This document describes a lab experiment where students modeled a motor/flywheel system using LabVIEW. They collected data for sinusoidal and square voltage waveforms and compared the experimental model to a theoretical model based on motor specifications. Key aspects of the comparison included transfer functions, step responses, and Bode plots. Students determined parameter values, created VIs to collect experimental data, and analyzed results to compare experimental and theoretical models.
MODELLING AND SIMULATION OF INVERTED PENDULUM USING INTERNAL MODEL CONTROLJournal For Research
The internal model control (IMC) philosophy relies on the internal model principle, which states that control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled. In particular, if the control scheme is developed based on an exact model of the process, then perfect control is theoretically possible. Transfer function of Inverted Pendulum is selected as the base of design, which examines IMC controller. Matlab/simulink is used to simulate the procedures and validate the performance. The results shows robustness of the IMC and got graded responses when compared with PID. Furthermore, a comparison between the PID and IMC was shows that IMC gives better response specifications.
MODELLING AND SIMULATION OF INVERTED PENDULUM USING INTERNAL MODEL CONTROLJournal For Research
The internal model control (IMC) philosophy relies on the internal model principle, which states that control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled. In particular, if the control scheme is developed based on an exact model of the process, then perfect control is theoretically possible. Transfer function of Inverted Pendulum is selected as the base of design, which examines IMC controller. Matlab/simulink is used to simulate the procedures and validate the performance. The results shows robustness of the IMC and got graded responses when compared with PID. Furthermore, a comparison between the PID and IMC was shows that IMC gives better response specifications.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
This project was developed for an Embedded systems class: we implemented a PID controller for a mechanical inverted pendulum. It was very interesting to experiment in practice with a simple control plant.
Applying Parametric Functional Approximations for Teaching Electromechanical ...IOSRJEEE
In this paper functional approximations for the parameters of a DC machine are proposed. These nonlinear algebraic approximations are based on the experimental data that are obtained by carrying out several steady state and transient tests, besides, this method links mathematics and practical analysis of electromechanical systems, allowing students to improve their academic performance and comprehension by comparing estimated values with measured data. An excellent dynamic model results of combining the well known state space description and these parametric functional approximations. This augmented model provides reliable results even during demanding large-excursion transient conditions
Mathematical model analysis and control algorithms design based on state feed...hunypink
XZ-Ⅱtype rotary inverted pendulum is a typical mechatronic system; it completes real-time motion control using DSP motion controller and motor torque. In this paper, we recognize XZ-Ⅱrotational inverted pendulum and learn system composition, working principle, using method, precautions and software platform. We master how to build mathematical model and state feedback control method (pole assignment algorithm) of the one order rotational inverted pendulum system and finish simulation study of system using Mat lab. In the end we grasp debugging method of the actual system, and finish online control of the one order rotational inverted pendulum system as well.
Linear quadratic regulator and pole placement for stabilizing a cart inverted...journalBEEI
The system of a cart inverted pendulum has many problems such as nonlinearity, complexity, unstable, and underactuated system. It makes this system be a benchmark for testing many control algorithm. This paper presents a comparison between 2 conventional control methods consist of a linear quadratic regulator (LQR) and pole placement. The comparison indicated by the most optimal steps and results in the system performance that obtained from each method for stabilizing a cart inverted pendulum system. A mathematical model of DC motor and mechanical transmission are included in a mathematical model to minimize the realtime implementation problem. From the simulation, the obtained system performance shows that each method has its advantages, and the desired pendulum angle and cart position reached.
LMI based antiswing adaptive controller for uncertain overhead cranes IJECEIAES
This paper proposes an adaptive anti-sway controller for uncertain overhead cranes. The state-space model of the 2D overhead crane with the system parameter uncertainties is shown firstly. Next, the adaptive controller which can adapt with the system uncertainties and input disturbances is established. The proposed controller has ability to move the trolley to the destination in short time and with small oscillation of the load despite the effect of the uncertainties and disturbances. Moreover, the controller has simple structure so it is easy to execute. Also, the stability of the closed-loop system is analytically proven. The proposed algorithm is verified by using Matlab/ Simulink simulation tool. The simulation results show that the presented controller gives better performances (i.e., fast transient response, no ripple, and low swing angle) than the state feedback controller when there exist system parameter variations as well as input disturbances.
