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In order to effectively mitigate the micro-vibration energy from the on-orbit flywheel and high-level vibration transmitted to flywheel system in the launching stage, a nonlinear vibration absorber (NVA) with Euler-buckled beams is developed and investigated in this paper. The NVA is composed of a linear supporting spring and a set of parallel Euler-buckled beams which is used as a negative stiffness corrector. In order to evaluate vibration reduction performance and stability characteristics of this developed nonlinear coupled dynamic system with NVA. First of all, a multi-degree-of-freedom compound dynamic model, including the flywheel system, the NVA and the supporting structural plate in the satellite platform, is built. Then, based on the systematic dynamic equations, the approximate steady-state solutions are derived by using the complexification-averaging (CX-A) method under on-orbit and launching loads, respectively. The analytical method and solutions are validated by using the numerical method. The proposed NVA can realize excellent vibration mitigation performance for the three-degree-of-freedom (3-DOF) coupled nonlinear system under the launching and on-orbit excitations. Next, the slow-variable manifold equation is analyzed to address the dynamic bifurcation behaviors of the nonlinear compound system and the influences of the excitation amplitude on the bifurcation characteristics are focused on. The results show that a 3-DOF system is more prone to instability and requires larger external excitation to escape the instability region. The calculation results also show that the stiffness ratio and excitation amplitude have significant effects on the bifurcation characteristics, and a proper stiffness ratio can be chosen to avoid bifurcations. Finally, compared with typical pure cubic stiffness NVA, the proposed NVA exhibits greater adaptability, and can work efficiently for a relatively larger range of excitation amplitude. [ABSTRACT FROM AUTHOR]

Hypergravity centrifugal shaking table is widely used in the field of civil engineering and is considered to be the most effective means to study geotechnical earthquake disaster effect in the world today. Here, the structure of hypergravity centrifugal shaking table system is briefly introduced, and then the necessity and difficulty of the precise control of the position ring of the airborne shaking table in the hypergravity centrifugal shaking table are explained. On this premise, the system modeling and analysis of the unidirectional airborne shaking table with hypergravity are carried out in this paper. A new two-degree-of-freedom controller of the unidirectional airborne shaking table with hypergravity is designed by combining the H ∞ control and an improved internal model control (IIMC) strategy, and the designed two-degree-of-freedom controller is experimentally verified. The experimental results show that compared with the traditional PID control strategy and the single H ∞ control strategy, the two-degree-of-freedom controller designed in this paper can make the position loop control of the unidirectional airborne shaking table with hypergravity have higher control accuracy and anti-interference ability. [ABSTRACT FROM AUTHOR]

The VIVACE device, which utilizes flow-induced vibration for harvesting ocean current energy, has been a research hotspot in the field of renewable energy. In this study, the flow-induced vibration characteristics and energy conversion efficiency of a D-section prism were investigated using the k-ω SST turbulence model and Newmark-β method. The vibration amplitude, frequency, equilibrium position offset, and energy conversion efficiency of the two-degree-of-freedom cylinder were systematically analyzed at seven angles of attack between 0 and 180 degrees. The Reynolds number ranged from 368 to 14,742, corresponding to equivalent speeds of 2 to 20. The results indicate that the angle of attack has a significant influence on the flow-induced vibration response of the D-section prism. As the angle of attack changes, the vibration amplitude of the cylinder continuously increases, and the cylinder sequentially enters the vortex-induced vibration, vortex-induced vibration-galloping, and fully galloping branches. The change in the angle of attack disrupts the symmetry of the cylinder's vibration in the streamwise direction, leading to a shift in the equilibrium position of the cylinder's vibration. When the angle of attack is 0°, the energy conversion efficiency of the column reaches a maximum of 11.75%. Additionally, at high Reynolds numbers, the vibration of the cylinder is not self-limiting, making it more advantageous for energy conversion devices compared to cylinders with circular cross-sections. [ABSTRACT FROM AUTHOR]

Diabetes Mellitus (DM) is emerging as a global concern, affecting people from early ages to adulthood and positioning itself as one of the leading causes of mortality worldwide. The post-COVID-19 era has been characterized by notable progress in the domains of medicine, science, and engineering, creating a favorable atmosphere for the investigation of innovative solutions. The present manuscript aims to investigate the problem of glucose regulation in adults diagnosed with Type 1 Diabetes mellitus (T1D) using a two-degree-of-freedom robust controller technique. A physiological mathematical model involving individuals with T1D serves as the foundation for the proposed closed-loop technique. The control algorithm approach successfully maintains safe glycemic levels in a virtual population of 10 adults using a sophisticated, well-known physiological T1D simulator. We evaluated this with continuous 24-hour simulations. Simulation results support the practicality of the presented approach, and we further validate it using a statistical analysis that incorporates a probability density function and control variability grid analysis (CVGA). Despite being a theoretical and simulation-based methodology, the results of this study demonstrate promise, offering promising opportunities for developments in the field of artificial pancreas technology using Mexican technology.

The issue of DC fault ride-through can now be resolved in a novel way thanks to flexible current limiting technology, but its practical worth cannot be realized due to flaws in the technology. This study examines the placement of a controlled current source on the secondary side of a current limiting inductor and the enhancement of clamping voltage stability on the primary side of a current limiting inductor from the standpoint of controlling flexible current limiting technology. It offers a theoretical foundation for the specified secondary-side controlled source through an analysis of the iron core's inductance properties. Two-degree-of-freedom algorithm and model predictive control are combined in a control strategy that is appropriate for flexible current limiting devices to address the issue of inadequate response time and control accuracy under standard control. In MATLAB/Simulink simulation software, the presented theory's soundness is lastly confirmed.

