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I n s t i t u t o P o l i t c n i c o I P U C
U n i d a d e C o r a o E u c a r s t i c o
B e l o H o r i z o n t e
A g o s t o d e 2 0 1 3
Disciplina EP2_MT
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PONTIFCIA UNIVERSIDADE CATLICA DE MINAS GERAIS
Instituto Politcnico/IPUCCurso de Engenharia Mecatrnica
Projeto 1:
Acionamento CC
Professor Lauro de Vilhena Brando Machado Neto
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Belo Horizonte
2013
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PROJETO I:
ACIONAMENTO A VELOCIDADE VARIVEL DE UMA MQUINA CC
ETAPAS DE DESENVOLVIMENTO:
1. Carga mecnica: sistemas rotacionais, acoplamento rgidos e no rgidos e
modelagem e simulao;
2. Mquina de corrente contnua: converso eletromecnica, mquina CC,
caracterstica torque versus velocidade e modelagem e simulao;
3. Fonte de alimentao / Conversores estticos: retificador controlado (tiristores),
conversor indireto de tenso (diodos mais transistores) e modelagem e simulao;
4. Circuitos de comando e controle: comando dos transistores, controle em malha
aberta e malha fechada modelagem e simulao e sistemas eletrnicos.
CRONOGRAMA DE DESENVOLVIMENTO E ACOMPANHAMENTO E AVALIAO:
1. Semana 1: Simulao utilizando o SystemVision;
2. Semana 2: Apresentao do sistema eletrnico Arduino e estudo e montagem dos
mdulos;
3. Semana 3: Apresentao do programa de linguagem grfica LabView e do toolkit do
Arduino;
4. Semana 4: Implementao do programa e primeiros testes;
5. Semana 5: testes e resultados obtidos
6. Semana 6: entrega relatrio final
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PROJETO I:
ACIONAMENTO A VELOCIDADE VARIVEL DE UMA MQUINA CC
COMPONENTES GRUPOS:
Grupo 1:
Marcos Vincius dos Santos Rocha
Cristiano Athayde Braga DinizDaniel de Oliveira Nogueira
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ORIENTAO 1: SIMULAO PONTE H, MQUINA CC E CARGA MECNICA
1. Faa o tutorial Parametric and Statistical Analyses, disponvel neste documento e
capture, explique, analise e comente as janelas dos circuitos e resultados obtidos;
2. Carga mecnica: descreva o modelo VHDL-AMS da carga mecnica utilizada;
3. Mquina de corrente contnua: descreva o modelo VHDL-MAS da mquina CC
utilizada;
4. Fonte de alimentao / Conversores estticos: descreva o funcionamento da ponte
H utilizada;
5. Salve o projeto com o seguinte nome: BeyondSPICE_Posio;
6. Troque a mquina CC, cuja sada posio, por uma mquina CC com sada em
velocidade. Refaa o tutorial.
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ORIENTAO 2: SISTEMA DE DESENVOLVIMENTO ARDUINO, SHIELDS EMQUINA CC
1. Descreva as principais caractersticas do sistema de desenvolvimento ARDUINO,
tais como especificaes, pinos digitais de entrada/ sada, PWMs, entradas
analgicas e memrias;
2. Descreva as principais caractersticas do Shield L298 de acionamento de mquinas
CC Ponte H. Descreva o diagrama de blocos do integrado L298;
3. Descreva o princpio de funcionamento do motor CC e descreva as principais
caractersticas do motor CC a ser utilizado no projeto;
4. Com base nos diagramas esquemticos do ARDUINO, do Shield L298 e do motor
CC, desenhe um diagrama da sua aplicao;
5. Considerando como exemplos os programas a seguir para acionamento de um
motor CC, descreva a lgica dos programas;
6. Monte o sistema do ARDUINO, Shield L298 e motor CC. Descarregue o programa
no ARDUINO e anlise o seu funcionamento.
