ME6105: Homework 3 Energy-Based Systems Modeling in Modelica

October 27 th , 2010
ME6105: Homework 3
Energy-Based Systems Modeling in Modelica
Project: SEGWAY
Jean-Vincent DEFRANCE Mickaël KARGULEWICZ
Guilhem TOURNAIRE Pascal TRANG

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Contents
1. GOALS AND PROBLEM DOMAIN .......................................................................................................3
2. SYSTEM AND SIMULATION SPECIFICATION .........................................................................................4
2.1. SYSTEMS APPROACH ........................................................................................................................... 4
2.2. INTERACTIONS ................................................................................................................................... 5
2.3. PHYSICAL PHENOMENA INCLUDED IN OUR MODEL: .................................................................................... 5
2.4. PHYSICAL PHENOMENA NOT INCLUDED IN OUR MODEL: ............................................................................. 5
3. DYMOLA MODELS AND VERIFICATIONS .............................................................................................6
3.1. DC MOTOR ...................................................................................................................................... 6
3.2. THE CONTROL LOOP ............................................................................................................................ 7
3.3. THE ROAD ......................................................................................................................................... 9
3.4. THE WHEELS.................................................................................................................................... 12
3.5. BATTERY ........................................................................................................................................ 13
3.6. CONVERTER .................................................................................................................................... 15
3.7. HANDLEBAR END PLATFORM ............................................................................................................... 19
3.8. THE SEGWAY PT .............................................................................................................................. 19
3.9. USER ............................................................................................................................................. 21
4. EXPERIMENTATION AND INTERPRETATION ...................................................................................... 21
4.1. SIMULATION OF THE SEGWAY BEHAVIOR ............................................................................................... 21
4.2. COMPARISON OF BATTERY DURATIONS ACCORDING TO THE SLOPE .............................................................. 22
4.3. VARIATION OF THE SEGWAY BEHAVIOR FOR DIFFERENT USER MASSES. ........................................................ 23
5. LESSONS LEARNED ...................................................................................................................... 24
5.1. WHERE WE STRUGGLED ..................................................................................................................... 24
5.2. WHERE WE WENT DOWN THE WRONG PATH AND HOW DID WE REVISE OUR APPROACH .................................. 25
5.3. HOW WOULD WE DO THINGS DIFFERENTLY IF WE WERE TO CREATE ANOTHER SIMULATION MODEL ................... 25
5.4. DID YOU LEARN ANYTHING NEW ABOUT THE BEHAVIOR OF THE SYSTEM YOU WERE MODELING? ....................... 25
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 2

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
1. Goals and problem domain
In our first homework, we identified two main trade-offs:
- The first was between the autonomy and the power of the Segway.
- The second was between the general technical performances and the overall costs of production and
assembly of the Segway.
Since the first homework, we used real Segways to feel how this vehicle really works:
The most striking fact is that the speed is limited by the control loop: when the Segway reaches a given
speed, the handlebar straightens up automatically to force the user to lean back and slow down. Thanks to this
experience, we will slightly change the first trade-off to better fit what we felt. Moreover, we will reduce the
scope of the second one to have a more feasible study:
Instead of trying to study the trade-off between the power of the motor and the autonomy, we will
look at the influence of the maximum speed allowed by the control loop on the autonomy. As a matter of fact,
the motor power has obviously an influence on the maximum speed reachable, but in practical use, the speed
is limited by the control loop, not by the motor power. Consequently, looking at the motor power is not
directly relevant for a Segway.
For the second trade-off, instead of looking at the general technical performances, we will only look at
the autonomy of the Segway, and instead of looking at the overall costs of production, we will only look at the
battery price.
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 3

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
To study these trade-offs, we will model a complete Segway and its environment: the driver of the
Segway, a road and the wind resistance. In the model, the Segway will move only in one direction (moving
forward and backward) without considering rotation. It will also be possible to model the Segway moving in a
slope.
For the first trade-off, we will look at the energy consumption of the Segway during a classic ride: flat
road, no wind, and regular accelerations and brakes to simulate a real use in a city with other road-users and
traffic lights. In order to shorten the simulation duration, we will underestimate the battery capacity and then
extrapolate the result to obtain the autonomy with a real battery.
For the second trade-off, we will use the extrapolated autonomy for different type of batteries and try
to find the best one considering their prices. Currently, battery stands for 25% of the Segway price, since the
price is the main reason why people do not buy Segway, we will be able to find a battery that bring the best
compromise between cost and autonomy.
2. System and Simulation Specification
2.1. Systems approach
Dc to dc converter
battery
Control loop
motor
gear box
driver
main body
(platform +
handle bar)
wheel
road
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 4