Frequency response capability is necessary for wind farms (WFs) in the power system with a high proportion of renewable energy. In frequency control, WFs need to meet the grid’s power demand and avoid obvious additional damage to wind turbines (WTs) due to frequency control. In terms of meeting the grid power demand, the actual power characteristics of WTs need to be accurately described. An improved Gaussian Mixture Model (GMM) is used to model the actual measured output of WTs. The wind farm control center can accordingly issue achievable effective power commands to the WTs in the frequency response. In terms of avoiding the structural fatigue increase of WTs, a two-degree-of-freedom control strategy is designed, which simultaneously controls the generator torque and pitch angle and achieves fatigue suppression through multi-objective model predictive control (MOMPC). The simulation results show that the proposed control system can improve the frequency response capability of the WF and reduce the fatigue load of WTs, which has obvious application prospects.

The VIVACE device, which utilizes flow-induced vibration for harvesting ocean current energy, has been a research hotspot in the field of renewable energy. In this study, the flow-induced vibration characteristics and energy conversion efficiency of a D-section prism were investigated using the k-ω SST turbulence model and Newmark-β method. The vibration amplitude, frequency, equilibrium position offset, and energy conversion efficiency of the two-degree-of-freedom cylinder were systematically analyzed at seven angles of attack between 0 and 180 degrees. The Reynolds number ranged from 368 to 14,742, corresponding to equivalent speeds of 2 to 20. The results indicate that the angle of attack has a significant influence on the flow-induced vibration response of the D-section prism. As the angle of attack changes, the vibration amplitude of the cylinder continuously increases, and the cylinder sequentially enters the vortex-induced vibration, vortex-induced vibration-galloping, and fully galloping branches. The change in the angle of attack disrupts the symmetry of the cylinder’s vibration in the streamwise direction, leading to a shift in the equilibrium position of the cylinder’s vibration. When the angle of attack is 0°, the energy conversion efficiency of the column reaches a maximum of 11.75%. Additionally, at high Reynolds numbers, the vibration of the cylinder is not self-limiting, making it more advantageous for energy conversion devices compared to cylinders with circular cross-sections.

Piezoelectric accurate actuation plays an important role in industrial applications. The intrinsic frequency of previous actuators is invariable. However, variable frequency can approach the range near the low-intrinsic-frequency and realize a high actuation capability. The frequency-variable linear and rotary motion (FVLRM) principle is proposed for rotor-blade-based two-degree-of-freedom driving. Inertial force is generated by frequency-variable piezoelectric oscillators (FVPO), the base frequency and vibration modes of which are adjustable by the changeable mass and position of the mass block. The variable-frequency principle of FVPO and the FVLRM are recognized and verified by the simulations and experiments, respectively. The experiments show that the FVLRM prototype moves the fastest when the mass block is placed at the farthest position and the prototype is at the second-order intrinsic frequencies of 42 Hz and 43 Hz, achieving a linear motion of 3.52 mm/s and a rotary motion of 286.9 mrad/s. The actuator adopts a lower operating frequency of less than 60 Hz and has the function of adjusting the natural frequency. It can achieve linear and rotational motion with a larger working stroke with 140 mm linear movement and 360° rotation. [ABSTRACT FROM AUTHOR]

This paper presents the design of the Two-Degree-of-Freedom (2DOF) based Model Reference Adaptive Control (MRAC) as a tracking control system for the Non-minimum Phase (NMP) system. Perfect set point tracking is possible by using a cascade-connected inverse and non-inverse transfer function model of the dynamic system. But this method is restricted to the minimum phase system only, whereas, NMP system produces unbounded output response using this inverse model technique. Though, adaptive inverse feed-forward control technique is an effective tracking control system, it also requires an inverse model of the system. To overcome this problem, a novel feed-forward MRAC scheme for the inverse NMP model and the State feedback controller of the non-inverse model has been proposed, and both the controller are decoupled in a 2DOF framework. The feed-forward control technique guaranteed the tracking performance using the Lyapunov stability theory, and the feedback counterpart enhances the steady-state performance of the NMP plant. The robustness of the asymptotic stability as well as tracking performance of the closed-loop NMP system has been ensured by the proposed 2DOF control based MRAC technique. The effectiveness of the proposed control structure initially has been verified by the MATLAB Simulink toolbox and, then the demand has been strengthened by the implementation of the same control logic in the real-time environment using analog simulation with Op-amp based hardware model. [ABSTRACT FROM AUTHOR]

The mechanical behavior, dynamic evolution, and flow-field distribution of a two-degree-of-freedom riserless drill string were simulated numerically by using FLUENT fluid simulation software with the user-defined function embedded. The rotation angular velocities before and after the critical rotation angular velocity were used as independent variables, and the reduced velocity range was 3–14. Fluid-structure coupling was realized based on the dynamic overset grid and the SST k-ω turbulence model. Results reveal that the dynamic response of the riserless drill string was considerably affected by rotation and flow velocity, which are coupled with each other. The cross-flow average dimensionless displacement increased with the rotation angular velocity, and rotation considerably enhanced the in-line maximum average dimensionless displacement. However, the cross-flow amplitude caused by vortex-induced vibration was suppressed when the rotation angular velocity reached a certain value. The in-line and cross-flow frequencies were the same, thereby causing the trajectory to deviate from the standard 'figure-eight' shape and become a closed circle shape. The vortex did not fall behind the cylinder at low reduced velocity with high-rotation angular velocity, and the structure of the near-wake vortex remained U-shaped. The wake of the cylinder was deflected along the cross-flow direction, thereby leading to vibration asymmetry and resulting in increased vibration instability and disordered vibration trajectories, especially at high-rotation angular velocities. [ABSTRACT FROM AUTHOR]

