Page 44 - IJEEE-2023-Vol19-ISSUE-1
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40 | Mohsin, Aldair & Al-Hussaibi
Rods Top layer output, and the PID controller that provides the sufficient
Middle layer
power to stabilize the robot. The Simulink into Physical signals
(S-PS) converter has been used to mimic the functioning of a
motor torque by estimating its ability to generate a linear
actuation signal for translation motion after receiving feedback
from the system rotational motion portion. According to [24]
and [25], a classical PID controller is utilized for the proposed
TWSBR. The PID control loop architecture is given by
Bottom layer ( = *!+ + *" ?$# +(/)0/ + *% %%&# (1)
Wheels The required pitch angle for a vertical position is 0 degree.
Pitch angle error is the difference between desired and
Fig.3: The structure of Two-Wheeled Self-Balanced Robot. measured angles. Based on these parameters the PID controller
calculates the angle error gains Kp, Ki and Kd. If this
Figure 4 shows a designed TWSBR with Simscape Multibody assumption is correct, the PID controller output should be
Library. The external force and torque block is introduced to supplied to the S-PS converter which is configured as an
apply an external disturbance force on the robot body for actuator force action to apply on the plant to accomplish system
controller evaluation as described in the following controller balancing. Obviously, the Simscape plant senses the robot
scheme. angle and feedbacks the deviation to the controller as an error
under road disturbances effects. Figure 5 shows how to connect
the 3D Simscape Multibody model of a TWSBR with controller
Simulink environment. The project goal is to construct a robust
design with the minimum response time while obtaining PID
controllers optimal performance.
The PID auto-tuning tool software in MATLAB Simulink is
successfully utilized to determine the best PID controller
parameters [26]. The best parameters values obtained by using
auto-tuner method as presented in Table I.
TABLE I
PID Controller Parameters of Auto-Tuning
Method
PID Parameter Value
Fig.4: TWSBR open loop Simscape Multibody modeling !" 0.563
III. CONTROLLER SCHEME !( 1.552
For the considered design of TWSBR, the wheels are moved !+ 0.02583
back and forth to keep the robot's vertical angle close to zero. A
stability criterion is given as: if the system is a Single Input B. LQR controller
Single Output (SISO) only, the robot body angle must be
dependable; and if Single Input Multi Output (SIMO) system is The robot moves back and forth under an inclination angle as
used, it is able to control the robot position as well. The robot is implemented by the PID controller with uncontrolled position.
challenged with several control primitives to achieve control TWSBR can be controlled using full-state feedback as
objectives. The robot tilt angle (%) and the wheel cart position described in [27]. The feedback control formula can be created
(!) represent the current condition that needs to be controlled. by finding the gain matrix (k) and applying it to the Simscape
These elements are discussed below. Multibody system. The LQR method can be used to determine
the robot position for improved target control [28]. The system
A. PID Controller can be given in the discrete state-space form as:
The self-balance robot control system must be capable to reject 2 ?(/) = 4!(/) + 56(/) (2)
external force perturbations from instability equilibrium to the
initial vertical body position. Accordingly, it must provide the 7(/) = 8!(/) + 96(/) (3)
correct input to the prismatic joint to achieve the desired system
behavior. To obtain the ideal input, a control loop is required The linearized system in the state-space model of TWSBR can
with three parts: the actual robot inclination angle, the be written in a mathematical form as [29], [30]:
summation process to compare with the robot desired angle