Troubleshooting and Enhancement of Inverted Pendulum System Controlled by DSP...Thomas Templin
An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart-and-pole system. A normal pendulum is always stable since the pendulum hangs downward, whereas the inverted pendulum is inherently unstable and trivially underactuated (because the number of actuators is less than the degrees of freedom). For these reasons, the inverted pendulum has become one of the most important classical problems of control engineering. Since the 1950s, the inverted-pendulum benchmark, especially the cart version, has been used for the teaching and understanding of the use of linear-feedback control theory to stabilize an open-loop unstable system.
The objectives of this project are to:
• Focus on hardware and software troubleshooting and enhancement of an inverted-pendulum system controlled by a DSP28355 microprocessor and CCSv7.1 software.
• Use the swing-up strategy to move the pendulum into the unstable upward position (‘saddle’). The cart/pole system employs linear bearings for back-and-forward motion. The motor shaft has a pinion gear that rides on a track permitting the cart to move in a linear fashion. Both rack and pinion are made of hardened steel and mesh with a tight tolerance. The rack-and-pinion mechanism eliminates undesirable effects found in belt-driven and free-wheel systems, such as slippage or belt stretching, ensuring consistent and continuous traction.
• The motor shaft is coupled to a high-resolution optical encoder that accurately measures the position of the cart. The angle of the pendulum is also measured by an optical encoder, and the system employs an LQR controller to stabilize the pendulum rod at the unstable-equilibrium position.
• Addition of real-time status reporting and visualization of the system.
For the project, the Quanser High Frequency Linear Cart (HFLC) was used. The HFLC system consists of a precisely machined solid aluminum cart driven by a high-power 3-phase brushless DC motor. The cart slides along two high-precision, ground-hardened stainless steel guide rails, allowing for multiple turns and continuous measurement over the entire range of motion.
Our team implemented a control strategy that consists of a linear stabilizing LQR controller, proportional-integral swing-up control, and a supervisory coordinator that determines the control strategy (LQR or swing-up) to be used at any given time. The function of the linear stabilizer is to stabilize the system when it is in the vicinity of the unstable equilibrium. When the pendulum is in its natural state (straight-down stable-equilibrium node), the swing-up controller provides the cart/pendulum system with adequate energy to move the pendulum to the unstable equilibrium inside the “region of attraction” in which the linearized LQR controller is functional.
Transfer Function and Mathematical Modeling
Transfer Function
Poles And Zeros of a Transfer Function
Properties of Transfer Function
Advantages and Disadvantages of T.F.
Translation motion
Rotational motion
Translation-Rotation counterparts
Analogy system
Force-Voltage analogy
Force-Current Analogy
Advantages
Example
Transient three dimensional cfd modelling of ceilng fanLahiru Dilshan
Ceiling fans are used to get thermal comfort, especially in tropical countries. With the increment of the usage of air conditioners, the emission of CO2 is increased. But ceiling fans are a limited solution, that saves much energy compared to air conditioners. Ceiling fans generate a non-uniform velocity profile, so that, there is a non-uniform thermal environment. That non-uniform environment does not imply lower thermal comfort, that will give enough thermal comfort with low energy cost by air velocity. Hence, there will be difficulties of analysing with simple modelling techniques in that environment. So, to predict the performance of the ceiling fan required more accurate models.
The accurate model of a ceiling fan will generate complex geometry that makes difficulties for the simulation process and requires higher computational power. Because of that, there are several methods used to predict the performance of the ceiling fan using mathematical techniques but that will give an estimated value of properties in the surrounding.
Мета заходу: ознайомити учнів 7 класу з творчою індивідуальністю Анатолія Свидницького — українського письменника-просвітителя, громадського діяча; прищепити почуття любові до літератури,пошани культурної спадщити; сформувати високі ідеали моральності,відповідальності за культурні надбання народу.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
This project was developed for an Embedded systems class: we implemented a PID controller for a mechanical inverted pendulum. It was very interesting to experiment in practice with a simple control plant.
Applying Parametric Functional Approximations for Teaching Electromechanical ...IOSRJEEE
In this paper functional approximations for the parameters of a DC machine are proposed. These nonlinear algebraic approximations are based on the experimental data that are obtained by carrying out several steady state and transient tests, besides, this method links mathematics and practical analysis of electromechanical systems, allowing students to improve their academic performance and comprehension by comparing estimated values with measured data. An excellent dynamic model results of combining the well known state space description and these parametric functional approximations. This augmented model provides reliable results even during demanding large-excursion transient conditions
Mathematical model analysis and control algorithms design based on state feed...hunypink
XZ-Ⅱtype rotary inverted pendulum is a typical mechatronic system; it completes real-time motion control using DSP motion controller and motor torque. In this paper, we recognize XZ-Ⅱrotational inverted pendulum and learn system composition, working principle, using method, precautions and software platform. We master how to build mathematical model and state feedback control method (pole assignment algorithm) of the one order rotational inverted pendulum system and finish simulation study of system using Mat lab. In the end we grasp debugging method of the actual system, and finish online control of the one order rotational inverted pendulum system as well.