The traditional canned electric valve consists of an induction motor and a reducer, which need to be matched with the position sensor to achieve precise control of valve position. The position sensor and reducer are not only easily damaged in high-temperature liquids, but also the slip rate of the induction motor is greatly affected by the liquid temperature, which makes it difficult to achieve accurate control. To address the above problems, this paper introduces a new topology of canned electric valve permanent magnet synchronous motor (CEV-PMSM), and a new maximum torque per ampere (MTPA) model is proposed. The new MTPA control equation considering the canned sleeve parameters is derived theoretically. By comparing it with id = 0 control and ideal MTPA control strategy, it is proved that the new MTPA model reflects the electric valve operation characteristics more realistically. In order to achieve sensorless control of the electric valve, and to achieve fast response and high-precision control under external disturbances and parameter uncertainties, the proposed control scheme combines sensorless control and two-degree-of-freedom (2-DOF) control. Consequently, the proposed control scheme can effectively improve the static and dynamic performances of the CEV-PMSM, as well as adjust the tracking and anti-disturbance performances independently. Finally, a 2 kW 100 r/min prototype was manufactured and corresponding experiments were conducted to verify the accuracy of the analysis. [ABSTRACT FROM AUTHOR]

This paper introduces a nonlinearity compensation based robust tracking controller for hypersonic flight vehicles. The controller focuses on robust control design with respect to the nonminimum phase feature and system uncertainties for the control-oriented model. Firstly, following the principle of decomposing the complex control problem into two simpler problems, the original robust tracking problem for nonlinear nonminimum phase hypersonic flight vehicles is decomposed into a simpler robust tracking problem for a linear nonminimum phase system with disturbances and a stabilization problem for a nonlinear system without disturbances. After the problem decomposition, a proportional–integral tracking controller and a feedback linearization controller are designed for the linear system and the nonlinear system, respectively. Then, the addition of the two designed controllers gives the final controller. By compensating for the system nonlinearity using the secondary system and its controller, the proposed control method can satisfy the robust tracking control requirements for nonlinear nonminimum phase hypersonic flight vehicles. The simulation results show, compared with a feedback linearization control method and a composite neural learning control method, the proposed method has superior tracking accuracy and robustness against system uncertainties and external disturbances. • The challenging nonlinear robust tracking problem for HFVs is well solved. • A novel same-order subsystem decomposition for HFVs is carried out. • A type of two-degree-of-freedom control combined by PI control and FLC is proposed. • Introducing nonlinearity compensation transforms the nonlinear NMP problem into a linear one. • The proposed control method guarantees superior tracking accuracy and robustness. [ABSTRACT FROM AUTHOR]

Piezoelectric accurate actuation plays an important role in industrial applications. The intrinsic frequency of previous actuators is invariable. However, variable frequency can approach the range near the low-intrinsic-frequency and realize a high actuation capability. The frequency-variable linear and rotary motion (FVLRM) principle is proposed for rotor-blade-based two-degree-of-freedom driving. Inertial force is generated by frequency-variable piezoelectric oscillators (FVPO), the base frequency and vibration modes of which are adjustable by the changeable mass and position of the mass block. The variable-frequency principle of FVPO and the FVLRM are recognized and verified by the simulations and experiments, respectively. The experiments show that the FVLRM prototype moves the fastest when the mass block is placed at the farthest position and the prototype is at the second-order intrinsic frequencies of 42 Hz and 43 Hz, achieving a linear motion of 3.52 mm/s and a rotary motion of 286.9 mrad/s. The actuator adopts a lower operating frequency of less than 60 Hz and has the function of adjusting the natural frequency. It can achieve linear and rotational motion with a larger working stroke with 140 mm linear movement and 360° rotation.

To overcome high periodic maintenance requirements, difficult replacement, and large application limitations of wireless sensor nodes powered by chemical batteries during the vibration control process of stiffened plates, a two-degree-of-freedom diagonal beam piezoelectric vibration energy harvester was proposed. Multidimensional energy harvesting and broadband work are integrated into one structure through the combined action of oblique angle, mass blocks, and piezoelectric beam. The mechanical model of the beam is established for theoretical analysis; the output characteristics of the structure are analyzed by finite element simulation; a piezoelectric energy harvesting experimental bench is built. The results show that: The structure has a wider harvesting band, multi-order resonant frequency, multi-dimensional energy harvesting, and higher output voltage and power than the traditional cantilever structures. The output performance of the specimens with 45° oblique angle, 5 g:5 g mass ratio, and 0.2 mm thickness of piezoelectric substrate is good in the frequency band of 10~40 Hz. When the excitation frequency is 28 Hz, the output voltage of the sextuple array structure reaches 19.20 V and the output power reaches 7.37 mW. The field experiments show that the harvester array can meet the requirements of providing auxiliary energy for wireless sensor nodes in the process of active vibration control of stiffened plates. [ABSTRACT FROM AUTHOR]

This paper presents a study of a two-degree-of-freedom (2DOF) piezoelectric energy harvester (PEH) under concurrent aeroelastic and base excitation. The governing equations of the theoretical model under the combined excitation are developed and solved analytically using the harmonic balance method. Based on the electro-mechanical analogies, an equivalent circuit model is established. The energy harvesting performance of the 2DOF PEH under different wind speeds but the same base excitation is investigated. Voltage amplitudes of various response components with different frequencies are predicted by the analytical method and verified by the circuit simulation. The root-mean-square (RMS) voltage is used to measure the actual performance of the 2DOF PEH. Around the resonance state, the 2DOF PEH has been found to produce a larger voltage output than the conventional SDOF PEH. Moreover, several interesting phenomena, such as the quasi-periodic oscillation and the peak-to-valley transition, have been observed in the circuit simulation and explained by the analytical solution. The developed methodology in this paper can be easily adapted to analyze other similar types of multiple-degree-of-freedom (MDOF) PEHs under concurrent aeroelastic and base excitation. [ABSTRACT FROM AUTHOR]

