ABSTRACT - Utah State University · of resolver-to-digital converter accuracy. This affects the...

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