Available via license: CC BY-SA 4.0
Content may be subject to copyright.
International Journal of Reconfigurable and Embedded Systems (IJRES)
Vol. 12, No. 3, November 2023, pp. 351∼359
ISSN: 2089-4864, DOI: 10.11591/ijres.v12.i3.pp351-359 ❒351
Self-balancing robot: modeling and comparative analysis
between PID and linear quadratic regulator
Lu Bin Lau, Nur Syazreen Ahmad, Patrick Goh
School of Electrical and Electronic Engineering, Universiti Sains Malaysia, Nibong Tebal, Malaysia
Article Info
Article history:
Received Oct 20, 2022
Revised Mar 19, 2023
Accepted Apr 4, 2023
Keywords:
Linear quadratic regulator
Modeling
Proportional-integral-derivative
Robot
Self-balancing
ABSTRACT
A two-wheeled self-balancing robot (TWSBR) is an underactuated system that
is inherently nonlinear and unstable. While many control methods have been
introduced to enhance the performance, there is no unique solution when it
comes to hardware implementation as the robot’s stability is highly dependent
on accuracy of sensors and robustness of the electronic control systems. In
this study, a TWSBR that is controlled by an embedded NI myRIO-1900 board
with LabVIEW-based control scheme is developed. We compare the perfor-
mance between proportional-integral-derivative (PID) and linear quadratic reg-
ulator (LQR) schemes which are designed based on the TWSBR’s model that
is constructed from Newtonian principles. A hybrid PID-LQR scheme is then
proposed to compensate for the individual components’ limitations. Experimen-
tal results demonstrate the PID is more effective at regulating the tilt angle of
the robot in the presence of external disturbances, but it necessitates a higher
velocity to sustain its equilibrium. The LQR on the other hand outperforms PID
in terms of maximum initial tilt angle. By combining both schemes, significant
improvements can be observed, such as an increase in maximum initial tilt angle
and a reduction in settling time.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Nur Syazreen Ahmad
School of Electrical and Electronic Engineering, Universiti Sains Malaysia
14300 Nibong Tebal, Penang, Malaysia
Email: syazreen@usm.my
1. INTRODUCTION
The past few decades have seen a growing interest in autonomous mobile robots (AMRs) in both
industries and academia due to rapid technological advancements and the extensive use of robotics particularly
for reducing costs and enhancing productivity [1]-[4]. A two-wheeled self-balancing robot (TWSBR) is one
type of AMRs that is underactuated and inherently unstable but has notable advantages of being able to move
on a zero-radius curve, high tolerance to impulsive force, and small footprints to move in dangerous places. The
Segway Personal Transporter and Ninebot scooters are examples of commercialized technologies that apply the
same concept of a TWSBR. Apart from being an alternative mode of transportation that can take the place of
an automobile for short commutes, they have also been demonstrated useful for populations with a range of
functional disabilities [5]. Although the user safety cannot be totally guaranteed [6]-[8], these technologies are
often equipped with multiple control systems to enhance their reliability in the event of failure in any one of
them, which in turn results in a higher cost.
In academia, the TWSBR is often used as a research platform to verify advanced control algorithms
as its behaviour is comparable to that of the classical inverted pendulum system. Its wheels are usually driven
Journal homepage: http://ijres.iaescore.com
352 ❒ISSN: 2089-4864
by an electrico-mechanical system which can be either direct current (DC) motors or stepper motors [9]. The
main control objective is to stabilize the robot by driving all the state variables, which are the robot’s position,
velocity, tilt angle and angular velocity, to approach their desired stable values in the shortest time possible. In
the TWSBR development, speed encoders, an accelerometer and a gyroscope are typically required to measure
these state variables [10]. Many techniques have been proposed to solve the problem in the literature, which can
be categorized into linear and nonlinear control approaches [11]-[14]. Examples of the latter include sliding
mode controls [15], fuzzy logic control [16], [17], artificial neural network [18], and deep learning [19]. Aside
from that, the Gaussian process (GP) has also been employed to its capability to create flexible nonlinear
nonparametric models [20]. Chen et al. [21] explained for instance, a control design based on a learned GP
regression model is proposed to alleviate the effects from modeling errors.