• This study examines the placement of a controlled current source on the secondary side of a current limiting inductor and the enhancement of clamping voltage stability on the primary side of a current limiting inductor from the standpoint of controlling flexible current limiting technology. • This study combines two-degree-of-freedom algorithm and model predictive control, which is appropriate for flexible current limiting devices to address the issue of inadequate response time and control accuracy under standard control. The issue of DC fault ride-through can now be resolved in a novel way thanks to flexible current limiting technology, but its practical worth cannot be realized due to flaws in the technology. This study examines the placement of a controlled current source on the secondary side of a current limiting inductor and the enhancement of clamping voltage stability on the primary side of a current limiting inductor from the standpoint of controlling flexible current limiting technology. It offers a theoretical foundation for the specified secondary-side controlled source through an analysis of the iron core's inductance properties. Two-degree-of-freedom algorithm and model predictive control are combined in a control strategy that is appropriate for flexible current limiting devices to address the issue of inadequate response time and control accuracy under standard control. In MATLAB/Simulink simulation software, the presented theory's soundness is lastly confirmed. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating the robust control problem for a class of singular systems with model structure uncertainty and external disturbance. Firstly, the uncertainty and disturbance estimator (UDE)-based robust control law is established for uncertain singular systems. Secondly, the two-degree-of-freedom (2DOF) nature of singular systems under the UDE-based robust controller is revealed, which shows that asymptotic reference tracking and disturbance rejection are decoupled. Additionally, on the basis of the small-gain theorem, sufficient conditions are established to ensure robust stability of the closed-loop system and to achieve asymptotic reference tracking and disturbance rejection. Finally, three numerical examples and a practical application to the multi-agent supporting systems are provided to illustrate the validity of the methods proposed.

This paper presents an improved analysis of a two-degree-of-freedom (2DOF) galloping-based piezoelectric energy harvester (GPEH). First, an overview of the 2DOF GPEH, together with some discussions on its physical implementation, are presented. The theoretical model of the 2DOF GPEH is then developed. The analytical solutions are derived using the harmonic balance method. The dynamic behaviour of the 2DOF GPEH is predicted according to the solution characteristics. Moreover, the mode activation mechanism of the 2DOF GPEH is theoretically unveiled: depending on the system parameters; there may exist a single or multiple stable solutions which correspond to different vibration modes of the 2DOF GPEH. Subsequently, an equivalent circuit model of the 2DOF GPEH is established. Circuit simulations are performed to verify the analytical solutions. Case studies through detailed theoretical analysis and circuit simulation give in-depth insights into the dynamic behaviour of the 2DOF GPEH. It is demonstrated that by tuning the stiffness of the auxiliary oscillator, either the first or the second mode vibration of the 2DOF GPEH can be activated, resulting in completely different dynamic behaviours and energy harvesting performance. Finally, from the perspectives of reducing the cut-in wind speed and improving the voltage output, several design guidelines are provided. [ABSTRACT FROM AUTHOR]

In recent years, vortex-induced vibration (VIV) has been widely employed to collect small-scale wind energy as a renewable energy source for microelectronics and wireless sensors. In this paper, a two-degree-of-freedom (2DOF) VIV-based piezoelectric energy harvester (VIVPEH) was designed, and its aerodynamic characteristics were thoroughly investigated. First, based on the traditional model theory and combined with the knowledge of vibration dynamics, the governing equations of the 2DOF VIVPEH were established. The dynamic responses, including the displacement and voltage output, were numerically simulated. Compared with the traditional 1DOF VIVPEH, the 2DOF VIVPEH proposed in this paper produced two lock-in regions for broadband wind energy harvesting. Furthermore, it was unveiled that the first- and second-order resonances were induced in the first and lock-in regions, respectively. Subsequently, a parametric study was conducted to investigate the influences of the circuit and mechanical parameters on the energy harvesting performance of the 2DOF VIVPEH. It was found that when the 2DOF VIVPEH was induced to vibrate in different lock-in regions, its optimal resistance became different. Moreover, by varying the masses and stiffnesses of the primary and secondary DOFs, we could adjust the lock-in regions in terms of their bandwidths, locations, and amplitudes, which provides a possibility for further customization and optimization.

To overcome high periodic maintenance requirements, difficult replacement, and large application limitations of wireless sensor nodes powered by chemical batteries during the vibration control process of stiffened plates, a two-degree-of-freedom diagonal beam piezoelectric vibration energy harvester was proposed. Multidimensional energy harvesting and broadband work are integrated into one structure through the combined action of oblique angle, mass blocks, and piezoelectric beam. The mechanical model of the beam is established for theoretical analysis; the output characteristics of the structure are analyzed by finite element simulation; a piezoelectric energy harvesting experimental bench is built. The results show that: The structure has a wider harvesting band, multi-order resonant frequency, multi-dimensional energy harvesting, and higher output voltage and power than the traditional cantilever structures. The output performance of the specimens with 45° oblique angle, 5 g:5 g mass ratio, and 0.2 mm thickness of piezoelectric substrate is good in the frequency band of 10~40 Hz. When the excitation frequency is 28 Hz, the output voltage of the sextuple array structure reaches 19.20 V and the output power reaches 7.37 mW. The field experiments show that the harvester array can meet the requirements of providing auxiliary energy for wireless sensor nodes in the process of active vibration control of stiffened plates.

