*Corr. Author’s Address: Bursa Technical University, Department of Mechatronics Engineering, Bursa, Turkey, onur.genc@btu.edu.tr 381
Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391 Received for review: 2023-12-16
© 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2024-04-12
DOI:10.5545/sv-jme.2023.899 Original Scientific Paper Accepted for publication: 2024-06-19
Cargo E-Bike Robust Speed Control Using  
an MPC Battery Thermal Lumped Model Approach
Genç, M.O.
Mehmet Onur Genç
Bursa Technical University, Department of Mechatronics Engineering, Turkey
Cargo e-bikes are expected to convey heavy loads in all aspects of daily life. Also, these vehicles are expected to maintain a consistent speed 
to meet mobility needs while optimizing the battery design. In this paper, a control model is developed to improve rotational speed motor 
control via the battery model predictive controller (MPC) thermal model designed based on experimental field test data. Experimental field 
tests are performed to provide the relation between battery surface and ambient temperatures in different road types and weight conditions. 
For this purpose, in different slope ranges, the pedal load/activity and voltage-current data are logged to use as experimental input in an MPC-
integrated 1D model. To obtain the desired thermal conditions in the Li-Ion battery, the MPC battery thermal model is defined based on the 
thermal lumped model approach. In the next step, the generated MPC model is used as a function for longitudinal speed control in the MPC 
motor torque control model subjected to uncertain road disturbances. Then, the outputs of the control models are compared using the MPC 
parameters oc weight factors and prediction horizon. Thus, the speed control model for cargo e-bikes is presented with increased robustness 
using the MPC battery thermal lumped model approach considering energy and Li-Ion battery life-cycle efficiency methods regardless of 
driving performance needs.
Keywords: cargo e-bike, e-micromobility, MPC, robust control, road uncertainty, lumped thermal model, state-space modelling
Highlights
• 	 The new model is proposed for cargo e-bike speed control using the MPC battery thermal lumped model approach.
• 	 The integrated robust speed control model is created by considering energy and battery life-cycle efficiency methods without 
taking driving performance needs into consideration.
• 	 The thermal condition of the battery is controlled by using this method before the battery reaches unsafe temperatures.
• 	 The lumped thermal model is used as the function of the longitudinal speed control model to provide thermally control-based 
driving. 
• 	 Sensitive weight factor selections have a significant effect on preventing overshoot within the robust control model, even if the 
same prediction horizon is used.
0  INTRODUCTION
E-micromobility has significantly improved 
transportation in various areas. As a result, optimizing 
motor torque consumption becomes more important 
for energy-efficient driving of cargo e-bikes. This 
study approaches the research from an experimental 
and model development point of view. The 
experimental test gives the energy capacity related to 
internal heat-up conditions under different ambient 
temperatures. The study is constructed based on two 
different steps: experimental tests and control model 
development. The experimental tests also include 
two stages: thermal and electro-mechanical tests to 
provide inputs for control model development. In the 
first stage, the experimental tests are performed to 
observe the thermal conditions of the two different 
capacities of batteries to cover the variety and 
uncertainty to provide a robust control methodology. 
The second step of the study includes pedal load and 
current-voltage measurements based on the slope 
and road conditions, with the pedal load vs. current-
voltage (Figs. 11 and 12) condition as model input. 
The increased scope of the experimental data is the 
input for an integrated robust MPC control model. 
MPC controllers can also be used for non-linear 
system controls. In this study, a linear MPC controller 
is selected and used in the modelling studies. Learning 
state-space models have also been used in plant 
models in recent years. In these models, the plant 
outputs are estimated via a data-training process, and 
results are found via neural network processing [1]. 
These models are preferred and accompanied by MPC 
control models [2]. 
MPC has recently also been investigated and 
validated for the battery developments in literature. 
Battery life-cycle studies using MPC control methods 
mainly focused on thermal management to control 
the battery ageing process. Ma et al. [3] developed 
an MPC trajectory tracking control model providing 
optimized battery energy consumption. To provide 
the model, the lateral and longitudinal deviations are 
derived with state selection into the plant, and then the 
battery energy consumption model is produced within 
the loss function to be used in the optimizer. Surya 
et al. [4] studied the energy consumption control 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391
382 Genç, M.O.
model development to improve battery management 
system (BMS) efficiency. In the study, they developed 
the optimization algorithm by considering the 
lump thermal model and used the base model to 
estimate battery surface temperature and battery core 
temperatures. Batiyah et al. [5] investigated a power 
management system (PMS) to provide optimized 
disturbances transients, overcharging the battery 
and effectively consuming the power. Masoudi and 
Azad [6] proposed a battery thermal management 
system (BTMS) for plug-in hybrid electric vehicles. 
They studied the non-linear model predictive control 
(NMPC) thermal controller for the system following 
the trajectory system. Shi et al. [7] studied an internal 
battery temperature estimator, developing an MPC 
controller for real-time state observer and Kalman 
filter.  
A three-wheel cargo e-bike is instrumented and 
experimentally real-time observed to provide an MPC-
integrated one-dimensional (1D) model (Fig. 1). As 
illustrated in Fig. 2, in discrete time variance, obtained 
measured data is processed via MPC optimizer to 
have a prediction in optimized levels. 
Fig. 2.  MPC operation chart
Eq. (1) represents the reference value for the 
manipulated variable (M
V
), Q, which stands for the 
weight factor for M
V 
data. U represents the input 
value, which is the input for the MPC controller. R 
is the weight factor for an input value and defines 
the effectiveness of the input factor in the control 
algorithm. The measured disturbances as input defined 
are indicated in U matrix; this enables visualizing the 
repercussions of the measured disturbances within the 
plant system [8]. Eq. (2) shows the discrete-time of the 
Loss function which is held to optimization. In this 
version, the matrix format is prepared, and the sum 
of the total values is calculated based on sample time 
during the total horizontal definition named N.
 (,)( )( ), xu xx Qx xR U
refr ef
T