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
2.2. Interactions
- Road-wheel : transmission of power from rotational to translation
- Wheel – gear box : transmission of torque
- Motor – gear box : transmission of torque with a gain
- Gear box – main body : fixed
- Motor – main body : fixed
- DC to DC converter – motor : electrical interface – motor input voltage
- Control loop – DC to DC converter : electrical interface – command
- Battery – DC to DC converter : electrical interface
- Driver – main body : fixed (in our model, not in reality)
2.3. Physical phenomena included in our model:
- Friction between tire and road
- Friction in motor
- Tire deformation
- Inertia of the body, driver, wheel and motor
2.4. Physical phenomena not included in our model:
- Air resistance
- Temperature of components (especially battery and motor)
- Slipping of the tire on the road
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 5

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
3. Dymola Models and Verifications
Model
3.1. DC Motor
We have decided to use a DC motor that has already been done in class before. Tests have already been
done for this motor so we are going to use the same for our model:
Test
Tests have already done previously with the following configuration:
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 6

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Model
3.2. The control loop
The control loop of a Segway, which permits the system to remain in equilibrium, is based on a PID
which regulates the angular velocity of the handlebars. As a result, if the driver leans forward, the PID will try
to reduce the angular velocity of the handlebars, and therefore it will accelerate the motor to catch up the
forward moving.
Moreover, there is an additional security system to limit the maximum speed: when the Segway reaches
a given speed, the motor quickly delivers more torque to straighten up the handlebars and force the user to
lean back and slow down.
These two systems are modeled as shown in the following figure:
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 7

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Although we are sure that the control loop of a Segway is based on a PID, we have no idea about how it
really works. We just know that a powerful computer is used, and that the software update is very expensive.
Therefore, we built this model with the aim to obtain the two main purposes of this control loop, which are
the equilibrium of the system and the speed limitation, but we admit that this model is probably very different
from the reality.
The equilibrium function is made with a simple PID which tries to reduce the error between the set and
the real angular velocities of the handlebars. For a better equilibrium of the Segway, the set angular velocity is
not 0 but a small value that is proportional and opposite to the real angular velocity. The real angular velocity
is given by the gyrometers attached to the body of the Segway.
The speed limit function is made with a test on the Segway velocity: if this velocity exceeds the limit, the
set angular velocity given to the PID is set to a large value in order to quickly straighten up the handlebars. The
Segway velocity is the derivative of its position, and this position is calculated with a rotary encoder.
Test
To test the control loop, we create input signals which could be found on a real situation with a Segway.
We assume that the user is leaning forward to reach the maximum velocity. Therefore, the angular
velocity of the body of the Segway increases and then remains constant, as shown with the blue curve.
Actually, the angular velocity is negative when the user leans forward because it is measured on the +z axis.
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 8

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
As a result, the Segway accelerates until it reaches the speed limit, here 4 m/s. This acceleration is
shown with the pink curve.
Before the speed limit is reached, the set angular velocity is small, proportional and opposite to the real
angular velocity in order to obtain a better stability. When the speed limit is reached, the set angular velocity
becomes suddenly larger to straighten up the handlebars. The evolution of this set angular velocity is shown
by the red curve.
Therefore, the error between the set and the real angular velocities is calculated (green curve) and
processed by the PID in order to drive the motor of the Segway.
Model
3.3. The road
The road is simply modeled with a prismatic joint allowing one translation for the Segway compared to
the World. For a horizontal road, the direction of the joint is {1,0,0}, and for a 10% positive slope, it is {1,0.1,0}.
Axis1 and support1 receive the translation generated by the rolling wheel of the Segway:
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 9

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Test
We tested the road by verifying that a mass placed on it does not fall vertically. If we inclinate the floor,
the mass should follow the profile of the road.
For this we just linked a point mass to the road. If the road is horizontal (vector [1,0,0]) the point mass
does not move. If we inclinate the road at 45° (vector [1,1,0]), the ball should fall. That is what we observe in
the simulation
Configuration:
Position of the mass as a function of time on the plane road:
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 10

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Position of the mass as a function of time for a 45° slope: mass falls down:
Trajectory of the mass:
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 11

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Model
3.4. The wheels
The wheels rotate around the body of the Segway and on the road, but it is important to notice that the
body of the Segway can lean forward and backward, and therefore the angular velocity of the wheel compared
to the road is not equal to the one compared to the body of the Segway. That is why we need two revolute
joints:
- The first one is between the wheel and the body of the Segway. The stator of the DC motor is linked to
the body of the Segway through support1, and its rotor is linked to the wheel through axis1.
- The other one is between the wheel and the road: the angular velocity between these two elements is
transformed into a linear velocity thanks to the rolling wheel, and a damper models the energy loss
due to the contact between the road and the tire.
The vertical prismatic joint coupled with an elastogap stands for the tire. In this model, we assume that
the Segway moves straight forward and backward. Therefore, we can consider that the two wheels have the
same angular velocity and are on the same transmission shaft. These two wheels are modeled by the two body
cylinders.
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 12

