Limit cycling in observer-based controlled mechanical systems with friction

In this paper, it is shown that observer-based controlled mechanical systems with friction may exhibit limit cycling. The limit cycling is induced by the interaction between friction and friction compensation, which is based on the estimated velocity. This limit cycling phenomenon, which is experimentally observed in a rotating arm manipulator, is analyzed through the shooting method and bifurcation analysis. The numerical results match well with laboratory experiments. The bifurcation analysis confirms that the limit cycling can be eliminated by enlarging the controller gains and the observer gains at the cost of a steady state error.