It was shown previously that the synergy of the multi-degree-of-freedom (multi-DOF) and the mechanical stopper techniques is an effective way to further broaden the operation bandwidth of vibration energy harvesters. Considering the stochastic factor at the same time, this paper is devoted to developing a theoretical method for analyzing the dynamical characteristics of an impact-engaged 2DOF energy harvesting system under stochastic excitation, in which the impact is modeled as a nonlinear piecewise function. The existence of the impact and multi-DOF brings complexity in analyses, and the main theoretical method utilized in this paper is the stochastic averaging method which is suitable for multi-DOF quasi-nonintegrable systems. After that, the joint and marginal probability density functions of the system are derived, and numerical examples are shown to verify the effectiveness of the theoretical method. It is noteworthy that the theoretical method has the potential to be extended to more complex multi-DOF systems with stoppers. Subsequently, the stochastic response, bifurcations in the stochastic and corresponding deterministic systems, and the relationship between the D-bifurcation and the mean square voltage are discussed. Effects of crucial system coefficients, the impact stiffness and distance on the system are investigated as well. [ABSTRACT FROM AUTHOR]

An experimental program investigating the behavior of glued laminated timber (glulam) assemblies with various bolted connections subjected to simulated blast loading was undertaken. A total of 14 full-scale tests on 137×267-mm glulam members with idealized and realistic boundary conditions were carried out using a shock tube apparatus capable of simulating the effects of far-field blast explosions. Full-scale glulam specimens with bolted connections designed to yield in bolt bending performed better than those that were overdesigned. Proper detailing of the bolt group geometry was found to be sufficient to achieve the desired failure sequence. Reinforcement with self-tapping screws changed the failure mode from that of splitting to a combination of bolt yielding and wood crushing and provided additional ductility in the assembly. A two-degree-of-freedom blast analysis was found to adequately capture the system response with reasonable accuracy. An investigation of the current Canadian blast design provisions showed that the design approach does not allow for energy dissipation in the assembly. An approach is proposed that requires more stringent provisions for the design of brittle failure modes in connections and ensures that ultimate failure will occur in load-bearing timber elements. [ABSTRACT FROM AUTHOR]

This paper investigates a novel control strategy that reduces the fatigue load of wind turbines during active power control. Based on the analysis of the reference power tracking of wind turbines, the proposed new control strategy considers simultaneous control of rotor speed and pitch angle. For this goal, a two-degree-of-freedom wind turbine active power control model based on the small-signal method is established, and the linearized fatigue load calculation is also completed in the model. For the effective control under this two-degree-of-freedom control framework, a model predictive control method suitable for multi-objective optimization is applied. Simultaneously, with the help of simulation tools, adaptive weight selection for multi-objective optimization is discussed and implemented. Simulation results show that the two-degree-of-freedom control system proposed in this paper can accurately implement reference power tracking and significantly reduce the fatigue load of wind turbines. The proposed method is valid not only on a single wind turbine but also in the wind farm's active power dispatching process. • Two-degree-of-freedom wind turbine control model is studied. • Fatigue load of wind turbines is modeled linearly. • Optimized multi-input multi-output MPC optimization control is adopted. • Fatigue load of wind turbine operation is significantly reduced. [ABSTRACT FROM AUTHOR]

This paper introduces a two-degree-of-freedom pipe selection mechanism using contraction and extension unit composed of single tube and a T branch experiment of an in-pipe mobile robot equipped with this mechanism. Household piping is used for gas transportation to each household. If the pipe is cracked or corroded due to long-term use, it becomes difficult to supply a stable gas. Therefore, inspection of household piping is necessary. The existing methods require a lot of time for the inspection or it is difficult to inspect the entire pipeline. Therefore, in this study we developed an inspection robot for home piping using a mobile robot. To date, the robots proposed have been able to bend in the direction along the pipeline, as the tip of the robot passively bends when passing through the curved pipe. However, at the branch pipe, there is no mechanism that actively bends the tip of the robot, and the pipe cannot be selected and moved in a specific direction. Therefore, this paper proposes the application of a small pipe selection mechanism combining a ball-point pen knock mechanism and a wire bending mechanism to an in-pipe mobile robot using the pressure difference of a single tube.

This article proposes an improved two-degree-of-freedom Smith predictive control method for typical industrial control systems. Smith predictive control is a classic control strategy designed for systems with pure lag. As an extension of Smith predictive control, internal model control can solve the time-delay problem effectively and make the controller design simple. Based on the two control algorithms, an enhanced control method with modified control structure is developed in this paper. In the design scheme, the set-point tracking and the disturbance rejection characteristics are decoupled, such that the set-point tracking and disturbance rejection controllers can be designed independently to achieve better control performance. The obtained control strategy possesses simple and convenient parameter tuning procedures. The validity of the proposed scheme is verified through theoretical analysis and simulation comparison with other control methods, and the results indicate that the proposed strategy shows better performance on set-point tracking and disturbance rejection. [ABSTRACT FROM AUTHOR]

In this paper, we propose a low-frequency (<100 Hz) piezoelectric MEMS energy harvester (PMEH) with a two-degree-of-freedom (2DOF) structure to work in two vibration modes for broadband operation. The PMEH is fabricated by bonding a piezoelectric ceramic lead zirconate titanate Pb(Zr,Ti)O3 (PZT) to phosphor bronze, which can work in a high-acceleration ambient with good durability. The maximum open-circuit voltage and output power of the PMEH are 23.6 V and 64.69 μW at the first resonant frequency of 27.4 Hz when the input vibration acceleration is 2 g (9.8 m/s2), while they are 14 V and 56.75 μW at the second resonant frequency of 93.4 Hz when the input vibration acceleration is 8 g, respectively. The fabricated PMEH scavenged the vibration energy of a vacuum compression pump and an ultrasonic cleaner and generated maximum output powers of 10.45 and 16.59 μW, respectively. The experimental results show that the device has good environmental adaptability. [ABSTRACT FROM AUTHOR]

