Proceedings of the American Control Conference Albuquerque, New Mexico June 1997 0-7803-3832-4/97/$10.00 0 1997 AACC Friction Compensation for Drives with and without Transmission Compliance t S. Jain F. Khorrami N. Ahmad S. Sankaranarayanan Control/Robotics Research Laboratory (CRRL) Department of Electrical Engineering Polytechnic University Brooklyn, New York 11201 Abstract In this paper, nonlinear robust adaptive controler is pro- posed for friction compensation. The design has been per- formed for a six parameter dynamic model of friction. The advocated control design does not utilize any knowledge of these six parameters and requires just an upper bound on the static friction level, which can be obtained experi- mentally. The controller is robust to dynamic uncertain- ties and can compesate the effect of friction which is sep- arated from the control input through drive compliance. Simulation and experimental results are also presented. I. Introduction In many applications, friction sets the limit for achiev- ing high positioning accuracy. For this reason, in many high speed ultra accurate machines, air bearings are uti- lized in order to avoid dealing with friction. One of the major problems in friction compensation is the fact that the friction force varies as a function of temperature, lu- bricant condition, load, etc. On the other hand, accurate models that describe the behavior and dynamics of fric- tion to a suficient degree are not available although a reasonable amount of progress have been made. In many applications where micron or submicron accuracies are not required, one can sufficiently compensate for friction ef- fects 1-61. In these earlier works, various techniques such and adaptive nonlinear controllers have been considered. An adaptive nonlinear control work is recently reported in [2] where a nominal friction model is utilized and one parameter adaptation is carried out. In this paper, the model advocated in [3] is used. Our controller design methodology utilizes a dynamic model of friction with unknown parameters in the model. To further mimic real physical systems, we consider the case where friction occurs both on the load and the drive side with transmission compliance. In this case, our results in conjunction with backstepping techniques are utilized. Experimental results are given for a brushless DC motor setup with variable friction and loads in this paper. 11. Friction Model as dit I, er, pulse-width modulation, observer based design, Several dynamic friction models have been proposed in literature[5]. We consider a dynamic model for friction developed in [3] which mimics many characteristics of fric- tion. In this model, the bodies in contact are modelled as elastic “bristles”. The model captures the average deflec- tion (z) of the bristles which is given as tThis work is supported in part by the U.S. Army Research Office under grant # DAAH04-93-G-0209, the National Science Foun- dation under grant # DMI-9413543 and OmniTek R&D, Inc. where v is the relative velocity between the two surfaces, and g(v) is a positive function and depends on material properties, lubrication, temperature, etc. A typical repre- sentation of g(v) is given by aog(w) = F, + (F, - F,)e-(%)’ (2) where F, and F, are the Coulomb and static friction levels respectively and U, is the Stribeck velocity. Note that g(v) decreases monotonically from g(0) as the velocity increases which is consistent with the decline in the friction force on commencement of motion (Stribeck effect). The total friction force is given by (3) The friction model given by (l), (2), and (3) is thus charac- terized by six parameters CTO, CT~, 02, U,, F, and F,. These parameters, in general time-varying, and are a function of material and environmental properties. 111. Robust Adaptive Friction Compensation Motivated b our earlier results in robust, adaptive non- linear control $], we here propose a friction compensation scheme for the above discussed frictionmodel. The design assumes no knowledge of any of the friction parameters or the measurement of the friction state z. Only the knowl- edge of an upper boundon the static friction force F, is required which can easily be obtained experimentally. The state space model of a servomotor driving a fric- tional load can be written as1 8 = w (4) where r is the input torque and rf is the friction torque which is modelled as discussed above: dx IWI Tf = L7ox+a1-+a2w, z = w - - dt 9(W) aog(w) = rc + (r, - T,)e-(:)z 5 7,. The following property of the friction model is employed in the compensator design: ‘The case where there is compliance between the actuator and the load is considered later. 2925