Two-degree-of-freedom Research Articles

Impact response of stainless steel tube locally-strengthened by concrete-filled steel tube

This paper proposes a novel stainless-steel tube locally strengthened by a concrete-filled steel tube to resist impact loads. A drop hammer impact test system was used to determine the failure modes, impact forces, and displacement responses of the strengthened tubes under an impact load. The effects of the strengthening length and thickness of the concrete and outer steel tubes on the impact responses of the strengthened tubes were investigated. The impact resistance was found to improve with an increase in the thickness of the concrete and outer steel thickness. The test results also indicated that the strengthened tubes exhibited a flexural failure mode with a combination of local and global deformations. An analytical model for predicting the dynamic responses of the locally strengthened tubes was established based on an equivalent two-degree-of-freedom (TDOF) model. The analytically predicted results were compared with the experimental results, and the good consistency between these two results demonstrated the accuracy of the established analytical model.

Study the bifurcations of a 2DoF mechanical impacting system

Impacting mechanical systems with suitable parameter settings exhibit a large amplitude chaotic oscillation close to the grazing with the impacting surface. The cause behind this uncertainty is the square root singularity and the occurrence of dangerous border collision bifurcation. In the case of one-degree-of-freedom mechanical systems, it has already been shown that this phenomenon occurs under certain conditions. This paper proposes the same uncertainty of a two-degree freedom mechanical impacting system under specific requirements. This paper shows that the phenomena earlier reported in the case of one-degree-of-freedom mechanical systems (like narrow band chaos, finger-shaped attractor, etc.) also occur in the two-degrees-of-freedom mechanical impacting system. We have numerically predicted that the narrowband chaos ensues under specific parameter settings. We have also shown that narrowband chaos can be avoided under some parameter settings. At last, we demonstrate the numerical predictions experimentally by constructing an equivalent electronic circuit of the mechanical rig.

Blast wave attenuation of nonlinear meta-isolation system: Theoretical analysis and experimental validation

In the field of protective engineering, wire rope isolators are usually applied in the isolation floor to mitigate the impact and vibration induced by explosive blast. In this paper, two kinds of meta-isolation systems were proposed and designed based on the local resonance, and investigated by means of theoretical analysis, numerical calculation and experimental research. First, the force-displacement hysteresis loops of the selected wire rope isolators are obtained by the cyclic loading tests, and identified by a mathematical model to make preparations for numerical calculation. Then, in order to discuss the influence of mass ratio, stiffness ratio and damping ratio on the shock isolation, the two-degree-of-freedom (TDOF) linear and nonlinear models are studied based on the mode superposition method and fourth-order Rugga-Kutta method respectively. Finally, the blast-induced ground shock experiments were conducted to evaluate the isolation efficiencies of conventional isolation systems and meta-isolation systems. The experiment results reveal that the isolation efficiency of meta-isolation system can increase by 10% points vertically and 16% points horizontally compared to conventional systems, which indicates that the meta-isolation system has great potential to be adopted in the engineering structures and provides a new idea and reference for protective engineering.

Behavior of novel steel-concrete-steel sandwich walls under low-velocity impact loading

This paper reported experimental and analytical studies on impact behaviors of steel-concrete-steel sandwich composite (SCSSC) walls using enhanced C-channels (ECs). Six SCSSC walls, designed with variations in impact energy levels and boundary columns, were tested by drop hammer and simulated by LS-DYNA. The main failure modes of the specimens after impact loading were global flexure and flexure-shear mode. As direct-link connections, the ECs provided strong interfacial shear and tensile resistances, which prevented local failure of SCSSC walls. Under three impact energy levels, boundary CSFT columns increased the ultimate impact resistance of SCSSC walls, and effectively reduces their peak displacements. Refined finite element (FE) models considering the effect of strain rate were established, and verified by reported impact test results. In addition, this study adopted modified two-degree-of-freedom (TDOF) model to estimate the impact force and displacement responses of this type of SCSSC walls. Validations against reported test results confirmed that the TDOF model provided reasonable predictions.

Broadband energy harvesting in a two-degree-of-freedom nonlinear system without internal resonance

In this paper, we propose a novel two-degree-of-freedom (TDOF) nonlinear energy harvester without internal resonance to realize broadband harvesting characteristic. To show the performance, a TDOF nonlinear electromagnetic harvester is designed. The electromechanical coupling system is established and solved by adopting the harmonic balance method. The modulation equations are constructed, the first-order harmonic solutions of the system are obtained and the frequency response curves of the displacement and current are plotted. The advantage of the proposed harvester is compared to the conventional single-degree-of-freedom (SDOF) nonlinear model and the corresponding TDOF linear system, the results achieve that the proposed scheme can enhance the bandwidth of the harvesting energy. Furthermore, the influences of system parameters on the response are discussed. The accuracy of the first-order harmonic results is revealed by numerical simulations. To further demonstrate the accuracy of analytical solutions, the finite element simulation is constructed in ANSYS finite element analysis (FEA) software. The performance predictions from the analytical solutions are compared with results from FEA. It is convincingly demonstrated that periodic solutions have a degree of good consistency for the behavior of frequency response curves.