Linear quadratic regulator and pole placement for stabilizing a cart inverted...journalBEEI
The system of a cart inverted pendulum has many problems such as nonlinearity, complexity, unstable, and underactuated system. It makes this system be a benchmark for testing many control algorithm. This paper presents a comparison between 2 conventional control methods consist of a linear quadratic regulator (LQR) and pole placement. The comparison indicated by the most optimal steps and results in the system performance that obtained from each method for stabilizing a cart inverted pendulum system. A mathematical model of DC motor and mechanical transmission are included in a mathematical model to minimize the realtime implementation problem. From the simulation, the obtained system performance shows that each method has its advantages, and the desired pendulum angle and cart position reached.
LMI based antiswing adaptive controller for uncertain overhead cranes IJECEIAES
This paper proposes an adaptive anti-sway controller for uncertain overhead cranes. The state-space model of the 2D overhead crane with the system parameter uncertainties is shown firstly. Next, the adaptive controller which can adapt with the system uncertainties and input disturbances is established. The proposed controller has ability to move the trolley to the destination in short time and with small oscillation of the load despite the effect of the uncertainties and disturbances. Moreover, the controller has simple structure so it is easy to execute. Also, the stability of the closed-loop system is analytically proven. The proposed algorithm is verified by using Matlab/ Simulink simulation tool. The simulation results show that the presented controller gives better performances (i.e., fast transient response, no ripple, and low swing angle) than the state feedback controller when there exist system parameter variations as well as input disturbances.
Troubleshooting and Enhancement of Inverted Pendulum System Controlled by DSP...Thomas Templin
An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart-and-pole system. A normal pendulum is always stable since the pendulum hangs downward, whereas the inverted pendulum is inherently unstable and trivially underactuated (because the number of actuators is less than the degrees of freedom). For these reasons, the inverted pendulum has become one of the most important classical problems of control engineering. Since the 1950s, the inverted-pendulum benchmark, especially the cart version, has been used for the teaching and understanding of the use of linear-feedback control theory to stabilize an open-loop unstable system.
The objectives of this project are to:
• Focus on hardware and software troubleshooting and enhancement of an inverted-pendulum system controlled by a DSP28355 microprocessor and CCSv7.1 software.
• Use the swing-up strategy to move the pendulum into the unstable upward position (‘saddle’). The cart/pole system employs linear bearings for back-and-forward motion. The motor shaft has a pinion gear that rides on a track permitting the cart to move in a linear fashion. Both rack and pinion are made of hardened steel and mesh with a tight tolerance. The rack-and-pinion mechanism eliminates undesirable effects found in belt-driven and free-wheel systems, such as slippage or belt stretching, ensuring consistent and continuous traction.
• The motor shaft is coupled to a high-resolution optical encoder that accurately measures the position of the cart. The angle of the pendulum is also measured by an optical encoder, and the system employs an LQR controller to stabilize the pendulum rod at the unstable-equilibrium position.
• Addition of real-time status reporting and visualization of the system.
For the project, the Quanser High Frequency Linear Cart (HFLC) was used. The HFLC system consists of a precisely machined solid aluminum cart driven by a high-power 3-phase brushless DC motor. The cart slides along two high-precision, ground-hardened stainless steel guide rails, allowing for multiple turns and continuous measurement over the entire range of motion.
Our team implemented a control strategy that consists of a linear stabilizing LQR controller, proportional-integral swing-up control, and a supervisory coordinator that determines the control strategy (LQR or swing-up) to be used at any given time. The function of the linear stabilizer is to stabilize the system when it is in the vicinity of the unstable equilibrium. When the pendulum is in its natural state (straight-down stable-equilibrium node), the swing-up controller provides the cart/pendulum system with adequate energy to move the pendulum to the unstable equilibrium inside the “region of attraction” in which the linearized LQR controller is functional.
Transfer Function and Mathematical Modeling
Transfer Function
Poles And Zeros of a Transfer Function
Properties of Transfer Function
Advantages and Disadvantages of T.F.