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Model
3.5. Battery
To model the battery, we used generic discharge graphs (V=f(A.h) ). Measuring the current provided to
the system with a current sensor, we integrate it in time to get the quantity of charges used. Interpolating the
graph in a table, the quantity of charges used can then give us the voltage provided by the battery.
To get the graphs, we used the battery block of Simulink which gives the data for different types of
batteries. In our case, we began by modeling an Ni-MH.
Plot given by Simulink:
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 13

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Test
To test our battery model, we just connected a small resistor to it. We should see a quick discharge of
the battery. If we also plot the quantity of charges used, we should find the same time for the voltage decay
and the quantity of charges reaching the capacity value.
Configuration:
Test results :
We took the capacity in A.sec so that the simulation does not take too much time. However, the
observations are the same as if we used Ah. We see in the previous figure that the quantity of charges
increases up to a value of 5.8A.sec, which is the total capacity of the battery. When it reaches this value, the
tension provided falls to 0, which corresponds to the moment when the battery is discharged.
We also observe that the discharge graph is really close to the one provided by Simulink, which confirms
the validity of our battery model.
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 14

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Model
3.6. Converter
A DC to DC converter has been added between the battery and the DC motor which allows modulating
the input voltage coming from the battery. Indeed, the PID controller gives us a desired angular speed for the
DC motor and the role of the DC to DC motor is to adapt the voltage in order to reach it.
Here is the block we created in order to model the DC to DC converter:
p1
n1
As you can see, it has 2 inputs (p1 and n1), 2 outputs (p2 and n2) and a Real Input (u) representing the
command. In order to control the DC to DC converter represented by this block, we have used the Modelica
language with the appropriate declarations and equations.
u
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 15
p2
n2

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Tests
We made different tests with the DC to DC converter model. The first one was to use the DC to DC
converter with a constant input voltage (150V) and a constant real input as command (50V).
Configuration:
Results:
constant...
[V]
160
140
120
100
80
60
+ -
ground
realExpression
50
dC_DC_converter
dC_DC_converter.p1.v resistor.v
ground1
40
0.0 0.5 1.0
As we can see, the output voltage is equal to the real input command so that the DC to DC motor functions.
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 16
R=2000
resistor

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
The second test we ran was the DC to DC converter coupled with the battery model and still a constant
real input (100V).
Configuration:
Results:
[V]
120
100
80
60
40
20
0
realExpression
100
battery_... dC_DC_...
Here, we can see that the output voltage is not always constant anymore. Indeed, we have to take into
account the fact that the battery discharges itself. In this case, the test shows that the output voltage follows
the real input command as long as the battery is not discharged, phenomenon which was expected.
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 17
R=20
ground
-20
0.0 0.2 0.4 0.6 0.8 1.0
resistor
dC_DC_converter.p1.v resistor.v dC_DC_converter.u

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
The third test we ran was the DC to DC converter coupled with the battery model and a ramp (duration
5s, height 200V) as real input.
Configuration:
Results:
[V]
250
200
150
100
50
0
ramp
duration=5
battery_... dC_DC_...
In this test, we can see that the output voltage follows the command (which is not constant in this case)
as long as the battery is not discharged.
ground
dC_DC_converter.p1.v resistor.v dC_DC_converter.u
-50
0 1 2 3 4 5
These 3 tests have shown that our DC to DC converter with a real input was valid.
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 18
R=20
resistor

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Model
3.7. Handlebar end platform
We have decided to model the handlebar and the platform in the same part. The handlebar is modeled
by a simple body cylinder while the platform is modeled by a bodybox:
Model
3.8. The Segway PT
The entire Segway is mainly divided into 4 parts: the body, the wheels, the control loop, and the
electrical propulsion.
The wheel is connected to the body of the Segway. The frame_a1 will be used to connect the user to the
Segway, the frame_a2 will be used to connect the Segway to the road, and the flangeT1 and supportT1 will be
used to move the Segway along the road. The relative angles sensor models the rotary encoder which
measures the angle between the body of the Segway and the wheels. The absolute angular velocity sensor
models the gyrometers which measure the angular velocity of the body of the Segway compared to an inertial
frame (here the "World").
Thanks to these two sensors, the control loop gives a command to the DC to DC converter. This
converter receives an almost constant voltage from the battery, and delivers a varying voltage to the DC motor
according to the command of the control loop. The DC motor drives the wheels through the gearbox, and
therefore the entire Segway is balanced.
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 19

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Complete Segway model:
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 20

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Model
3.9. User
The user is modeled very simply because we consider that he doesn’t move on the platform. He is
modeled using a simple body cylinder. We do not have modeled reactions of the user during the motion of the
segway.
4. Experimentation and Interpretation
4.1. Simulation of the Segway behavior
Simulation configuration:
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 21

