Ayesha Sayed, M.S. StudentDionysios Aliprantis, Associate Professor of Electrical and Computer Engineering

Impact of Resolver Error in ElectricVehicle Traction Systems

SELECT Annual Meeting and Technology Showcase – Logan, Utah – September 27-28, 2016

ABSTRACT

Resolvers are used in various motor drive applications, e.g. robotics, HEV/EV’s and

in the aerospace industry.

Position measurement error occurs due to manufacturing imperfections or limitations

of resolver-to-digital converter accuracy.

This affects the field orientation control in permanent magnet (PM) machines and

leads to substantial oscillations in currents, torque etc.

Here, a survey on the effects of non-ideal resolver signal characteristics is presented.

IDEAL RESOLVER (VR)

𝑉sin = 𝐾𝑉0sin(𝜃𝑟)sin 𝜔𝑒𝑡𝑉cos = 𝐾𝑉0cos(𝜃𝑟)sin 𝜔𝑒𝑡

𝑉e= 𝑉0sin 𝜔𝑒𝑡

𝑉e

𝑉sin

𝑉cos

2 lobes 4 lobes3 lobes

All windings are on the stator.

Rotor lobes usually equal motor poles

so that induced output is ~ sin/cos of

electrical rotor angle 𝜃𝑟.

TRACKING MECHANISM

Input to demodulation block

= 𝐾𝑉0 sin 𝜔𝑒𝑡 sin(𝜃𝑟 − 𝜙𝑟) Different control schemes e.g.

PLL, Type-II tracking loops etc.

are used to estimate 𝜙𝑟 .

Errors in resolver signals

introduce error in output of R/D

converter.

AMPLITUDE IMBALANCE

𝑉sin= 𝐾𝑉0sin(𝜃𝑟)sin 𝜔𝑒𝑡𝑉cos = 𝐾 1 + 𝛼 𝑉0cos(𝜃𝑟)sin 𝜔𝑒𝑡

𝜙𝑟 ≈ 𝜃𝑟 −𝛼

2sin(2𝜃𝑟)

Position error occurs at twice

the electrical rotor speed.

Causes:

Unequal inductances in the phases.

Variation in gain between resolver

and R/D converter

IMPERFECT QUADRATURE

𝑉sin= 𝐾𝑉0sin𝜃𝑟sin 𝜔𝑒𝑡𝑉cos = 𝐾𝑉0cos(𝜃𝑟 + 𝛽)sin 𝜔𝑒𝑡

Position error here also exists at

twice the electrical rotor speed.

This error has non-zero average

value

Cause:

Output phases not in perfect

spatial quadrature

Approximations: sin 𝛽 ≈ 𝛽cos𝛽 ≈ 1

DC OFFSET

Causes:

Asymmetrical coil locations due to

three layers of winding on stator

tooth in VR resolvers

Rotor eccentricity during assembly

or operating

𝑉sin = (𝐾0 + 𝐾𝑉0sin 𝜃𝑟 )sin 𝜔𝑒𝑡𝑉cos = (𝐾0 + 𝐾𝑉0cos(𝜃𝑟))sin 𝜔𝑒𝑡

Position error occurs at

fundamental frequencyConventional VR resolver Rotor eccentricity

IMPACT OF RESOLVER ERROR

Variable Reluctance (VR) resolver – 2X Brushless Type resolver

(Resolver-to-Digital Converter)

Output of R/D converter:

error

𝜙𝑟 ≈ 𝜃𝑟 +𝛽

2(1 − cos(2𝜃𝑟))

Output of R/D converter:

error

𝜙𝑟 ≈ 𝜃𝑟 + 2𝐾0 cos 𝜃𝑟 +𝜋

4

Position error introduces oscillations

in qd currents.

First and second harmonics are

reflected in the torque.

Position error introduced at:

Fundamental of 1∘ magnitude

Second harmonic of 2∘ magnitudePosition error affecting the system

𝑉sin

𝜙𝑟

Error

cos

Demodulation

Control

𝑉cos

sin

𝑉e

𝑻𝒆Current

Controlqd/abc Inverter Machine

𝜽𝒓 + ∆𝜽𝒓 𝒊𝒒𝒅∗

Ƹ𝒊𝒒𝒅 𝒗𝒒𝒅∗ 𝒗𝒂𝒃𝒄

𝒊𝒂𝒃𝒄

𝜽𝒓 + ∆𝜽𝒓

abc/qd