While the aforementioned nonlinear control methods have been demonstrated to provide robustness
against uncertainties, the resulting complexity will typically limit their applicability to low-cost embedded
controllers. The linear control approaches on the other hand are relatively simpler in terms of their imple-
mentations on hardware. The most popular methods are proportional-integral-derivative (PID) [22]-[24] and
linear quadratic regulator (LQR) schemes [25]. Nevertheless, a notable downside of the PID control algorithm
for controlling the TWSBR is the difficulty of parameter tuning [26], [27]. Although there are many software
tools available to aid the optimization of the PID parameters, the resulting control law may not be desirable
for the TWSBR which can be easily driven to the instability region. In contrast, controlling the TWSBR via
the LQR scheme is relatively more straightforward as its optimal parameters can be obtained by minimizing
the cost function that can also preserve the closed-loop stability at the same time. However, utilization of this
controller requires prior knowledge and skills in analysing the trade off between the control performance and
power consumption.
Most of the aforementioned work focused on developing new control strategies that can be validated
via simulations. In practice, the system is not only inherently nonlinear and unstable, but is prone to random
noise and disturbances [28]. Plus, there is no unique solution when it comes to hardware implementation as
the robot’s stability is highly dependent on the robustness of the electronic control systems. In this study, a
TWSBR that is controlled by an embedded NI myRIO-1900 board with LabVIEW-based control scheme is
developed. We compare the performance between PID and LQR schemes which are designed based on the
robot’s model that is constructed from Newtonian principles. A hybrid PID-LQR scheme is then proposed
to compensate for the individual components’ limitations. Experimental results demonstrate the PID is more
effective at regulating the tilt angle of the robot in the presence of external disturbances, but it necessitates a
higher velocity to sustain its equilibrium. The LQR on the other hand outperforms PID in terms of maximum
initial tilt angle. By combining both schemes, significant improvements can be observed, such as an increase
in maximum initial tilt angle and a reduction in settling time.
2. METHOD
2.1. TWSBR design and modeling
The TWSBR built in this study is shown in Figure 1 which consists of an NI myRIO-1900 board, two
brushed DC motors with encoders, an external gyroscope (i.e. PmodGyro) to improve the tilt angle estimation
(explained further in section 2.3), a 12 V Li-Ion power supply, a printed circuit board (PCB) containing the
motor driver and voltage regulators, the wheels and the chassis. Figure 1(a) illustrates the built TWSBR while,
Figure 1(b) visualizes the connection between each unit. The control scheme is constructed via model-based
design approach in LabVIEW which is also used as a user interface to display and log the data wirelessly during
the experiment.
The robot can be modeled from first principles by taking into account the dynamics of the motors,
robot chassis, and the forces on the wheels. The inputs to the TWSBR are the torques applied to the left and
right wheels, which are assumed to be similar. Figure 2 illustrates the free body diagram of the TWSBR. The
diagram for the robot’s wheel is depicted in Figure 2(a) where Twdenotes the torque applied to it, θis the
angular position, Fwis the force applied to the wheel by the chassis, and Ffis the friction force by the surface
contact. With regard to the robot chassis which includes the NI-myRIO board, batteries, gyroscope and the
printed circuit board, it acts similar to an inverted pendulum as illustrated in Figure 2(b) whose base is attached
to the wheels.
Int J Reconfigurable Embedded Syst, Vol. 12, No. 3, November 2023: 351–359
Int J Reconfigurable Embedded Syst ISSN: 2089-4864 ❒353
(a) (b)
Figure 1. The TWSBR’s prototype built in (a) this study and (b) its connection diagram
(a) (b)
Figure 2. Free body diagrams of (a) the wheel and (b) the TWSBR’s chassis
Let Jwbe the moment of inertia of the wheel, rbe its radius, mwbe mass of the wheel, and xbe the
horizontal position of the center of the wheel relative to a defined origin. Using Newton’s law of motion, the
sum of forces in the horizontal x-direction can be written as (1):
mw¨x=Ff−Fw(1)
for each wheel. Assuming there are no tire deformation and rolling resistance, the sum of torques is given by
(2):
Jw¨
θ=Tw−Ffr(2)
for each wheel. From the DC motor dynamics, the torque relates to the input voltage as Tw= (km/R)Vin −
(kmke/R)˙
θ, where Ris the electrical resistance of the motor, and Vin is the applied voltage, and kmand ke
are torque and back EMF constants respectively. Substituting this expression into (2), we will get (3).