Translation motion
Rotational motion
Translation-Rotation counterparts
Analogy system
Force-Voltage analogy
Force-Current Analogy
Advantages
Example
Transient three dimensional cfd modelling of ceilng fanLahiru Dilshan
Ceiling fans are used to get thermal comfort, especially in tropical countries. With the increment of the usage of air conditioners, the emission of CO2 is increased. But ceiling fans are a limited solution, that saves much energy compared to air conditioners. Ceiling fans generate a non-uniform velocity profile, so that, there is a non-uniform thermal environment. That non-uniform environment does not imply lower thermal comfort, that will give enough thermal comfort with low energy cost by air velocity. Hence, there will be difficulties of analysing with simple modelling techniques in that environment. So, to predict the performance of the ceiling fan required more accurate models.
The accurate model of a ceiling fan will generate complex geometry that makes difficulties for the simulation process and requires higher computational power. Because of that, there are several methods used to predict the performance of the ceiling fan using mathematical techniques but that will give an estimated value of properties in the surrounding.
Мета заходу: ознайомити учнів 7 класу з творчою індивідуальністю Анатолія Свидницького — українського письменника-просвітителя, громадського діяча; прищепити почуття любові до літератури,пошани культурної спадщити; сформувати високі ідеали моральності,відповідальності за культурні надбання народу.
Check out the blog post on the importance of building your content marketing destination:
http://marketinginsidergroup.com/content-marketing/content-marketing-destination/
A content hub is a valuable way of interacting with your customers and connecting them with information, ideas, images, and stories. Once you have this content to pass along, you need a place to house it all. Somewhere that is capable of handling a constant feed of new content, from a variety of sources, covering a variety of topics, while still looking aesthetically pleasing and functioning so well that a customer will want to spend hours browsing what it has to offer.
This isn’t an easy task, but one that will be simplified and attainable after reading this guide. The guide is split into four sections, two dealing with your main hub page and two dealing with your specific article page. For both page types the guide is split into a form and function section. Form being your most basic layout, the pieces you need for the page and how to handle them stylistically. Function guides you through how a user will experience each page and the added elements to help improve this experience.
Each suggestion is analyzed on its own page and is accompanied by a screenshot of a site that demonstrates the topic. If you want to explore the entirety of the site, you can click the magnifying glass in the upper left corner of the screenshot on each example page to launch the full site on your browser.
Check it out and less us know what you think?
Sharepoint implementation quick points to graspNeha Rai
SharePoint Implementation- some key factors to be considered for successful results. #SharePoint
if you are looking for SharePoint new/ongoing development/maintenance where we can assist you. Please reach to us for getting experts assistance. Share your feedbacks on email: Neha.rai@adapt-india.com.
Field-Oriented Control of PMSM Drive Based on SVPWM Using MATLABIJERA Editor
The space vector PWM has the character of wide linear range, little higher harmonic and easy digital
realization. The FOC theory and SVPWM technique make the PMSM can achieve the performance as well as
DC motor. The mathematical model of PMSM is analyzed and the system model of FOC vector control has
been established. The control system has been also simulated by MATLAB/Simulink. The simulation results
accord with the real motor’s performance and provide the theory basis for the designing of real system.
A Novel Direct Torque Control for Induction Machine Drive System with Low Tor...IAES-IJPEDS
The conventional Direct Torque Control (DTC) is known to produce a quick and robust response in AC drives. However, during steady state, stator flux and electromagnetic torque which results in incorrect speed estimations and acoustical noise. A modified Direct Torque Control (DTC) by using Space Vector Modulation (DTC-SVM) for induction machine is proposed in this paper. Using this control strategy, the ripples introduced in torque and flux are reduced. This paper presents a novel approach to design and implementation of a high perfromane torque control (DTC-SVM) of induction machine using Field Programmable gate array (FPGA). The performance of the proposed control scheme is evaluated through digital simulation using Matlab\Simulink and Xilinx System Generator. The simulation results are used to verify the effectiveness of the proposed control strategy.
The experiment is on the DC motor modelling along with DC motor validation. The system of DC analysed in this experiment by the connection of hardware and software. The bump test method is done which depends on responses of the stable system.
A NEW FUZZY LOGIC BASED SPACE VECTOR MODULATION APPROACH ON DIRECT TORQUE CON...csandit
The induction motors are indispensable motor types for industrial applications due to its wellknown
advantages. Therefore, many kind of control scheme are proposed for induction motors
over the past years and direct torque control has gained great importance inside of them due to
fast dynamic torque response behavior and simple control structure. This paper suggests a new
approach on the direct torque controlled induction motors, Fuzzy logic based space vector
modulation, to overcome disadvantages of conventional direct torque control like high torque
ripple. In the proposed approach, optimum switching states are calculated by fuzzy logic
controller and applied by space vector pulse width modulator to voltage source inverter. In
order to test and compare the proposed DTC scheme with conventional DTC scheme
simulations, in Matlab/Simulink, have been carried out in different speed and load conditions.
