A Novel Stability Analysis Method for the DC-AC Inverter with Nonlinear Loads Based on Harmonic Balance and Floquet Theory

Hong Li,Jing Bian,Jianing Shang,Trillion Q. Zheng,Ruxiang Hao 전력전자학회 2015 ICPE(ISPE)논문집 Vol.2015 No.6

The nonlinear loads exist widely in practical engineering applications. Due to the nonlinear characteristic of the loads, the nonlinear loads firstly need to be linearized to a resistor with constant value using the traditional stability analysis method based on the Routh-Hurwitz stability criterion and the method based on the stroboscopic map. In this paper, a novel stability analysis method is proposed based on the harmonic balance and Floquet theory for the inverters with nonlinear loads, which can present all characteristics of the nonlinear loads. In detail, the model of the inverter with nonlinear loads is established. Following, the approximate analytical periodic expressions of the inverter with nonlinear loads are obtained by using the harmonic balance method; and then, the stability analysis of the above inverter versus PI parameters is carried out according to Floquet theory. Finally, simulation and experimental results are given to verify the accuracy of the stability analysis method proposed in this paper.

축 방향 추진력을 받는 자유 비행 구조물의 동적 안정성 해석

은성진(Sung Jin Eun),유홍희(Hong Hee Yoo) 대한기계학회 2005 대한기계학회 춘추학술대회 Vol.2005 No.11

Dynamic stability of a free flying structure undergoing axially driving force is investigated in this paper. The equations of motion of a free-free beam are derived using the hybrid deformation variable method and the assumed mode method. Unstable regions due to periodical driving force are obtained by using the Floquet’s theory. Stability diagrams are presented to illustrate the influence of the dimensionless driving force, amplitude, and frequency. Also, buckling occurs when the driving force exceeds a certain value. It is found that relatively large unstable regions exist around the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

Complex harmonic modal analysis of rotor systems

한동주 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.7

Complex harmonic analysis for rotor systems has been proposed from the strict complex modal analysis based upon Floquet theory. Inthis process the harmonic balance method is adopted, effectively associated with conventional eigenvalue analysis. Also, the harmoniccoefficients equivalent to dFRFs in harmonic mode has been derived in practice. The modes are classified from identifying the modalcharacteristics, and the adaptation of harmonic balance method has been proven by comparing the results of the stability analyses fromFloque theory and the eigen analysis. The modal features of each critical speed are depicted in quantitatively and qualitatively by showingthat the strengths of each component of the harmonic coefficients are estimated from the order of magnitude analysis according totheir harmonic patterns. This effectiveness has been verified by comparing with the numerical solutions.

Automotive brake squeal analysis with rotating finite elements of asymmetric disc in time

Elsevier [etc.] 2017 Journal of sound and vibration Vol.393 No.-

<P>The new finite element brake squeal model is proposed where the finite elements of a real brake disc rotate in time. Contact nodal forces between the rotating disc and stationary pads are allocated to the moving contact area at every time step. When the proposed model is applied to an asymmetric automotive brake disc, it becomes the periodic time varying brake system. The stability boundary of the discrete time-varying system is numerically calculated by the Floquet theory. Also, the quasi-static linearized eigenvalue analysis is conducted to show that the unstable modes repeatedly appear at the short interval of the disc rotation angle. The results are consistent with the angle-dependent local phenomenon of squeal termed squeal periodicity in the squeal experiment. In the nonlinear time-domain analysis, the squeal vibration increases and then decays in time for the rotating mode shape functions. It demonstrates that the rotation of an asymmetric disc can change the nonlinear squeal behavior as well as the linear stability character drastically. (C) 2017 Elsevier Ltd. All rights reserved.</P>

매개변수 가진력을 받아 비행하는 구조물의 동적 모델링 및 안정성 해석

현상학,유홍희 한국소음진동공학회 1999 소음 진동 Vol.9 No.6

Dynamic stability of a flying structure undertaking constnat and pulsating thrust force is investigated in this paper. The equations of motion of the structure, which is idealized as a free-free beam, are derived by using the hybrid variable method and the assumed mode method. The structural system includes a directional control unit to obtain the directional stability. Unstable regions due to periodically pulsating thrust forces are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the constant force, the location of gimbal, and the frequency of pulsating force. The validity of the diagrams are confirmed by direct numerical simulations of the dynamic system.

