mathworks technology session at ge closed-loop motor

1 © 2012 The MathWorks, Inc.

MathWorks Technology Session at GE

Closed-Loop Motor Control

Development

February 28, 2013

Brad Hieb

Tom Priestley

Marc Semma

http://www.google.com/url?sa=i&rct=j&q=synchronous+motor&source=images&cd=&cad=rja&docid=fB8yL0IMqSekGM&tbnid=OFHM1ru63s2Q8M:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.nhpa40.org%2Fb2b%2Fradio_and_tv_equipment%2F6%2F&ei=kDouUazwF8K30QXz0IDABA&bvm=bv.42965579,d.d2k&psig=AFQjCNEnnL3hh96sj_2T6ssr_LuykK71kw&ust=1362070223890219

2

Design Controller

Control System Toolbox

Robust Control Toolbox

Model Predictive Control Tbx

Optimize Control System

Simulink Control Design

Simulink Design Optimization

Model Physical Plant

System Identification Toolbox

Model-Based Calibration Tbx

Simscape

data model

http://www.google.com/url?sa=i&rct=j&q=feedback+control+loop&source=images&cd=&cad=rja&docid=XbdPYXu_6laCPM&tbnid=9wiYqNlpyGZ_rM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.peterkrantz.com%2F2011%2Fenergy-feedback-loops%2F&ei=Y74sUfCLFOfy0QHUhoGIDw&bvm=bv.42965579,d.dmQ&psig=AFQjCNHwhXwVGcQcLkR2RNtr52Z8Uw8xjg&ust=1361973133251793

3

Embedded System

Motor

Hardware

Controller

C Code

System Model

Model Based Design for Embedded Controls

Controller

C Code

Controller

Model

Motor

Model

Motor

Hardware

4

Embedded System

Motor

Hardware

Controller

C Code

System Model

System Modeling and Simulation

GE Tech

Session, Tues.

March 26

Controller

C Code

Controller

Model

Motor

Model

Motor

Hardware

5

What’s Next

Introduction and overview

PMSM motor characterization Characterization tests

Test data to model parameters

Validating the characterized model

Control system design Control model architecture

Tuning control parameters

Verifying closed-loop performance

Q&A

http://www.google.com/url?sa=i&rct=j&q=feedback+control+loop&source=images&cd=&cad=rja&docid=XbdPYXu_6laCPM&tbnid=9wiYqNlpyGZ_rM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.peterkrantz.com%2F2011%2Fenergy-feedback-loops%2F&ei=Y74sUfCLFOfy0QHUhoGIDw&bvm=bv.42965579,d.dmQ&psig=AFQjCNHwhXwVGcQcLkR2RNtr52Z8Uw8xjg&ust=1361973133251793

http://www.google.com/url?sa=i&rct=j&q=permanent+magnet+synchronous+motor&source=images&cd=&cad=rja&docid=kFKr55HbkRc6eM&tbnid=Dvv1gpkXRvkllM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.jmag-international.com%2Fcatalog%2F103_PMMotor_Efficiency.html&ei=tbssUZqsBcXW0gGD74GYDQ&bvm=bv.42965579,d.dmQ&psig=AFQjCNFMLUYrlGEGtULFY-V-OSbekFCBLg&ust=1361972477287942

6 © 2012 The MathWorks, Inc.

Characterizing a Permanent Magnet

Synchronous Machine

Brad Hieb – Application Engineer

7

Motivation

Why characterize the motor?

– To develop a plant model

Why develop a plant model?

– To simulate the system

Why simulate the system?

– Simulation is a safe environment to try out new ideas without

the risk of damaging prototype hardware.

– Visualization and analysis of the complex data in our system.

– Gain confidence in our controller design before deploying on

hardware.

8

Example use of simulation

Develop a velocity controller to meet performance

requirements

9

But Does it Work on Hardware?

10

Key Point

Create accurate plant models by executing tests,

identify parameter values and verifying against real-

world data

Test Identify

Parameters Verify

11

What do These Particular Models Look Like?

