* Corresponding author. Tel.: #82-42-869-3042; fax: #82-42-869- 3210. E-mail address: kwonds@me.kaist.ac.kr (D.-S. Kwon). Control Engineering Practice 9 (2001) 159}167 A nonlinear friction compensation method using adaptive control and its practical application to an in-parallel actuated 6-DOF manipulator Jee-Hwan Ryu, Jinil Song, Dong-Soo Kwon* Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, ME 3042 Taejon, South Korea Department of Automation and Design Engineering, Korea Advanced Institute of Science and Technology, Seoul, South Korea Received 15 October 1999; accepted 9 June 2000 Abstract This paper presents a simple and e!ective nonlinear friction compensation method which is derived from an adaptive control strategy and its practical application to a linear actuator. The proposed adaptive friction compensation method is shown to be equivalent to the reversed integral controller that is easily applied to the conventional PID controller. The reversed integral controller reverses the sign of the integrator output as the sign of the velocity changes. It analyzes how the reversed control action can compensate for friction. The e!ectiveness of this approach is demonstrated by experiments on a 3-PRPS (Prismatic-Revolute-Prismatic-Spherical joints) in-parallel 6-DOF manipulator.  2001 Published by Elsevier Science ¸td. All rights reserved. Keywords: Nonlinear friction; Friction compensation; Adaptive control; Reversed integral control; Parallel manipulator 1. Introduction In servo systems, steady-state errors and tracking er- rors are mainly caused by static friction (stiction), which depends on the velocity's direction, and the viscous fric- tion that increases the damping of a system. The main way to remedy friction is to formulate a nonlinear friction model, identify its parameters, and suggest compensation algorithms. Friction models have been widely studied by numer- ous researchers (Armstrong-Helouvry, 1993; Canudas de Wit, Astrom & Lischinsky, 1995; Canudas de Wit, Olsson, Astrom & Lischinsky, 1993). Friction is commonly modeled as a linear combination of Coulomb friction, stiction, viscous friction, and the Stribeck e!ect. However, the modeling of exact friction characteristics is not easy because friction characteristics are sensitive to various environmental factors: variations of the load, temperature, lubrication, and the assembly status of machines. A wide range of friction compensation schemes have been proposed (Armstrong-Helouvry, Dupont & Canudas de Wit, 1994). Traditional PD con- trollers will not achieve satisfactory results because of steady-state errors. Even though the errors may be re- duced using a high-gain PD controller (Wu & Paul, 1980), the high gain controller can cause system instabil- ity. The integrator of a PID controller can compensate for steady-state errors, but this will cause the generation of a limit cycle due to the fact that stick}slip friction is time-varying (Radclittle & Southward, 1990; Townsend & Salisbury, 1987). As a model reference feed-forward method, adaptive schemes (Ge, Lee & Harris, 1998; Lewis, Jagannathan & Yesildirek, 1998; Polycarpou & Ioannou, 1993) have been proposed to compensate for nonlinear friction in a variety of mechanisms (Canudas de Wit, Astrom & Braun, 1987; Canudas de Wit, Noeol, Auban & Broglianto, 1991), but these are usually based on certain linearized models or models with linearized parameters that are approximations of the nonlinear phenomenon. To strengthen the compensation of nonlin- ear friction, a new adaptive scheme was developed re- cently (Canudas de Wit & Ge, 1997), based on a new friction model (Canudas de Wit et al., 1995). Since the model reference feed-forward compensation depends on the friction model, the model error of friction can induce 0967-0661/01/$ - see front matter  2001 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 0 ) 0 0 1 0 3 - 9