Journal for Research| Volume 01| Issue 12 | February 2016 ISSN: 2395-7549
Position Control of Brushed DC Motor using PID controller in MATLAB Smeeta C. Maheriya PG student Department of Applied Instrumentation Atmiya Institute of Technology & Science, Rajkot, Gujarat, India
Hardik V. Kannad Assistant Professor Department of Instrumentation & control Atmiya Institute of Technology & Science, Rajkot, Gujarat, India
Abstract This research paper provides knowledge about the position control of Brushed DC motor. This motors are two wire control device. It has Replaceable brushes for extended its life. These motors are Simple and inexpensive as compare to other types of DC and AC motors. There is no required controller for fixed position operates. It is used in extreme environment due to lack of electronics. This motors are easy to drive, and are readily available in all sizes and shapes. These motors are used in various applications like Automated Guided Vehicle, Conveyer belt, Self-Guided Vehicle, home appliance and also in industries for real time application. Here, shows the mathematical modeling of Brushed DC motor and simulation of closed loop model of DC Brushed motor. For the Position control of DC motor in almost applications, PID controller is used. The PID controllers have a long history in control engineering and they have been proven to be robust, simple and stable for many real world applications. Roughly, P action is related to the present error, I action is based on the past history of error, and D action is related to the future behavior of the error. From estimation point of view P, D, and I correspond to filtering, smoothing and prediction problems respectively. This control mode is combination of the Proportional, the Integral, and the Derivative mode. This is most powerful but complex controller mode. It provides accurate and stable control of the three controller mode. It is recommended in system where the load changes frequently. Even complex industrial control systems may comprise a control network whose main control building block is a PID control module. The three-term PID controller has had a long history of use and has survived the changes of technology from the analogue era in to the digital computer control system age quite satisfactorily. It was the first (only) controller to be mass produced for the high-volume market that existed in the process industries. There are many types’ open loop and closed loop methods for tunning of PID controllers. here given the comparision of trial and error method, ZieglerNicholas Closed Loop method and good Gain method. Keywords: Brushed DC motor, MATLAB/Simulink, PID controller, Tunning Methods Nomenclatures: s=Laplace operator, ď ˇ = Natural frequency of oscillations, K= gain of the system, Km=Motor size constant, Kb=Back emf constant, J= Inertia of the motor, ess=steady state error, Z-N method= Ziegler Nichols method, , C(t)= time domain output response, Tr = Rising time, Mp= overshot in %, Ts= settling time, Ku=ultimate gain , Pu=ultimate time, Ti=integrated time , Td=differentiated time _______________________________________________________________________________________________________
I. INTRODUCTION A Brushed DC motors are an important machine in the most control systems such as electrical systems in trains, vehicles, homes, and process control system. It is well known that the mathematical model is very crucial in a control system design. For DC motor, there are many models which represent the machine behavior with a good accuracy. Although, the parameters of the model are also very important because the mathematical model can’t provide a correct behavior without correct parameters in of the model. A brushed DC motor is internally commutated electric motors designed to be run from a direct current power source. Brushed motors were the first commercially important application of electric power to driving mechanical loads, and DC distribution systems were used for few eras to operate motors in commercial and industrial buildings. PID control mode is combination of the Proportional, the Integral, and the Derivative mode. This is most powerful but complex controller mode. It provides accurate and stable control of the three controller mode. It is recommended in system where the load changes frequently. Three-term, PID controllers are most widely used industrial controller. In advance complex industrial control system may comprise a control network whose main control building block is a PID control module. The threeterm PID controller has had a long history of use and has survived the changes of technology from the analogue era in to the digital computer control system age quite satisfactorily. It was the first controller to be mass produced for the high-volume in market that existed in the process industries. The PID control remains an important control tools due to three reasons: past record of success, simplicity in use and, wide availability. Also in the case where the complexity of the process demand a multiloop or multivariable control solution, a network based on PID control building blocks is often used. In control system, different tuning methods have been proposed for PID controllers. Our purpose in this study is comparison of these tuning methods for single input and single output (SISO) systems using computer simulation. An Integral of the absolute value of the errors has been
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Position Control of Brushed DC Motor using PID controller in MATLAB (J4R/ Volume 01 / Issue 12 / 005)
used as the criterion for comparison. These tuning methods have been implemented for first order, second and third order systems with dead time and for two cases of set point tracking and load rejection.