Post critical characteristics of a side-box steel concrete composite girder: Experimental investigation and mechanism analysis

The present study is aimed to investigate the post-critical behavior of a side-box steel-concrete composite girder under varying wind angles of attack, by conducting a series of section model testing with single-degree and two-degrees of freedom. The essence of flutter, as well as the adverse impact of vortex shedding lock-in on exacerbating post-critical flutter responses, was revealed in detail. The results indicate that the coupled motion of flutter for the prototype composite girder can be characterized as a supercritical Hopf bifurcation with significant phase shifting between motions. The circular character of the limit cycle oscillation (LCO) expressed in the phase diagram is altered to a non-circular form due to the apparent aerodynamic stiffness nonlinearity within a wide range of wind speeds. Interestingly, the coupling vibration between vortex-induced vibrations (VIV) and flutter, i.e., VIV-flutter coupling vibration is observed for the prototype girder, due to the evolution of total damping ratio concave shape with wind speed. Two mitigation countermeasures, i.e., a L-shaped skirt plate and a sharpened wind fairing, were proposed to improve the aeroelastic stability, caused by a significant increase in uncoupled positive aerodynamic damping and alternation of VIV-flutter coupling. In addition, the specific effects of structural damping on the VIV-flutter coupling were discussed in detail.

Robust QFT control design for a multivariable torsion/bending of rotational nanoscanner

This paper proposes a reasonable, practical, and novel method for designing a robust controller for two degrees of freedom nano-electromechanical scanners based on the combination of quantitative feedback theory (QFT) and the Taguchi method. Although the main primary of this paper devotes to rotational control, an investigation of two-degree freedom (rotational/bending) is studied by employing the Taguchi method. A moveable main plate suspended by two nano-beams over a fixed substrate electrode is used to represent the scanner. The nanoscanner is thoroughly analyzed using the most comprehensive modeling design, considering the elastic, electrical, Casimir force and moment, and squeezes film damping. The nanoscanner’s governing equations are initially derived by considering both rotation and deformation. In addition, because the size dependency of materials is significant in ultra-small structures, we developed the constitutive equations within the context of the modified couple stress theory to integrate the effect of scale dependency. Next, system uncertainties have been wholly addressed to achieve an accurate model. As a result, using robust control methods such as quantitative feedback theory to precisely control nano-scanners in the presence of uncertainties is inevitable. The quantitative feedback approach transforms the nonlinear plant into a family of linear uncertain plants in the first part. This is accomplished using a fixed-point theorem, after which appropriate disturbance rejection boundaries are discovered. In this problem, quantitative feedback controllers and checking the system’s stability at any frequency and time are intended to solve the tracking problem and the disturbance rejection issue. Due to the uncertainty associated with the system model’s complexity and accuracy, we employ a QFT controller to control the system. Moreover, because this system has only one input and two outputs, and changing the controller’s gain is complicated, the Taguchi method has been employed to enhance better performance. Nonlinear simulations of the tracking issue are carried out, and the results demonstrate the effectiveness of the developed controllers and prefilters. The findings show that using the suggested approach effectively overcomes the challenges to robust control of a nonlinear rotational nanoscanner, and also the system achieves the best angle and deflection adjustment accuracy.

Nonlinear analysis of vibration attenuation of ring-spring-resonator based meta-isolation system

Ring-spring-resonator (RSR) based nonlinear meta-isolation system (RSR-M) was proposed and its vibration attenuation characteristic was investigated experimentally and theoretically. The force–displacement hysteresis loops of the selected wire rope isolators (WRIs) exhibit softening under compression and hardening under extension, and are identified by a modified mathematical model combined with the normalized Bouc-Wen model. Frequency response curves of conventional isolation system and RSR-M−2 were calculated based on the single-degree-of-freedom (SDOF) and two-degree-of-freedom (TDOF) models, along with the fourth-order Runge-Kutta method. Shaking table experiments were carried out to evaluate the nonlinear dynamic response and vibration attenuation property of the RSR-M, which proves to be in good agreement with the numerical results of acceptable validity. Dynamic hysteresis loops and phase portraits were plotted to study the dynamic responses and stability of the RSR-M. The experimental results show that, no matter vertical or horizontal direction, the RSR-M possesses better vibration attenuation performance compared to conventional isolation system. In general, the meta-isolation vibration system provides a new reference and idea for the practice designing of the isolation system in some sense.

