טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentLichtsinder Arkady
SubjectReciprocity of Friction and Backlash in Servo Control
Systems
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Emeritus Per-Olof Gutman
Full Thesis textFull thesis text - English Version


Abstract

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.