Ff= (km/Rr)Vin −(kmke/Rr2) ˙x−(Jw/r2)¨x. (3)
Replacing Ffin (1) with this expression gives (4).
Fw= (km/Rr)Vin −(kmke/Rr2) ˙x−mw+ (Jr/r2)¨x(4)
The sum of forces in the x-direction can be written as (5):
Nx=mc¨x+mcℓ¨
βcos β−mcℓ˙
β2sin β(5)
where Nxis the combination of forces from both wheels, mcis the mass, ℓis the distance to the center of the
mass, θis the angle between vertical line and the pendulum, and ¨xis the robot’s acceleration in the x-direction.
The sum of forces perpendicular to the pendulum is simply:
Nysin β+Nxcos β−mcgsin β−mcℓ¨
β=mc¨xcos β(6)
Self-balancing robot: modeling and comparative analysis between PID and linear quadratic ... (Lu Bin Lau)
354 ❒ISSN: 2089-4864
where Nyrefers to the force in the ydirection, and grefers to the gravity constant. The sum of torques acting
at the center of the pendulum is:
−Nyℓsin β−Nxℓcos β−2Tw=Jc¨
β(7)
where Jcis the pendulum’s moment of inertia. Assuming αis sufficiently small, we have sin β= sin(π+α)≈
−α; cos β= cos(π+α)≈ −1; β2=α2≈0, which lead to the following approximations.
Nx=mc¨x−mcℓ¨α(8)
−Nyα−Nx+mcgα −mcℓ¨α=−mc¨x(9)
Nyℓα +Nxℓ−2Tw=Jc¨α(10)
By substituting the expression of Twinto (10), we will obtain.
Nyℓα +Nxℓ−2km
RVin +2kmke
Rr ˙x=Jc¨α(11)
Let x1=x,x2= ˙x,x3=α,x4= ˙α,u=Vin, and q= [x1x2x3x4]T, the state space representation
of the TWSBR can be constructed as ˙q=Aq +Bu;y=Cq with:
A=
0 1 0 0
0−2kmke(Jc+mcℓ2−mcℓr)
ΩRr2
m2
cℓ2g
Ω0
0 0 0 1
02kmke(Λr−mcℓ)
ΩRr2
mcgℓΛ
Ω0
;B=
0
2km(Jc+mcℓ2−mcrℓ)
ΩRr
0
2km(mcℓ−Λr)
ΩRr
(12)
C=0010(13)
2.2. Control schemes for TWSBR
Figure 3 illustrates the difference between the PID control (Figure 3(a)), LQR control (Figure 3(b))
and the PID-LQR scheme (Figure 3(c)) which is proposed to overcome the limitation of each component. For
the LQR control scheme, the control parameter KL=k1k2k3k4is optimized by minimizing the
following cost function J=R∞
0qTQ+KT
LRKLq dt where Q≥0and R > 0. The optimal value of
KLcan be obtained by using the formula KL=R−1BTPwhere Pis the solution to the Ricatti equation
ATP+P A −P B R−1BTP+Q= 0. With regard to the PID control scheme, the parameters for Kp,Kiand
Kdwere tuned based on the Ziegler-Nichols approach as presented in [29].
