and flux of the PMSM independently. The standard Proportional Integrator Derivative (PID) controller

regulates the speed in FOC, which is noted for its increased resilience in linear systems, however in nonlinear

ones, the PID controller responds poorly to changes in the system’s variables. In this case, the best solutions are

frequently based on optimization techniques that produce the controller’s gains in every period. Optimizing the

PID’s behavior in response to the system’s nonlinear behavior. The novel proposed strategy for enhancing the

gains of the PID controller by employing a cost function such as Integral Time Absolute Error (ITAE) is based

on PID speed regulation and is optimized using the Ant Colony Optimization algorithm (ACO) for FOC. To

confirm the strategy’s aims, the suggested method is implemented on Matlab/Simulink. The simulation results

demonstrated the efficiency of the intelligent ACO-FOC control, which delivers good performance in terms of

stability, rapidity, and torque fluctuations.

1 Introduction

Researchers have already been grappling with the

regulation of variable-speed electrical machinery

since the birth of industrialization. This is why

electrical motors are becoming increasingly

demanding in terms of efficiency, dependability,

and cost reduction, [1], [2], [3]. This difficulty was

rectified in the nineteenth century with DC motors;

however, these drives cannot be utilized in corrosive

(PMSM) provide several advantages, including a

high-power factor, a high-power density, high

efficiency, and low-maintenance operation, [6], [7].

controls, which have advantages but are limited by

percent of all control loops are PID, spanning

applications ranging from process management to

motor drives, transportation, and aviation control.

Because of their linear form, these linear control

techniques have the benefit of being simple to

implement and simple to synthesize. Its applications

will be unsuccessful, especially if the structures that

have to be controlled have complex and nonlinear

properties, [12], and because of the PID regulator’s

renowned characteristics, which fail to be adaptable

performance of the PID controller, intelligent

optimization techniques such as Particle Swarm

Optimization (PSO) [14], autotuning [15], Fuzzy

Logic [16], Genetic Algorithm (GA) [17], [18],

[19], Evolutionary Programming (EP) [20] and

Future Search Algorithm (FSA) [21], have been

used.

is employed in this study to control the speed of the

PMSM using DFOC. ACO has attracted widespread

genuine ant colonies. It was originally suggested in

1992 by Marco Dorigo. ACO is used in [22], for

Dynamic path optimization; it is a crucial part of

intelligent transportation systems. Where the results

are more accurate. The application of Ant Colony

Optimization in [23], is in the field of Image

Processing. Application/Improvements: ACO has

been used successfully in a variety of applications

that deal with images such as edge linking, edge

detection, segmentation, image compression, and

reasons, including the ability to reply at a faster rate

and with no static error in response speed,

employing ACO to control the speed of the PMSM

using DFOC is useful. The work in this paper

focuses on the analytical analysis and design of

FOC control applied to PMSM, and the parameters

way back if the designated road leads to food.

Simultaneously, the shorter way will be used with

greater frequency, strengthening and tempting it,

[24]. A network scenario can be used to depict the

challenge of developing the PID controller utilizing

the ACO algorithm (Figure 3). Three separate

vectors were used to organize all of the information

for each gain (P, I, D). The vectors in question can

be thought of as roads connecting nests to form a

graphical representation of the scenario. During the

Fig. 3: ACO structure as a neural network problem

integral time absolute error (ITAE). Where the

ITAE will be employed for this work. Equation 12

expresses it.

󰇛󰇜

the ACO block structure is shown in Figure 4.

Fig. 4: PID Controller Optimization Using ACO

the examination of field-oriented control: variable

load with variable reference speed and dynamic

speed with no load. The simulation results are

depicted in the following figures.

As shown in Figure 7-a, the PMSM is in

acceleration mode. Where there is no load, the speed

increased from 80 rad/s to 110 rad/s at t=3 s. The

torque response of the system is shown in Figure 7-

b, and the load torque follows the electromagnetic

torque, which has a value of 0 Nm. The quadrature

current generated by the ACO method speed

b- Torque response, c- Quadrature current, d- Direct

current

and no peak time of the speed as shown in Figure 8-

a. The torque, as seen in Figure 8-b, follows the

quadrature current path (Figure 8-c), thanks to the

ACO-FOC method, which allows for torque control

by adjusting the proportionate quadrature currents

and as presented in their responses there is small

ripple that render this control well performed.

Figure 8-d shows that the flux has been oriented,

deceleration speed performance of the PMSM using

the ACO-FOC algorithm to optimize the PID gains,

which results in good performance (Figure 11-a), as

well as the reliability of ACO-FOC in torque control

utilizing current control (Figure 11-b). Where the

motor accelerates to 100 rad/s, and decelerates to -

100 rad/s after 3 seconds (Figure 11-a) with the

same performance discussed previously.

Furthermore, Figure 11-b depicts the performance

this control is reliable where the quadrature current

is still zero.

Fig. 11: Response under load: a- Acceleration and

deceleration of speed response, b- Torque response,

c- Quadrature current, d- Direct current

5 Conclusion

In this paper, an optimization technique known in

terms of ACO implemented in PMSM using the

state error.

ripples owing to the FOC strategy. In addition, due

to this strategy, both currents; quadrature and direct

are well regulated.

environment, the proposed FOC approach and ACO

algorithm have not yet been put into practice in real