7. Com o osciloscpio, capture e anlise as principais formas de ondas do sistema;
8. Faa a redao do relatrio sobre este experimento.
PROGRAMA 1 Sadas digitais:
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int pin2 = 2;
int pin3 = 3;
void setup (){
pinMode(pin3,OUTPUT);pinMode(pin2,OUTPUT);
}
void loop(){
{
digitalWrite(pin2,HIGH);
digitalWrite(pin3,LOW);
delay(2000);digitalWrite(pin3,HIGH);
digitalWrite(pin2,LOW);
delay(2000);
}
}
PROGRAMA 2 PWM constant:
int pin2 = 2; // IN4
int pin3 = 3;
int pin4 = 4; // enable da ponte B em high
// Definindo variveis de controle de velocidade e sentido dos motores
const int Motor1 = 6; //PWM motor 1//const int DirMotor1 = 2;// Direo motor 1
//Definindo PWM como zero
int pwm =0;
void setup (){
pinMode(pin3,OUTPUT);
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pinMode(pin2,OUTPUT);
pinMode(pin4,OUTPUT);
}
void loop(){{
digitalWrite(pin4,HIGH);
digitalWrite(pin2,LOW);
//digitalWrite(pin3,LOW);
analogWrite(Motor1, 90);
delay(10000);
//digitalWrite(pin3,HIGH);//digitalWrite(pin2,LOW);
delay(2000);
}
}
PROGRAMA 3 Partida Suave:
int pin2 = 2; // IN4
int pin3 = 3;
int pin4 = 4; // enable da ponte B em high
// Definindo variveis de controle de velocidade e sentido dos motores
const int Motor1 = 6; //PWM motor 1
//const int DirMotor1 = 2;// Direo motor 1
//Definindo PWM como zero
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int pwm =0;
int i = 0;
void setup (){
pinMode(pin3,OUTPUT);
pinMode(pin2,OUTPUT);
pinMode(pin4,OUTPUT);
}
void loop(){
{
i = i + 10;
digitalWrite(pin4,HIGH);
digitalWrite(pin2,LOW);
//digitalWrite(pin3,LOW);
analogWrite(Motor1, i);
//delay(10000);
//digitalWrite(pin3,HIGH);
//digitalWrite(pin2,LOW);
delay(1000);
}
}
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PROGRAMA 4 Rotao nos dois sentidos com acelerao e frenagem suave:
int pin4 = 4; // enable da ponte B em high
// Definindo variveis de controle de velocidade e sentido dos motores
const int Motor1 = 6; //PWM motor 1 IN4
const int Motor2 = 3; //PWM motor 2 IN3
//Definindo PWM como zero
int pwm =0;
int i = 0;
void setup (){
pinMode(pin4,OUTPUT);
pinMode(Motor1, OUTPUT);
pinMode(Motor2, OUTPUT);
}
void loop(){
{
do{
i = i + 10;
digitalWrite(pin4,HIGH);
digitalWrite(Motor1,LOW);
analogWrite(Motor2, i);
delay(1000);
}while(i
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delay(3000);
do{
i = i - 10;digitalWrite(pin4,HIGH);
digitalWrite(Motor1,LOW);
analogWrite(Motor2, i);
delay(1000);
}while(i>=0);
do{i = i + 10;
digitalWrite(pin4,HIGH);
digitalWrite(Motor2,LOW);
analogWrite(Motor1, i);
delay(1000);
}while(i=0);
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}
}
SystemVision How To Tutorials
The following tutorials include a diverse collection of designs that highlight
SystemVisions design and analysis capabilities. If you are new to SystemVision, it is
recommended that you begin with the Getting Startedtutorial.
To begin a tutorial, click on the desired icon below. The corresponding tutorial
instructions will be automatically loaded into a new browser window. In some cases, anadditional menu will be presented that offers multiple design choices related to the icon
you have chosen.
You can go to the previous page at any time by clicking on the Back button, in the
SystemVision Toolbar, or the link at the top of a given page.