(a) (b) (c)
Figure 3. Illustrations on (a) the LQR and PID, (b) the proposed hybrid PID-LQR, and (c) control schemes for
the TWSBR
2.3. Software implementation
In this work, the control schemes were designed in the LabVIEW software and deployed to the em-
bedded NI myRIO-1900 board. The board consists of a built-in accelerometer which provides the angular
acceleration from x,y, and z axes. The tilt angle from the accelerometer can be obtained as (14):
αacc = (arctan val(y)/val(z))×180◦/π (14)
Int J Reconfigurable Embedded Syst, Vol. 12, No. 3, November 2023: 351–359
Int J Reconfigurable Embedded Syst ISSN: 2089-4864 ❒355
where val(y)is the accelerometer value from the y-axis, val(z)is the accelerometer value from the z-axis,
and Tsis the sampling time. However, any shock or vibration will produce sudden spikes on the tilt angle
which can lead to instability of the robot. Therefore, the pitch angle of the robot was obtained through sensor
fusion by combining readings from the accelerometer and a gyroscrope, αgyro, which was externally connected
to the board. A low pass filter was applied to the accelerometer to attenuate the high frequency vibration
noise produced by the motors of the TWSBR. The drift from the PmodGyro’s readings was minimized by
applying a high pass filter. The filtered readings were then combined to obtain a more stable reading for the
TWSBR. The output of the sensor fusion block is considered as the actual tilt angle of the robot, i.e. α. The
corresponding angular velocity, ˙α, of the robot can be obtained by a simple mathematical calculation, i.e.
˙α= (α(k)−α(k−1))/Ts.
To measure the robot’s position and speed, i.e. xand ˙x, the angular speeds of the DC motors were
firstly measured using hall-effect magnetic encoders. Since each of the hall sensors gives a resolution of 390
lines per revolution, quadruple outputs from the two hall sensors give an effective resolution of 1,560 lines per
revolution. Therefore, the angular speed (in rad/s) of each motor can be calculated as follows:
ωi= (C(k)−C(k−1))/Ts×(2π/1560), i =R, L (15)
where C(k)is the encoder count at iteration k, and ωR(ωL)is the angular speed of the right (left) wheel. The
robot’s speed and position can then be written as follows: ˙x= (ωR+ωL)r/2and x= ˙xTs+x0respectively
where x0is the previous position. As the controller’s output will send a command that is linearly proportional
to the speed, a closed-loop speed control technique from [17] is employed to ensure the actual speed of the
robot follows the reference value.
3. RESULTS AND DISCUSSION
Based on the TWSBR model parameters in Table 1, the resulting transfer function Gαis:
Gα=39.77s
s3+ 66.1s2−0.514s−26.88,
and the Aand Bmatrices are:
A=
0 1 0 0
0−1.1237 6.9748 0
0 0 0 1
0−255.26 128.9962 0
;B=
0
10.30
0
39.77
.(16)
Table 1. Model parameters of the robot
Notation Definition Value/unit
gGravitational acceleration 9.81 ms−2
mcMass of the chassis 0.7604 kg
mwMass of each wheel 0.048 kg
JcMoment of inertia of the chassis 0.0032 kgm2
JwMoment of inertia of the wheel 0.000074 kgm2
RElectrical resistance of the motor 1.6 Ω
rRadius of the wheel 0.034 m
kmMotor torque constant 0.2182 Nm/A
keBack EMF constant 0.2182 V/(rad/s)
ℓHalf length of the chassis 0.0 m
To accurately model the built robot, its linear speed is constrained within ±100 cm/s. Using the LQR
control design techniques in section 2.2, the values of Qand Rwere set to Q=diag(10,10,0,0) and R= 1
respectively to give the following state feedback gain KL=−3.1623 6.9428 −3.9015 −0.4482. For
the PID, the optimal values obtained were Kp= 300; Ki= 5500; Kd= 1.5. A filter coefficient of
10,000 was included in the PID control scheme to make the transfer function realizable. In the proposed hybrid
method, some parameter tunings need to be performed to maintain the stability and improve the performance of
Self-balancing robot: modeling and comparative analysis between PID and linear quadratic ... (Lu Bin Lau)
356 ❒ISSN: 2089-4864
the closed-loop system. The optimal values obatined were ˆ
KL= [−207.84 245.64 −220.47 −18.25],
ˆ
Kp= 0.1,ˆ
Ki= 0.3and ˆ
Kd= 0.7.
In order to evaluate the performance of the three control schemes on the TWSBR, they were tested
experimentally when the robot was placed on two types of surface, i.e. rough and smooth. For each scheme,
the initial tilt angle was slowly increased after each trial until the controller was no longer able to maintain the
stability of the TWSBR. To provide a fair comparison, only the maximum initial tilt angle that the robot was
able to self-balance and its corresponding settling time were used to evaluate the performance since the noise
and disturbances entering the system were random and unmeasurable. The settling time in this case is defined
as the time it takes for the tilt angle to reach within ±1◦region.
