Experimental Control of a Fast Chaotic Time-Delay Opto-Electronic Device
DUKE UNIV DURHAM NC DEPT OF PHYSICS
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The focus of this thesis is the experimental investigation of the dynamics and control of a new type of fast chaotic opto-electronic device an active interferometer with electronic bandpass filtered delayed feedback displaying chaotic oscillations with a fundamental frequency as high as 100 MHz. To stabilize the system, I introduce a delayed feedback control suitable for fast time-delay systems. The new opto-electronic device consists of a semiconductor laser, a Mach-Zehnder interferometer, and an electronic feedback loop. Both the nonlinearity and the timescale of the oscillations are easily manipulated experimentally. The system displays a route to chaos that begins with a Hopf bifurcation from a steady state to a periodic oscillation at the so-called fundamental frequency. Further bifurcations give rise to a chaotic regime with a broad, flattened power spectrum. I develop a mathematical model of the device that shows very good agreement with the observed dynamics. To control chaos, I introduced modification of a well known control approach called time-delay autosynchronization TDAS in which the control perturbation is formed by comparing the current value of a system variable to its value at a time in the past equal to the period of the orbit to be stabilized. The current state of a time-delay dynamical system retains a memory of the state of the system one feedback delay time in the past. As a result, the past state of the system can be used to predict the current state. In order to take advantage of this effect, the new control method forms a perturbation according to the TDAS scheme but delays actuation of the control perturbation by a time equal to the feedback delay time of the system to be controlled. This effectively sets the control-loop latency equal to the feedback delay time of the uncontrolled system.
- Electrooptical and Optoelectronic Devices