Gyroscopic modes decoupling method in parametric instability analysis of gyroscopic systems

Traditional procedures to treat vibrations of gyroscopic continua involve direct application of perturbation methods to a system with both a strong gyroscopic term and other weakly coupled terms.In this study,a gyroscopic modes decoupling method is used to obtain an equivalent system with decoupled gyroscopic modes having only weak couplings.Taking the axially moving string as an example,the instability boundaries in the vicinity of parametric resonances are detected using both the traditional coupled gyroscopic system and our system with decoupled gyroscopic modes,and the results are compared to show the advantages and disadvantages of each method.

EIGENVALUE PROBLEM OF A LARGE SCALE INDEFINITE GYROSCOPIC DYNAMIC SYSTEM

Gyroscopic dynamic system can be introduced to Hamiltonian system. Based on an adjoint symplectic subspace iteration method of Hamiltonian gyroscopic system, an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gyroscopic system was proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system. The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero was used. The eigenvalues that Hamiltonian function is negative can be separated so that the eigenvalue problem of positive definite Hamiltonian function system was presented, and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system was used to solve the separated eigenvalue problem. Therefore, the eigenvalue problem of indefinite Hamiltonian function gyroscopic system was solved, and two numerical examples were given to demonstrate that the eigensolutions converge exactly.

RESEARCH ON CONTROL OF FLYWHEEL SUSPENDED BY ACTIVE MAGNETIC BEARING SYSTEM WITH SIGNIFICANT GYROSCOPIC EFFECTS

Traditional PID controllers are no longer suitable formagnetic-bearing-supported high-speed flywheels with significant gyroscopic effects. Becausegyroscopic effects greatly influence the stability of the flywheel rotor, especially at highrotational speeds. Velocity cross feedback and displacement cross feedback are used to overcomeharmful effects of nutation and precession modes, and stabilize the rotor at high rotational speeds.Theoretical analysis is given to show their effects. A control platform based on RTLinut and a PCis built to control the active magnetic bearing (AMB) system, and relevant results are reported.Using velocity cross feedback and displacement cross feedback in a closed loop control system, theflywheel successfully runs at over 20000 r/min.

Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function

In a dissipative gyroscopic system with four degrees of freedom and tensorial variables in contravariant(right upper index)and covariant(right lower index)forms,a Lagrangian-dissipative model,i.e.,{L,D}-model,is obtained using second-order linear differential equations.The generalized elements are determined using the{L,D}-model of the system.When the prerequisite of a Legendre transform is fulfilled,the Hamiltonian is found.The Lyapunov function is obtained as a residual energy function(REF).The REF consists of the sum of Hamiltonian and losses or dissipative energies(which are negative),and can be used for stability by Lyapunov’s second method.Stability conditions are mathematically proven.

Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system

This study presents a kinematic calibration method for exoskeletal inertial motion capture (EI-MoCap) system with considering the random colored noise such as gyroscopic drift.In this method, the geometric parameters are calibrated by the traditional calibration method at first. Then, in order to calibrate the parameters affected by the random colored noise, the expectation maximization (EM) algorithm is introduced. Through the use of geometric parameters calibrated by the traditional calibration method, the iterations under the EM framework are decreased and the efficiency of the proposed method on embedded system is improved. The performance of the proposed kinematic calibration method is compared to the traditional calibration method. Furthermore, the feasibility of the proposed method is verified on the EI-MoCap system. The simulation and experiment demonstrate that the motion capture precision is significantly improved by 16.79%and 7.16%respectively in comparison to the traditional calibration method.

Response analysis of NMRG system considering Rb-Xe coupling

The dynamic range of the nuclear magnetic resonance gyroscope can be effectively improved through the closedloop control scheme,which is crucial to its application in inertial measurement.This paper presents the analytical transfer function of Xe closed-loop system in the nuclear magnetic resonance gyroscope considering Rb–Xe coupling effect.It not only considers the dynamic characteristics of the system more comprehensively,but also adds the influence of the practical filters in the gyro signal processing system,which can obtain the accurate response characteristics of signal frequency and amplitude at the same time.The numerical results are compared with an experimentally verified simulation program,which indicate great agreement.The research results of this paper are of great significance to the practical application and development of the nuclear magnetic resonance gyroscope.

