NCEEERE 2008, Sikkim Manipal Institute of Technology, Sikkim – 737 132, INDIA
Mathematical Modeling & Simulation of DC Servomechanism Using MATLAB/SIMULINK and Their Integration into Undergraduate Control Engineering Courses P. M. Menghal Abstract-Today, with the advent of computers and various easily accessible software packages, computer aided teaching tools have become an essential part of both classroom lectures and laboratory experiments in any kind of education curriculum. The computational tools, as a part of control engineering laboratory experiments, enhance lab experience by providing students with the opportunity to verify the results of the experiments and to compare them with those obtained by computer aided simulations. A case is made for the use of MATLAB/SIMULINK as a teaching and research tools in engineering education. This paper will also emphasize on the use of mathematical modeling and simulation of DC Servo Mechanism and study of their behaviour by using the MATLAB/SIMULINK models and Graphical User Interface (GUI).[1-2] As the user can change the parameters of the systems as per his choice or required condition, this computational tool as a part of laboratory experiments will enhance laboratory experience by providing students with the opportunity to compare the results of laboratory experiments with those obtained by computer simulation. Such an opportunity helps students of all courses realise the limitations of hardware
C. S. Kudarihal
II. MATHEMATICAL MODELING AND SIMULATION A DC servomechanism (ES-130) is a device used to provide control of a desired operation through the use of feedback. Servos are commonly electrical or partially electronic in nature, using an electric motor as the primary means of creating mechanical force. The experimental setup of DC Servomechanism is shown in fig 1
Keywords: DC Servomechanism, GUI, MATLAB/SIMULINK I. INTRODUCTION
A
virtual laboratory for Automatics and Control Engineering can provide university students with easy access to engineering applications at anytime and from any computing environment. This interactive learning environment, consisting of simulations, demonstrations and exercises, can fulfill the role of a bridge from passive learning to active engagement and thus stimulate deeper thinking; grounding a problem based-learning environment. The applications are also very important for relating theory to practice, so that the students can develop engineering judgment and understand how process behavior can be captured using mathematical models. The undergraduate control engineering at engineering colleges is based on a strong “hands-on” laboratory experience. Regardless of how many fine lectures are given or how many homework problems assigned, the students do not see how control systems work in the real world until they get into the laboratory. [3]They do not understand that they can modify the performance of a physical system to meet design specifications. Only after they complete the laboratory course do they understand the power that they have to become “control gods.” After completing the lab experiments on virtual laboratory, the students first characterize the performance of a second order system (a dc servomechanism ES-130).This paper describes the mathematical modeling of DC Servomechanisms (ES-130) and study of their behaviour by using MATLAB/SIMULINK model and GUI. A graphical user interface is developed which is user friendly and not required the knowledge of Matlab.
Fig (1) Experimental setup of DC Servomechanism This experimental setup has following main components: (i) DC Servomotor (ii) Tachogenerator (iii) Input & output Potentiometer (iv) Reduction gears (v) Flexible coupling (vi) Input & Output shafts The mathematical modeling of DC servo motor in armature control and field control mode has been carried out by writing the differential equation as follows : e – La dia/dt –Ra ia - eb = 0 (1) T α Ø Ia (2) T = Jd2θ/dt2 + fodθ/dt (3) eb = Kbω (4) The simulated model after doing mathematical modeling for DC servomechanism (ES130) in armature controlled and field control mode are shown in fig 2(a) and (b)
NCEEERE 2008, Sikkim Manipal Institute of Technology, Sikkim – 737 132, INDIA
1 Step Input
2.5
Polarity
Amp
Gear Ratio
Rad Speed
Tm
1
600
2s+7
In1
1/16
Out1
DC motor
Ia
1
1
In1
Angle
5s+4
s
TF2
Integrator
Kt
TF1
1
Output
1 Out1
(b) Field Controlled mode Fig-(4) Characteristics of DC Servomechanism
0.045 Kb
1
1
If
Tm
3s+5
In1
1
5 Kt
TF1
Speed
1
Angle 1
s+1
s
TF2
Integrator
Out1
Fig -2 Simulink Model for DC Servomechanism (a) Simulink model for Armature control of DC motor (b) Simulink model for Field control of DC motor The simulated model can be used to perform following experiments: (i) Open Loop (ii) Closed Loop (iii) Characteristics of DC servo motors. (iv) Frequency Response (v) PID Control and (vi) System Time Constant. The developed simulation model of closed loop system with PID controller is shown in fig.3
du/dt
4
(b) Field Controlled mode
Summer Derivative D-Gain 1
1
Step Input Polarity
P-Gain
2.5 Add
In1
Out1
Amp DC motor
1 s
(a) Armature Controlled mode
1/16 Gear Ratio
Output
Fig-(5) Characteristics of DC Servomechanism with PID Controller
.5
Integrator I-Gain 0.76 Tacho
Fig-(3) The Simulink model Servomechanism with PID controller. III. RESULTS & ANALYSIS The characteristics of the DC servo mechanism for different experiments are shown in fig.4 and 5
(a) Armature Controlled mode
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The following inferences are drawn from the simulation results of DC Servomechanism: (i) In Armature Controlled mode characteristics, it is observed that for increase in input voltage the output response (i.e. Angular Displacement, Speed and Torque) also increases and reaches its steady state value faster. (ii) In filed control mode the response is oscillatory and takes more settling time to reach the steady state value. (iii) By using PID controller the transient as well as steady state response improves. (iv) As seen from the graphs in Fig(6), when a step input is given to field controlled motor, a large time constant (11 sec) is obtained, shows a sluggish system and in case of Armature controlled motor, a small time constant (6 sec) is obtained corresponds to a fast response as shown in fig. 6(a)
NCEEERE 2008, Sikkim Manipal Institute of Technology, Sikkim – 737 132, INDIA (k) A button to see the SIMULINK diagram of DC Servomechanism in both the modes. (m) Menu bar to see different values in the graph, to zoom in/out and other controls. (n) A course ware for each experiment is prepared and successfully integrated in to the control engineering laboratory at Radar and Control Engg.Dept.Faculty of Electronics, Military College of Electronics & Mechanical Engineering, Secunderabad .
