Robust and Efficient Control of an Induction Machine
for an Electric Vehicle
Arbin Ebrahim and Dr. Gregory Murphy
University of Alabama
Outline
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Project Objectives
What is Adaptive Control?
Definition of Adaptive Backstepping
Advantages of Using a Adaptive Backstepping Controller
Problem Formulation
Design Procedures
Project Work Summary
Project Objectives

Robust and efficient control of an induction motor for an electric vehicle
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Track the speed of an induction motor to a desired reference trajectory under timevarying load torque for an electric vehicle

Robust control of an electric vehicle induction motor under varying changes in the
motor parameters.
What is an Adaptive Controller?

Learning Mechanisms
(Parameter Adaptation)
Coordination
Mechanisms
Robust
Feedback
r (t)
Adjustable
Model Compensation

u
x
Plant
To invent, design and build systems capable of controlling unknown plants or
adapting to unpredictable changes in the environment
y
What is Backstepping?
x= f x +
=u
u
∫
V = 1 x2
2
δ
des =  x , V ≤ 0
z =  - des
Va = 1 x 2 + 1 z 2
2
2
u = c x , V a ≤ 0
V,Va = Lyapunov Functions
x,  = State Variables
z = Virtual State
 (x) = Virtual Control
u = plant input

∫
x
f (x)
u
-
∫
z
∫
x
f ' (x)
Backstepping is to design a controller for a system recursively by considering some of the
state variables as “Virtual Controls” and designing for them intermediate control laws
Advantages of Adaptive Backstepping
Controller Design Procedure
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Both the stability properties and control law can be ensured in this same step
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The Control Law can be obtained in steps no greater than the order of the system
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In adaptive backstepping unknown plant parameters can be easily dealt with to
design control laws
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Observers can be easily incorporated in the design procedure to perform observer
backstepping
Problem Formulation
Flux
Command

r
+-
ids
Vds
*
Vds
Flux
Controller
 ref
iqs
ref
*
Vqs
Speed
Controller
+Speed
Command
*
r
*
Rotating
Stator
Frame to
Stationary
Stator Frame
Conversion
cos 
Va
Space
Vector
Modulation
Vqs
sin 
ia
ib
ic
Flux
Estimator
Where
ids
iqs
*
= Flux component of the Stator Current
*
= Speed component of the Stator Current
*
Vds , Vqs *=
Voltages in the rotating stator frame
r
= Measured Speed of the Motor
r
= Estimated Flux of the motor

i a , ib , ic
= Measured Stator Currents
Va , Vb , Vc
= Applied three phase stator voltages
Power
Stage
Vc

r
3
Vb
r
IM
Time
varying
Load Torque
Design Procedure
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Modeling-:
The equations representing the dynamics of motion of the Induction Motor is
derived in the three phase, stationary and rotating stator frame co-ordinates and
analyzed for the application of Adaptive Backstepping procedure.

Controller Design-:
Flux Controller-:
An Observer Backstepping Flux Controller is designed using flux observers to make
the estimated flux track a desired reference trajectory to ensure that sufficient torque
is delivered to Load
Speed Controller-:
An Adaptive Backstepping Speed Controller is designed to make the measured
speed of the motor track a desired reference trajectory under varying Load Torque
Conditions
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Simulation-:
The adaptive controllers designed are simulated in the Simulink environment to
verify the results
Design Procedure……………………Continued
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Hardware Implementation-:
The Adaptive Controllers developed are verified in real time using an Induction
Motor tied to a varying load. The results are observed and conclusions made
Project Work Summary

Model the Induction Motor in the stationary and rotating stator frames so that Vector
Control can be applied to develop a speed controller as well as a flux contoller
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Apply adaptive backstepping procedure to develop a speed controller for the motor
speed to track a desired reference speed under time varying load conditions
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Design flux observers to estimate the flux and design an observer based
backstepping controller for the flux to track a desired reference trajectory so that
sufficient torque can be supplied to the Load
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Develop a modular design in Simulink environment for the motor models, observer
models, controller models, and etc for simulation
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Implement real-time controller application to an Induction Motor for verifying and
comparing the simulation results to the real-time results; to make conclusions and
recommendations on future research