Investigation of the Stability of Control Systems with Double (Frequency and Width) Pulse Modulation by the Direct Lyapunov Method

摘要

Discussion is based on a typical control system comprised of a continuous linear section (CLS) and combined pulse modulator (CPM). The modulator converts continuous output signal into a sequence of pulses of constant amplitude and modulated in sign, frequency, and duration. The modulation law is expressed. The development consists of the following: application of the direct Lyapunov method to the study of stability of a system with double pulse modulation; the Lyapunov function and its first difference; conditions of complete stability of a static system; and conditions of complete stability of a set of equilibrium positions of astatic systems. The method presented is applicable not only to systems with double pulse modulation but to all pulse systems which may be regarded as a special case of such a system.