Modeling Nonstationary Time Series for Gyroscopic Drift Analysing

A state space aproach for modeling nonstationary time series is employed in analysing gyro transient process. Based on the concept of smoothness priors constraint, the overall model is using the Kalman filter and Akaike's AIC criterion.Some numerical results of gyro drift models are obtained for analysis of gyro system. As the trend and irregular components of the observed time series can be modeled simultaneously, it is statistically more accurate and efficient than that modeled separately.

THE ANALYTICAL APPROACH FOR LARGE SCALE NON-CLASSICALLY DAMPED DYNAMIC SYSTEM

This paper gives a dynamic decoupling approach for the analysis of large scale non-classically damped system, in which the complex variable computations were completely avoided not only in solving for the eigenvalue problem but also in the calculation of the dynamic response. The analytical approaches for undamped gyroscopic system, non-classically damped system, including the damped gyroscopic system were unified. Very interesting and useful theoretical results, practical algorithms were obtained which are applicable to both non-defective and defective systems.

Simulation Analysis and Experimental Verification of Spiral-tube-type Valveless Piezoelectric Pump with Gyroscopic Effect

The current research of the valveless piezoelectric pump focuses on increasing the flow rate and pressure differential. Compared with the valve piezoelectric pump, the valveless one has excellent performances in simple structure, low cost, and easy miniaturization. So, their important development trend is the mitigation of their weakness, and the multi-function integration. The flow in a spiral tube element is sensitive to the element attitude caused by the Coriolis force, and that a valveless piezoelectric pump is designed by applying this phenomenon. The pump has gyroscopic effect, and has both the actuator function of fluid transfer and the sensor function, which can obtain the angular velocity when its attitude changes. First, the present paper analyzes the flow characteristics in the tube, obtains the calculation formula for the pump flow, and identifies the relationship between pump attitude and flow, which clarifies the impact of flow and driving voltage, frequency, spiral line type and element attitude, and verifies the gyroscopic effect of the pump. Then, the finite element simulation is used to verify the theory. Finally, a pump is fabricated for experimental testing of the relationship between pump attitude and pressure differential. Experimental results show that when Archimedes spiral θ=4π is selected for the tube design, and the rotation speed of the plate is 70 r/min, the pressure differential is 88.2 Pa, which is 1.5 times that of 0 r/min rotation speed. The spiral-tube-type valveless piezoelectric pump proposed can turn the element attitude into a form of pressure output, which is important for the multi-function integration of the valveless piezoelectric pump and for the development of civil gyroscope in the future.

Study on Steering Law of Large Spacecraft SGCMG System Based on Fuzzy Decision

A single gimbal control moment gyro system is the best choice for large spacecraft attitude control systems, as executive components of spacecraft guidance, navigation, and control system. But the phenomenon of singularity exists in this system. This increases the difficulty in designing the steering law. Singularity of SGCMG system is analyzed in this paper. The singularity measurement is determined making use of a fuzzy decision. A singularity avoidance steering law of large spacecraft SGCMG system based on fuzzy decision is designed according to the idea of searching the singularity measurement's gradient. The simulation experiments show this method guarantees singularity avoidance of SGCMG system. This method provides a new idea for the steering law of large spacecraft.

Application of Ultrasonic Motor to Control of Moment Gyroscope Gimbal Servo System

Attitude control system is one of the most important subsystems in a spacecraft.As a key actuator,the control moment gyroscope(CMG)mainly determines the performance of attitude control system.Whereas,the control accuracy and output torque smoothness of the CMG depends more on its gimbal servo system.Considering the constraints of size,mass and power consumption for a small satellite,here,a mini-CMG is designed,in which the gimbal servo system is driven by an ultrasonic motor.The good performances of the CMG are obtained by both the ultrasonic motor and the rotary inductosyn.The direct drive of gimbal improves its dynamic performance,with the output bandwidth above 20 Hz.The angular and speed closed-loop control obtains the 0.02°/s gimbal rate,and the output torque resolution better than 2×10^(-3) N·m.The ultrasonic motor provides 1.0N·m self-lock torque during power-off,with 12arc-second position accuracy.