축 방향 가속을 받는 보 구조물의 동적 안정성 해석

은성진(Eun, Sung-Jin),유홍희(Yoo, Hong-Hee) 한국소음진동공학회 2005 한국소음진동공학회 논문집 Vol.15 No.9

Dynamic stability of an axially accelerating beam structure is investigated in this paper. The equations of motion of a fixed-free beam are derived using the hybrid deformation variable method and the assumed mode method. Unstable regions due to periodical acceleration are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the dimensionless acceleration, amplitude, and frequency. Also, buckling occurs when the acceleration exceeds a certain value. It is found that relatively large unstable regions exist around the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

Period doubling of the nonlinear dynamical system of an electrostatically actuated micro-cantilever

Y.M. Chen,J.K. Liu 국제구조공학회 2014 Smart Structures and Systems, An International Jou Vol.14 No.5

The paper presents an investigation of the nonlinear dynamical system of an electrostatically actuated micro-cantilever by the incremental harmonic balance (IHB) method. An efficient approach is proposed to tackle the difficulty in expanding the nonlinear terms into truncated Fourier series. With the help of this approach, periodic and multi-periodic solutions are obtained by the IHB method. Numerical examples show that the IHB solutions, provided as many as harmonics are taken into account, are in excellent agreement with numerical results. In addition, an iterative algorithm is suggested to accurately determine period doubling bifurcation points. The route to chaos via period doublings starting from the period-1 or period-3 solution are analyzed according to the Floquet and the Feigenbaum theories.

Period doubling of the nonlinear dynamical system of an electrostatically actuated micro-cantilever

Chen, Y.M.,Liu, J.K. Techno-Press 2014 Smart Structures and Systems, An International Jou Vol.14 No.5

The paper presents an investigation of the nonlinear dynamical system of an electrostatically actuated micro-cantilever by the incremental harmonic balance (IHB) method. An efficient approach is proposed to tackle the difficulty in expanding the nonlinear terms into truncated Fourier series. With the help of this approach, periodic and multi-periodic solutions are obtained by the IHB method. Numerical examples show that the IHB solutions, provided as many as harmonics are taken into account, are in excellent agreement with numerical results. In addition, an iterative algorithm is suggested to accurately determine period doubling bifurcation points. The route to chaos via period doublings starting from the period-1 or period-3 solution are analyzed according to the Floquet and the Feigenbaum theories.

Control of an underwater biomimetic vehicle using Floquet theory

Plamondon, Nicolas,Nahon, Meyer Techno-Press 2014 Ocean systems engineering Vol.4 No.3

Aqua is an underwater biomimetic vehicle designed and built at McGill University that uses six paddles to produce control and propulsion forces. It has the particularity of having time-periodic thrust due to its oscillating paddles. Using an existing model of the vehicle, two types of controller were developed: a PD controller and a Floquet controller. The Floquet controller has the advantage of explicitly addressing the time-periodicity of the system. The performance of the controllers was assessed through simulation and experimentally in the Caribbean Sea. We find that the vehicle was able to follow the prescribed trajectories with relative accuracy using both controllers, though, the Floquet controller slightly outperforms the PD controller. Furthermore, a key advantage of the Floquet controller is that it requires no tuning while the PD controller had to be tuned by trial and error.

Floquet 이론과 섭동법에 의한 Mathieu Equation의 안정성해석

박찬일(Park, Chan Il) 한국소음진동공학회 2013 한국소음진동공학회 논문집 Vol.23 No.8

In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from the linear natural frequencies. The Mathieu equation is the simplest differential equation with periodic coefficients, which lead to the parametric excitation. The Mathieu equation may have the unbounded solutions. This work conducted the stability analysis for the Mathieu equation, using Floquet theory and numerical method. Using Lindstedt's perturbation method, harmonic solutions of the Mathieu equation and transition curves separating stable from unstable motions were obtained. Using Floquet theory with numerical method, stable and unstable regions were calculated. The numerical method had the same transition curves as the perturbation method. Increased stable regions due to the inclusion of damping were calculated.