Comparison of EKBF-based and Classical Friction Compensation Ashok Ramasubramanian 1 e-mail: ashokr@alum.dartmouth.org Laura R. Ray e-mail: Laura.Ray@dartmouth.edu Thayer School of Engineering, Dartmouth College, Hanover, NH 03755 In servo control, traditionally, models that attempt to capture the friction-velocity curve and interactions at contacting surfaces have been used to compensate for friction-introduced tracking errors. Recently, however, extended Kalman-Bucy filter (EKBF)- based approaches that do not use a phenomenological or struc- tured model for friction have been proposed. In addition to being cast as a friction estimator, the EKBF can also be used to provide parameter adaptation for simple friction models. In this paper, a traditional motor-driven inertia experiment is used to demonstrate the usefulness of EKBF in friction compensation. In addition, a numerical simulation is used to test the robustness of the new methods to normal force variations. Using root mean square po- sition tracking error as the performance metric, comparisons to traditional model-based approaches are provided. DOI: 10.1115/1.2431817 1 Introduction The motion control precision of many mechanical systems is severely compromised due to friction. Precise positioning systems that involve repeated velocity reversals are particularly vulner- able. Examples of such systems include airborne navigation sys- tems, systems used in computer controlled manufacturing, semi- conductor manufacturing and inspection systems, robotics, and automated surgical instruments. A primary feature of these appli- cations is low velocity, bidirectional position tracking. In cases where it is feasible to measure or estimate friction accurately in real time, it is possible to use the measurement or estimate to provide instantaneous feedforward compensation. Friction is thus monitored in real time, and corrective action is taken simultaneously. Optimized proportional-integral-derivative PID control combined with feedforward friction compensation provides high tracking accuracy with smaller control gains. In general, real-time friction measurement is difficult and an ob- server is used to estimate friction using measured quantities, such as position, velocity, and input torque. This estimate is then used to provide a compensating torque at the input of the machine Fig. 1. This topology is considered in a number of previous studies 1–5. Friction observers are typically model-based, i.e., phenomeno- logical or empirical modeling is used to characterize the surface interactions leading to friction. Dahl developed the first successful friction model for use in servo machines and used it to cancel bearing friction 1. This model accounts for presliding displace- ment sometimes referred to as the “Dahl effect”. Bliman studied the Dahl model as a map between the displacement or velocity and friction force and showed the existence of bounded hysteresis loops 6. A simplified version of the Dahl model was used by Walrath to compensate for bearing friction in an airborne tracking system 2. Friction modeling in motion control is a widely stud- ied field with a rich body of literature. Reference 7 gives a comprehensive survey. The most significant recent development in model-based fric- tion compensation for servo control has been the development of the LuGre model 8 and various schemes to adapt its six param- eters 4,5. This model improves Dahl’s work and includes the Stribeck effect. Common friction phenomena, such as hysteresis, presliding displacement, frictional lag, and stick-slip motion, are also captured 8. It has been applied successfully to cancel fric- tion in a DC motor-driven inertia 5 and is also used in industrial applications 9. Following their successful application in estimating aerody- namic forces 10 and tire forces 11, extended Kalman-Bucy filter EKBF-based methods have been introduced as an addition to model-based friction compensation 12,13. These methods ap- pend the friction state to the system state using a Gauss-Markov GM formulation, and no attempt is made to capture the surface level interactions leading to friction. Instead, friction is calculated from simple Newtonian dynamics using the known plant model and motion measurements Sec. 2.1. An earlier comparative study performed by the authors 12 demonstrated the effectiveness of the EKBF as a friction estima- tor. In this paper, we investigate this method further and address the following issues: i Whereas the earlier study used a second order GM formulation for friction, it is possible that higher-order formulations give better performance at an increased computa- tional cost. First-, second-, and third-order formulations are tested in this study, and the optimal order is selected. ii Using a nu- merical simulation, we test the robustness of EKBF-based meth- ods to friction level uncertainty. Also, the simulation uses a two- body system with dynamics significantly different compared to the traditional DC motor-driven inertia test bed and we test how the EKBF performs in this case. iii At least two previous com- parative studies that involve experimental validation of friction compensation have reported that the simple and elegant Dahl fric- tion compensator either had the best performance or was statisti- cally similar to the best compensator for a wide array of operating conditions 3,12. However, both these studies point out the diffi- culty in tuning the free parameters of the Dahl model: a time constant  and the level of Coulomb friction, T c . In this paper, we consider an adaptive Dahl model where the EKBF is used to es- timate T c in real time. iv Because of continued interest in the EKBF-based methods, certain implementation aspects are covered in more detail in this paper. In order to compare the various friction compensation algo- rithms, a sinusoidal position tracking experiment is used. The an- gular position of a load inertia is used as the controled variable in a PID-controlled system, where friction-related performance losses are significant. Such position tracking experiments have been used in previous comparative studies 3,12,14. Following the example set by these prior studies, root mean square RMS position error is used as the performance metric. In addition, a numerical simulation tests the efficacy of friction compensation when friction levels change over time. 2 Friction Compensation Methodologies 2.1 EKBF-Based Friction Compensation (KF Estimator). In many mechanical systems, the rigid-body dynamics are well known, whereas certain external forces acting on the system are poorly understood. Often, the well established rigid-body dynam- ics, along with motion measurements, can be exploited to recover these unknown external forces. The basic idea behind EKBF- based friction estimation can be summarized as follows: Extract friction force by exploiting the well-known motion equations and using the information from motion measurements. This funda- 1 Corresponding author. Contributed by the Dynamic Systems, Measurement, and Control Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS,MEASUREMENT, AND CON- TROL. Manuscript received October 18, 2005; final manuscript received June 23, 2006. Assoc. Editor: George Chiu. 236 / Vol. 129, MARCH 2007 Copyright © 2007 by ASME Transactions of the ASME