Adaptive position control of a cart moved by DC motor using Grey Wolf Optimizer Algorithm

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Adaptive position control of a cart moved by DC motor using Grey Wolf Optimizer Algorithm

Tarek Hassan Mohamed¹, Ahmed Mohamed A.El-Hady²,Asmaa Fawzy Rashwan³

1,3Facultyof Energy Engineering, Aswan University, Egypt

2Hydro-plants generation company, Aswan, Egypt

1[email protected], ²[email protected],

3[email protected]

Abstract

Recently, the importance of DC motors becomes from its Function and reliability.

Those are two important factors that modern mechanisms, processes and products require to success. So DC motor control technology has a very important part to play at origin of machinery design evolution. Its flexibility, efficiency, power, speed and position will have a flow on effect throughout the machine. Our paper presents an investigation of a positioning control system for a DC motor (with Position-Velocity controller) using a Grey Wolf Optimizer algorithm. The parameters of the used conventional PV controller are tuned by GWO to improve the system performance of the DC motor system. The GWO simulates the realistic performance of the leadership hierarchy and hunting mechanism of grey wolves. There are four types of grey wolves which are delta, beta, alpha and omega.

These four types can be used for representing and simulating the leadership hierarchy. In order to complete the GWO process, three main procedures of hunting are implemented, searching for prey then pursuing or keep tracking of prey and finally attacking prey. The GWO method is used for a DC motor to avoid the load disturbance problem and its bad effect on the system performance. The simulating results showed the improvement efficiency of the system performance when using GWO.

Keywords:Grey Wolf Optimizer, DC motor, Load disturbance

1. Introduction

According to user demands and the great acceleration in the evolution of industries like robotics, DC motors with a wide variation of high performance and a certain amount of controllability are feasible and practice. DC motors used for many purpose applications like robotics, electric trains, electric cars, medical industries, etc. they have some important advantages such as: high reliabilities, simplicity, easy to control their speed by regulate the armature voltage and they have a superior speed torque characteristics more than that of AC motors. In all applications, DC motors should have an accurate controller to achieve the desired performance [1-3].

Controlling position and speed of a DC motor can be done by many types of controllers such as: proportional integral derivative (PID), model predictive control (MPC), Fuzzy Logic Controller (FLC), Particle Swarm Optimization Algorithm (PSO), Grey Wolf Optimizer (GWO)Algorithm, etc. [4, 5]

In this paper, we will develop a model of the DC motor with system identification to get an appropriate transfer function to be simulated in Matlab, and then a Grey Wolf Optimizer is used to improve the control performance of the position-velocity controller of the servo system. Grey Wolf Optimizer (GWO) algorithm is proposed by S. Mirjalili in 2014 [6], as one of the efficient meta-heuristics swarm intelligence optimization technique, which designed to give a solution near-optimal for optimization problems [7].

GWO includes no deviation information in the initial search and it's easy to use make it simple and flexible [8].

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This paper has been organized as below:

Section 2 system dynamics of DC motor is explained thereafter the motor transfer function and the standard closed-loop position control system are shown. In section 3, the Grey Wolf Optimizer Algorithm is reviewed. Section 4 includes subsections 4.1 Position- Velocity (PV) controller of DC servo motor and 4.2 GWO of DC servo motor, which illustrate the desired parameters and the Simulink diagram of the two controllers.

Subsection 4.3 Simulation Results examines system performance by simulating the results. Finally the paper is concluded in section 5.

2. System dynamics of DC motor

In this paper, the positioning servo system studied is a cart driven by a DC motor and controlled by a position-velocity (PV) controller as shown in Figure1.

Figure1: Description ForThe Studied Positioning Servo System The optical encoder measures the cart position, and then sends it to the data acquisition system to perform a feedback signal to the closed control system. After that a control signal is provided back to the DC motor, which depending on the designation scheme of the controller [9].Figure2 shows the equivalent electric circuit of DC motor

Figure2: DC Motor Circuit Diagram

From the schematic of the dynamic DC motor in Figure2, we can find the transfer function of the DC motor as Eq. 1[11].

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Gp S = ^2.46

S²+17.14S(1)

Then representing the PV control system in the standard closed-loop position control system shown in Figure3.

Figure 3: Standard closed-loop position control system

Then by using measurements of the system's input and output signals in Matlab system identification tool we can build a mathematical model represents a new transfer function as shown in Eq. 2. This new transfer function is fitted to the response of the transfer function model of the DC motor by 99.73%.