SystemVision Design & Analysis Tutorials
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Getting Started Sensitivity, Monte Carlo, WCA
Create Symbols for Models Create Models from Datasheets
Import SPICE/PSpice Models Graphical Component Modeling
Create Behavioral Models Use C Code in a Design
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Switch Characteriztion &
ModelingPlace Symbols with DxDataBook
PCB/Library Setup Automation Scripts, Tips
Read S-ParametersGlobal Params, Sim Options,
etc.
Experiment Manager (SV Excel)
Parametric and Statistical Analyses Tutorial
In this tutorial you will use Parameter Sweeps, Sensitivity, Monte Carlo and Worst-Caseanalyses in SystemVision to analyze the performance of a simple H-Bridge Motor
Controller. This example combines SPICE models for the electronics with VHDL-AMS
models for the motor and loads. The ability to simulate these together is made possible
by SystemVisions support for multiple industry standard languages. Combining this with
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Parametric Analyses makes SystemVision a powerful tool for robust mixed-technology
system design.
Related Documents:
For further information on the subjects discussed in this exercise, please refer to the
SystemVision Help (Help > SystemVision Help).
Open Beyond SPICE Project
The first step for designing and simulating a design is to open a SystemVision project.
If you have already gone through the initial steps of this tutorial and created
this project, you should just open the project as follows: select File > Open
> Project, browse to the location you specified when creating theproject, and open the Beyond_Spice.dproj file. You can then continue this
tutorial wherever you left off.
When you open any of the pre-installed SystemVision tutorials (like the Beyond SPICE
project) for the first time, you will follow these steps.
1. Select File > New
2. Click on the Project tab in the New dialog.
3. Click on the TutorialProjects folder under Categories.
4. Select the Parametric icon under Types.
The name of the project, Beyond_Spice, will appear in the Name field.
5. Browse into a location where you would like to copy the Beyond_Spice project
files.
6. Click OK.
The Beyond_Spice project files are copied to the location you specified, and the
project is then loaded into SystemVision and is ready to run.
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To open this project in the future, select File > Open > Project, browse to the location
you specified when creating the project, and open the Beyond_Spice.dproj file.
H-bridge Motor Controller
The design tb_hbridge_spice_ams, shown in Figure 1, is an H-bridge circuit combining
SPICE level transistors with digital (VHDL) stimulus and VHDL-AMS drivers, DC motor
and loads. Using SystemVision, the power of VHDL-AMS can be seamlessly integrated
with existing SPICE models or subcircuits, to provide a multi-language, mixed-
technology system simulation.
Figure 1 - tb_hbridge_spice_ams schematic.
Design Selection/Exploration
1. From the Simulation tab, click on TestBenches > tb_hbridge_spice_ams to open
the schematic.
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2. Explore some of the component models.
For example, select the DC Motor Symbol and right-click > Push VHDL to view the
VHDL-AMS model (repeat for other VHDL-AMS models as desired).
3. View some of the model properties that have been assigned to various symbols:
Double-click on a VHDL-AMS or SPICE model to access model attributes .
Simulating the Circuit (Nominal Simulation)
First you will perform a nominal simulation to verify that the circuit is operating as
intended.
1. Return to the schematic and from the menu, select Simulation > Simulate to
invoke the Simulation Control window (there is also a simulation icon available on
the icon bar).
2. In the Simulations tab enable the Time-Domain Analysis and set End Time to 1
sec e em Run colocar nominal.
3. Leave the settings in the Results tab as they are.
The Results tab allows you to select the signals for viewing. The default selection
for this design is Selected Waveforms, with which individual waveforms have
been selected for analysis.
4. Click on the Multi-Run tab, and select Nominal for the Multi-Run Type, if
necessary.
The Multi-Run tab is for performing variations on component parameters.
5. No settings will be needed for the Advanced tab.
The Advanced tab is used for advanced simulation settings (normally not
required).
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6. Click the OKbutton to run the simulation.
Viewing Results
The simulation results will automatically be loaded into the Waveform Analyzer uponcompletion of a successful simulation (if not, look in the Output Window for any error
messages).
Individual signals can be viewed by double-clicking with the left-mouse button or by
using the drag-and-drop feature. You can also plot a signal from the schematic by
selecting the desired signal and using right-click > Plot Waveform.