Table 2 records the numerical results while Figure 4 to Figure 6 illustrate the performance of the
TWSBR with PID, LQR, and hybrid PID-LQR control schemes on both surfaces. Durations of oscillations
and settling time are seen longer on smooth surface for all control schemes due to a higher probability of the
robot to have wheel slips. Comparing Figure 4(a)-Figure 4(d) against Figure 5(a)-Figure 5(d), the PID is seen
to be more effective at regulating the tilt angle of the robot, but it necessitates a higher linear velocity (i.e. back
and forth) to sustain its equilibrium as can be observed from the trajectories of x2in Figure 4(a), Figure 4(c),
Figure 5(a), and Figure 5(c). The LQR on the other hand outperforms the PID in terms of both maximum tilt
angle and settling time. Nonetheless, a significant improvement is achieved when both schemes are hybridized
as can be observed from Figure 6 and the last column in Table 2 where the settling time is reduced and the
maximum initial tilt angle is increased (Figure 6(a) and Figure 6(c)). Figure 6(b) and Figure 6(d) also show a
considerable reduction in the amplitudes of x3and x4.
Table 2. Performance evaluations between PID, LQR, and hybrid LQR-PID schemes by experiments
Control scheme
Type of surface Performance metric PID LQR Hybrid
Rough Maximum initial tilt angle (deg) 2.01 7.42 9.22
Settling time (s) 2.78 2.12 2.04
Smooth Maximum initial tilt angle (deg) 1.04 3.21 10.11
Settling time (s) 3.02 2.13 2.12
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-30
-20
-10
0
10
20
30
x1 (cm), x2 (cm/s)
Performance with PID on Rough Surface
x1
x2
(a)
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-10
-8
-6
-4
-2
0
2
4
6
8
10
x3 (deg), x4 (deg/s)
Performance with PID on Rough Surface
x3
x4
(b)
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-30
-20
-10
0
10
20
30
x1 (cm), x2 (cm/s)
Performance with PID on Smooth Surface
x1
x2
(c)
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-10
-8
-6
-4
-2
0
2
4
6
8
10
x3 (deg), x4 (deg/s)
Performance with PID on Smooth Surface
x3
x4
(d)
Figure 4. Performance of the TWSBR with PID control in terms of trajectories of (a) x1, x2on a rough
surface, (b) x3, x4on a rough surface, (c) x1, x2on a smooth surface, and (d) x3, x4on a smooth surface
Int J Reconfigurable Embedded Syst, Vol. 12, No. 3, November 2023: 351–359
Int J Reconfigurable Embedded Syst ISSN: 2089-4864 ❒357
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-30
-20
-10
0
10
20
30
x1 (cm), x2 (cm/s)
Performance with LQR on Rough Surface
x1
x2
(a)
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-10
-8
-6
-4
-2
0
2
4
6
8
10
x3 (deg), x4 (deg/s)
Performance with LQR on Rough Surface
x3
x4
(b)
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-30
-20
-10
0
10
20
30
x1 (cm), x2 (cm/s)
Performance with LQR on Smooth Surface
x1
x2
(c)
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-10
-8
-6
-4
-2
0
2
4
6
8
10
x3 (deg), x4 (deg/s)
Performance with LQR on Smooth Surface
x3
x4
(d)
Figure 5. Performance of the TWSBR with LQR control in terms of trajectories of (a) x1, x2on a rough
surface, (b) x3, x4on a rough surface, (c) x1, x2on a smooth surface, and (d) x3, x4on a smooth surface
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-30
-20
-10
0
10
20
30
x1 (cm), x2 (cm/s)
Performance with Hybrid PID-LQR on Rough Surface
x1
x2
(a)
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-10
-8
-6
-4
-2
0
2
4
6
8
10
x3 (deg), x4 (deg/s)
Performance with Hybrid PID-LQR on Rough Surface
x3
x4
(b)
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-30
-20
-10
0
10
20
30
x1 (cm), x2 (cm/s)
Performance with Hybrid PID-LQR on Smooth Surface
x1
x2
(c)
0 0.5 1 1.5 2 2.5 3 3.5
Time (s)
-10
-8
-6
-4
-2
0
2
4
6
8
10
x3 (deg), x4 (deg/s)
Performance with Hybrid PID-LQR on Smooth Surface