Summary: The efficient exploitation of ubiquitous low‐frequency mechanical excitations through electromagnetic induction is important for implementing self‐sustained low‐power electronics. Conventional electromagnetic energy harvesters (EMEHs) have been usually designed as a 1‐degree‐of‐freedom (1‐DOF) linear system with a high resonant frequency, resulting in poor performance under low‐frequency excitations. To solve this key issue, this paper presents four 2‐DOF cylindrical EMEHs with various configurations. Theoretical models for the four EMEHs are built and then validated by experiment. With the theoretical models, a parametric study is carried out to reveal the energy harvesting performance of the four 2‐DOF EMEHs. The results indicate that supporting a 1‐DOF EMEH within a large tube using springs or magnetic coupling to construct a 2‐DOF EMEH can lower the operating frequency, endowing the 2‐DOF EMEH with improved performance under low‐frequency excitations. Moreover, the 2‐DOF EMEH can always provide higher power outputs than the corresponding 1‐DOF EMEH except the linear 2‐DOF EMEH configuration with overly stiff inner springs. Furthermore, for the nonlinear 2‐DOF EMEH, the output power can be optimized by adjusting the spring stiffness and the length of the inner tube. In addition, increasing the mass of the inner center magnet can enhance the power output and in the meanwhile make the operational frequency shift toward the left (lower frequency). [ABSTRACT FROM AUTHOR]

Abstract Converting the ambient waste energy into electricity has been considered as an effective approach for sustaining low-power devices. One of the key issues is how to generate more electricity from ultra-low frequency excitations that are ubiquitous in our environment. To tackle this problem, this paper presents a two-degree-of-freedom (2-DOF) electromagnetic energy harvester (EMEH) that is realized simply by magnetically levitating a 1-DOF EMEH in a cylindrical housing. Both experiment and simulation exhibit the advantages of the proposed design, including the tunable operating frequencies, improved power output, and extended operating bandwidth. The experimental measurements show that, under a sinusoidal excitation with an amplitude of 0.5 g (1 g = 9.8 m/s2), nearly 40% increase in the magnitude of the power and 152% increase in the operating bandwidth are achieved by the proposed harvester. Under the hand-shaking induced excitation, the 2-DOF EMEH can enhance the voltage of a capacitor (33 μF) from 0 V to 5 V within half a second, showing a charging performance much better than that of the 1-DOF EMEH. Moreover, the 2-DOF EMEH successfully sustains the continuous operation of a hygrothermograph using the energy converted from human body motions, demonstrating its potential application in powering some wearable electronics. Highlights • The proposed harvester features tunable operating frequencies and extended bandwidth. • The enhanced voltage and power outputs are achieved. • The harvester can produce substantial power output under ultra-low frequency excitations. • The continuous operation of a hygrothermograph is sustained by the harvester when excited by human body motions. [ABSTRACT FROM AUTHOR]

Control of real-time pressure process is quite challenging due to high nonlinearity and sensitivity. PID controllers being the most employed for industrial applications have the potential for control of such processes. This is due to the PID's advantages of simple structure, ease of tuning and implementation. However, its performance degrades during set-point change and high external disturbances due to high sensitivity and nonlinearity of the pressure plant. Therefore, this paper proposes the two-degree-of-freedom fractional-order PID (2DOF-FOPID) controller for real-time control of pressure process in both parallel and series configurations. Furthermore, the controller parameters are obtained experimentally using Ziegler-Nichols and closed-loop set-point approaches. The controller has the advantages of improving set-point tracking and disturbance rejection performance through smoother control action over the conventional PID. From the real-time experimental results obtained, the proposed approach outperforms PID, fractional-order PID and 2DOF-PID controllers in terms of overshoot and settling time. Hence, the approach has better set-point tracking ability and disturbance rejection capability. Furthermore, the control action of the approach is less affected by undesired oscillations and derivative kick effect thereby extending the life of actuator. [ABSTRACT FROM AUTHOR]

Abstract Two-degree-of-freedom (2-DOF) vortex-induced vibration (VIV) of an elliptic cylinder is numerically investigated at a Reynolds number R e = 150. The incompressible Navier–Stokes equations in arbitrary Lagrangian–Eulerian formulation are solved by a four-step fractional finite element method. The elliptic cylinder, with a variety of aspect ratios (AR = 1.0–2.5), is free to vibrate in both transverse and azimuthal directions. At each AR , the computations are conducted within a wide range of reduced velocities (2 ≤ U r ≤ 15). For comparison, the one-degree-of-freedom (1-DOF) responses of the cylinder vibrating only transversely are also provided. The results show that significant rotations occur under a condition of frequency synchronization similar to the lock-in condition of VIV in the transverse direction. Under the rotation effect, the transverse peak amplitude at AR = 1.0 reaches a higher value about 20% larger than its counterpart of 1-DOF VIV, whereas it fells by more than half at AR = 2.0 and 2.5, and the corresponding wake patterns present distinct characteristics. The typical phenomenon of phase switch can be captured successfully between the torque and rotation response, which occurs at the same reduced velocity to the phasing between the transverse force and motion. Our simulation results also elucidate that the free rotation may significantly affect the statistics of the drag, lift and moment coefficients. The most striking observation is that all of the force responses at AR = 2.0 and 2.5 collapse onto a very low level compared to those of the transverse-only VIV. This is consistent with the dramatic drop in the transverse vibration amplitude at the same AR. [ABSTRACT FROM AUTHOR]

Symmetries play very important in the dynamics of robot systems. The relevant control of robot arm motion with fault diagnosis including the optimized fuzzy algorithm based on the error rate adjustment P, I, D value (Fuzzy PID algorithm) model relies on symmetry principles. A robot is a kind of mechanical device that can program and perform certain operations and mobile tasks under automatic control. The manipulator is a very complex multi-input multi-output non-linear system and the main actuator of the robot. This paper focuses on the design of a control algorithm for a two-degree-of-freedom (2-DOF) manipulator. First, the mathematical model of a 2-DOF articulated manipulator is established, that is, the functional relationship between the input driving force vector and the output rotation angle vector of a 2-DOF manipulator. Then, a set of trajectory planning algorithms are designed by using gradient model control, which can calculate the trajectory of the end-effector of a 2-DOF manipulator according to the user’s task requirements. The experimental results verify the effectiveness of the proposed algorithm.