 
2
 (1)
   
min, .., (, )
() () () ). (
UU JxU
xiQx iU iR Ui
Nk k
TT
i
N
1
1

 





 (2)
Eq. (3) shows the state-space model in continuous 
time frame. In the MPC controller and optimization-
based control algorithms, the calculations are done 
in a discrete-time system. Eq. (4) shows the discrete-
time system definition based on k sample time.
 
 xA XB U
yC XD U
   
   
,
,
 (3)
 
xk AXkB Uk
yk CXkB Uk
dd
xk
     
    
1,
.
 (4)
During the test, a three-wheeler e-bike was used 
(Fig. 3). During the experimental tests, the first gear 
was used, meaning 2:1 torque transmission from pedal 
torque. Due to the one-wheel torque transmission, 
e-bike dynamics are differentiated from two-wheelers, 
creating challenging control of steering due to the 
created continuous force on the right section of 
the bike. The left wheel is without power, so the 
unbalanced condition needs extra effort to control 
the bike. The used bike has a 26-inch (around 66 cm 
diameter) wheel dimension.
Fig. 1.  Proposed control model – battery MPC control model as input reference for longitudinal MPC speed control

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391
383 Cargo E-Bike Robust Speed Control Using an MPC Battery Thermal Lumped Model Approach 
Fig. 3.  Three-wheeler powertrain chart
Fig. 4 shows the instruments used and capacity 
details during experimental tests. The three-wheeler 
e-bike consists of a hub motor (36 V , 250 W continuous 
power, 35 Nm maximal torque), controller, and battery 
packets. Fig. 5 shows the general equipment and 
instrumentation places of the e-bike. The pedal load 
sensor is placed on the pedal, and thermal sensors and 
voltage-current recorder are placed at the rear carrier 
of the bike. 
Fig. 4.  Instrument data used in the study
Fig. 5.  Three wheelers e-bike using experimental tests
1  THERMAL FIELD TESTS UNDER VARIABLE AMBIENT 
TEMPERATURES WITH DIFFERENT BATTERY CAPACITIES
During experimental tests, drives were performed 
with two different batteries with different energy 
capacities in two different test roads for each battery 
to increase the diversity and sensitivity of the control 
model robustness. Fig. 6 shows the handmade battery. 
The cells are designed as serial, with a total of 10 
cells providing 36 V total nominal voltage (max. 42 
V, 29-V cut-off voltage) and a total 3.2 Ah energy 
capacity due to serial connection. The second battery 
has a total of 40 cells with 13 Ah energy capacity 
with serial-parallel combinations. The cells also have 
18650 geometrical dimensions and a 3.2 Ah unique 
cell capacity.  
Fig. 6.  Handmade test battery; 36 V nominal / 3.2 Ah capacity
Fig. 7.  Experimental test flow chart
Fig. 7 explains the workflow during the 
experimental test driving with both battery types.  Fig. 
8 shows the general equipment of the test e-bike. The 
normal bike weighs 30.5 kg, with an additional 30 
kg of weight made up of two different gravel sands, 
each weighing 15 kg. Including driver weights and 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391
384 Genç, M.O.
the other additional weights, the driving is performed 
with a total of 137.5 kg. 
Fig. 8.  Experimental test boundary condition  