Data⁃Based Feedback Relearning Algorithm for Robust Control of SGCMG Gimbal Servo System with Multi⁃source Disturbance

Single gimbal control moment gyroscope(SGCMG)with high precision and fast response is an important attitude control system for high precision docking,rapid maneuvering navigation and guidance system in the aerospace field.In this paper,considering the influence of multi-source disturbance,a data-based feedback relearning(FR)algorithm is designed for the robust control of SGCMG gimbal servo system.Based on adaptive dynamic programming and least-square principle,the FR algorithm is used to obtain the servo control strategy by collecting the online operation data of SGCMG system.This is a model-free learning strategy in which no prior knowledge of the SGCMG model is required.Then,combining the reinforcement learning mechanism,the servo control strategy is interacted with system dynamic of SGCMG.The adaptive evaluation and improvement of servo control strategy against the multi-source disturbance are realized.Meanwhile,a data redistribution method based on experience replay is designed to reduce data correlation to improve algorithm stability and data utilization efficiency.Finally,by comparing with other methods on the simulation model of SGCMG,the effectiveness of the proposed servo control strategy is verified.

Kinetic Analysis of Vectored Electric Propulsion System for Stratosphere Airship

To enhance the controllability of stratosphere airship,a vectored electric propulsion system is used.By using the Lagrangian method,a kinetic model of the vectored electric propulsion system is established and validated through ground tests.The fake gyroscopic torque is first proposed,which the vector mechanism should overcome besides the inertial torque and the gravitational torque.The fake gyroscopic torque is caused by the difference between inertial moments about two principal inertial axes of the propeller in the rotating plane,appears only when the propeller is rotating and is proportional with the rotation speed.It is a sinusoidal pulse,with a frequency that is twice of the rotation speed.Considering the fake gyroscope torque pulse and aerodynamic efficiency,three blade propeller is recommended for the vectored propulsion system used for stratosphere airship.

Three-mode optomechanical system for angular velocity detection

We propose a scheme for measuring the angular velocity of absolute rotation using a three-mode optomechanical system in which one mode of the two-dimensional （2D） mechanical resonator is coupled to an optical cavity. When the total system rotates, the Coriolis force acting on the 2D mechanical resonator due to the absolute rotation will affect the mechanical motion and thus change the phase of the output field from the cavity. The angular velocity of the absolute rotation can be estimated by monitoring the spectrum of the output field from the cavity via homodyne measurement. The minimum measurable angular velocity, which is determined by the noise spectrum, is calculated. The working range of the gyroscope for measuring angular velocity is discussed.

Motionplanningof UAVgroupusing modifiedgyroscopic force forguidance and avoidance

It is comment that unmanned aerial vehicles （UAVs） have limitation on information cap- turing in reality applications. Therefore, online method of motion planning is necessary for such UA- Vs. Gyroscopic force （GF） is used for obstacle avoidance as an online method. However, classical GF has shortcoming in generating orbit for UAV with high velocity because the GF results in a time- varying turning radius. Modified gyroscopic force （MGF） given by function of velocity can overcome this shortcoming and help get a more practical control law for avoidance. MGF can also be used to implement the guidance of UAV by designing particular active conditions. Interactions in forms of stress function and damping force are introduced so that an UAV group can have coordinated motion. By combining controls of MGF and interactions, motion planning of UAV group in obstacle environ- ment can be implemented.

Study on Gyroscopic Effect of Floating Offshore Wind Turbines

Compared with bottom-fixed wind turbines,the supporting platform of a floating offshore wind turbine has a larger range of motion,so the gyroscopic effects of the system will be more obvious.In this paper,the mathematical analytic expression of the gyroscopic moment of a floating offshore wind turbine is derived firstly.Then,FAST software is utilized to perform a numerical analysis on the model of a spar-type horizontal axis floating offshore wind turbine,OC3-Hywind,so as to verify the correctness of the theoretical analytical formula and take an investigation on the characteristics of gyroscopic effect.It is found that the gyroscopic moment of the horizontal axis floating offshore wind turbine is essentially caused by the vector change of the rotating rotor,which may be due to the pitch or yaw motion of the floating platform or the yawing motion of the nacelle.When the rotor is rotating,the pitch motion of the platform mainly excites the gyroscopic moment in the rotor’s yaw direction,and the yaw motion of the platform largely excites the rotor’s gyroscopic moment in pitch direction,accordingly.The results show that the gyroscopic moment of the FOWT is roughly linearly related to the rotor’s inertia,the rotor speed,and the angular velocity of the platform motion.