1. Use one of these methods to plot the digital command signals d_fcmd and d_rcmd
indicated by the symbol next to the waveform name.
2. Next plot the motor current ydcmotor1/i.
Notice the effect of the back-emf voltage as modeled in the motor equations,
which levels out the current as the motor spins.
3. Plot the waveform position.
This is the position of the motor shaft over time. Notice that the motor does notreturn to its original position due to the short length of the reverse command
signal.
4. Verify that the waveforms match those shown in Figure 2.
5. Bring up a new graph window by selecting File > New. This window will be used
shortly.
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Figure 2 - Nominal Simulation Results.
dada a partida no motor em aproximadamente 0,2s para o sentido positivo (dc_fcmd).
Inicialmente tem-se um pico devido inercia do indutor. O motor permanece neste
sentido durante 0,2 segundos. O sentido inverso est defasado de 0,2 segundo do
sentido direto, entretanto o sentido reverso tem durao de 0,1 segundo. Isso implica
que ele no consegue retornar posio inicial permanecento na metade do caminho.
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Figura 01: Circuito de comando.
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Figura 02: Forma de ondas
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Parameter Sweeps
Parameter sweeps are useful for automatically varying specific circuit parameters and
running simulations.
Setup Sweeps
You will next examine the effects of the component parameters on the motor position.
You will do this by sweeping a parameter (motor winding resistance) over a specified
range.
1. Return to the tb_hbridge_spice_ams schematic and from the menu, select
Simulation > Simulate to invoke the Simulation Control window
2. Select the Multi-Run tab.
3. Change the Multi-Run Type to Sweep Values.
4. Click on the Parameter Editbutton to invoke the Sweep Parameter dialog.
5. Click on the browse button () to invoke the Select Parameterdialog.
6. Select ydcmotor1.r_wind and click OK.
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7. Set the Sweep Type to List and the Sweep List to 50.0 100.0 200.0.
8. Click the Replace current sweep parameters checkbox.
This will remove any previous sweep commands. The dialog should appear similar to
that shown in Figure 3.
Figure 3 - Sweep parameter dialog box.
9. Click OK in the Sweep Parameter dialog.
10. Click OK in the Simulation Control dialog.
11. When the simulation runs are complete, plot the digital command signals
(d_fcmd and d_rcmd) along with the motor position as shown in Figure 4.
Note the sweep values shown are annotations that were added manually.
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Figure 4 - Parameter Sweep Results.
Figura 03:
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Performing Measurements
As expected, these results show that the winding resistance has a significant effect on
the final angular position. SystemVision allows you to quantify relationships between
system performance and component parameters by performing measurements on thesimulation results. In this section you will re-run the previous analysis with additional
sweep values. The extra data that is generated will allow you to create correlation plots.
1. Re-invoke the Simulation Controldialog and click on the Multi-Run tab.
2. Click the Parameter Edit button and modify the existing fields as follows:
Parameter:E(ydcmotor1,r_wind) (unchanged from previous analysis)
Sweep Type:Increment
Sweep Start:10.0
Sweep Stop:100.0
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Sweep Increment:10.0
3. Click the Replace current sweep parameters checkbox.
4. Click OK in the Sweep Parameter dialog.
5. Click OK in the Simulation Control dialog.
6. When the simulation runs complete, plot the position waveform into a new graph
(select File > New to create a new graph window).
7. Click the Add Cursor button twice to place two cursors (C1 and C2) at locations
similar to those shown in Figure 5.
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Figure 5 - Parameter Sweep Results with Measurements.
8. Click the Measurement Tool icon and fill in the dialog as shown in Figure 6 to
annotate the Risetime measurement results to the graph.
Be sure to Apply Measurements Between Two Cursors.
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Figure 6 - Measurement Tool for Risetime Measurement.
9. Click Apply. The measurements are annotated to the graph.
The measurement can be moved from one waveform to another by clicking on
the handle at either the top or bottom of the result markers, and holding and
dragging to another waveform. All measurement results can be viewed by right-
clicking with the cursor over the measurement and selecting Measurement
Results.
