Ph.D Student | Lichtsinder Arkady |
---|---|

Subject | Reciprocity of Friction and Backlash in Servo Control Systems |

Department | Department of Civil and Environmental Engineering |

Supervisor | Professor Emeritus Per-Olof Gutman |

Full Thesis text |

The analysis and
the synthesis control problems of a non-linear servo system under the impact of
both friction and backlash are addressed. Backlash and friction *reciprocal*
effect on limit cycle existence is investigated for the one-mass, and two-mass
non-linear servo systems with simplified models of friction and backlash. By
the describing function method, it is shown that the upper boundary for limit
cycle existence, in the backlash-friction plane, is a *straight line*
starting in the origin. This fact provides a simple condition of the limit
cycle existence in terms of the friction-to-backlash ratio. It is also shown
that for different pairs of friction torque and backlash gap such that their
ratio is constant, the system under consideration will oscillate with the same
limit cycle frequency. This property is used to suggest a friction and backlash
identification algorithm that exploits the self-oscillating mode.

Experimental measurements are provided to demonstrate the applicability of the theoretical results. This outcome forms the basis for studies into the effect of backlash and friction for more realistically modeled systems including the modern "exact" backlash model combined with the Karnopp and the LuGre friction models.

Thus,
quasi-linear analytical approximations for the Karnopp friction model and for
the "exact" backlash model are presented for the first time using the
describing functions method. It is shown that the proposed quasi-linear
descriptions are more appropriate to describe a realistic behavior of friction
and backlash in the frequency domain in contrast to the classical describing
functions of the Coulomb friction and dead-zone backlash models. The
reliability of these novel quasi-linear approaches is experimentally verified
by the common sine-scan frequency response technique. The analytical form of the proposed descriptions enables
for rapid computation, and can therefore be of use in real-time control
algorithms. It is also shown that the friction and backlash models and
their describing functions are based on similar mathematical descriptions, or,
in a certain sense, they are *reciprocal* of each other from a structural
standpoint.

The experimental
results of design and implementation of a cascade control scheme on the real
industrial servo system of a stabilized platform is presented to verify the
theoretical findings concerning friction and backlash effect. The presented
control design methodology is based on the *Quantitative feedback theory*
synthesis method, integrated with the novel quasi-linear analytical approach
for stick-slip friction and "exact" backlash phenomena, providing
the modeling of the non-linear dynamics via a set of the describing functions.