Gp S =_S₂^1.437_+6.18S(2)

3. Grey Wolf Optimizer Algorithm

The inspiration of the GWO algorithm comes through the simulation of the grey wolf pack lifestyle in leadership and hunting prey. Grey wolves prefer to live and hunt in groups, Each pack has a specific leader, this leader represents Alpha which is not necessarily the strongest one but the best to manage the pack, and it has the right and authority to make decisions concerning the pack members, and they must follow all these decisions. Other wolves in the pack represent beta, they dedicated to the pack leader and serves as his advisor, and they are the best wolves after Alpha to take alpha's place in case of death or retirement. The wolf delta follows the orders and hunts. The omega wolves are the lowest and must follow the orders of all the other dominant and higher wolves in the order Figure4. [10-12]

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Figure 4: Hierarchy of grey wolf (dominance decreases from top down) The essential stages of hunting include [13]:

1- Tracking, chasing and approaching the prey.

2- Keep tracking with encircling, and harassing the prey until it stops moving.

3- Attacking towards the prey Figure5.

Figure 5: Hunting behavior of grey wolves: (a)–(c) chasing and tracking prey;(d) encircling prey; and (e) attacking prey.

For modeling the social behaviour of wolves, alpha (α) is considered as the fittest solution, and the others beta (β) and delta (δ) are the second and third best solutions respectively. Also there is a number of parameters need to be set in the GWO algorithm such as: initializing the number of search agents, initialize alpha, beta, delta, maximum number of iterations and the stopping criterion [15]. Thus the encircling behaviour can be characterized by the following equations [16]:

𝐷 = 𝐶 . 𝑋 𝑡 − 𝑋 𝑡 (3)_𝑝 𝑋 𝑡 + 1 = 𝑋 𝑡 − 𝐴 . 𝐷𝑝 (4) Where,

t : the current iteration.

A and C : coefficient vectors.

X_p

t : the position vector of the prey.

The vectors A and C are calculated as follows:

𝐴 = 2𝑎 . 𝑟 − 𝑎 (5)₁ 𝐶 = 2. r (6) ₂

Where the components of a are linearly decreases from 2 to 0 over the course of iterations and r₁, r₂ are random vectors in [0, 1].

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After the encircling process, they start hunting. Whereas, the first three best solutions obtained are saved so far and force the other search agents (including omegas) to update their position depending on the position of the best search agents. The following formulas are proposed in this regard.

𝐷_𝛼

= 𝐶 . 𝑋₁ − 𝑋 _𝛼 , 𝐷 = 𝐶_𝛽 . 𝑋₂ − 𝑋 _𝛽 , 𝐷 = 𝐶_𝛿 . 𝑋₃ − 𝑋 _𝛿 (7) 𝑋₁

= 𝑋 − 𝐴_𝛼 . (𝐷₁ )_𝛼 , 𝑋 = 𝑋₂ − 𝐴_𝛽 . (𝐷₂ )_𝛽 , 𝑋 = 𝑋₃ − 𝐴_𝛿 . 𝐷₃ (8)_𝛿 𝑋 𝑡 + 1 =^𝑋 𝑡 +𝑋¹ 𝑡 +𝑋₂ (𝑡) ₃

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Attacking prey is the final step which is done by linearly decreasing the value of afrom 2 to 0. With this fluctuation of A is also reduced.

4. Implementations

4.1 Position-Velocity (PV) controller of DC servo motor

The closed-loop structure of the DC motor with PV control of the controlled DC motor with PV control scheme is shown in Figure6, where G(s) is the transfer function of the DC motor shown in Eq. 1 and Eq. 2 respectively, and an external equivalent load disturbance d affects the DC servo motor input system.

Figure 6: PV control scheme

The PV controller consists of a position control loop cascaded with a speed control loop, and the output of the controller is obtained from the sum of two correction signals, one is proportion gain (𝑘_𝑝) to the position error and the other is proportional gain (𝑘_𝑣) to the velocity.

Calculation of (𝑘_𝑝) and (𝑘_𝑣) based on some satisfying performance requirements, those requirements are as follows:

- Percentage overshoot PO ≤ 10٪ - Time to first peak tp ≤ 0.15 sec - Settling time t_s ≤ 0.2 sec

Then, (𝑘_𝑝) and (𝑘_𝑣) has been calculated as 274.62 v/m, and 5.532 v.sec/m respectively.

Now, simulate the PV controller using MATLAB simulink package Figure7.

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Figure 7: PV control system Simulink diagram 4.2 GWO of DC servo motor

An intelligent control of a Positioning system through auto-tuning the parameters of a position-velocity controller using GWO algorithm is investigated. GWO Algorithm is exploited to achieve the optimal parameters of DC motor. The GWO has been executed to search according to the following parameters:

- Number of Search Agents : 5 - Number of iterations : 100

- Number of variables (dimension of the problem) : 2

Figure8 shows the DC motor based on GWO Algorithm using MATLAB simulink package.