The simulation results showed that a significant improvement in the dynamic torque and speed
responses when compared to the conventional DTC scheme.
EE380-4 Course project Experimental determination of a Ser.docxjack60216
EE380-4 Course project
Experimental determination of a Servo-Motor State Space Model
Dr. A. Masoud, Course Project, Posted Thursday, October 8, 2015, Due a week before the end of the semester 151.
Objective: To determine experimentally the state space model and the transfer function of the
control laboratory servo-trainer using physical measurements instead of mathematical
derivations. In addition, to be familiarized with the mathematical tools needed for doing this task
Background: The servo-process you will be examining in the EE380 laboratory is the DC
motor (figure-1). By now, you are familiar with how to model theoretically this process. To do
this, you need to know beforehand all the parameters of the system. These parameters are
usually not readily available. Computing them may be difficult or not possible. Therefore, the
only other alternative is to determine the model of the servo-process experimentally.
Figure-1: Equivalent circuit of a DC motor
The motor used in the laboratory servo-trainer is a permanent magnet DC motor. The field is
generated by the permanent magnet is a constant. This makes the armature voltage (Va) the
only means of control available, i.e the motor is in an armature control mode.
The state of the overall system (X) consists of the state of the electrical part which is the current
in the inductor (the armature current Ia), the angular position ( )θ and the velocity of the
mechanical part (θ ). As for the output, it can be selected as anyone of these variables. This
makes writing the output equation of the state space model of the motor a simple and a
straightforward task. The state vector of the overall system is: X=[ Ia θ θ ]T. However, we are
going to use a simplified model that neglects the electrical component and focus only on the
mechanical one. The state vector of the simplified model is: X=[θ θ ]T. The state equation of
the simplified model in (1)
Va,
dc
ba
⎥
⎦
⎤
⎢
⎣
⎡
+⎥
⎦
⎤
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
=⎥
⎦
⎤
⎢
⎣
⎡
f
e
θ
θ
θ
θ (1)
Determining the model means that the input (Va(t)), the states (θ (t), θ (t)) and their derivatives
can be directly measured or reliably computed. The parameters (a,b,c,d,e,f) are the unknowns
that need to be determined from the measurements.
To determine the parameters, we first need to change the form of the state space equations into
the form in (2)
,
f
e
d
c
b
a
Va0(t)(t)00
0Va00(t)(t)
(t)
(t)
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
=⎥
⎦
⎤
⎢
⎣
⎡
θθ
θθ
θ
θ
(2)
Now take “n” measurements of the states, their derivatives and the input and form the equations
in (3). Determining the time instants (t1, t2,..,tn) at which measurements are to be taken are left
up to the student. However, one should make sure that the measurements are distinct, i.e. do
not take the same measurement more than once. ...
Linear Control Hard-Disk Read/Write Controller AssignmentIsham Rashik
Classic Hard-Disk Read/Write Head Controller Assignment completed using MATLAB and SIMULINK. To see the diagrams in detail, please download first and zoom it.
Experimental dataset to develop a parametric model based of DC geared motor i...IJECEIAES
This paper presents the application of a System Identification based on Particle Swarm Optimization (PSO) technique to develop parametric model of experimental dataset of DC Geared motor in feeder machine. The experimental was conducted to measure the input (voltage) and output (speed) data. The actual data is used to be optimized using PSO algorithm. The parameter emphasized is Time, Man Square Error (MSE) and Average Time. One of the best model has been chosen based on the optimum parameters.
THIS DOCUMENT MAINLY CONTAINS THE HOW TO MODLE DC SERVO MOTOR BY USING THE MATLAB SIMULINK AND HOW IT WILL BEHAVE IS SHOWN IN THE MATHEMATICAL EQUATIONS AND THE PLOTTINGS ARE ALSO KEPT IN THIS DOCUMENT SO BY THIS IT IS USEFUL TO STUDY THE CHARACTRISTICS OF A DC SERVO MOTOR
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Simulation of Direct Torque Control of Induction motor using Space Vector Mo...IJMER
This paper presents simulation of Direct Torque Control (DTC) of Induction Motor using Space
Vector Modulation (SVM). Direct Torque Control is a control strategy used for high performance torque
control of Induction Motor. This SVM based DTC technique reduces torque ripple and improves torque
response. The performance is explained using simulation in MATLAB environment. Result of the
simulation done in the paper shows improvement in flux and torque. These results verifies the merits of
DTC- SVM over conventional Direct Torque Control technique.
