scholarly journals Limit Cycle Oscillation Suppression Controller Design and Stability Analysis of the Periodically Time-varying Flapping Flight Dynamics in Hover

2021 ◽  
Author(s):  
Liang Wang ◽  
Wuyao Jiang ◽  
Zongxia Jiao ◽  
Longfei Zhao
Keyword(s):  
Stability Analysis ◽  
Limit Cycle ◽  
Controller Design ◽  
Stability Result ◽  
Multiple Shooting ◽  
Limit Cycle Oscillation ◽  
Time Varying ◽  
Oscillation Suppression ◽  
Cycle Oscillation ◽  
The Stability

Abstract The periodically time-varying forces make the equilibrium state of Beihawk, an X-shaped flapping-wing aircraft, to be a periodic limit cycle oscillation. However, traditional controllers based on averaging theory fail to suppress this oscillation and the derived stability result may be inaccurate. In this study, a period-based method is proposed to design the oscillation suppression controller, locate the corresponding cycle and analyze its stability. A periodically time-varying wing–tail interaction model is built and Discrete Fourier Transform is applied to adapt the model for controller design. The harmonics less than quintuple flapping frequency account for more than 96 percent of the total harmonics and are reserved to present a concise model. Based on this model, Active Disturbance Rejection Controller (ADRC) is designed and its Extended State Observer can observe the disturbance to suppress the oscillation. Poincaré map is introduced to convert the stability analysis of the cycle to a fixed point. A multiple shooting method is adopted to locate several points on the cycle and the map is obtained by calculating the submaps between the adjacent points with the Floquet theory. The located points are proved to be accurate compared with the numerical solved cycle and the stability analysis result of the cycle is verified by the dynamic evolution. Compared with the State Feedback Controller, the ADRC performs better in suppressing the limit cycle oscillation and eliminating the attitude control error. The oscillation suppression is meaningful in maintaining a stable flight and capturing high quality images.

Nonlinear Control Methods for High Energy Limit Cycle Oscillations

1999 ◽  
Author(s):  
Thomas Strganac ◽  
John Junkins ◽  
J. Ko ◽  
Andrew J. Kurdila
Keyword(s):  
Nonlinear Control ◽  
Limit Cycle ◽  
Active Control ◽  
High Performance ◽  
High Energy ◽  
Limit Cycle Oscillation ◽  
Limit Cycle Oscillations ◽  
Cycle Oscillation ◽  
The Stability ◽  
Flight Regimes

Abstract Limit cycle oscillations, as they manifest in high performance fighter aircraft, remain an area of scrutiny by the aerospace industry and military. Tools for the simulation and prediction of the onset for limit cycle oscillations have matured significantly over the years. Suprisingly, less progress has been made in the derivation of active control methodologies for these inherently nonlinear dynamic phenomena. Even in the cases where it is known that limit cycle oscillation may be observed in particular flight regimes, and active control methodologies are employed to attenuate response, there are very few analytical results that study the stability of the closed loop system. In part, this may be attributed to the difficulty in characterizing the nature of the contributing nonlinear structural and nonlinear aerodynamic interactions that account for the motion. This paper reviews recent progress made by the authors in the derivation, development and implementation of nonlinear control methodologies for a class of low speed flutter problems. Both analytical and experimental results are summarized. Directions for future study, and in particular technical barriers that must be overcome, are summarized in the paper.

scholarly journals Limit cycle oscillation control and suppression

1999 ◽  
Vol 103 (1023) ◽  
pp. 257-263 ◽  
Author(s):  
G. Dimitriadis ◽  
J. E. Cooper
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Harmonic Balance Method ◽  
Limit Cycle Oscillation ◽  
Aeroelastic System ◽  
Oscillation Control ◽  
Control Scheme ◽  
Non Linear ◽  
Cycle Oscillation ◽  
The Stability

Abstract The prediction and characterisation of the limit cycle oscillation (LCO) behaviour of non-linear aeroelastic systems has become of great interest recently. However, much of this work has concentrated on determining the existence of LCOs. This paper concentrates on LCO stability. By considering the energy present in different limit cycles, and also using the harmonic balance method, it is shown how the stability of limit cycles can be determined. The analysis is then extended to show that limit cycles can be controlled, or even suppressed, by the use of suitable excitation signals. A basic control scheme is developed to achieve this, and is demonstrated on a simple simulated non-linear aeroelastic system.

Impact of the Fear Effect on the Stability and Bifurcation of a Leslie–Gower Predator–Prey Model

2020 ◽  
Vol 30 (14) ◽  
pp. 2050210
Author(s):  
Xiaoqin Wang ◽  
Yiping Tan ◽  
Yongli Cai ◽  
Weiming Wang
Keyword(s):  
Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Cycle Oscillation ◽  
The Stability ◽  
Coexistence Equilibrium ◽  
Predator Behavior

In this paper, we investigate analytically and numerically the dynamics of a modified Leslie–Gower predator–prey model which is characterized by the reduction of prey growth rate due to the anti-predator behavior. We prove the existence and local/global stability of equilibria of the model, and verify the existence of Hopf bifurcation. In addition, we focus on the influence of the fear effect on the population dynamics of the model and find that the fear effect can not only reduce the population density of both predator and prey, but also destabilize the coexistence equilibrium, which are beneficial to the occurrence of limit-cycle-induced oscillation, or prevent the occurrence of limit cycle oscillation and increase the stability of the system.

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