Dc Motor Speed Control Matlab

International Journal of Power Electronics and Drive System (IJPEDS)

Journal Homepage: Http://Ijpeds.Iaescore.Com

Design and implementation speed control system of DC Motor

Based On Pid Control And Matlab Simulink

Salman Jasim Hammoodi1, Kareem Sayegh Flayyih2, Ahmed Refaat Hamad3

Accepted Aug 4, 2019

In this paper, we first write a description of the operation of DC motors taking into account which parameters the speed depends on thereof. The PID (Proportional-Integral-Derivative) controllers are then briefly described, and then applied to the motor speed control already described, that is, as an electronic controller (PID), which is often referred to as a DC motor. The closed loop speed control of a Brush DC motor is developed applying the well-known PID control algorithm. The objective of this work is to designed and simulate a new control system to keep the speed of the DC motor constant before variations of the load (disturbances), automatically depending to the PID controller. The system was designed and implementation by using MATLAB/SIMULINK and DC motor.

Figure: System Model & Simulation Flow for Dc Motor Speed Control Matlab

Speed Control

This is an open access article under the CC BY-SA license.

Al-Za’Franiya, 10074 Baghdad, Iraq

1.

Introduction

At present, most of the motors in the industry are handled directly from the electrical distribution lines, whether they are DC or AC motors. Because of this, the behaviour of the motor depends on the nature of the load coupled to the axis of the machine . In the case of a light load the motor develops a relatively high speed and a low torque because it is the load requirement. On the contrary, if a heavy or difficult to move load is available, the motor will move at a lower speed and deliver more torque as a higher load demands it .

Figure: System Model & Simulation Flow for Dc Motor Speed Control Matlab

As can be seen by directly connecting the motor to the AC or DC electrical network, its behaviour is defined and it will remain unchanged for a certain fixed voltage in the power supply line. However, in a large part of the industrial sector, there are processes in which the management of the operating characteristics of said machines is required, which is why parameter control devices such as speed and frequency variations are used. In the case of AC motors, these devices are commonly used and have a relatively low cost, however, when working with DC motors the variable speed drives have an excessively high cost which makes them little accessible to many industries that require its use .

Figure: System Model & Simulation Flow for Dc Motor Speed Control Matlab

In this paper to design and implementation speed control system of DC Motor based on PID control and Matlab Simulink, the motor is divided into two main parts the electrical part of the armature and the mechanical part [11, 12]. The armature is modelled as a circuit with resistance R connected in series to a conductor L, a source of voltage V and constant Kb of force against electromotive in the armature. The

128

mechanical part of the motor is the rotor which, when in motion, has a moment of inertia J, a Torque T, a viscous friction coefficient b, a position θ and an angular velocity bθ = ω . The PID controller is responsible for correcting the error it receives from the difference of the input signal and the output signal of the tachometer, the corrected error enters an amplification stage before entering the plant. In this paper the development of a speed and direction motor for an autonomous race robot is presented. Both controls use the PID control algorithm [13, 15-20].

Figure: System Model & Simulation Flow for Dc Motor Speed Control Matlab

The paper aims to provide a solution to the difficult access that economic conditions have for these automation technologies, developing an own speed control system for any DC motor that requires it, economically viable and applicable to any type of machine, of easy use and implementation in all types of industrial processes.

Figure: System Model & Simulation Flow for Dc Motor Speed Control Matlab

2.

The Basics Of Dc Motors

The history of the development of the construction of electric machines began in 1831 with the discovery of Faraday's law until the middle of the eighth decade of the last century. The DC motors are machines that convert electrical energy into mechanical energy, causing a rotary movement. There were several reasons for the prolonged popularity of dc motors. One was that DC power systems are common even in cars, trucks and airplanes. When a vehicle has a DC power system, it makes sense to use DC motors. DC motors were also applied when wide variations in speed were required. Before the widespread use of electronic power rectifier inverters, dc motors were not matched in speed control applications. Even if there were no dc power source, the solid-state rectifiers and the trimmer circuits were used to create the necessary power; dc motors were used to provide the desired speed control (induction motors with groups of solid-state controllers are now preferred for most speed control applications.) However, there are still applications where DC motors).