1. Abstract— In this lab, students modeled a motor/flywheel
system using LabVIEW, the SADIDAQ and hardware in the lab.
Using LabVIEW, data was collected for sinusoidal and square
voltage wave forms and compared with a theoretical model of the
system using the given motor specifications. Transfer functions,
step responses and bode plots were the primary means of
performing the comparison.
Index Terms—Bodine DC motor, bode plots, step response,
transfer functions
I. INTRODUCTION
ransfer functions are used to model a system’s dynamic
characteristics. A Transfer function is the ratio of the
system’s output response to input command signal. Any type of
control system can be modeled in this fashion. In this lab,
LabVIEW is used to experimentally collect data and this data
enables student to model the system’s transfer function, step
response and bode plots. The theoretical transfer function
model is found using the motor data sheet [1] located on
Canvas. Initially, the experimental input command consists of
a sinusoidalvoltage signal with the following frequencies (Hz):
0.1, 0.2, 0.5, 1, 2, 5, 7.5, 10, 15, 20. At each frequency,5 cycles
of data were obtained for the experimental model. After this
data is found, a square wave input command was used at a
frequency of 0.2 Hz in order to find the system’s velocity step
response.
II. PROCEDURE
A. Determining the system transfer function
The first step of this lab is to find the system’s transfer function
based on the given systemparameters. Fig.1 shows the system
dynamics/parameters. This diagram is used as a basis for
creating the system’s transfer function.
Fig. 1. Diagram of system dynamics
The system’s input/output dynamics and parameters are
located in the following table. The electrical dynamics are
modeled using the following formula.
𝑉 = 𝑖𝑅 +
𝐿𝑑𝑖
𝑑𝑡
+ 𝑒 (1)
Where 𝑉 is the input voltage, 𝑖 is the current, 𝑅 is the
resistance, 𝐿 is the motor inductance,
𝑑𝑖
𝑑𝑡
is the time rate of
change of the current and 𝑒 is the back electromotive force of
the motor. The motor dynamics are modelled using the
following equation:
𝐽Ӫ = 𝑇 − 𝑏 𝑚 𝜔 (2)
Where 𝐽 is the rotational inertia, Ӫ is the motors angular
acceleration, 𝑇 is the motor torque, 𝑏 𝑚 is the viscous friction
coefficient and 𝜔 is the angular velocity of the motor. In order
to relate the electrical dynamics with the motor dynamics,
electromechanical relations are used. The following equations
represent the systems electromechanical relations:
𝑒 = 𝐾𝑒 𝜔 (3)
𝑇 = 𝐾𝑇 𝑖 (4)
Where 𝐾𝑇 is the motor torque constant. To find the system
transfer function, the Laplace transform is taken of the motor
dynamics and the electrical dynamics and through algebraic
manipulation, the system transfer function relating the input
voltage to the motor velocity is obtained [1]. The following
equation represents the system’s transfer function.
𝜃(𝑠)
𝑉(𝑠)
=
𝐾𝑇
( 𝐽𝐿) 𝑆3 + ( 𝐽𝑅 + 𝑏 𝑚 𝐿) 𝑆2 + (𝑏 𝑚 𝑅 + 𝐾𝑒 𝐾𝑇 )𝑆
(5)
B. Creation of LabVIEW VI to obtain theoretical transfer
function/step response/Bode plots
In order to find the theoretical system transfer function/step
response/Bode plots, students must create a LabVIEW VI that
allows for the input of the symbolic systeminputs (symbolic
denominator) and the symbolic system outputs (symbolic
Lab 1: Modeling a Motor/Flywheel System
Ballingham, Ryland
Section 7042 9/10/16
T
2. <Section####_Lab#> Double Click to Edit 2
2
numerator). This is done by following the motor/flywheel
system tutorial provided online [1]. Once the parameter
constants are found using the motor data sheet, the theoretical
systemtransfer function/step response can be found.