12

Surface Mount PMSM Equations

Mechanical Model

Electrical Model

𝑣𝑑 = 𝑅𝑖𝑑 − 𝐿𝑞𝑝𝜔𝑟 𝑖𝑞 + 𝐿𝑑

𝑑

𝑑𝑡𝑖𝑑

𝑣𝑞 = 𝑅𝑖𝑞 + 𝑝𝜔𝑟 𝐿𝑑 𝑖𝑑 + 𝜆 + 𝐿𝑞

𝑑

𝑑𝑡𝑖𝑞

𝜔𝑒 = 𝑝𝜔𝑟

𝑇𝑒 = 1.5𝑝 𝜆𝑖𝑞 + 𝐿𝑑 − 𝐿𝑞 𝑖𝑑 𝑖𝑞

𝑇𝑒 = 𝐾𝑡𝑖𝑞 𝑎𝑠𝑠𝑢𝑚𝑒𝑠 𝑟𝑜𝑢𝑛𝑑 𝑟𝑜𝑡𝑜𝑟, 𝐿𝑑 = 𝐿𝑞

𝑑

𝑑𝑡𝜔𝑟 =

1

𝐻 𝑇𝑒 − 𝑠𝑔𝑛 𝜔𝑟 𝐽0 − 𝑏𝜔𝑟 − 𝑇𝑙𝑜𝑎𝑑

13

Required Parameters

Electrical Model

Mechanical Model

𝑣𝑑 = 𝑅𝑖𝑑 − 𝐿𝑞𝑝𝜔𝑟 𝑖𝑞 + 𝐿𝑑

𝑑

𝑑𝑡𝑖𝑑

𝑣𝑞 = 𝑅𝑖𝑞 + 𝑝𝜔𝑟 𝐿𝑑 𝑖𝑑 + 𝜆 + 𝐿𝑞

𝑑

𝑑𝑡𝑖𝑞

𝜔𝑒 = 𝑝𝜔𝑟

𝑇𝑒 = 1.5𝑝 𝜆𝑖𝑞 + 𝐿𝑑 − 𝐿𝑞 𝑖𝑑 𝑖𝑞

𝑇𝑒 = 𝐾𝑡𝑖𝑞 𝑎𝑠𝑠𝑢𝑚𝑒𝑠 𝑟𝑜𝑢𝑛𝑑 𝑟𝑜𝑡𝑜𝑟, 𝐿𝑑 = 𝐿𝑞

𝑑

𝑑𝑡𝜔𝑟 =

1

𝐻 𝑇𝑒 − 𝑠𝑔𝑛 𝜔𝑟 𝐽0 − 𝑏𝜔𝑟 − 𝑇𝑙𝑜𝑎𝑑

14

Mapping parameters to PMSM model

𝑅

𝐿𝑑 , 𝐿𝑞

𝜆

𝐾𝑡

𝐻

𝑏

𝑝

𝐽0

15

Tests to Characterize Motor and Load

Motor Tests Parameters Identified Identification method

Back EMF Test

Number of Pole Pairs (p)

Flux Linkage Constant (λ)

Torque Constant (Kt)

Calculation

Friction Test

Viscous Damping Coefficient (b)

Coulomb Friction (J0)

Curve fitting

Coast Down Test

Rotor Inertia (H) Curve fitting

DC Voltage Step Test Resistance (R)

Inductance (L)

Parameter estimation

Load Tests Parameters Identified Identification method

Bifilar Pendulum Test Disc inertia (Hd) Calculation

16



Back EMF Test




Calculation

Friction Test



Curve fitting

Coast Down Test


DC Voltage Step

Test

Resistance (R)

Inductance (L)



Bifilar Pendulum

Test

Disc inertia (Hd) Calculation

17



Back EMF Test




Calculation

Friction Test



Curve fitting

Coast Down Test



Inductance (L)




18

Coast Down Test

Coast down test used to identify:

Rotor inertia (H)

Test Extract

Parameters Verify

19

Identify Rotor Inertia (H)

𝑑𝜔𝑟

𝑑𝑡=

1

𝐻𝑇𝑒𝑚 − 𝑏𝜔𝑟 − 𝐽0 − 𝑇𝑙𝑜𝑎𝑑

𝑇𝑙𝑜𝑎𝑑 = 0

𝜔𝑟 = 𝜔𝑟0 + 𝐽0𝑏

𝑒−𝑏𝐻𝑡 −

𝐽0𝑏

NRMSD = Normalized Root Mean Square Deviation

Note: J0 and b are known from friction

test. Curve fit equation for ωr to find H.