x3
x4
(d)
Figure 6. Performance of the TWSBR with a hybrid PID-LQR in terms of trajectories of (a) x1, x2on a rough
surface, (b) x3, x4on a rough surface, (c) x1, x2on a smooth surface, and (d) x3, x4on a smooth surface
Self-balancing robot: modeling and comparative analysis between PID and linear quadratic ... (Lu Bin Lau)
358 ❒ISSN: 2089-4864
4. CONCLUSION
In this study, we developed a TWSBR controlled by an embedded NI myRIO-1900 board with a
model-based control scheme. Our experimental results showed that PID is more effective in regulating the
robot’s tilt angle in the presence of external disturbances, but it requires a higher velocity to maintain equilib-
rium. On the other hand, LQR outperforms PID in terms of the maximum initial tilt angle. By combining both
schemes, we observed significant improvements, such as an increase in the maximum initial tilt angle and a re-
duction in settling time. While the experimental results presented in this study provide valuable insights into the
performance of the TWSBR, future research could focus on evaluating its performance in real-world scenarios,
such as navigating through complex environments or performing specific tasks. Machine learning techniques,
such as reinforcement learning, could also be used to train the TWSBR to adapt to changing environmental
conditions or to optimize its performance based on specific performance criteria.
ACKNOWLEDGEMENT
The authors would like to thank Ministry of Higher Education Malaysia for the financial support under
Fundamental Research Grant Scheme with Project Code: FRGS/1/2021/TK0/USM/02/18.
REFERENCES
[1] G. Fragapane, R. de Koster, F. Sgarbossa, and J. O. Strandhagen, “Planning and control of autonomous mobile robots for intralo-
gistics: literature review and research agenda,” European Journal of Operational Research, vol. 294, no. 2, pp. 405–426, Oct. 2021,
doi: 10.1016/j.ejor.2021.01.019.
[2] A. Loganathan and N. S. Ahmad, “A systematic review on recent advances in autonomous mobile robot navigation,” Engineering
Science and Technology, an International Journal, vol. 40, p. 101343, Apr. 2023, doi: 10.1016/j.jestch.2023.101343.
[3] J. H. Teo, A. Loganathan, P. Goh, and N. S. Ahmad, “Autonomous mobile robot navigation via RFID signal strength sens-
ing,” International Journal of Mechanical Engineering and Robotics Research, vol. 9, no. 8, pp. 1140–1144, 2020, doi:
10.18178/ijmerr.9.8.1140-1144.
[4] I. Arrouch, N. S. Ahmad, P. Goh, and J. Mohamad-Saleh, “Close proximity time-to-collision prediction for autonomous robot
navigation: an exponential GPR approach,” Alexandria Engineering Journal, vol. 61, no. 12, pp. 11171–11183, Dec. 2022, doi:
10.1016/j.aej.2022.04.041.
[5] B. Sawatzky, I. Denison, S. Langrish, S. Richardson, K. Hiller, and B. Slobogean, “The segway personal transporter as an alternative
mobility device for people with disabilities: a pilot study,” Archives of Physical Medicine and Rehabilitation, vol. 88, no. 11, pp.
1423–1428, Nov. 2007, doi: 10.1016/j.apmr.2007.08.005.
[6] J. Ashurst and B. Wagner, “Injuries following segway personal transporter accidents: case report and review of the literature,”
Western Journal of Emergency Medicine, vol. 16, no. 5, pp. 693–695, Sep. 2015, doi: 10.5811/westjem.2015.7.26549.
[7] A. Pourmand, J. Liao, J. M. Pines, and M. Mazer-Amirshahi, “Segway® personal transporter-related injuries: a systematic literature
review and implications for acute and emergency care,” The Journal of Emergency Medicine, vol. 54, no. 5, pp. 630–635, May 2018,
doi: 10.1016/j.jemermed.2017.12.019.
[8] K. Hoffeld et al., “Is the use of segways or e-scooters in urban areas a potential health risk? a comparison of trauma consequences,”
Medicina, vol. 58, no. 8, p. 1033, Aug. 2022, doi: 10.3390/medicina58081033.