The dc motors are driven by a dc power source. Unless otherwise specified, it is assumed that the input voltage is constant, since this assumption simplifies the analysis of the motors and the comparison between the different types of them. There are five types of general purpose DC motors:



Independent excitation direct current motor.



Direct current motor in derivation.



Permanent magnet direct current motor.



Direct current motor in series.



Composite direct current motor. The Figure 1 show the full equivalent circuit of the dc motor. The equivalent circuit in Figure 1 is similar to the generator circuit only the current directions are different. The operation equations are, (1) is present the Armature voltage equation .

(1)

The induced motor voltage and motor speed vs angular frequency of the motor is present in (2). The combination is present in (3) and the output power and torque are present in (4).



Design and implementation speed control system of DC Motor based on PID ... (Salman Jasim Hammoodi)

(4)

3.

3.1. The Control Systems

Automatic control is of vital importance in the world of engineering. In addition to being essential in robotic systems or modern manufacturing processes, among others applications, has become essential in industrial operations such as pressure control, temperature, humidity and viscosity, and flow in the processing industries. Figure 2 shows a generic block diagram of a control system, in the Laplace domain.

Figure 2. The Block Diagram Of A Control System

Typically, the feedback contains a sensor or transducer element that measures a physical parameter, such as speed or temperature, and converts it into a voltage or current. The basic function of a controller is to compare the real value of the output of a plant c(t), with the reference input r(t) (desired value), determine the error e(t), and produce a control signal that will reduce the error to a value close to zero.

Figure 3 present the specifications for a control problem are often given in the time domain, and usually include a certain transient response and an error in state stationary, for a specific entry as is usually a step.

Figure 3. The specifications for a control problem One way to achieve this is by placing a transfer driver Gc (s), in the control loop, as shown in the Figure 3. The error signal E (s) is the input to the controller, and U (s) is the output of the same and at the same time the input to the plant, and the purpose of the controller is to make the output of the system follow the input. In Figure 4 we observe the different types of response according to the controller that is used.

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Figure 4. Response to the step of a closed-loop feedback system given by: (a) Controller P (b) Controller PD

3.2. The Pid Controllers Method

error is changing with respect to time. In this way, the controller can estimate future values of the error signal and compensate accordingly. It should be taken into account that even if the error is constant and the derivative term does not contribute, if it is variant in time this term can be used to reduce the offset called steady-state error. Another problem associated with the PD is that it works like a high-pass filter. Therefore, the PD controller amplifies the high frequency noise, which reduces the stability of the total system.

To eliminate the steady state error, an integral term is added. That term it gives the PID controller the ability to remember the past, also allowing an output non-zero for a null entry. So this controller allows to have a status error stationary equal to zero. In return, the integrator adds a pole in the function of closed loop, with which the stability of the system declines. From the above, the PID is an excellent controller. The

(5)

It should be clarified that if a mathematical model of the plant can be deduced, it is possible apply several techniques to determine the controller parameters, which comply with the transient and steady state specifications of the closed loop system. However, if the plant is so complicated that you cannot easily obtain your mathematical model, the analytical design model of the PID controller is possible. Then you have to resort to experimental procedures for the design of this type of controller. The process of select the parameters of the controller so that it meets the specifications of operation is known as tuning or tuning the controller. Ziegler and Nichols suggested rules for tuning PID controllers, that is, setting the values of Kp, Kd and Ki.

3.3. Types Of Pid Controllers

for PIDs The transfer functions for the different types of PID drivers are: a. PID not interacting or ideal form : is present in (6).

(6)

b. Interactive PID or series form : is present in (7).

(7)

c. PID parallel form : is present in (8).

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Figure: System Model & Simulation Flow for Ansys Airbag Injury Simulation

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

0.150

Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

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