Study of Limit Cycles in Pulse Control Systems

Abstract

This paper presents a method for the study of limit cycles in sampled-data systems containing relay with dead-band and hysteresis and control systems with pulse-width and frequency modulation. The linear sub-system is characterized by real, non-positive and distinct eigenvalues. Using state-variable techniques, intrinsic equations for the response of systems in the state of symmetrical oscillations are derived. These equations provide necessary conditions for existence of limit cycles. The parameters of limit cycles satisfying necessary conditions may be found by solving intrinsic equations by numerical methods. In addition to this, the method allows an effective visualization of the effect of parameters of linear sub-system and pulse controller on behaviour of system.

Indexing Terms:

• Limit Cycles
• Pulse Control Systems