This study aims to present a new two-degree-of-freedom (DOF) linear resonant actuator (LRA) and its motion control method without a position sensor. The design method of 2-DOF LRA which resonates with only detent force without a mechanical spring is proposed. Since the information of displacement and direction is required to control 2-DOF LRA, a sensor or an estimator is needed. Therefore, we proposed a position estimator and a motion controller for 2-DOF LRA. This paper proved that reciprocating motion, elliptical motion, and scrolling motion can be controlled without a position sensor. Finite element analysis (FEA) and dynamic simulation results validated the proposed method as well.

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This paper presents an additive-state-decomposition-based attitude tracking control method for a class of bank-to-turn aerial vehicles subject to unknown disturbances and nonlinear coupling. This method ‘additively’ decomposes the original tracking problem into two more tractable problems, namely a tracking problem for a deterministic nonlinear ‘primary’ system, and a disturbance rejection problem for a linear time-invariant ‘secondary’ system. Based on the decomposition, a backstepping controller is designed for the primary system to track the reference attitude signal, and a proportional-integral controller is applied to the secondary system to compensate for the disturbances. Finally, the two designed controllers are combined to achieve the original control objective. By using additive state decomposition, the proposed control method with two degrees of freedom can consider tracking task and disturbance rejection task respectively. Simulation results illustrate that the proposed controller can track the reference attitude signal and compensate for disturbances meanwhile. Additionally, the ASD-based controller outperforms the traditional backstepping controller in the presence of unknown disturbances and input delay, and the robustness of the full system can be improved by adjusting the controller parameters of the secondary system. [ABSTRACT FROM AUTHOR]

In the displacement measurement of the wafer stage in lithography machines, signal quality is affected by the relative angular position between the encoder head and the grating. In this study, a two-degree-of-freedom fiber-coupled heterodyne grating interferometer with large operating range of rotation is presented. Fibers without fiber couplers are utilized to receive the interference beams for high-contrast signals under the circumstances of large angular displacement and ZEMAX ray tracing software simulation and experimental validation have been carried out. Meanwhile, a reference beam generated inside the encoder head is adopted to suppress the thermal drift of the interferometer. Experimental results prove that the proposed grating interferometer could realize sub-nanometer displacement measurement stability in both in-plane and out-of-plane directions, which is 0.246 nm and 0.465 nm of 3σ value respectively within 30 s.

A two-degree-of-freedom direct-drive induction motor (2DoFDDIM), whose solid rotor is coated with a copper layer, is capable of linear, rotary, and helical motions and has widespread applications. For solid-rotor motors, the calculation and analysis of rotor total eddy current loss (TECL) are crucial in studying the factors causing such a loss and possible loss reduction methods. In this study, a new nonlinear analytical method considering the saturation of the rotor core is proposed to solve the fundamental magnetic field. The new method divides the time period into segments. The magnetic field distribution at any time is obtained using Maxwell equations. The eddy current losses in the copper layer and rotor core caused by the fundamental magnetic field are calculated. The surface eddy current losses in the copper layer and rotor core caused by harmonics are calculated using a 2D analytical method. TECL is determined by the sum of eddy current and surface eddy current losses. Coefficients are utilized to consider eddy, saturation, and end-region effects when calculating the rotor core TECL. The new method is verified using 3D FEM, and the results show the proposed method has higher accuracy than the original method. The errors of the rotor core and copper layer TECLs are less than 6 % and 7.3 % , respectively.

Active disturbance rejection control (ADRC) treats the external disturbance and internal uncertainties as a general disturbance, and uses an extended state observer (ESO) to estimate it in real-time and feeds it back in the control loop, thus can achieve good disturbance rejection performance. However, ADRC is not quite suitable for unstable delayed processes due to its inherent structure. In this paper, a two-degree-of-freedom (2DOF) control structure is proposed for unstable time- delayed systems. Set-point tracking and disturbance rejection are separated in this structure and ADRC is solely responsible for disturbance rejection. A method to tune the ADRC parameters using all the information of the system is proposed, and robustness and performance of the proposed method are analyzed. Simulation examples show that 2DOF-ADRC can achieve good tracking and disturbance rejection performance. [ABSTRACT FROM AUTHOR]

In this study, the flow-induced vibration of two-degree-of-freedom staggered circular cylinders at subcritical Reynolds numbers is studied numerically with overset dynamic mesh. The streamwise spacing ratio S x / D of 4 and the transverse spacing ratio S y / D ranging from 0 to 2 are employed to explore the influence of staggered arrangement on the vibrations and fluid forces of cylinders. It is found the upstream cylinder mainly experiences the vortex-induced vibration while vortex-induced and wake-induced vibrations happen for the downstream one, which may be interfering or independent depending on the transverse spacing of cylinders. The phase lag between the displacement and fluid force of the downstream cylinder changes from 0° to 180° with the increasing of inflow velocity, which leads negative add mass and serves as the reason of wake-induced vibration. The theoretical formulae to estimate the critical velocity, fluid coefficient and vibration amplitude of wake-induced vibration are proposed and validated by the numerical simulations. • The flow-induced vibration of staggered circular cylinders is accurately simulated. • The characteristics of vibration response and fluid forces of the cylinders are analyzed. • The features of wake-induced vibration of cylinders are predicted theoretically. [ABSTRACT FROM AUTHOR]

