Limit cycles are periodic motions of a system that can be described with the equations
$$u(t)=u(t+T)$$
Where \(T\) is the period of the motion. Limit cycles can be either stable or unstable. And portions of the limit cycle can be classified as stable or unstable, as shown in the figure “b” below. Rate limiters in control systems can cause limit cycles.
[[Limit Cycles for Flying Squirrels]]
[[Unstable Limit Cycles around a Stable Point]]
[[Low AOA Wing Rock]] – becomes a limit cycle
[[Van Der Pol Equation]] – example of a limit cycle
[[HL-10 Flight Control System]] – had limit cycles in the control system.
[[Control Surface Rate Limits]] – can cause limit cycles in the dynamics.
[[Phase Plot of a stationary Gravity Well]] – Orbital capture is a limit cycle in the phase plot of a gravitational well.
[[MH-96 AFCS]] – exhibited limit cycle close to the natural frequency of the sevo-actuator loop
Pilot-Induced Oscillations – limit cycle analysis does not give any information on PIO susceptibility.
[[X-29 Flight Testing]] – used limit cycle margin tests for ground testing.
[[Superaugmentation Architecture]] – The \(\int a_Z\ dt, \ G_{wo}q\rightarrow \delta_e\) mechanization exhibits a bias with roll limit cycles
Sources
- Bifurcations in 2D, Part 3: Hopf Bifurcation Physical Examples, (Apr. 07, 2021). Accessed: Aug. 30, 2023. [Online Video]. Available: https://www.youtube.com/watch?app=desktop&v=4vOC7zw2YME
- W. D. Painter and G. J. Sitterle, “HL-10 LIFTING BODY FLIGHT CONTROL SYSTEM CHARACTERISTICS AND OPERATIONAL EXPERIENCE”.
- M. Román and E. Ponce, “The describing function method accuracy in first order plants with rate-limited feedback,” European Control Conference, ECC 2003, Apr. 2015.
- “Wing Rock Prediction Method for a High Performance Fighter Aircraft”.
Backlinks
[[Hopf Bifurcations]]
[[Orbit]]
Wing Rock