Limit cycle oscillations in a satellite attitude control system

Limit cycle oscillations in an attitude control system using an integral-pulse-frequency modulator are studied. A previous paper showed, through a study of some geometrical properties of the state transition equations, the necessary and sufficient relationships among the physical parameters for the ultimate behavior to be a two-pulse limit cycle for arbitrary initial states 1]. Here it is shown that two-pulse limit cycles can exist if those relationships are not satisfied provided the initial state lies in a certain region near the origin of the state space. The boundaries of this region are established analytically by geometrical means and are verified by simulator experiments. These experiments also show the existence of four-pulse, six-pulse and higher order limit cycles for certain initial states and combinations of physical parameter values.