C. Creation of LabVIEW VI to obtain experimental transfer
function/step response
In order to properly collect data, a LabVIEW VI must be
created that takes an input frequency and voltage signal and
outputs the system’s tachometer voltage, motor velocity, motor
rotation and command signal. A LabVIEW template file found
on Canvas is used as a basis for the VI creation. During lab, data
is obtained for both sinusoidal and square wave form input
voltages. For the sinusoidal waveform input, the voltage is set
to 2V and data is obtained for five cycles over the following
frequency range (Hz): 0.1, 0.2, 0.5, 1, 2, 5, 7.5, 10, 15, 20. For
the square wave input, the voltage is set to 2V and data is
obtained for only 0.2 Hz for 5 steps. The data obtained for both
waveform inputs was exported to Excel for analysis.
D. Bode Magnitude/Phase Diagrams
In order to find both the Bode magnitude/phase diagrams for
the sinusoidal input voltage data, the motor velocity derivative
is plotted versus time at each individual frequency. Using these
plots, the motor velocity derivative minimum/maximu m
magnitudes are found and an average magnitude is found at
each frequency using the following formula:
𝑀𝑜𝑢𝑡 = 0.5 ∗ (𝜔 𝑚𝑎𝑥 − 𝜔 𝑚𝑖𝑛 ) (6)
Also,the tachometer voltage offset is found using the following
formula:
𝑂𝑜𝑢𝑡 = 0.5 ∗ (𝜔 𝑚𝑎𝑥 + 𝜔 𝑚𝑖𝑛 ) (7)
Once these calculations are complete, the same steps must be
performed for the input waveform (command signal). Once this
is complete, the input sinusoid must be scaled to match the
output sinusoid,and then it is shifted by the offset. This data is
then plotted on the same plot as the motor velocity derivative.
The following plot shows this for 1 Hz frequency range:
Fig. 2. Output/scaled and shifted input vs time for 2 Hz frequency
Once all these plots are made for all frequencies, the next step
is to find the time of several corresponding input/output peaks
for all frequencies. The time difference between each
corresponding input/output peakis the systems delay. Once the
delay is found for each frequency, the phase delay (𝜙)(for each
frequency can be found using the following formula:
𝜙 = 𝑑𝑒𝑙𝑎𝑦 ∗ 𝑠𝑖𝑔𝑛𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 ∗ 360 (8)
Since the voltage input magnitude entered into LabVIEW was
2 V, the Bode magnitude (𝑀 𝐵𝑜𝑑𝑒 ) can be found using the
following formula:
𝑀 𝐵𝑜𝑑𝑒 = 20 ∗ 𝐿𝑜𝑔10 (
𝑀𝑜𝑢𝑡
𝑀𝑖𝑛
) (9)
Now that both the Bode magnitudes and phase delays have been
found, both Bode plots can be made.
E. Velocity step response plot square wave data
In order to find the velocity step response for the square wave
data, students need to download the given excel file on
Canvas. With this excel file, the motor velocity derivative data
found in lab for the first step wave is pasted into this excel file
as well as the time. When this is done, a plot is created over
the existing plot.
F. Calculating parameter constants
In order to find the theoretical transfer function, bode plots
and pole-zero equations in LabVIEW, the parameter constants
must be calculated. 𝑘 𝑇 , 𝐿, 𝑅, can be found on the given motor
data sheet [2]. 𝑏 𝑚 and 𝐽 must be calculated by hand. 𝑏 𝑚 can be
calculated by using the following formula:
𝑏 𝑚 =
𝑇
𝜔
(10)
𝜔 can be found on the motor data sheet. To calculate the
motor torque, the following formula can be used:
𝑇 = 𝐾𝑇 ∗ 𝑖 (11)
Once the torque is calculated, 𝑏 𝑚 can be found. The rotational
inertia can be found by creating the flywheel in SolidWorks.
G. Estimated gain/ pole locations/parameter values for the
system
The theoretical gain for the systemcan be found by using the
following formula:
𝐾𝑉 =
𝐾𝑇
𝑏 𝑚 𝑅 + 𝐾𝑒 𝐾𝑇
(12)
The experimental gain can be found be looking at the
experimental Bode magnitude plot.
The theoretical pole locations of the systemcan be looking
3. <Section####_Lab#> Double Click to Edit 3
3
at pole-zero equation found in LabVIEW. In this equation,
setting the denominator equal to 0 and solving for S roots will
yield the system’s pole locations. The experimental pole
locations can be found by looking at fig. 4.
The theoretical system parameter values (𝑎, 𝑑) can be
derived from the system transfer function using the following
formulas:
𝑎 =
𝑏 𝑚 + 𝐾𝑒 𝐾𝑇
𝐽𝑅
(13)
𝑑 =
𝐾𝑇 𝐾𝑎𝑚𝑝
𝐽𝑅
(14)
Where 𝐾𝑎𝑚𝑝 is 90 V. The experimental parameter values can
be found by importing the motor velocity derivative lab data
into the provided step response excel file. Using the solvertool,
𝑎 and 𝑑 can be calculated.