10. In the Measurement Tool, select the Plot New Waveform option under
Measurement Results and re-apply to create a plot of Risetime vs. motor winding
resistance.
11. In necessary, click Continue in the Open New Window dialog.
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You now have a waveform that displays Risetime as a function of motor winding
resistance.
12. Bring back up the graph window with the waveforms shown in Figure 5.
13. Reposition the cursors so that they enclose the falling edges of the swept
waveforms.
14. In the MeasurementTool, select Falltime as the Measurement.
15. Be sure to specify that the measurement is to be performed between the cursors.
16. Re-apply to create a plot of Falltime vs. motor winding resistance.
17. The results are shown in Figure 7.
The waveforms were super-imposed by copying and pasting (or dragging) a
waveform from one graph window to another graph window.
The individual measurement points can be displayed by selecting the waveform
name (in the signal pane) and selecting right-click > Data Point > Symbols.
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Figure 7 Risetime/Falltime Plots.
Figura 04: Tempo de subida e tempo de descida.
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Figure 7 clearly shows the effect the value the motor winding resistance has on the shaft
position rise- and fall-times when used with the H-bridge driver circuit. This is a simple
example of how SystemVision can be used to turn simulation data into engineering
information that can be used to help improve a system design.
Note that rise- and fall-times are measured relative to the minimum and maximum value
of each individual waveform, which explains why fluctuations such as those shown
above are possible (as opposed to a continuous increasing or decreasing pattern).
18. Exit out of the Waveform Analyzer. Do not save the waveforms.
19. Descrio dos cdigos em VHDL:
19.1. Descrio do bloco clock pulse:
No SystemVision, o Bloco Clock Pulse tem a seguinte representao grfica:
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Figura 05: Bloco do Clock_Pulse
Abaixo segue o cdigo em VHDL que descreve as funcionalidades do bloco
Clock Pulse. O smbolo \* *\ representa delimitao de comentrios dos integrantes
deste relatrio.
library IEEE;
use IEEE.std_logic_1164.all;
\* Determina qual biblioteca dever ser utilizada. Contm a maioria dos comandos
utilizados na linguagem VHDL*\
entity clock_pulse is
\* a parte principal do projeto, a interface do Sistema que descreve as
entradas e sadas. Neste caso a entrada o bloco clock_pulse.
generic (initial_delay : time; -- Delay Time [Sec]
width : time; -- pulse width [Sec]
period : time); -- Period [Sec]
\* generic : Declarado naentitypara definir constantes. Neste caso, as
constantes so width e period, que so dados de entrada a serem determinados pelo
usurio. *\
port (out_state : out std_logic);
end entity clock_pulse;
architecture ideal of clock_pulse is
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signal out_signal : std_logic;
constant off_time : time := period - width;
\* generic : Operao para determinar a constante de tempo *\
\* -----------------------------------------------------------------------------------------------*\
Begin
\* Inicia o processo de criao do sinal de sada do clock.*\
-- purpose: Creates events on signal "out_signal"
-- type : combinational
-- inputs :
-- outputs: out_signal
CreateEvent : process
Begin \* Incio do processo de repetio que dar origem ao clock pulse .*\
out_signal
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end process CreateEvent;
out_state
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Figura 06: Bloco do Transistor.