with 3.2 Ah handmade battery usage
Fig. 9 shows the battery surface temperature 
data during test routes recorded at different ambient 
temperatures with handmade batteries. The maximum 
slope that exists in this test route is 6 %, and the 
average slope rate is found to be 2.6 % via GPS data. 
The drives were performed starting on the 18
th
 of July 
at 23 °C degree ambient temperature, then continued 
on July 19
th 
with 28 °C ambient temperature, which 
was the hottest weather condition in all test drives, then 
on July 24
th
 at 20 °C, and finalized on July, 26
th
 with 
15 °C, which is the coldest weather condition between 
in all test drives. Fig. 10 shows the colour map taken 
temperatures vs. time for battery surface temperature 
based on the different ambient temperatures. Red and 
blue represent the hottest and coldest temperatures 
Fig. 9.  Battery surface temperature vs time – handmade battery 3.2 Ah, 5.73 km route north-west Ulm 
Fig. 10.  Battery surface temperature vs time – e-bike original battery 13 Ah,  5.82 km route west Ulm

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391
385 Cargo E-Bike Robust Speed Control Using an MPC Battery Thermal Lumped Model Approach 
vs the time graph taken by 13 Ah battery capacity. 
The maximum slope rate in this route is 5 %, and the 
average slope rate is 2.3 % based on GPS data. 
2 PEDAL ACTIVITY vs. VOLTAGE – CURRENT 
MEASUREMENTS IN HILL-START CONDITION 
In this section, the pedal activity vs. voltage [V] 
and current [I] values are obtained to use these data 
as MPC model input. Pedal load is the disturbance 
needed to obtain the target motor torque level. Pedal 
load creates a disturbance for the desired motor torque 
level controlled by the thermal MPC battery model, 
and the pedal load/pedal activity values are measured 
depending on real-time voltage-current values.
Figs. 11 and 12 show the hill-starting driving 
conditions in which the voltage-current measurements 
and pedal load/pedal activity measurements are done 
simultaneously at 4 % and 6 % incline. Fluctuations 
occurred in voltage output data due to terminal 
voltage. Blue represents the terminal voltage; current 
and pedal activity are defined respectively in orange 
and black. The hill-starting tests are performed via 
handmade batteries having a 3.2 Ah capacity. The 
obtained data are used in Section 4 within Figs. 16 and 
17 as powertrain electro-mechanical inputs.
Fig. 11.  Real-time voltage – current meas. vs pedal activity  
on 4 % slope hill driving with handmade battery 3.2 Ah
Fig. 12.  Real-time voltage – current meas. vs. pedal activity  
on 6 % slope hill driving with hand-made battery 3.2 Ah
3  MPC DESIGN WITH THERMAL  
AND LONGITUDINAL MODELLING 
In this section, the complete cargo e-bike model is 
modelled based on the experimental test data taken 
from the field tests. The controller model is designed 
to be used to provide optimized electric motor energy 
consumption despite measured disturbances pedal 
load torque and slope (gradient) torque (Eq. (5)). The 
generated thermal model is the function of the 
integrated longitudinal speed control model explained 
in detail in Section 4. M
dv
dt
M
 
