Page 178 - IJOCTA-15-1

Y. Olmez et al. / IJOCTA, Vol.15, No.1, pp.166-182 (2025)
where max it is the number of the iterations (it). usage of the controller is ensured within the spec-
R is a constant value and taken as 0.2. r denotes ified range. The settings of the parameters and
the random number. their definitions for all metaheuristic methods are
given in Table 3. Additionally, Table 4 presents
3. Experimental studies the common control parameters used in all meth-
ods.
The experiments and coding are carried out on
MATLAB software with version 2020a on a per-
sonal computer that contains an IntelCore-i7 9 th
Gen processor, and 16GB RAM. The control of As shown in Table 4, the maxit and the number
the speed and the balance angle for the two-
of solutions are taken to be the same in all al-
wheeled robot is provided using the PI controllers.
gorithms, with values of 500 and 20, respectively.
The mentioned metaheuristic methods in Section
All considered algorithms run under 5-times. The
2 are utilized for tuning the controllers’ param-
parameters of the two PI controllers, which each
eters. The model of two-wheeled robots is illus-
have four parameters, denote the dimension of the
trated in Figure 1. In this figure, R denotes the
problem and are set to the same value in all algo-
radius of the wheel. The width, depth, and height
rithms. To make an accurate comparison of the
of the body are represented as W, D, and H, re-
optimization algorithms, the ranges of PID con-
spectively. Table 2 presents the vehicle’s param-
trol parameters were investigated in a wide search
eter and their definitions.
space as (0-800).
The model of the optimized control system for 4. Results and discussion
the two-wheeled vehicle is given in Figure 2. The
fitness value of each candidate solution set gen- Performance evaluations of the current meta-
erated by metaheuristic methods is sent to the heuristic algorithms are carried out on the same
control part of the robot. The equation of the platform and the system. The performances of
fitness value is calculated using Eq. (34): nine algorithms proposed in the last four years
(detailed above) are analyzed by comparing them
with five older algorithms, which are Whale, Grey
f (t) = 0.6e + 0.4M (34) Wolf, Crow Search, Covariance Matrix Adapta-
tion Evolution Strategy, and Flower Pollination
Where M represents the maximum overshoot and
optimization algorithms. Each method is em-
e is the steady-state error of the system. The
ployed in the optimization stage of the control pa-
error acquired from the control model is passed
rameters to perform speed and balance controls of
through the function of the Integral Square Er-
the two-wheeled vehicle. For a fair evaluation, all
ror (ISE) given in Eq. (35). In the metaheuris- algorithms are performed under equal conditions.
tic algorithm, the fitness value is minimized by PI controllers are used for the balance and the
searching for the optimal solution until the stop- speed control of the two-wheeled vehicle. The pa-
ping criteria are achieved.
rameters of the PI controllers (Kp 1 , Ki 1 , Kp 2 , Ki 2 )
are obtained using the determined iteration and
2
ISE = ∫ e (t) dt (35) number of the search agents (see Table 4). The
optimal PI controller parameter values obtained
where the e(t) function is calculated as presented for all methods are presented in Table 5. In this
in Eq. (36). table, Kp 1 and Ki 1 indicate the parameters of the
speed controller, while Kp 2 and Ki 2 represent the
parameters of the balance controller.
e (t) = e velocity (t) + e balance (t) (36)
Table 5 shows that controller parameters are sim-
A control signal is obtained with each candidate ilar in the PO, AO, GOA, POA, GJO, FDA, EO,
solution created by the metaheuristic algorithm, ARO, CSA, GWO, and FPA optimizers. For both
as shown in the control block diagram of the controllers, Kp values which are obtained by using
two-wheeled vehicle above. The effectiveness of CO, WOA, and CMA-ES are bigger than the ob-
the controller is assessed with the acquired con- tained Kp values with other methods. The Ki pa-
trol signal, and further effective solutions are at- rameters of the balance controllers with CO and
tempted to be developed in conjunction with the WOA are smaller, whereas these parameters ac-
prior solutions. As a result, the most efficient quired with CMA-ES are slightly bigger than the
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