TRENDS OF MECHANICALLY DITHERED SYSTEM OF RLG

As mechanical dither is widely applied to reduce frequency “Lock in” of RLG(ring laser gyroscope) that is based on the principle proposed by Sagnac in 1913, it is necessary to know the recent development it the field The proper design of dither mechanism that decides the effect of bias to some extent is discussed The proper dither signal and its control have a direct influence on dither efficiency Real,stable and accurate error compensation can improve the performance of RLG further Some proposals, which are helpful to future research on the field,are concluded

ARNOLDI REDUCTION ALGORITHM FOR LARGE SCALE GYROSCOPIC EIGENVALUE PROBLEM

Based on Arnoldi's method, a version of generalized Arnoldi algorithm has been developed for the reduction of gyroscopic eigenvalue problems. By utilizing the skew symmetry of system matrix, a very simple recurrence scheme, named gyroscopic Arnoldi reduction algorithm has been obtained, which is even simpler than the Lanczos algorithm for symmetric eigenvalue problems. The complex number computation is completely avoided. A restart technique is used to enable the reduction algorithm to have iterative characteristics. It has been found that the restart technique is not only effective for the convergence of multiple eigenvalues but it also furnishes the reduction algorithm with a technique to check and compute missed eigenvalues. By combining it with the restart technique, the algorithm is made practical for large-scale gyroscopic eigenvalue problems. Numerical examples are given to demonstrate the effectiveness of the method proposed.

Design and simulation of a silicon-based hybrid integrated optical gyroscope system

By combining a silicon-based lithium niobate modulator and a silicon-based Si3N4resonator with silicon-based photonics technology,a highly systematic design of a hybrid integrated optical gyroscope with enhanced reciprocity sensitivity and a dual micro-ring structure is proposed for the first time in this paper.The relationship between the device's structural parameters and optical performance is also analyzed by constructing a complete simulation link,which provides a theoretical design reference to improve the system's sensitivity.When the wavelength is 1550 nm,the conversion frequency of the dual-ring optical path is 50 MHz,the coupling coefficient is 0.2,and the radius R is 1000μm,the quality factor of the silicon-based Si_(3)N_(4)resonator is 2.58×10^(5),which is 1.58 times that of the silicon-on-insulator resonator.Moreover,the effective number of times the light travels around the ring before leaving the micro-ring is 5.93,which is 1.62 times that of the silicon-on-insulator resonator.The work fits the gyro dynamic output diagram,and solves the problem of low sensitivity at low speed by setting the phase offset.This results provide a basis for the further optimization of design and chip processing of the integrated optical gyroscope.

Control System Design for Low PowerMagnetic Bearings in a Flywheel Energy Storage System

This paper presents a theoretical and experimental study on controller design for the AMBs in a small-scale flywheel energy storage system,where the main goals are to achieve low energy consumption and improved rotordynamic stability.A H-infinity optimal control synthesis procedure is defined for the permanent-magnet-biased AMB-rotor system with 4 degrees of freedom.Through the choice of design weighting functions,notch filter characteristics are incorporated within the controller to reduce AMB current components caused by rotor vibration at the synchronous frequency and higher harmonics.Experimental tests are used to validate the controller design methodology and provide comparative results on performance and efficiency.The results show that the H-infinity controller is able to achieve stable rotor levitation and reduce AMB power consumption by more than 40%(from 4.80 to 2.64 Watts)compared with the conventional PD control method.Additionally,the H-infinity controller can prevent vibrational instability of the rotor nutation mode,which is prone to occur when operating with high rotational speeds.