is the net excitation 
force obtained after negative forces of Air drag 
(F
Airdrag
), Slope (F
Slope
), and Rolling Resistance (F
R.
Res
)
 
are removed from total positive forces Electric 
Motor (F
Motor
) and Pedal forces (F
Pedal
).
 M
dv
dt
FFFF F
MotorP edal AirdragS lope
 
R.Res
. (5)
The lumped model is used for the battery 
thermal model. During experimental tests, surface 
temperatures are provided via an Arduino thermal 
datalogger to provide input data for the model. The 
battery model is also defined as a simple version 
in Fig. 13. R
i
, C
i,
 and T
i
 represent the resistance, 
capacitance, and temperature for the battery's internal 
region simulated with an electric circuit, and C
S
 and 
T
S
 represent the resistance and capacitance for battery 
surface in order, and R
A
 and T
A
 represent resistance 
and temperature for ambient conditions.    
Fig. 13.  Battery thermal lumped model – simplify circuit
The measured disturbance is ambient temperature, 
which is the factor for battery surface temperature 
control [7] and [9]. The reference temperature is the 
targeted battery surface temperature that can be 
defined by the model (Fig. 14). The equation of the 
lumped model defined for this model is shown in Eq. 
(6). 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391
386 Genç, M.O.
Fig. 14.  MPC battery surface temperature controller  
algorithm flow
The terms T
is 
and
 
T
ss 
explain, respectively,
 
the temperature difference between cell internal 
temperature and ambient temperature (T
is
 = T
internal
 
– T
ambient
) and the temperature difference between 
surface temperature and ambient temperature (T
ss
 
= T
surface
 – T
ambient
) represented via measured output 
(MO) in Fig. 15. In T
is
,
 
the input heat (generated 
internal heat) is placed into Eq. (7). The internally 
generated (Q
i
) heat can be defined in Eq. (6). V
OC 
defines the open circuit voltage, V
T 
is the terminal 
voltage, and I is the current flow in the circuit. The 
time-dependent temperature difference between 
surface and ambient includes radiation heat occurrence 
created by sun-related emission factor-based heat 
generation (Q
r
) and forced convection heat transfer 
(Q
fc
) due to airflow and battery surface contact during 
movement in an e-bike.
 
QVVI
iO CT
  ,
 (6)
   
dT
dt RC
T
RC
T
VV
C
I
dT
dt RC
T
RC
is
ii
is
ii
ss
OC T
i
ss
is
is
is
 

 
11
11
,
 







1
0
RC
TQQ
s
ss rf c
. (7)
Eq. (8) shows the state-space model of the 
thermal lumped model adapted to Li-Ion battery 
thermal behaviour. The input value is selected as 
internally generated Heat energy (Q
i
). Because the 
battery surface temperature measurement is easy to 
measure and gives more accurate data, the output 
factor is selected as T
ss 
, explaining the temperature 
difference between the battery surface and ambient 
(Eq. 9). 
 


