An Adaptive Control Technique for Systems with Lightly Damped Resonances

Citation

Pinson, Elliot Neil (1961) An Adaptive Control Technique for Systems with Lightly Damped Resonances. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/6HPW-4V89. https://resolver.caltech.edu/CaltechTHESIS:04122011-150702576

Abstract

An Adaptive Controller capable of stabilizing dynamic systems containing multiple lightly damped resonances is synthesized. The controller acts to stabilize the dynamic system by introducing cascade compensation which has zeros of transmission very close to the critical resonant frequencies. Very little a priori knowledge is needed about the frequencies at which the resonances occur because the Adaptive Controller itself measures these frequencies while the system is operating. It then adjusts its internal parameters on the basis of these measurements to insure that the overall system performance is satisfactory. Since the measurement process can be performed continually, this adaptive control technique is applicable to systems whose resonant frequencies change slowly with time. Both the measurement and compensation functions are performed by a digital computer. The resonant frequencies are measured by cross-correlating a signal generated by the dynamic system with a set of periodic signals whose frequencies span the frequency intervals in which the resonances are known to occur. The necessary compensation is instrumented in a set of difference equations stored in the digital computer. Certain coefficients which appear in these difference equations are adjusted according to logic programmed into the computer. Necessary and sufficient conditions are derived to describe the conditions under which the proposed system can be successful. The fact that the system can perform successfully is demonstrated by a detailed digital simulation of an adaptive autopilot for a highly flexible ballistic missile.

Thesis Files