[9] J. A. Borja, I. Alvarado, and D. M. Pe˜
na, “Low cost two-wheels self-balancing robot for control education powered by stepper
motors,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 17518–17523, 2020, doi: 10.1016/j.ifacol.2020.12.2660.
[10] J.-H. Park and B.-K. Cho, “Development of a self-balancing robot with a control moment gyroscope,” International Journal of
Advanced Robotic Systems, vol. 15, no. 2, p. 172988141877086, Mar. 2018, doi: 10.1177/1729881418770865.
[11] J. Iqbal, M. Ullah, S. G. Khan, B. Khelifa, and S. ´
Cukovi´
c, “Nonlinear control systems - a brief overview of historical and recent
advances,” Nonlinear Engineering, vol. 6, no. 4, Dec. 2017, doi: 10.1515/nleng-2016-0077.
[12] N. S. Ahmad, J. Carrasco, and W. P. Heath, “LMI searches for discrete-time Zames-Falb multipliers,” in 52nd IEEE Conference on
Decision and Control, Dec. 2013, pp. 5258–5263, doi: 10.1109/CDC.2013.6760716.
[13] N. Bekiaris-Liberis and M. Krstic, Nonlinear control under nonconstant delays. Philadelphia, PA: Society for Industrial and Applied
Mathematics, 2013.
[14] L. R. Silva, R. C. C. Flesch, and J. E. Normey-Rico, “Analysis of anti-windup techniques in PID control of processes with measure-
ment noise,” IFAC-PapersOnLine, vol. 51, no. 4, pp. 948–953, 2018, doi: 10.1016/j.ifacol.2018.06.100.
[15] I. Jmel, H. Dimassi, S. Hadj-Said, and F. M’Sahli, “Adaptive observer-based sliding mode control for a two-wheeled self-balancing
robot under terrain inclination and disturbances,” Mathematical Problems in Engineering, vol. 2021, pp. 1–15, Jan. 2021, doi:
10.1155/2021/8853441.
[16] ´
A. Odry, R. Full´
er, I. J. Rudas, and P. Odry, “Fuzzy control of self-balancing robots: A control laboratory project,” Computer
Applications in Engineering Education, vol. 28, no. 3, pp. 512–535, May 2020, doi: 10.1002/cae.22219.
[17] N. S. Ahmad, “Robust H∞-fuzzy logic control for enhanced tracking performance of a wheeled mobile robot in the presence of
uncertain nonlinear perturbations,” Sensors, vol. 20, no. 13, p. 3673, Jun. 2020, doi: 10.3390/s20133673.
[18] A. Unluturk and O. Aydogdu, “Adaptive control of two-wheeled mobile balance robot capable to adapt different surfaces using a
novel artificial neural network–based real-time switching dynamic controller,” International Journal of Advanced Robotic Systems,
vol. 14, no. 2, p. 172988141770089, Mar. 2017, doi: 10.1177/1729881417700893.
[19] M. M. Rahman, S. M. H. Rashid, and M. M. Hossain, “Implementation of Q learning and deep Q network for controlling a self
balancing robot model,” Robotics and Biomimetics, vol. 5, no. 1, p. 8, Dec. 2018, doi: 10.1186/s40638-018-0091-9.
Int J Reconfigurable Embedded Syst, Vol. 12, No. 3, November 2023: 351–359
Int J Reconfigurable Embedded Syst ISSN: 2089-4864 ❒359
[20] N. S. Ahmad, J. H. Teo, and P. Goh, “Gaussian process for a single-channel EEG decoder with inconspicuous stimuli and eyeblinks,”
Computers, Materials & Continua, vol. 73, no. 1, pp. 611–628, 2022, doi: 10.32604/cmc.2022.025823.
[21] K. Chen, J. Yi, and D. Song, “Gaussian processes model-based control of underactuated balance robots,” in 2019 International
Conference on Robotics and Automation (ICRA), May 2019, pp. 4458–4464, doi: 10.1109/ICRA.2019.8794097.
[22] J. Velagic, I. Kovac, A. Panjevic, and A. Osmanovic, “Design and control of two-wheeled and self-balancing mobile robot,” in 2021
International Symposium ELMAR, Sep. 2021, pp. 77–82, doi: 10.1109/ELMAR52657.2021.9550938.