Experimental and numerical study on 2-DOF wind-induced vibration and energy harvesting of triangular prism

The two-degrees of freedom (2-DOF) wind-induced vibration (WIV) response and energy harvesting performance of an equilateral triangular prism were conducted by numerical and experimental studies under different attack angles. The piezoelectric patch is applied in this work to extract power. To enhance the output power of the prism, an omnidirectional piezoelectric system is used to harvest energy in flow and cross flow directions simultaneously. It's found that the attack angle (α0) is a key factor influencing the power extraction performance of the system. The output power of the prism almost keeps around zero when 0° ≤ α0 ≤ 30° and increases monotonously with the increase of wind velocity for 30° < α0 ≤ 60°. Especially for α0 ≥ 55°, the power output experiences a rapid increase. The highest output power of 1.30 mW can be obtained when α0 = 60°. The WIV responses show that the amplitude in the direction perpendicular to incoming flow can reach 3.00b (b is the side length of the triangular cross section for the prism) when α0 = 60°. And the lock-in region can be observed in high reduced velocity range when 30° ≤ α0 ≤ 60°. In addition, due to the transition of vortex pattern from 2S to P + S for high attack angles, the unsteady aerodynamic loading acting on the prism results in strong WIV responses with high vibration amplitude, which then leads to the improvement of energy harvesting performance from WIV.

Identification and control of Maglev system using fractional and integer order PID controller

System identification techniques have proved to be the most effective methodologies for the modeling highly non-linear and system. For the purpose of real-time parameter estimation of a Maglev system, a Teaching Learning Based Optimization (TLBO) for updating the weights of Functional Link Artificial Neural Network (FLANN) model is proposed and implemented in this research. Moreover, we proposed a one &amp; two-Degree of Freedom (one-DOF &amp; two-DOF) Fractional Order PID (FOPID) controller, where the parameters are optimized by using the Teaching Learning Based Optimization (TLBO) and the recently proposed Black Widow Optimization (BWO) algorithm. To investigate the robustness of the proposed controller, a pulse signal disturbance is added at equal intervals of the output of the identified model of the Maglev system. It is found that the suggested two-DOF FOPID controller with TLBO performs better than its counterpart in terms of both in time domain specifications (i.e., maximum overshoot = 1.2648%, settling time = 1.3884 sec and rise time = 0.8685 sec) and in robustness analysis (i.e., system is sufficiently robust, because the infinity norms of the sensitivity and the complementary sensitivity functions of the system are less than two). The TLBO algorithm has performed better for both identification and optimization of controller parameter due to very less number of algorithmic parameter is as compared to other algorithm.

Modeling and Control of Robotic Manipulators Based on Symbolic Regression.

Model-based design is an important method of addressing problems associated with designing complex control systems. For complex dynamic systems in the presence of uncertainties, the modeling process from the first principles becomes extremely tedious and simplification in mechanism and parameter measurement may result in model inaccuracy. On the contrary, machine learning has the characteristic of fitting complicated equations, which makes it widely used in the research of model identification. However, it only brings a black-box model where the design schemes based on an analytical model cannot be applied. In this article, a simple and novel scheme for modeling and control of robotic manipulators is proposed; without prior knowledge, a dynamic model in an analytical form is obtained from artificially excited training data using the symbolic regression technique, and then, a controller is designed based on the dynamic model. Due to the ingenious experimental design, on one hand, the amount of training data is far less than the system identification method by machine learning. On the other hand, a decoupling feature is used in the model that greatly simplifies controller design. The experimental results on two-degree of freedom (DOF) and 6-DOF robotic manipulator simulators verify that the scheme is feasible and effective.

Two-Degree-of-Freedom Control of a Micro-Robot Using a Dual-Rate State Observer

This brief presents a novel tracking control algorithm for a micro-robot based on dynamics and positional measurements. The algorithm improves the tracking performance and response time. We designed a two-degree-of-freedom (TDOF) control, which is widely utilized in industrial servo systems, for a micro-robot. Our TDOF control prevents undesirable effects, such as model uncertainty. The dynamic characteristics of a micro-robot were analyzed using the frequency response function (FRF), and a dynamic model specific for micro-robot motion was derived. This brief also addresses the dual-rate problem of micro-robot control systems by designing a dual-rate state observer (DSO) that provides positional information for the micro-robot when no camera updates are available. Thus, the TDOF controller provides feedback control at higher sampling frequencies. The performance of the controller was experimentally verified.