Figure 8: Simulink diagram used for DC motor based on GWO 4.3 Simulation Results

Simulating the results using MATLAB/Simulink package software is to examine system performance with the conventional PV controller and the GWO controller respectively, also testing the impact of load disturbance (with value 0.2 N appeared at t=3 sec) on the system performance of the DC motor with the transfer function in Eq. 2.

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Figure9 and Figure10, compare the obtained results based on the conventional PV controller with those obtained using the GWO based adaptive controller. It is clearly from the simulation results that the performance specifications of the conventional PV controller have a good remarkable improvement with those auto-tuned controller based on the GWO (with and without load disturbance). GWO based adaptive controller has a good performance with decreased percentage overshoot.

Figure 9: Response of the PV & GWO controllers without load disturbance

Figure 10: Response of the PV & GWO controllers with load disturbance

5. Conclusion

In this paper, an effective control for the PV controller of a DC motor system with auto-tuned parameters using GWO algorithm has been investigated. A comparison

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between the system performance using proposed controller and the conventional PV controller has been presented.

Simulation results were carried out to confirm the effectiveness of using GWO based adaptive controller against conventional PV controller with the existence of the load disturbance and results assured that system with proposed controller can achieve the desired required response.

References

[1] Mohamed Abdelhamid Mohamed, Tarek Hassan Mohamed, Ammar Mostafa Hassan, Adel BedirAbdelMoaty, (2019). Position control of a cart moved by DC motor using 2DOF-DFC method.

Youth Research Conference

[2] Jimmy Linggarjati, (2017). DC servo motor positioning with anti-windup implementation using C2000 ARM-Texas Instrument, IOP conf. ser.: Earth Environ. Sci. 109 012016.

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[7] Rezaei H, Bozorg-Haddad O, Chu X. (2018). Grey Wolf optimization (GWO) algorithm, O. Bozorg- Haddad (Ed.) Advanced optimization by nature-inspired algorithms, Springer, Singapore.

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[9] Esam H. Abdelhameed, Tarek Hassan Mohamed, Marwa Mahmoud Hamed, Gaber El-saady Ahmed, (2018). Fuzzy-Based Position-Velocity Controller Gain Scheduling for Load Disturbance Rejection in a Positioning Servo System. Twentieth International Middle East Power Systems Conference (MEPCON).

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[11] IP01 and IP02, Linear Experiment #1, PV position control, https://bearspace.baylor.edu/Paul_Grabow/public/Baylor%20SysML/Furuta%20Pendulum/InvertedPen dulum/IP01_2%2520Position_PV_Student_504.pdf

http://www.ece.uprm.edu/control/manual/quanser/linear/IP01_2%20Position_PV_Student_504.pdf [12] Madhusmita Panda and Bikramaditya. (2019). Grey Wolf Optimizer and Its Application: A Survey,

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Authors

Tarek Hassan Mohamed was born in 1975. He received the B.Sc. in control engineering from Minoufta University, Egypt and he received M.Sc. and Ph.D. degrees in Electrical engineering from Minia University, Egypt in 2006 and 2012

From 2006 to 2012, he was an assistant lecturer with the Faculty of Energy Engineering, Aswan University. Since 2017, he has been an Assistant Professor with the Electrical Engineering Department, Faculty of Energy Engineering, Aswan University, Egypt. In addition, from 2018 he is the Head of the Department. He is the author of more than 40 articles. His research interests include automatic control, power system control, and renewable energy.

Asmaa Fawzy Rashwanis an associate professor of Electrical Engineering at Aswan University, Egypt.

She received her B.SC and M.SC degrees in Electrical EngineeringfromFaculty of Energy Engineering,Aswan University andAssuit University, Egypt in 2002 and 2008,respectively.She joined to Electrical Engineering departmentof Faculty of Energy Engineering, Aswan Universityas a demonstrator in 2004.She received P.HDin 2015 fromFaculty of Engineering ,Aswan University. HerResearch areas includes linear control system, adaptivecontrol system ,neural network and system identification.

Ahmed Mohamed A.El-Hadywas born in 1985. He received the B.Sc. in Electronicsengineeringand Communication technology from Modern Academy for Engineering and Technology, Egypt in 2007.

He received Diploma degree in ElectricalControl engineering from the Faculty of Energy Engineering, Aswan University, Egypt in 2017.He has been a master’s student since 2017 at the Faculty of Energy Engineering, Aswan University.

In addition,Since 2009,he has been an electrical engineer at High Dam power station, Hydro Plants Generation Company, Egypt.