II. MODELLING OF BRUSHED DC MOTOR A common actuator in control systems is the DC motor. Here given the modeling of armature voltage control of DC motor and field current is constant. It directly provides rotary motion and, coupled with wheels or drums and cables, can provide transitional motion. The electric circuit of the armature and the free body diagram of the rotor are shown in the following figure1:
Fig. 1: DC Motor Equivalent Circuit
Applying KVL to circuit, đ?‘‘đ?‘–đ?‘Ž đ?‘Ł = đ?‘…đ?‘Ž ∗ đ??źđ?‘Ž ∗ + đ??¸ đ?‘‘đ?‘Ą Since, field current is constant and flux will be constant, Now, when armature is rotating an e.m.f is Induce, đ??¸= đ?œ‘∗ đ?œ” đ??¸ = đ??žđ?‘? ∗ đ?œ” Here, w = angular velocity Kb = back e.m.f constant Now, torque delivered by the motor will be the product of the armature current and flux, đ?‘‡ đ?›ź đ?œ‘ ∗ đ?‘–đ?‘Ž đ?‘‡ = đ??ž ∗ đ?‘–đ?‘Ž Here, K is the motor torque constant The dynamic Torque equation with moment of inertia and co-efficient will be given as, đ?‘‘2đ?œƒ
(1)
(2) (3)
(4) (5)
đ?‘‘đ?œƒ
đ?‘‡=đ??˝âˆ— 2+ đ??ľâˆ— (6) đ?‘‘đ?‘Ą đ?‘‘đ?‘Ą Now, taking Laplace of equation no. (1), (4), (5), (6) đ?‘‰ (đ?‘ ) − đ??¸ (đ?‘ ) = đ??źđ?‘Ž (đ?‘ ) ∗ (đ?‘…đ?‘Ž + đ?‘ ∗ đ??żđ?‘Ž) (7) đ??¸(đ?‘ ) = đ??žđ?‘? ∗ đ?‘ ∗ đ?œƒ(đ?‘ ) (8) đ?‘‡(đ?‘ ) = đ??ž ∗ đ??źđ?‘Ž(đ?‘ ) (9) đ?‘‡(đ?‘ ) = (đ?‘ 2 ∗ đ??˝ + đ?‘ ∗ đ??ľ) ∗ đ?œƒ(đ?‘ ) (10) đ?‘‡(đ?‘ ) = (đ?‘ ∗ đ??˝ + đ??ľ)đ?‘ ∗ đ?œƒ(đ?‘ ) (11) Here, the transfer function Model [4] shows in Figure.2. Which is shows that the input voltage V (s) , to the output angle (position) θ, directly follows : đ?œƒ(đ?‘ ) đ??ž = (đ?‘…đ?‘Ž+đ?‘ ∗đ??żđ?‘Ž)(đ??˝âˆ—đ?‘ +đ??ľ)đ?‘ +đ??žâˆ—đ??žđ?‘?∗đ?‘ (12) đ?‘‰(đ?‘ )
Fig. 2: Block diagram of DC motor Transfer function Model
As above given transfer function we can find the speed and position of motor. For the modeling of DC motor Its physical parameters are required. The modeling of motor is very important for the control of motor [1]. All rights reserved by www.journalforresearch.org
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Position Control of Brushed DC Motor using PID controller in MATLAB (J4R/ Volume 01 / Issue 12 / 005)
Serial No. 1. 2. 3. 4. 5. 6.
Table - 1 Physical Parameters of Motor Physical Parameter Symbol Quantity Input voltage V 6V Motor Inductance La 0.5 H Armature Resistance Ra 2 Ohm Motor inertia J 0.03 Kg.m2 Torque Constant Ka 0.01 N.m/Amp Damping Co-efficient B 0.1 N.m.s/rad
III. PID CONTROLLER PID controllers are designed from 1890. PID controllers were subsequently developed in automatic ship steering. One of the earliest examples of a PID type controller was developed by Elmer Sperry in 1911, when the first published theoretical analysis of a three term controller was by Russian American engineer Nicolas Minorsky, (Minorsky 1922). Minorsky was designing automatic steering systems for the US Navy, and based his analysis on observations of a helmsman, noting the helmsman controlled the ship based not only on the current error, and also on past error as well as the rate of change current; this was then made mathematical by Minorsky. His goal was the stability, not a general control, which was simplified the problem significantly. While proportional control provides stability against the small disturbances, it was insufficient for dealing with a steady state disturbance, notably a stiff gale (due to the droop), which was required adding the integral term. Finally, the derivative term was added for improve stability and control [7]. Trial and Error Method: The gain of the PID controller is obtained using trial and error method. In this method, the I and D terms are set to be Zerofirst and the proportional gain is increased until the output of the loop oscillates. As once increase the proportional gain the system becomes faster but care must be taken not make the system unstable .once P has been set to obtain a desired fast response, the integral term is increased to stop the oscillation. The integral term reduce the steady state error but increase the overshoot. Once P and I have been set to get the desired fast control system with minimum steady state error the derivative term is increased until the loop is acceptably quick to set point. Increase derivative term decreases the overshoot and cause higher gain with stability but would cause the system to be highly sensitive to noise. Ziegler-Nicholas Tuning Method: There are a range of methods for PID tuning available. Ziegler-Nichols Method typically used for PID tuning. Two classical methods for determining the parameter of PID controllers were Present by Ziegler and Nichols in 1942.These method is still widely used, either in their original or in some modification form. They often from the basis for tuning procedures used by controller manufacture and process industries. Table shows the value of Kp, Ti, and Td using Ziegler-Nicholas steps to design Ziegler-Nicholas tunning method is given below. Here, Ku =0.2 (ultimate gain) and Pu=1.21sec (ultimate period) which is find out using Routh-hurwitz Criterian. Table - 1 Ziegler Nichols Tuning Rules Type of controller Kp Ti Ku/2 P Controller Ku/2.2 Pu/1.2 PI Controller Ku/1.7 Pu/2 PID controller
