Periodic Modes of Oscillations in Non-linear Control Systems

Abstract

A state variable approach is presented in this paper for investigating the possible modes of oscillations in a non-linear control system. Intrinsic equations have been developed, which represent the oscillatory response of a non-linear system and can be suitably adopted to ascertain whether or not a system has symmetrical and asymmetrical limit cycles and if it does to identify them completely. This technique can be adapted to a pulse width modulated system, sampled data system with a saturation non-linearity and an amplitude quantizer, a relay sampled data system, a continuous system with a saturation non-linearity and a discontinuous control system. Suitable examples have been taken to demonstrate the analytical procedure in each case. This approach of obtaining information on the periodic modes of oscillations is not restricted to the type of non-linearity or the order of the system and hence can be applied to various forms of non-linear systems. However, it is based on the assumption that the modes of the limit cycles should be specified, as can be done in certain cases, and the method can then suggest whether these modes are possible or not in that system.