For beam control during acceleration, it is conventional to derive the frequency from an external reference, be it a field marker or an external oscillator. In addition, phase and radius feedback loops are also provided to ensure the phase stability, radial position and emittance integrity of the beam. The open and closed loop behaviors of both feedback controls and their responses under the possible frequency, phase and radius errors are derived from fundamental principles and equations. The stability of the loops is investigated under a wide range of variations of the gain and time delays. Actual system performance of the AGS Booster is analyzed and compared with commissioning experiences. Such analysis is useful for setting design criteria and tolerances for new proton synchrotrons.