T
T
RC RC
RC RC RC
is
ss
ii ii
is is s
























11
11 1
0
 











 










T
T
VV
C i
is
ss
oc T
i
0
, (8)
 T
T
T
VV
ss
is
ss
OC T
 






   01 0. (9)
Fig. 15 shows the general chart of the MPC 
integrated battery thermal control model. The target of 
the model is to allow cargo e-bikes to arrange their 
surface temperature values based on the experimental 
field data behaving in experimental-based modelling. 
The outputs of the battery model are state of charge 
(SoC) and terminal voltage [V]. MPC controller model 
is identified with T
ambient 
as measured disturbance 
(M
D
). Reference temperature can be defined by the 
user to have a safe battery surface temperature. Also, 
low-temperature occurrence needs low Q
i
 occurrence, 
including a reduction in current (I) consumption. The 
manipulated variable (M
V
) is selected as the input of 
the longitudinal model reference speed belonging to 
the longitudinal MPC controller [10] (Fig. 15).
4 ELECTRIC MOTOR STATE MODEL INTEGRATED 
LONGITUDINAL SPEED CONTROL MODEL
In this section, the longitudinal speed controller model 
is explained. The thermal battery MPC controller 
Fig. 15.  MPC battery surface temperature controller via thermal lumped state-space model

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391
387 Cargo E-Bike Robust Speed Control Using an MPC Battery Thermal Lumped Model Approach 
is designed, and M
V
 is selected as the temperature 
difference between the battery surface and ambient 
temperature based on experimental field test data (Fig. 
16). Eq. (10) shows the rotational Newton mechanics 
equation in the driving system. The driving torque 
equals electric motor (T
m
) and pedal sourced torque 
(T
p
) total value minus slope (gradient) torque, air drag 
force torque (T
A
), and rolling resistance (T
R
) [11] and 
[12]. In the force domain, Eq. (5) explains the general 
equality of the system. 
Fig. 16.  MPC longitudinal speed controller algorithm flow
 JT TTTT
xm PSAR

  . (10)
The system is solved based on Newtonian 
mechanics. To perform this, electric motor torque (T
m
) 
is selected as the control parameter, and pedal torque 
(T
P
) and slope torque (T
S
) are selected as measured 
disturbances [13]. The unmeasured disturbances T
A
 
and T
R
 are defined by the damping factor multiplied 
by wheel diameter. b is the equal damping factor, 

θ is 
angular velocity obtained by the battery thermal 
model as experimental field data [14]. J
x
 is the equal 
inertia value of the e-cargo bike in pitch movement 
direction based on cartesian coordinates (Eq. (11)).
 Jb rT TT
xS mP
 
   . (11)
Eq. (12) explains the state-space model selected 
for the longitudinal control model. The state is 
selected as the angular velocity (

Q ) of the electric 
motor, including the internal reducer. [B] × [U] 
matrices are composed of control parameter T
M
 and 
measured disturbances T
p
 and T
S
. The output is 
selected as angular velocity (

Q ) compiling [C] × [X] 
matrix [15].
   

 
x
br
JJ JJ
T
T
T
xx xx
m
P
S
 




 
























11 1
 


  










,
. yQ
T
T
T
m
P
S
1 000 (12)
Fig. 17 shows the 1D model of the MPC-
integrated longitudinal control chart. In this model, 
the reference speed (T
S
 – T
A
-based speed data from the 
1D look-up table, see Fig. 15) is assigned to the 
battery thermal MPC controller model. MD is selected 
as pedal torque (T
P
) and slope torque (T
S
) and linked 
via Simulink 1D model into the related block. M
O
 
(measured observations) is recorded via GPS speed 
calculation and converted into angular velocity (

Q ) to 
provide feedback to MPC.  
The manipulated variable (M
V
) is the selected     angular velocity (

Q ) which is the input for the 1D 
look-up table. First, the M
V
 value is converted into 
RPM (revolution per minute), and then the RPM vs. 
motor efficiency table is processed based on the 
obtained BLDC (brushless direct current) motor data. 
5  RESULTS AND DISCUSSIONS
In this section, the control model results obtained 
in Section 4 are investigated, and the comparison is 
discussed. The proposed innovative model used in the 
study is also discussed, and key control parameters 
and improved outputs are presented.
Fig. 17.  MPC longitudinal speed controller 1D model chart via angular to velocity longitudinal converter