TDOF model for UHPC members under lateral low-velocity impact

The dynamic behaviors of ultra-high performance concrete (UHPC) members under lateral low-velocity impact loading have been intensively studied by experiment and numerical simulation, while the corresponding structural design approach is still limited and mainly concerned in this study. Firstly, through comprehensively considering the compression arch action, strain rate effect, and unloading stiffness, the dynamic resistance function of UHPC members, e.g., reinforced UHPC (R-UHPC) and UHPC-filled steel tube (UHPC-FST) beams/columns, are built and verified. Then, a two degrees of freedom (TDOF) model of the drop hammer test on UHPC members is improved by considering the P-δ effect and stress wave propagation effect. Furthermore, the impact force- and mid-span deflection-time histories of the existing five series of drop hammer tests on UHPC members are applied to verify the validity and applicability of the established TDOF model. The influence of considering the stress wave propagation effect, strain rate effect, and steel fibers in UHPC for predictions of the TDOF model are discussed by parametric analyses. Finally, based on the energy balance, the explicit formulae are proposed to predict the maximum and residual mid-span deflections of the flexural critical UHPC members under the lateral low-velocity impact, which can be helpful for the design of UHPC structures under lateral impact loadings.

Effective Load Frequency Control of Power System with Two-Degree Freedom Tilt-Integral-Derivative Based on Whale Optimization Algorithm

Nowadays, the operation and control of power systems are a big challenge. An essential part of the power system (PS) control is load frequency control (LFC). Different secondary controllers are implemented for the frequency control problem. Hence, cascaded two-degree freedom and a tilt-integral-derivative controller having a filter (2DOFTIDF) are intended in this paper and implemented for load frequency control. In order to determine the efficiency of the 2DOFTIDF controller, a well-known non-reheat thermal system with/without a governor dead band is considered. A new whale optimization algorithm (WOA) is used to enhance the suggested controller parameters. The predominance of the presented method is exhibited by comparing the consequences with different heuristic techniques tuned to controllers published recently. Further, the simulation results for two test cases indicate that system enactments are enhanced by introducing the suggested controller and are also best suited in the presence of system nonlinearity. Finally, random load fluctuation along with noise and changing the system parameters are also used to determine the reliability of the suggested controller. Compared to the WOA-tuned TIDF controller, the settling time of ΔF1, ΔF2, and ΔPTie is improved by 45.45%, 56.77%, and 20.26%, respectively, with the WOA-tuned 2DOFTIDF controller and by 40%, 48.27%, and 20%, respectively, with the DE-tuned TIDF controller. Experimental validation using the hardware-in-the-loop real-time simulation based on OPAL-RT has been carried out to confirm the viability of the proposed approach.

A Modification to the Enhanced Correction Factor Technique for the Subsonic Wing–Body Interference Model

In this work, the enhanced correction factor technique (ECFT) is modified for a subsonic wing–body interference model, which can consider the forces on both the lifting boxes and the body elements of an idealized airplane, termed the advanced ECFT method. A passenger aircraft model is chosen as the simulation model, and the longitudinal static aeroelasticity at the transonic situation for two-degree freedom, including the α (angle of attack) degree and ϕ (angle of horizontal tail) degree, is simulated in this paper. The corresponding CFD results are used to correct the aerodynamic influence coefficients (AIC) matrix, which is then simulated by MSC.NASTRAN. The pressure distribution results of different aircraft components received by the advanced ECFT method indicate that it is suitable for the subsonic wing–body interference model. Compared with the uncorrected linear method and the diagonal corrected method, it is generally more consistent with the CFD/CSD coupling method, not only for the lifting boxes, but also for the body elements. In addition, the aerodynamic derivative results also show good agreement with the flight test data, which solidly verifies the advance ECFT method.

Impact response analysis of vibration system with inerter

This research investigates using an inerter system to control the impact-induced vibration response of a single degree of freedom(SDOF) and two degrees of freedom(TDOF) vibration system. An analytic model of the SDOF system with an inerter is first derived, and simulation is performed to compare the inerter performance in suppressing the maximum acceleration response under shock load. Next, a more complex TDOF vibration model with an inerter is derived, and the effectiveness of the inerter in reducing the large acceleration amplitude is evaluated. The energy analysis is conducted to investigate the energy transfer mechanism during impact. The simulation study shows that one can significantly decrease the maximum acceleration response with an appropriate selection of the inerter parameters. For the SDOF vibration system with an inerter, response reduction is greatly influenced by the system’s natural frequency. In the TDOF vibration system, the maximum acceleration response attenuation is caused by two factors. For a large inerter radius, the acceleration response reduction is mainly influenced by energy transfer between unsprung and inerter mass. However, for a big inerter mass, attenuation of the acceleration response is caused by decreasing the system’s natural frequency. It is observed from the simulation that the maximum acceleration response can be reduced up to 35% by adjusting the inerter radius of gyration. Furthermore, the optimum condition for reducing the acceleration response occurs when the inerter mass is half the unsprung mass ( m i = 0.5 m u). An experimental study is conducted to validate the simulation results.

