Introduction: Eccentricity and Cogging

Motor Model

Step response of non-reduced model of permanent magnet DC-Motor

Order Reduction For many DC motors, the time constant of the armature, is negligible. This produces a reduced transfer function :

Control Requirements Notatio n NameValue Bandwidth Resonant Peak Steady State Error :

Bode diagram of system with desired PI controller

Bode diagram of disturbance-output transfer function

Step response for a constant angular velocity input command

Sinusoidal angular velocity input command near =100Hz frequency

Sinusoidal angular velocity input command near 10Hz frequency

Reaction to a constant torque disturbance

Reaction to a sinusoidal torque disturbance

Tracking error for sinusoidal input command and sinusoidal disturbance

Tracking error for position dependent disturbance and sinusoidal 100[rad/sec] input command

Tracking error results for different phase position dependent torque disturbance and fixed parameter disturbance compensation

Tracking error results for different amplitude position dependent torque disturbance and fixed parameter disturbance compensation

LYAPUNOV ANALYSIS

Tracking error for adaptive eccentricity compensator

Desired and Actual Angular Velocity for adaptive eccentricity compensator

Predicted and actual disturbance using an adaptive eccentricity compensator

Angular position tracking error for adaptive eccentricity compensator

Actual and predicted disturbance

Disturbance Prediction Error

Angular Position Observer Error

Angular Velocity Observer Error

Tracking error for adaptive eccentricity compensation of two harmonic position dependent disturbances

Desired and Actual Angular Velocity for adaptive eccentricity compensator

Predicted and actual disturbance using an adaptive eccentricity compensator

SUMMARY