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391
388 Genç, M.O.
Fig. 19.  Scenario 1. Prediction horizon N: 23 vs W
Q
: 0.1 –U:1
Fig. 20.  Difference between Battery surface temperature and 
ambient temperature; Blue: Reference curve (from experimental 
tests shown in Figs. 14 and 15) – Red: Model output
          Fig. 21.  Electric motor angular velocity [rad/s] for Model 1; 
 Blue: Reference curve (obtained from the integrated model side; 
see Figs. 16 and 17)  – Red: Model output
Figs. 20 and  21 show the thermal modelling 
results and thermally controlled motor angular 
velocity (

θ ) MPC control data is modelled based on 
Fig. 19. The green curve represents the reference input 
in which the target of the temperature difference 
between the surface and ambient temperature is 
experimentally obtained from the road tests (Figs. 9 
The integrated robust control model with the 
experimental thermal lumped model approach is 
shared via step response, temperature sensor data, and 
dependent motor torque graphs. The model scenarios 
include the control tuning parameters to have a 
sensitive battery life cycle and energy consumption 
against battery thermal ageing.
In model scenario 1, to provide the robust 
prediction horizon, the weight factor (W
Q
) is kept 
constant, and the thermal and speed control outputs 
are observed based on 23 due to sensitive step 
response compared to 

Q . In model scenario 2, the 
input and output weight factors are changed to observe 
the thermal and speed output behaviours. After the 
second scenario, the correct weight factor is detected, 
and the robust control model is provided.
Model Scenario 1 
Scenario 1 compares the models as an 
unconstrained state-space model condition with W
Q
(1) 
= 0.1 Weight factor, U(1) is also measured outputs 
multiplied with weight factor W
Q
(1) (Eqs. (1) and 
(2)). Eqs. (1) and (2) are the mathematical definition 
of MPC modelling in Simulink MPC Designer. In this 
scenario, based on the experimental input data, the 
prediction horizon effects are investigated to see the 
over-shoot of the catching reference value in the step 
response model. The first prediction horizon with the 
defined weight factors is determined as 10 (Fig. 18); in 
the next step, the model is run for prediction 23 (Fig. 
19). The prediction horizon using W
Q
(1) is obtained 
more stable and robust by using  After defining the 
prediction horizon, the next step is to see the thermal 
fluctuation by comparing the reference curve obtained 
from experimental road tests and model results (Fig. 
21).
Fig. 18.  Scenario 1. prediction horizon N: 10 vs W
Q
: 0.1 – U:1

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391
389 Cargo E-Bike Robust Speed Control Using an MPC Battery Thermal Lumped Model Approach 
and 10). The control model behaves smoothly starting 
from the second minute.
The control model is now simulated to investigate 
motor torque output stability (Fig. 17). The blue 
curve represents the desired rotational speed, which 
provides the target longitudinal speed (Fig. 17). The 
model shows smooth control in rotational angular 
velocity (Fig. 21) from 0 rad/s to around 100 rad/s 
during 30 seconds. 
Model Scenario 2
Model 2 approaches the model outputs from 
Weight factor effects. To see the model behaviour, 
the input weight factor in the model changed to 0.25 
W
Q
(2) instead of W
Q
(1): 0.1 (Scenario 1). The output 
weight factor is defined as 0.75 U(2). The prediction 
horizon is kept in Fig. 23, and the model is run (Fig. 
22). 
          Fig. 22.  Scenario 2. Prediction horizon 
N: 23 vs. W
Q
: 0.25 – U: 0.75  
Fig. 23.  Scenario 2. Prediction horizon  
N: 10 vs  W
Q
: 0.25 – U: 0.75  
Between Figs. 19 and 22, the overshoot difference 
is observed in parallel to input and output weight 
factor changes even in the use of the same prediction 
horizon. The model outputs on the MPC side show 
a higher delay in response to input data compared to 
Scenario 1 (Figs. 18 and 19). Also, the overshoot is 
prominent compared with Scenario 1 curves. If the 
prediction horizon goes to 10, the step response drops 
and delays (Fig. 23). 
          Fig. 24.  Difference between Battery surface temperature and 
Ambient temperature; Blue: Reference curve (from experimental 
tests shown in Figs. 14 and 15) – Red: Model output
Fig. 24 shows the difference between the battery 
surface temperature and ambient temperature during 
30 minutes, similar to the experimental tests. As seen 
in around two seconds, the measured outputs (in 
yellow) present prominent overshoot values compared 
to Fig. 20. Fig. 25 is the angular velocity data 
providing longitudinally measured outputs. Similar to 
the thermal model, around two seconds, the over-shoot 
occurs; after this time range, up to 30 seconds, the 
smooth correlation is observed. Compared to Fig. 21, 
the weight factor is observed with higher overshoot 
also in rotational motor speed control integrated with 
the MPC thermal battery model.
Fig. 25.  Electric motor angular velocity [rad/s] for Model 2;  
Blue: Reference curve (obtained from the integrated model side;  
see Figs. 16 and 17) – Red: Model output