Direct yaw-moment control of electric vehicles based on adaptive sliding mode.

The direct yaw-moment control (DYC) system consisting of an upper controller and a lower controller is developed on the basis of sliding mode theory and adaptive control technique. First, the two-degree of freedom (2-DOF) model is utilized to calculate the ideal yaw rate. Then, the seven-degree of freedom (7-DOF) electric vehicle model is given to design the upper controller by employing first-order sliding mode (FOSM) method, which is constructed to guarantee the actual yaw rate to approach the ideal value and gain the additional yaw moment. On this basis, an adaptive first-order sliding mode (AFOSM) controller is designed to enhance the system robustness against probable modelling error and parametric uncertainties. In order to mitigate the chattering issue present in the FOSM controller, a novel adaptive super-twisting sliding mode (ASTSM) controller is proposed for the design of DYC. Furthermore, the lower controller converting the additional yaw moment into driving or braking torque acting on each wheel is also developed. Finally, The simulation results indicate that the proposed DYC system can improve the electric vehicle driving stability effectively.

Research on robust fuzzy logic sliding mode control of Two-DOF intelligent underwater manipulators.

This study investigates the independent motion control of a two-degree-of-freedom (Two-DOF) intelligent underwater manipulator. The dynamics model of two-DOF manipulators in an underwater environment is proposed by combining Lagrange's equation and Morison's empirical formulation. Disturbing factors such as water resistance moments, additional mass force moments and buoyancy forces on the intelligent underwater manipulator are calculated exactly. The influence of these factors on the trajectory tracking of the intelligent underwater manipulator is studied through simulation analysis. Based on the design of the sliding mode surface of the PID structure, a new Fuzzy-logic Sliding Mode Control (FSMC) algorithm is presented for the control error and control input chattering defects of traditional sliding mode control algorithm. The experimental simulation results show that the FSMC algorithm proposed in this study has a good effect in the elimination of tracking error and convergence speed, and has a great improvement in control accuracy and input stability.

Two Degree of Freedom Dynamic Model Parameter Identification of Accelerometer Using Feature Point Coordinate Estimation and Amplitude Correction

The accurate identification and characterization of the accelerometer dynamic model parameters play an important role in improving the dynamic performance of the device or system with an accelerometer. To overcome the problem that the traditional single degree of freedom (SDF) dynamic model of the accelerometer cannot describe the dynamic characteristics beyond the first resonant frequency of the accelerometer, a two degree of freedom (TDF) dynamic model of the accelerometer was constructed. On this basis, a parameter identification method for the TDF dynamic model of the accelerometer based on the feature points coordinate estimation and amplitude correction was proposed. First, the zero frequency point coordinates of the accelerometer frequency response were obtained by the Hv method. The first and second resonance point coordinates were estimated by discrete spectrum correction and the least square (DSC-LS) method. Then, the amplitude correction coefficient was applied to eliminate the influence of series coupling on the amplitude. Finally, the TDF dynamic model parameters of the accelerometer were calculated through the feature point coordinates. The experimental results show that the method has high accuracy and can avoid the influence of series coupling on the parameter identification accuracy of the accelerometer’s TDF dynamic model without complex derivation and decoupling operations. The identified TDF dynamic model of the accelerometer can represent the dynamic characteristics with a higher frequency range.

A Lateral Control Method of Intelligent Vehicles Based on Shared Control

This paper studies the lateral control problem for intelligent vehicles based on the concept of shared control. Considering the participation of drivers in the control loop, a shared control-based lateral controller is designed, which consists of two differed controllers: one is an LQR-based autonomous driving controller and the other is a driver’s intention-based fuzzy controller. For the vehicle dynamic model with two-degrees of freedom, an autonomous driving controller based on LQR and a driver’s intention-based fuzzy controller are designed. Then, the lateral controller based on shared control is constructed, which integrates the aforementioned two controllers. Finally, the co-simulation by MATLAB/Simulink and Carsim is presented. Furthermore, simulation results show that the designed lateral controller can track the desired path with better performance than the LQR-based autonomous driving controller.