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Limit cycle stability of systems containing a pulse ratio modulator

Most spacecraft attitude control systems employing mass-expulsion techniques use some form of pulse modulation at the output from the control system to the gas control valves. In a number of early designs such modulation was introduced almost accidentally by surrounding simple relay-type switching logic with a feedback loop containing a first-order lag to provide ‘derived rate’ damping. This arrangement gives pulse width and pulse frequency modulation (Combined pulse modulation). Such a modulation scheme was devised by Schaefer in 1962 which he called a Pulse Ratio Modulator (PRM). His main concern was the mechanisation of the quasistatic equations of the modulator and he did not investigate the stability of systems containing a PRM.