme forms a NOMA cluster to perform power domain multiplexing and formulates a NOMA cluster pairing strategy according to the user location to reduce the CCI of the CEU. After NOMA cluster pairing, the optimal carrier frequency of the NOMA cluster is selected by a reinforcement learning algorithm. The simulation results verify the excellent performance of the proposed NCBH scheme regarding the user’s received power, transmission rate, and outage probability.

Co-doped BaFe_(2)As_(2) Josephson junction fabricated with a focused helium ion beam

Josephson junction plays a key role not only in studying the basic physics of unconventional iron-based superconductors but also in realizing practical application of thin-film based devices,therefore the preparation of high-quality iron pnictide Josephson junctions is of great importance.In this work,we have successfully fabricated Josephson junctions from Co-doped BaFe_(2)As_(2)thin films using a direct junction fabrication technique which utilizes high energy focused helium ion beam(FHIB).The electrical transport properties were investigated for junctions fabricated with various He^(+)irradiation doses.The junctions show sharp superconducting transition around 24 K with a narrow transition width of 2.5 K,and a dose correlated foot-structure resistance which corresponds to the effective tuning of junction properties by He^(+)irradiation.Significant J_c suppression by more than two orders of magnitude can be achieved by increasing the He^(+)irradiation dose,which is advantageous for the realization of low noise ion pnictide thin film devices.Clear Shapiro steps are observed under 10 GHz microwave irradiation.The above results demonstrate the successful fabrication of high quality and controllable Co-doped BaFe_(2)As_(2)Josephson junction with high reproducibility using the FHIB technique,laying the foundation for future investigating the mechanism of iron-based superconductors,and also the further implementation in various superconducting electronic devices.

Cubature Kalman Filter Based Millimeter Wave Beam Tracking for OTFS Systems

In this paper,a Millimeter wave(mmWave)beam tracking problem is studied in orthogonal time frequency space(OTFS)systems.Considering the nonlinearity of beamforming and the constraints of existing Kalman-filtering based beam tracking schemes,we propose a novel Cubature Kalman Filter(CKF)framework tracking the channel state information(CSI)to manage the challenge of highspeed channel variation in single-user moving scene for OTFS systems.Aiming for low complexity for mobile settings,this paper trains only one beam pair to track a path to maintain the reliable communication link in the analog beamforming architecture.Simulation results show that our proposed method has better tracking performance to improve the accuracy of the estimated beam angle compared with prior work.

Beam Training and Tracking in mmWave Communication:A Survey

Communicating on millimeter wave(mmWave)bands is ushering in a new epoch of mobile communication which provides the availability of 10 Gbps high data rate transmission.However,mmWave links are easily prone to short transmission range communication because of the serious free space path loss and the blockage by obstacles.To overcome these challenges,highly directional beams are exploited to achieve robust links by hybrid beamforming.Accurately aligning the transmitter and receiver beams,i.e.beam training,is vitally important to high data rate transmission.However,it may cause huge overhead which has negative effects on initial access,handover,and tracking.Besides,the mobility patterns of users are complicated and dynamic,which may cause tracking error and large tracking latency.An efficient beam tracking method has a positive effect on sustaining robust links.This article provides an overview of the beam training and tracking technologies on mmWave bands and reveals the insights for future research in the 6th Generation(6G)mobile network.Especially,some open research problems are proposed to realize fast,accurate,and robust beam training and tracking.We hope that this survey provides guidelines for the researchers in the area of mmWave communications.

Natural vibration and critical velocity of translating Timoshenko beam with non-homogeneous boundaries

In most practical engineering applications,the translating belt wraps around two fixed wheels.The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries.In this paper,non-homogeneous boundaries are introduced by the support wheels.Utilizing the translating belt as the mechanical prototype,the vibration characteristics of translating Timoshenko beam models with nonhomogeneous boundaries are investigated for the first time.The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle.The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations,critical velocities,natural frequencies,and modes,are numerically calculated and analyzed.The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels.The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models.Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels.When the two wheels are of equal size,the critical velocities of both beam models reach their respective minima.In addition,the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%.Furthermore,as the axial velocities increase,the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant.Although dealing with non-homogeneous boundaries is challenging,beam models with non-homogeneous boundaries are more sensitive to parameters,and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries.

Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.

Nonlinear vibration of Timoshenko FG porous sandwich beams subjected to a harmonic axial load

In this study,the instability and bifurcation diagrams of a functionally graded(FG)porous sandwich beam on an elastic,viscous foundation which is influenced by an axial load,are investigated with an analytical attitude.To do so,the Timoshenko beam theory is utilized to take the shear deformations into account,and the nonlinear Von-Karman approach is adopted to acquire the equations of motion.Then,to turn the partial differential equations(PDEs)into ordinary differential equations(ODEs)in the case of equations of motion,the method of Galerkin is employed,followed by the multiple time scale method to solve the resulting equations.The impact of parameters affecting the response of the beam,including the porosity distribution,porosity coefficient,temperature increments,slenderness,thickness,and damping ratios,are explicitly discussed.It is found that the parameters mentioned above affect the bifurcation points and instability of the sandwich porous beams,some of which,including the effect of temperature and porosity distribution,are less noticeable.

Orbital angular momentum conversion of acoustic vortex beams via planar lattice coupling

Orbital angular momentum(OAM)conversion is critical in understanding interactions between a structural sound field and a planar lattice.Herein,we explore the evolution of a monochromatic acoustic vortex beam(AVB)that is scattered by a phononic crystal(PnC)or a correlated random lattice.The phenomenon is ascribed to the enhanced orbit–orbit angular momentum coupling induced by the band structure.By modifying the coupling condition,accurate and continuous micromanipulation of AVBs can be achieved,including the transverse/lateral gravity shift,the dynamics of the phase singularities,and the spatial distribution of acoustic pressure,etc.This research provides insight to the inhomogeneous coupling of AVBs with both propagating Bloch waves and localized Anderson modes,and may facilitate development of novel OAM-based acoustic devices for active sound field manipulation.