[23] C. V. Samak And T. V. Samak, “Design of a two-wheel self-balancing robot with the implementation of a novel state feedback for
PID controller using on-board state estimation algorithm,” International Journal of Robotics Research and Development, vol. 8, no.
2, pp. 1–10, 2018, doi: 10.24247/ijrrddec20181.
[24] F. F. Rabbany, A. Qurthobi, and A. Suhendi, “Design of self-balancing virtual reality robot using pid control method and comple-
mentary filter,” in 2021 IEEE International Conference on Industry 4.0, Artificial Intelligence, and Communications Technology
(IAICT), Jul. 2021, pp. 15–19, doi: 10.1109/IAICT52856.2021.9532576.
[25] M. O. Asali, F. Hadary, and B. W. Sanjaya, “Modeling, simulation, and optimal control for two-wheeled self-balancing
robot,” International Journal of Electrical and Computer Engineering (IJECE), vol. 7, no. 4, pp. 2008–2017, Aug. 2017, doi:
10.11591/ijece.v7i4.pp2008-2017.
[26] K. M. Goher and S. O. Fadlallah, “Bacterial foraging-optimized PID control of a two-wheeled machine with a two-directional
handling mechanism,” Robotics and Biomimetics, vol. 4, no. 1, p. 1, Dec. 2017, doi: 10.1186/s40638-017-0057-3.
[27] J. Lin, R. Zheng, Y. Zhang, J. Feng, W. Li, and K. Luo, “CFHBA-PID algorithm: dual-loop PID balancing robot attitude con-
trol algorithm based on complementary factor and honey badger algorithm,” Sensors, vol. 22, no. 12, p. 4492, Jun. 2022, doi:
10.3390/s22124492.
[28] B. Kim and B. Park, “Robust control for the segway with unknown control coefficient and model uncertainties,” Sensors, vol. 16,
no. 7, p. 1000, Jun. 2016, doi: 10.3390/s16071000.
[29] J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic controllers,” Journal of Dynamic Systems, Measurement, and
Control, vol. 115, no. 2B, pp. 220–222, Jun. 1993, doi: 10.1115/1.2899060.
BIOGRAPHIES OF AUTHORS
Lu Bin Lau was born in Penang in 1998. He received the B.Eng. degree in electronic
engineering from School of Electrical and Electronic Engineering, Universiti Sains Malaysia (USM)
in 2022. His research interest centers around control systems and robotics. During his undergraduate
studies at USM, he was actively involved in various national and international robotics competitions.
He joined National Instruments as an intern in 2021, and is currently working as an electrical engineer.
He can be contacted at email: laulubin@student.usm.my.
Nur Syazreen Ahmad received the B.Eng. degree in electrical and electronic engineer-
ing from the University of Manchester, United Kingdom and Ph.D. degree in control systems from
the same university. She is currently an associate professor at the School of Electrical and Elec-
tronic Engineering, University Sains Malaysia (USM), specializing in embedded control systems,
sensor networks and mobile robotics. Her main research interest revolves around autonomous mo-
bile robots, with a particular focus on sensing, identification, intelligent control and indoor naviga-
tion. She is a member of the IEEE Young Professional and Control System societies, and has gained
a recognition as a certified LabVIEW Associate Developer by NI. She can be contacted at email:
syazreen@usm.my.
Patrick Goh received the B.S., M.S., and Ph.D. degrees in electrical engineering from the
University of Illinois at Urbana-Champaign, Urbana, IL, USA in 2007, 2009, and 2012 respectively.
Since 2012, he has been with the School of Electrical and Electronic Engineering, Universiti Sains
Malaysia, where he currently specializes in the study of signal integrity for high-speed digital designs.
His research interest includes the development of circuit simulation algorithms for computer-aided
design tools. He was a recipient of the Raj Mittra Award in 2012 and the Harold L. Olesen Award
in 2010, and has served on the technical program committee and international program committee
in various IEEE and non-IEEE conferences around the world. He can be contacted at email: eep-
atrick@usm.my.
Self-balancing robot: modeling and comparative analysis between PID and linear quadratic ... (Lu Bin Lau)
