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1. Robust and Efficient Control of an Induction Machine
for an Electric Vehicle
Arbin Ebrahim and Dr. Gregory Murphy
University of Alabama

2. Outline
 Project Objectives
 What is Adaptive Control?
 Definition of Adaptive Backstepping
 Advantages of Using a Adaptive Backstepping Controller
 Problem Formulation
 Design Procedures
 Project Work Summary

3. Project Objectives
 Robust and efficient control of an induction motor for an electric vehicle
 Track the speed of an induction motor to a desired reference trajectory under time-
varying load torque for an electric vehicle
 Robust control of an electric vehicle induction motor under varying changes in the
motor parameters.

4. What is an Adaptive Controller?
 To invent, design and build systems capable of controlling unknown plants or
adapting to unpredictable changes in the environment
Learning Mechanisms
(Parameter Adaptation)
Coordination
Mechanisms
Plant
Adjustable
Model Compensation
Robust
Feedback
y
x
r (t) u


5. ∫
f (x)
∫
∫
f ' (x)
∫
-
u
u x
x
x = f x + 
 = u
V = 1
2
x2
des =  x
z =  - des
Va = 1
2
x2
+ 1
2
z2
u = c x
V,Va = Lyapunov Functions
x, = State Variables
z = Virtual State
(x) = Virtual Control
u = plant input
z
δ
V
, ≤ 0
Va ≤ 0
,



What is Backstepping?
 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

6. Advantages of Adaptive Backstepping
Controller Design Procedure
 Both the stability properties and control law can be ensured in this same step
 The Control Law can be obtained in steps no greater than the order of the system
 In adaptive backstepping unknown plant parameters can be easily dealt with to
design control laws
 Observers can be easily incorporated in the design procedure to perform observer
backstepping

7. Problem Formulation

r

r


r


r

ref

Speed
Flux
Controller
Rotating
Stator
Frame to
Stationary
Stator Frame
Conversion
Speed
Controller
ref

r

Flux
Command
Command
-
+
-
+
Space
Vector
Modulation
Power
Stage
IM
Flux
Estimator

3

cos 
sin
Where
= Flux component of the Stator Current
= Speed component of the Stator Current
qs
V
ds
V
= Measured Speed of the Motor
a
V
b
V
c
V
= Estimated Flux of the motor
r

a
i
b
i
c
i
Time
varying
Load Torque
b
i c
i
a
i , , = Measured Stator Currents
b
V c
V
a
V , , = Applied three phase stator voltages
*
ds
i
*
ds
i
*
qs
i
*
qs
i
*
ds
V
*
ds
V *
qs
V
,
*
qs
V
= Voltages in the rotating stator frame

8. Design Procedure
 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
 Simulation-:
The adaptive controllers designed are simulated in the Simulink environment to
verify the results

9. Design Procedure……………………Continued
 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

10. 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
 Apply adaptive backstepping procedure to develop a speed controller for the motor
speed to track a desired reference speed under time varying load conditions
 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
 Develop a modular design in Simulink environment for the motor models, observer
models, controller models, and etc for simulation
 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