Test Extract

Parameters Verify

20

Validate Coast Down Test


Test Extract

Parameters Verify

21



Back EMF Test




Calculation

Friction Test



Curve fitting

Coast Down Test


DC Voltage Step

Test

Resistance (R)

Inductance (L)




22

DC Voltage Step Test

Used to identify:

Phase resistance (R)

Phase inductance (L)

Test Extract

Parameters Verify

23

Identify Phase Resistance (R)

𝑣𝐼𝑛 𝑡 = 𝑅𝐿𝑖𝑚𝑖𝑡𝑖 𝑡 + 𝑅 𝑖 𝑡 + 𝐿 𝑑𝑖

𝑑𝑡

𝑣𝐼𝑛 𝑡 = 𝑅𝑇𝑖 𝑡 + 𝐿 𝑑𝑖

𝑑𝑡

𝑖 𝑡 = 𝑉𝐼𝑛

𝑅𝑇 1 − 𝑒

−𝑅𝑇𝐿

𝑡

𝑤𝑕𝑒𝑟𝑒: 𝑅𝑇 = 𝑅𝐿𝑖𝑚𝑖𝑡 + 𝑅

𝑅 = lim𝑡→∞

𝑣𝐼𝑛 𝑡

𝑖 𝑡

𝑅 = 𝑅

2

𝐿 = 𝐿

2

Test Extract

Parameters Verify

24

Identify Inductance (L) using

Parameter Estimation

Test Extract

Parameters Verify

25

Validate DC Voltage Step Test


Test Extract

Parameters Verify

26



Back EMF Test




Calculation

Friction Test



Curve fitting

Coast Down Test



Inductance (L)



Bifilar Pendulum

Test

Disc inertia (Hd) Calculation

27

Bifilar Pendulum Test

Bifilar pendulum test used to

identify:

Disc inertia (Hd)

Test Extract

Parameters Verify

28

Identify Disc Inertia (Hd)

𝐻𝑑 = 𝑚𝑑𝑔 𝑇2𝑏2

4𝜋2𝐿

𝑤𝑕𝑒𝑟𝑒: 𝑚𝑑 = 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑑𝑖𝑠𝑐 𝑔 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑇 = 𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 𝑑𝑖𝑠𝑐 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛

Measurements:

L = 2.356 (m)

b = 0.0565 (m)

md = 0.0425 (kg)

T = 2.21 (sec)

Test results

Hd = 6.993e-5 (kg-m2)

Test Extract

Parameters Verify

30

Validate Bifilar Pendulum Test

Simulation result

T = 2.21 (sec)

Parameters:

L = 2.356 (m)

b = 0.0565 (m)

md = 0.0425 (kg)

Hd = 6.993e-5 (kg-m2)

Test result

T = 2.21 (sec)

Test Extract

Parameters Verify

31

Key Point

Create accurate plant models by executing tests,

identify parameter values and verifying against real-

world data

Test Identify

Parameters Verify

32

Putting the pieces together

33

Control Design

34

Compare Closed Loop Simulation with

Hardware

35

Where can I find more information?

Explore a demo on generating C code from a controller and verifying its compiled behavior and execution time

>> docsearch "Field-Oriented Control of Permanent Magnet

Synchronous Machine"

http://mathworks.com/products/demos/shipping/rtw/rtwdemo_pmsmfoc_script.html

Watch a recorded webinar: “Embedded Code Generation for AC Motors” http://www.mathworks.com/company/events/webinars/wbnr61549.html

Watch 2012 MathWorks Automotive Conference recording of: “Parameterizing and Verifying a Permanent Magnet Synchronous Motor Model” http://www.mathworks.com/company/events/conferences/automotive-conference-michigan/2012/proceedings/registration.html?video=3

Enroll in SAE Course: “Model Based Design: Delivering Quality Electronic Products Faster” http://www.sae.org/pdevent/C0806

http://mathworks.com/products/demos/shipping/rtw/rtwdemo_pmsmfoc_script.html

http://www.mathworks.com/company/events/webinars/wbnr61549.html

http://www.mathworks.com/company/events/webinars/wbnr61549.html

http://www.mathworks.com/company/events/conferences/automotive-conference-michigan/2012/proceedings/registration.html?video=3






http://www.sae.org/pdevent/C0806



36

Questions

37

End

38

Backup Slides

41


Motor Tests Parameters Identified

Back EMF Test

Number of Poles (P)

Flux Linkage Constant (Λ𝑝𝑚)


Friction Test



Coast Down Test

Rotor Inertia (H)


Inductance (L)

Load Tests Parameters Identified

Bifilar Pendulum Test Disc inertia (Hd)

42



Back EMF Test

Number of Poles (P)



Friction Test



Coast Down Test

Rotor Inertia (H)


Inductance (L)



43



Back EMF Test

Number of Poles (P)



Friction Test



Coast Down Test

Rotor Inertia (H)


Inductance (L)



mathworks technology session at ge closed-loop motor

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