Piezoelectric energy harvesting techniques provide a promising way to transform the vibration energy into electric energy. Since the voltage output peak can drop due to the frequency excitation moving away from the resonance region, the on broadening the bandwidth of operation frequency has drawn great attention. In the paper, a novel two-degree-of-freedom piecewise-linear piezoelectric energy harvester is proposed to achieve wide operation frequency bandwidth by combining the multimodal harvesting technique and nonlinear method. Based on the average method, the analytical solution of the proposed device is achieved. From analytical and experiment results, at an excitation acceleration of 0.3 g, as the excitation frequency is up sweeping, the system achieves frequency bandwidth operation of 7.4 Hz which is about 5.2 times higher to that of conventional two-degree-of-freedom linear harvester, and the power outputs for the first and second resonances can reach up to 429 μW and 411 μW, respectively. Due to the close agreement between the calculated values and experiment results, the analytical solution and the theoretical model could be applied to further MEMS fabrication process and optimized design. [ABSTRACT FROM AUTHOR]

In this research, numerical simulation of two-dimensional fluid flow around a circular cylinder was performed considering two-degree-of-freedom for the cylinder under a turbulent flow regime using a hybrid random vortex-boundary element method. For fluid flow simulation, a code was developed where the cylinder vibrations in the x – y plane were modeled as a system of mass, spring, and damper. Numerical results were obtained at a Reynolds number of 10 4 , and a cylinder mass ratio and damping coefficient of 2.6 and 0.005, respectively, at different reduced velocities in the range of 2–14. A comparison between the simulation results of the present study and experimental data show that the maximum error of the hybrid random vortex-boundary element method in the present study was as low as 9%, indicating its superior accuracy in predicting the flow behaviour compared to the DES turbulence model. Furthermore, comparing the results of the simulations performed in this study to those of the modeling in ANSYS FLUENT based on the DES turbulence model, it was figured out that the present methodology could significantly shorten the processing time. The results further indicated that, at reduced velocities where the cylinder tended to exhibit small-amplitude streamwise responses (e.g. , U r = 4.5, 13), the cylinder motion was dominantly in the cross-flow direction and, given the response amplitude in the cross-flow direction, the vortex shedding turned from 2 S to P in mode. Moreover, resonance occurred as the vibration frequency of the structure approached that of the vortex shedding (e.g. , U r = 8) where the cylinder had its response amplitude increased in both directions. Under such circumstances, the streamwise motion of the cylinder effectively determines the flow pattern, with the vortex shedding occurred under a 2 T flow pattern. The results obtained in terms of drag and lift coefficients show that the proposed hybrid method, in contrast to existing numerical procedures, can well demonstrate temporal variations of these coefficients in such a turbulent flow regime. • Simulation of FIV around 2DOF cylinder using Combined RVM-BEM. • Comparison between accuracy and computational time of Combined RVM-BEM and DES turbulence model. • At U r = 8 , the cylinder exhibited the maximum response amplitude in the streamwise direction. • At U r = 13 , the cylinder motion was dominant in the vertical direction. [ABSTRACT FROM AUTHOR]

Friction induced vibration (FIV) and its application for energy generation through two-degree-of-freedom (2-DOF) piezoelectric coupled structure are modelled, described, and studied in this work. The FIV mathematical model of 2-DOF system in the direction of friction is established. A 2-DOF energy generator is designed as a sample structure to transform single direction continuum friction motion to high frequency vibration for energy generation. During the operation of a moving plate compressed and sliding on top of the friction excitation module, varying friction force and contact status (sliding and stick) will lead to the dynamic piezoelectric compression deformation, which can generate continuum electrical power for energy absorbing and harvesting applications. Through numerical simulation and parameter studies, the influences of different stiffness ratios, mass ratios, normal force, velocity, acceleration, structure parameter and friction coefficients on the system power generation are analyzed. Through simple structural design, W level power generation can be obtained with few piezoelectric materials. This work revealed the possibility of transforming low frequency excitation to high frequency vibration of general 2-DOF structure for energy generation. • FIV mathematical model of 2-DOF system in the direction of friction is established. • A 2-DOF energy generator is designed based on diamond-shaped structure. • Influences of structural and friction parameters on power generation are analyzed. • Through simple structural design, W level power generation can be obtained. • Low frequency excitation is converted to high frequency FIV for energy generation. [ABSTRACT FROM AUTHOR]

In order to promote the tolerance and controllability of the multi-degree-of-freedom (M-DOF) ultrasonic motor, a novel two-degree-of-freedom (2-DOF) spherical ultrasonic motor using three traveling-wave type annular stators was put forward. Firstly, the structure and working principle of this motor were introduced, especially a spiral spring as the preload applied component was designed for adaptive adjustment. Then, the friction drive model of 2-DOF spherical motor was built up from spatial geometric relation between three annular stators and the spherical rotor which was used to analyze the mechanical characteristics of the motor. The optimal control strategy for minimum norm solution of three stators' angular velocity was proposed, using Moore-Penrose generalized inverse matrix. Finally, a 2-DOF prototype was fabricated and tested, which ran stably and controllably. The maximum no-load velocity and stall torque are 92 r/min and 90 mN·m, respectively. The 2-DOF spherical ultrasonic motor has compact structure, easy assembly, good performance and stable operation. [ABSTRACT FROM AUTHOR]