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
Observations:
Since the user don’t move on the platform the segway move forward and when it reaches the speed
limit, the handlebar and the user begins to lean backward in order to slow down the segway. When the
segway is leant backward, it begins to slow down in order to reach a speed equal to zero. When this is done,
since the user don’t move, the segway is leant backward and therefore it begins to move backward. The
behavior is correct and close to what was expected. Since the user does not move on the platform, the segway
is going to do round trips.
4.2. Comparison of battery durations according to the slope
To perform this comparison, we choose a small enough battery so that the Segway does not have the
time to stop and move back.
We see on the resulting figure that the battery duration is smaller when the Segway has to climb a
slope. Moreover, if we perform this simulation with a negative slope, we also obtain a smaller battery duration
because the Segway has to brake more in order not to exceed the speed limit.
Results:
Accelerating/Moving forward Braking/Moving backward
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 22

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
4.3. Variation of the Segway behavior for different user masses.
In this case, we just change the mass of the user in order to see its influence on the segway behavior.
After simulation, we can see that the frequency of round trips is smaller with the heavier user, but the
amplitude of the movement is almost the same. Therefore, the accelerations are smaller.
Evolution of the segway position on the road with two different users:
( blue user is 1.5 times heavier than the red one)
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 23

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
5. Lessons learned
First, we can say that this assignment was very challenging. We do not pretend to be expert on the
Segway system but we certainly have improved our knowledge on it through our modeling study. In the same
time, by facing the difficulties regarding the modeling of such a system, we also had to improve our knowledge
on both Dymola software and Modelica language.
5.1. Where we struggled
Here are the stages where we have struggled the most:
• understanding the behavior of the Segway and its control
At the beginning, we did not know that the driver in a leaning forward position was experiencing a
force-feedback control through the handle bar, forcing him to lean backward when the system reaches a given
maximum speed.
Concerning the control, we can say that we did not expect such a complexity. We had to think about an
easiest way to model it without having a resulting behavior of our model that is too far from the reality.
• finding data concerning Segway components
For instance, we only know the overall weight of the system. We have not succeeded in finding enough
data regarding its mass distribution so that we had to make approximation. It can be problematic for a system
which is based on balance sensing.
• finding a way to model the driver
Indeed, the driver has an influence on the stability of the Segway during the motion. When the Segway
reaches its speed limit, in reality the driver can feel a force-feedback through the handle bar and should decide
to brake by moving its gravity center backward instead of insisting leaning forward. In this situation, the driver
helps the Segway to regulate its speed. Modeling such a behavior was quite hard since it means we had to
create a model representing the driver with the help of an additional controller.
• the discovery of some standard components of the Dymola library and their utilization in the model
In particular, the multi-body library was not very intuitive when we had to give a shape in 3D to our
Segway model in order to respect its inertia.
• debugging our model, finding the error
Sometimes, we have forgotten components that have quickly slowed down our work progress like
grounds or fixed parts. In general, we can say that finding the reason why Dymola was upset was quite timeconsuming.
ME 6105 – October 27 th , 2010
Homework 3: Energy-Based Systems Modeling in Modelica 24

Jean-Vincent DEFRANCE, Guilhem TOURNAIRE
Mickaël KARGULEWICZ, Pascal TRANG
5.2. Where we went down the wrong path and how did we revise our approach
At the beginning, we did not know how to stabilize the Segway and which parameter had to be
controlled: angular speed, position or acceleration in order to obtain a Segway that does not fall at the first
acceleration. We did many trials by attempting to set different conditions on these different parameters, it
was quite unsuccessful. By doing some research on how to model the Segway control, we found that many
people that have attempted to create a Segway by themselves have used a PID controller on the angular
speed. It seemed to be a good idea to use this tool as a controller but we still had to adapt the PID control to
our model. So, we can say that the major problem we had with our model was to find the way to control it in
realistic and not too complex way, which took us time and many trials.
5.3. How would we do things differently if we were to create another simulation model
It would have been better to have ridden a Segway before the previous assignment for instance. For
another simulation model, we would try this time to have more concrete knowledge on how works the system
we are using, instead of basing our knowledge only on theoretical principles.
Then, we can say that we would have made more efforts concerning our time management. That is to
say, we would try to improve our efficiency through a better sharing of the work load and a better
organization.
5.4. Did you learn anything new about the behavior of the system you were modeling?
Yes, we have learnt new things about the behavior of the system, especially concerning the behavior
when the system reaches its speed limit. We also have learnt about the behavior of the battery and its
discharge when combined with a DC to DC converter that sets an output voltage.
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Homework 3: Energy-Based Systems Modeling in Modelica 25