A sampled-data extremum-seeking approach for accurate setpoint control of motion systems with friction

This paper presents an extremum-seeking approach for accurate setpoint control of motion systems with friction, performing a repetitive motion. The classical PID controller, often used in industry for frictional motion systems, suffers from severe performance limitations. In particular, friction-induced limit cycling (hunting) is observed when integral control is employed on systems with unknown Stribeck friction, thereby compromising stability. Moreover, even if stability is warranted, transient performance highly depends on the particular frictional characteristic, which is typically uncertain. To deal with such uncertainty and to warrant optimal setpoint performance for the actual frictional properties, we propose a PID-based learning controller that achieves improved transient performance. Hereto, we consider a PID-type controller with a time-varying integral controller gain, which is adaptively obtained by employing a sampled-data extremum-seeking approach, resembling iterative learning control. The proposed approach does not require any knowledge on the friction characteristic. The working principle is illustrated by means of a representative simulation example.