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)7-8, 381-391
390 Genç, M.O.
6  CONCLUSION 
In this study, a cargo e-bike is investigated based on 
thermal and longitudinal control with MPC control 
design to provide optimal motor torque generation 
in pedal assist system (PAS) used plants. The field 
tests are performed via batteries with different 
capacities to show internal resistance-based surface 
temperature. Then, the desired thermal conditions 
are defined as a function to provide robust control 
for longitudinal speed control subjecting to uncertain 
road disturbances. The target of the integrated robust 
control model is constructed based on the thermal 
lumped model approach by predicting compulsive 
road disturbances under a weight load. The new 
model is based on the uncertain experimental road 
data configured with the MPC controller, in which 
the battery and longitudinal robust control have 
been designed for the three-wheeler cargo e-bike. 
The model is developed based on experimental test 
data by measuring the thermal conditions of Li-Ion 
batteries and pedal load vs. voltage-current input data 
for electro-mechanical model development. To cover 
the sensitivity, the most used battery energy capacities 
are selected to create reference curves and avoid 
uncertainty.  
The weight factor and prediction horizon selection 
sensitivities are comparatively investigated to increase 
robustness in the developed model. In this direction, 
the performance of the control model can be controlled 
within the simulation phase. During the control model 
simulations, the step response, thermal model, and 
integrated rotational motor speed are observed for 10 
seconds, 30 minutes, and 30 seconds, respectively, to 
create a similar environment to the experimental tests. 
The model also presents a cost-effective methodology 
by giving life-expansion possibilities for Li-Ion 
batteries. In addition, the proposed control model 
can be performed and analysed on fully electrified 
e-micromobility vehicles in which the battery thermal 
conditions and cost-effectiveness are concerned.      
7  ACKNOWLEDGEMENT 
This study is funded by TUBITAK 2219 (The 
Scientific and Technological Research Council of 
Turkey) entitled ‘An Experimental Battery Model 
Development for PAS (Pedal Assist System) of 
E-Quadricycle under Hill Hybrid Driving Modes 
at Different Ambient Temperatures’. The author is 
extremely grateful to the ‘Institute of Measurement, 
Control, and Microtechnology, Ulm University, 
Germany’ for supporting the research project and 
providing testing opportunities.
 
8 NOMENCLATURES
T
is
 battery temperature difference,
 
T
internal
 – T
ambient, 
[°C]
T
ss
 battery temperature difference,
 
T
surface
 – T
ambient
, [°C]
Q
i
 battery internally generated heat, [J]
V
OC
 open circuit voltage, [V]
Q
r
 radiation-based heat,
 
[J]
Q
fc
 forced convection heat, [J]
T
m
 cargo e-bike electric motor torque, [N·m]
T
P
 cargo e-bike driver pedal-generated torque, [N·m]
T
S
 gradient based negative slope torque, [N·m]
T
A
 aerodynamic drag based negative torque, [N·m]
T
R
 road based negative rolling resistance torque, [N·m]
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