Date of Award

Spring 1994

Document Type


Degree Name

Doctor of Philosophy in Electrical Engineering - (Ph.D.)


Electrical and Computer Engineering

First Advisor

Bernard Friedland

Second Advisor

Timothy Nam Chang

Third Advisor

Denis L. Blackmore

Fourth Advisor

Avraham Harnoy

Fifth Advisor

F. Khorrami

Sixth Advisor

Brian Armstrong-Helouvry


The research reported in this dissertation concerns the estimation and cancellation of friction in control systems. For purposes of analysis, the Coulomb friction model, the "extended" Coulomb friction model as well as dynamic friction models are used. In addition, for systems with multiple degrees-of-freedom, a general matrix representation of friction is presented.

For the design of the friction estimators, the theory of nonlinear observers is applied. In particular, for a system with multiple degrees-of-freedom, holonomic constraints, and multiple friction sources, three different observers are presented to estimate the friction force or torque. The first (Generalized Coulomb Friction Observer) is designed by assuming that friction is described by the classical Coulomb model; the second (Generalized Tracking Observer) considers friction as a system unknown constant input; and the third (Generalized Dynamic Friction Observer) is designed by assuming that friction is described by a dynamic model.

For the analysis of the performance of the proposed estimators, two cases are considered. First considered is the case where both the system "positions" and "velocities" are available for measurements. Second considered is the case where only the system "positions" can be measured. In the first case, the observers use the measurements of the states to estimate the friction forces. In the second case, an additional reduced-order velocity observer is used to estimate the unmeasured "velocities".

The problem of friction cancellation in a system with multiple degrees-of-freedom, external inputs and friction sources is also addressed. Necessary and sufficient conditions are derived for cancellation of the friction. The conditions are based on the relative distribution of the system inputs and friction sources at the different system degrees-of-freedom. When cancellation is possible, a control law for accomplishing it is presented.

The effectiveness of the proposed algorithms for friction estimation and cancellation is demonstrated by simulations. The observers are applied and compared in systems with linear as well as nonlinear dynamics.

Finally, experimental data for the different friction compensators are taken and compared, using an experimental apparatus built for this purpose. The results of the experiments confirm the theory and demonstrate that friction can be estimated and cancelled by the algorithms developed in this research.