Page 47 - IJEEE-2023-Vol19-ISSUE-1

Mohsin, Aldair & Al-Hussaibi | 43

(a) (b)
(b)

(c) (c)
Fig.10: Continued. Fig.12: TWSBR 3D visualization with additional weight is
loaded up. (a): on the top layer. (b): on the middle layer. (c): on
Case 4: Robustness test of proposed PID controller
The robustness of the proposed controller is studied by the bottom layer
changing the carried weights on the TWSBR layers. In the three
different cases 1kg, 2kg, and 3kg of additional weight are TABLE III
loaded to each layer of TWSBR, respectively as shown in The Key Va3ues Res765se 6f
Fig.12. Two disturbances are introduced to the controlled S04u3at065 Resu3ts f69 T67
system in order to validate the robustness and effectiveness of Laye9.
the proposed controller. To evaluate the performance of the
robustly designed controller, the top, middle, and bottom layers Mass Self-Balancing Rise Overshoot steady-state
are compared in terms of their ability to handle the loaded extra
weights and achieve the stability of these situations in the (kg) Time Time (%) error
presence of two road disturbances. Figures 13, 14, and 15 show
the PID control efforts and effectiveness for the three layers of (seconds) (seconds)
the robot body construction when 0, 1, 2, and 3 kilograms are
loaded. Furthermore, comparisons between the robot's 0 0.5 0.0278 61.6 0
desired angle and the robot's actual angle under two different
scenarios of disturbance are used in road design. Based on the 1 0.765 0.0324 77.6 0
findings of the figures, the Tables III, IV and V shows the
transient response of the simulation results to each robot layer 2 1.11 0.0329 97 0
for the self-balancing time (settling time), overshot, rise time,
and steady-state error along with the corresponding suggested 3 1.62 0.033 125 0
additional weights that are being loaded on three layers. When
compared to the bottom layer, the top and middle robot layers TABLE IV
have a faster self-balancing time when loading up extra
weights. Moreover, they have a greater capacity for carrying The Key Values Response of Simulation Results for Middle
and transferring the suggested additional loads of weight than
the bottom layer. Layer.

Mass Self-Balancing Rise Overshoot steady-state

(kg) Time Time (%) error

(seconds) (seconds)

0 0.5 0.0278 61.6 0

1 0.774 0.0269 73.7 0

2 0.905 0.0267 88.4 0

3 1.63 0.0267 108 0