Experimental Control of Instabilities and Chaos in Fast Dynamical Systems

摘要

I investigate experimentally and theoretically the application of controltechniques in systems that display temporal instabilities, including chaos, on very short timescales. My study includes two distinct systems: a fast chaotic electronic circuit called the diode resonator, and a compound-cavity semiconductor laser system that exhibits an instability called low-frequency fluctuations. Control of fast unstable systems presents several experimental challenges. It is also a topic of broad interest, since it requires the development of new control techniques, and addresses technologically important devices such as the semiconductor laser. The diode resonator is a well-understood system, and when modified for 10 MHz operation serves as a good testbed for the application of novel control techniques. I develop a new high-speed time-delay feedback control technique that is based on the comparison of the present value of a system variable with a series of its past values. The principles of operation of this technique are studied in both time and frequency domains, as well as possible methods for its implementation. I develop a detailed analog electronic implementation that addresses the experimental needs of rapid processing and faithful reproduction of the feedback signal. This control system successfully stabilizes unstable periodic orbits in the diode resonator, the fastest experimental instability controlled to date. This technique also increases significantly the regions of parameter space in which control is effective, in comparison with previous methods. The improvement is gained by incorporating more information from further in the system's past.