**On Methods for Low Velocity Friction Compensation**

Theory and Experimental Study

Theory and Experimental Study

**Abstract**

A study of different classes of controllers for mechanisms

under the influence of low velocity friction is conducted.

Many methods are proposed in the literature for friction

compensation, but there has been no significant analysis

of these methods with respect to each other. Also lacking

in the literature is some form of categorization, under which

it is possible to describe and study their performance.

This paper provides an experimental and analytic study of

controllers previously proposed for low velocity friction

compensation. Since each controller will be evaluated on

the same experimental platform, the results can be quantified

to provide an approach by which to evaluate the performance

of the controllers relative to each other. Some simulations will

also be performed to show the effect of certain system

parameters on the performance of these controllers.

**1 Introduction**

**2 System Description**

**3 Linear Methods**

3.1 PD schemes

3.2 PID Control

**4 Nonlinear Methods**

4.1 Smooth Continuous Nonlinear Compensation

4.2 Discontinuous Compensation

**5 Experimental Results**

5.1 Experimental Setup

5.2 Results and Discussion

**6 Conclusions**

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**Adaptive Compensation of Friction Forces with Differential Filter**

Kouichi Mitsunaga, Takami Matsuo

**Abstract:**

In this paper, we design an adaptive controller to

compensate the nonlinear friction model when the output is the

position. First, we present an adaptive differential filter to estimate

the velocity. Secondly, the dynamic friction force is compensated

by a fuzzy adaptive controller with position measurements. Finally,

a simulation result for the proposed controller is demonstrated.

Keywords: nonlinear friction, adaptive controller, fuzzy basis

function expansion, adaptive differential filter.

**Introduction**

Friction is one of the greatest obstacles in high precision positioning

systems. Since it can cause steady state and tracking errors, its

influence on the response of the systems must be considered

seriously ([10]). Many friction models have been proposed that differ

on the friction effects that are modeled in a lubricated contact.

These models are divided into two categories: the kinetic and dynamic

Friction models. The kinetic friction models take into account the

friction effects such as the viscous friction, the

Coulomb friction, and the Stribeck effect. Another category of friction

model includes dynamic friction model that embody the natural

mechanism of friction generation such as the LuGre model

**Adaptive differential filter**

Nonlinear friction model

Controller design

Nonlinear friction model

Controller design

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**New Results in NPID Control: Tracking,**

Integral Control, Friction Compensation

and Experimental Results

Integral Control, Friction Compensation

and Experimental Results

Brian Armstrong†, David Neevel, Todd Kusik

**Abstract**

Nonlinear (NPID) control is implemented by varying the controller

gains as a function of system state. NPID control has been previously

described and implemented, and recently a constructive Lyapunov

stability proof has been given. Here, NPID control analysis and design

methods are extended to tracking, and to systems with state feedback

and integral control. Experimental results are presented showing

improved tracking accuracy and friction compensation by NPID control.

Here we are interested in NPID control applied to linear systems with

the objective of improved performance. Past and recent studies have

shown that for linear systems NPID control can provide:

1. Increased damping,

2. Reduced rise time for step or rapid inputs,

3. Improved tracking accuracy, and

4. Friction Compensation.

2 NPID control in state space

2.1 System model

Theorem 1. Asymptotic stability of NPID regulator control for

state space systems

2.2 Design of NPID control

3 Tracking NPID control

Theorem 2. Bounded Input – Bounded Output stability of

NPID tracking control.

4 Augmented state vector: integral control

5 Friction compensation

Proposition 3. Friction compensation by NPID control.

6 Experimental results

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