Analysis of oscillations in systems with relay and friction

Deals with systems containing a relay-type nonlinearity (referred to as "plant relay") and in feedback with another relay ("identification relay"). This system structure is inspired by mechanical systems affected by friction. We consider two different system configurations-with common entry point of the control signal and the friction force and with a dynamics between them. For the first case, we found a relation between the identification relay amplitude and the limit cycles frequency resulting from the harmonic analysis. The conclusions of the analysis are verified by simulation of a single-mass system with friction modelled in different ways. For the second case, results of simulations and of the harmonic analysis are presented together with some practical measurements realised on a pneumatic actuator (the structure of which contains dynamics between the control signal and the friction).