Limit Cycles in a Class of Systems under PID-type of Relay Feedback

This paper investigates the limit cycles within a class of linear system under PID-type of relay feedback. The problem is generalised from identification of friction models of servo mechanical systems via limit cycle experiments under dual- channel relay feedback. Locations of limit cycles are given so that the exact durations between two consecutive switchings of relays can be determined via numerical computation. After this, local stability of limit cycles can be checked via Jacobian of Poincare map. Examples are analysed using proposed theorems.