Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch
- Univ. of Wisconsin, Madison, WI (United States)
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
- Research Organization:
- Univ. of Wisconsin, Madison, WI (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- FG02-96ER54345
- OSTI ID:
- 656820
- Report Number(s):
- DOE/ER/54345-T2; ON: DE98007453; BR: AT0530020; AT5010902; TRN: 99:000497
- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); PBD: Jun 1998
- Country of Publication:
- United States
- Language:
- English
Similar Records
Controlling chaos in low and high dimensional systems with periodic parametric perturbations
Extraction of dynamical equations from chaotic data