Td Pu/8
Good gain Mehod: The Good Gain method is a simple, experimental method which can be used on a real process or simulated system The Good Gain method aims at giving the control loop better stability than what the famous Ziegler-Nichols’ methods are, the Closed-loop method and the Open-loop method . The Ziegler-Nichols’ methods are designed to give an amplitude ratio between subsequent oscillations after a step change of the set point equal to 1/4 (“one-quarter decay ratio”). This is often regarded as poor stability. The Good Gain method gives better stability. Furthermore, the Good Gain method does not require the control loop to get into oscillations during the tuning, which is another benefit compared with the Ziegler-Nichols’ methods. Here, gives the steps to design Good Gain tuning method. Here, KpGG = 0.12 where, KpGG is the Kp of Ziegler- Nicholas tuning method and T ou = 0.22 sec where, Tou is the time between the overshoot and the undershoot of the step response (a step in the set point) with the P controller.values of Kp,Ti, and Td is show in Table.3: Table - 3 Tunning Rules of Good Gain method Type of Controller PID controller
Kp 0.8 KpGG
Ti 1.5 Tou
Td Ti/4
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Position Control of Brushed DC Motor using PID controller in MATLAB (J4R/ Volume 01 / Issue 12 / 005)
IV. PID CONTROLLER As per explained above figure gives comparison of the position control of brushed DC motor model using different type of PID tuning methods in MATLAB/simulink library. Here, shows the output signal is tracking the input signal and reducing the steady state error and make system stable. In the simulation work there is given 6V step signal as an input.
Fig. 3: Position control of Brushed DC motor model using PID methods
Fig. 4: Comparison response of different tuning methods
According to the simulation in the matlab we can measure the steady state and transient parameter of the system.the values of this parameter with different tuning methods is given below in table: Table – 4 Resultant values of Brushed DC motor model using PID controller methods Parameter of system Without controller Trial and error method Ziegler-Nicholas method Overshoot in (Mp) % 73 % 36.6 % 24.6 % Steady State error 0.8 volt 0.65 volt 0.2 volt Setling Time (Ts) 1.05 sec 0.95 sec 0.22 sec Rise Time (Tr) 0.03 sec 0.111 sec 0.010 sec
Good Gain method 20.5 % 0.19 volt 0.215 sec 0.01 sec
V. CONCLUSION The present research paper elaborates the simulation of the Brushed DC motor model system in MATLAB/SIMULINK. Main aim of this work is to reduce steady state error, less settling time, and less overshoot. Moreover, its gives information about different types of PID tuning methods. These methods are more suitable for the set point tracking as per the input values. All rights reserved by www.journalforresearch.org
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Position Control of Brushed DC Motor using PID controller in MATLAB (J4R/ Volume 01 / Issue 12 / 005)
According to simulation result we can concluded that the Good Gain method is more suitable then the Ziegler-Nicholas tunnning method. A proportional–integral–derivative controller (PID controller) is a generic feedback controller (Thomas. B, 2004). It can be used whenever a mean position has to be achieved but the controls of the system do not react instantaneously and accurately. The PID algorithm, takes in account the following three things are to be taken in account- the existing error, the time the system has stayed away from the mean position and the possibility of overshooting the mean position. Using these three quantities, the system is controlled better, allowing it to reach the mean position faster and without over shooting it.
ACKNOWLEDGMENT This is the time to express my deep sense of gratitude to my college, Atmiya Institute of Technology & Science, Rajkot & Gujarat Technological University for providing me a great opportunity to prepare this research work. I am humbly expressing thanks to my respected guide Prof. Mr. Hardik V. Kannad forgive me his valuable time and constant help give to me, from the concept stage to this stage. I would like to thanks Head of Instrumentation and control Engineering Department, Dr. Komal R. Borisagar for Her precious help & guidance who always bears and motivate me with technical guidance throughout this semester period. Also I would like to thank to the other respected faculties of department and my respected sir Mr. Priyam A. parikh. Most importantly, I would like to thank My Friends and My Parents, my for their inspiration and ever encouraging moral support and for everything that they have done for me throughout my life. Much of my success has been because of their love & encouragement.
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