H. Calibrating the tachometervoltage
In order to obtain a proper tachometer voltage reading, the
tachometer voltage needs to be calibrated. This is done by
plotting the motor velocity derivative vs the tachometer
voltage reading. Once this is done,a linear trend line is found
and the resulting slope is the calibration constant. This is done
to convert the voltage reading from the tachometer to a
velocity. Using this calibration constant,a new motor velocity
derivative reading can be found.
III. RESULTS
Fig. 3. Experimental Bode magnitude plot
Fig. 4. Experimental pole location
Fig. 5. Experimental Bode phase plot
Fig. 6. Velocity step response of square wave data
Fig. 7. Theoretical Bode magnitude plot
Fig. 8. Theoretical Bode phase plot
4. <Section####_Lab#> Double Click to Edit 4
4
Fig. 9. Theoretical transfer function found in LabVIEW
Fig. 10. Theoretical pole-zero equation found in LabVIEW
Fig. 11. Motor velocity derivative vs time for square waveform plot
Fig. 12. Calibratedmotor velocitytachometer vs timefor square waveformplot
Fig. 13. Motor velocity tachometer vs motor velocity derivative with linear
trendline
TABLE I
THEORETICAL PARAMETER VALUES
Parameter Value
𝐾𝑇 [(N-m)/A] 0.4202
𝐾𝑒 [V/(rad-s)] 0.4202
J [N-m^(2)] 0.0064
R [Ohms] 11
L [H] 0.00028
𝑏 𝑚 [(N-m)/(rad/s)] 0.003157
TABLE II
A AND D PARAMTER VALUES
Parameter Theoretical Experimental
𝑎 2.97 10.31
𝑑 (rad/s) 9.35 6.79
Gain 1.99 1.33
TABLE III
THEORETICAL/EXPERIMENTAL POLE LOCATIONS
Parameter Theoretical Experimental
𝑆1 0 0
𝑆2 -3.00154 4.4
𝑆3 -39,283.2 -
IV. DISCUSSION
A. Comparison of experimental/theoretical Bode plots
Both Bode magnitude plots (figures 3 & 7) have the same
general trend and shape. The main difference is the magnitude
values at which the plots begin/end. The same is true for the
Bode phase plots (figures 5 & 8). The reason for this could be
due to the additional gain constant on the experimental transfer
function.
B. Numerical time derivative vs tachometer voltage
Using the tachometer voltage yields a better reading then the
motor time derivative. This is because the numerical derivative
is a calculated value in LabVIEW which is based on a position
reading. Since a series of calculations has to be performed to
get a motor derivative value, it is more prone to error
propagation. The tachometer voltage is based on a sensor
reading with no intermediate calculations, thus providing a
more accurate reading.
C. Parameter comparison
A 71% difference was calculated between the theoretical 𝑎
value and the experimental 𝑎 value while a 27% error was
calculated between the theoretical 𝑑 value and the
experimental 𝑑 value. These errors are likely due to estimation
errors and noise during data collection.
D. Model improvements
In order to make this model better, closed-loop control could
be used instead of open-loop. This will help account for
numerical errors in the systemby accounting for the system
error in the input command signal. This will help reduce
overshoot and steady-state errors in the system.
5. <Section####_Lab#> Double Click to Edit 5
5
V. CONCLUSION
This lab is a good demonstration of a basic control system.
Using the hardware in lab, an experimental systemmodel was
created to compare to a theoretical system model. This lab
demonstrated that using a motor velocity derivative doesn’t
work as well as using a tachometer voltage reading due to
intermediate calculation errors that propagate. Also, closed-
loop control should be used to account for calculation errors in
LabVIEW.
REFERENCES
[1] N. Instruments, "ModelingDC motorposition,"2008. [Online].
Available: http://www.ni.com/tutorial/6859/en/#toc1.Accessed: Sep. 11,
2016.
[2] Bodine Electric Company, 33ASeries Permanent Magnet DC Motor:
Model 6435specifications. http://www.bodine-
electric.com/Products/Asp/ProductSpecs.asp?Co%E2%80%A6&Name=
33A%20Series%20Permanent%20Magnet%20DC%20Motor&Model=6
[3] S. Banks. “Simplified MF model, EML4312C