Maximum Speed Response of motor
8
14 (a) Armature Control
Maximum Speed Response of motor
8
19 (a) Field Control Fig-(6) Determination of time constant
Fig (7) Simulated DC Servomechanism
V. THE EDUCATIONAL USE OF THE MODELS
IV. NOTABLE FEATURES OF DC SERVOMECHANISM SIMULATION MODEL The DC Servomechanism Simulation Model with graphical user interface is shown in fig 6 .It consists of the complete detail of mathematical modeling using the modules available in SIMULINK for open loop, close loop, PID control, frequency response and system time constant experiments in both armature controlled and field controlled mode. Then the programming of each selected module was carried out. For the ease of the user a graphical user interface was modeled for all the above said experiments on a single platform. The platform includes: (a) Buttons to perform all the experiments. (b) Controls to change the system parameters. (c) View the results of the experiments in the graphical form. (d) Compare system response for angular displacement, speed and torque of different experiments performed in armature and field controlled motors. (e) A menu bar on activation of which brief description along with the transfer function of the experiments performed can be viewed. (f) A menu bar to simulate directly the SIMULINK circuits diagrams and see the results in separate window. (g) SIMULINK diagram of the current experiment. (h) An EXIT button to come out of the GUI page of project. (j) A refresh button to clear all the graphs and diagram displayed earlier.
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DC Servomechanisms is very useful for performing experiments and understanding the basic concepts of feedback systems in the control system laboratory. Its is a fundamental system useful to any course of instruction including basic subjects in electronics and Electrical Engg at undergraduate courses. The MATLAB/SIMULINK models and GUI representation of closed loop, open loop, PID Control, etc of ES-130 servo system will definitely work as teaching tool and support the classroom teaching by enabling the instructor, through the computer-generated graphics, to illustrate transient and steady-state performance and stability analysis of control system under various parameter controls. The user can change the parameters of the systems as per his choice or required condition, thus this computational tool as a part of laboratory experiments will enhance laboratory experience by providing students with the opportunity to compare the results of laboratory experiments with those obtained by computer simulation. Such an opportunity helps students of all courses realise the limitations of hardware. VI. CONCLUSION The MATLAB/SIMULINK models and GUI representation of DC servo system will definitely work as teaching tool and support the classroom teaching by enabling the instructor, through the computer-generated
NCEEERE 2008, Sikkim Manipal Institute of Technology, Sikkim – 737 132, INDIA graphics. As the user can change the parameters of the systems as per his choice or required condition, this computational tool as a part of laboratory experiments will enhance laboratory experience by providing students with the opportunity to compare the results of laboratory experiments with those obtained by computer simulation. Such an opportunity helps students of all courses realise the limitations of hardware. A Virtual laboratory for Automatic Control (AC) allows students an easy access to different applications, simulations related to the theory they study. These interactive demos present in a tutorial manner the influence of the different parameters of the mathematical model to the system behavior. These simulations provide a more intuitive and more practical approach for the abstract theory of AC. The advantage of the approach presented here is the use of the available simulations tools. The user can focus on the learning and understanding of problems and concepts, as he/she doesn’t have to master the Matlab programming environment. APPENDIX The parameter of ES-130 DC Servo mechanism Kt = 600 Kb = 0.045 Ra = 7 ohm La = 2 H
fo = 4
J=5
REFERENCES [1] Saffet Ayasun, Chika O. Nwankpa “Induction motor tests using MATLAB/SIMULINK and their integration in to undergraduate electric machinery courses” IEEE Transactions on education, vol 48 No.1Feb 2005 pp 37-46. [2] O. I. Okoro C.U. Ogbuka M.U.Agu “Simulation of D.C. machines transient behaviours : Teaching and Research” Pacific journal of science and technology vol.9 No.-1 MayJune 2008 pp.142-148. [3] Erin Harley ,G.R.Loftus “MATLAB and graphical user interfaces: Tools for experimental management” Behaviour Research Methods, Instruments and Computers 2000 vol 32(2) pp 290-296. [4] M. Javed, H. Aftab, M.Qasim, M.Sittar “RLC Circuit response and Analysis (using State Space Method)” International journal of computer science and network security vol.8.No.4 April 2008 pp-48-54.
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P.M.Menghal is working as a faculty in Radar and Control System Department, Faculty of Electronics, Military College of Mechanical Engineering, Secunderabad, A.P., India. He received Master Degree in Control Systems, from Government College of Engineering, Pune,University of Pune. He is a Member of Institute of Engineers (MIE), India and Life member of Indian Society of Technical Education(ISTE). His current research interest are in the areas of Control system, Mathematical Modeling and Simulation. Email :
[email protected] C S Kudarihal is working as a faculty in Radar and Control System Department, Faculty of Electronics, Military College of Mechanical Engineering, Secunderabad, A.P., India. He received Master of Technology in Energy Systems Engineering, from Visveshwaraih Technological University, Belgaum, Karnataka. He is a member of instate of engineers (MIE), India and life member of Indian Society of Technical Education (ISTE). His research is focused on Microcontrollers, Embedded Systems and Energy management.