* Model 2N3904
\* Determina qual transistor dever ser utilizado na simulao.*\
.MODEL 2N3904 NPN ( IS=11.3161F
+ BF=174.8327 NF=1.017 VAF=102.2265 IKF=64.3415M
+ ISE=59.1356F NE=1.5412 BR=23.1889 NR=1.024
+ VAR=12.7191 IKR=0.1342 ISC=13.4919P NC=1.5092
+ RB=5 IRB=8.8078M RBM=2.2344 RE=0.4831
+ RC=1.3075 CJE=6.622P VJE=0.5954 MJE=0.2753
+ TF=75.9047P XTF=3.5 ITF=11.5542M CJC=3.42P
+ VJC=0.5 MJC=0.2024 TR=10.7163N EG=1.11 )
\* Este cdigo determina as caractersticas intrnsecas do transistor escolhido para a
simulao e em cada ponto descreve um parmetro caracterstico dele*\
19.3. Descrio do cdigo VHDL que descreve o motor dc:
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Figura 07: Bloco do Motor DC
- Use proposed IEEE natures and packages
library IEEE;
\*Bibliotecapadro que contm comandos de execuo para linguagem VHDL */
use IEEE.mechanical_systems.all;
\*Permite utilizar definies e comandos que no esto na biblioteca padro. Neste
caso usa uma biblioteca especifica para comandos ou definies mecnicas do
motor DC */
use IEEE.electrical_systems.all;
\*Permite utilizar definies e comandos que no esto na biblioteca padro. Neste
caso usa uma biblioteca especifica para comandos ou definies elticas do
motor DC */
entity DCMotor_r is
\*Determina o comportamento do motor dc */
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generic (
pos_ic : angle := real'low; -- Initial value for shaft angle
\*Determina o o ngulo inicial do eixo do motor */
r_wind : resistance; -- Motor winding resistance [Ohm]
\*Determina o a resistncia da bobina do motor dc */
kt : real; -- Torque Constant [N*m/Amp]
\*Recebe o valor do torque do motor dc */
l : inductance; -- Winding inductance [Henrys]
\*Recebe o valor da indutncia da bobina do motor dc */
d : real; -- Damping coefficient [N*m/(rad/sec)]
\*Determina o valor do coeficiente de amortecimento do motor dc */
j : moment_inertia); -- Moment of inertia [kg*meter**2]
\*Determina o momento de inrcia da carga do motor dc */
port (terminal p1, p2 : electrical;
terminal shaft_rot : rotational);
end entity DCMotor_r;
-------------------------------------------------------------------------------
-- Basic Architecture
-- Motor equations: V = Kt*W + I*Rwind + L*dI/dt
-- T = -Kt*I + D*W + J*dW/dt
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-------------------------------------------------------------------------------
architecture basic of DCMotor_r is
quantity v across i through p1 to p2;
quantity theta across torq through shaft_rot to rotational_ref;
begin
if domain = quiescent_domain and pos_ic /= real'low use
theta == pos_ic;
v == kt*theta'dot + i*r_wind + l*i'dot;
\* Observa o valor da posio angular do eixo e partir dele calcula a velocidade
angular *\
else
torq == -1.0*kt*i + d*theta'dot + j*theta'dot'dot;
\* Calcula o valor do torque a partir da variao do ngulo do eixo *\
v == kt*theta'dot + i*r_wind + l*i'dot;
\* Calcula o valor da velocidade a partir da variao do ngulo do eixo *\
end use;
end architecture basic;
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19.4.Descrio do cdigo VHDL que descreve o bloco do momento de inrcia
Figura 08: Bloco da Carga (momento de inrcia)
-- Use proposed IEEE natures and packages
library IEEE;
use IEEE.mechanical_systems.all;
entity inertia_r is
generic (j : moment_inertia); -- Value of moment of inertia [Kg*m^2]
\* Determina o valor do momento de inrcia de massa (j) da carga acoplada aoeixo*\
port (terminal rot1 : rotational);
end entity inertia_r;
-------------------------------------------------------------------------------
-- Ideal architecture
-- Tload = J*dW/dt
-------------------------------------------------------------------------------
architecture ideal of inertia_r is
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quantity theta across torq through rot1 to rotational_ref;
begin
torq == j * theta'dot'dot;
\* Calcula o valor do torque a partir da variao do ngulo do eixo e do momento de
inrcia da carga *\
end architecture ideal;
------------------------------------------------------------------------------
-- Copyright (c) 2003 Mentor Graphics Corporation
19.5. Descrio do cdigo que modela o fim de curso rotacional:
library IEEE;
use IEEE.MATH_REAL.all;
use IEEE.MECHANICAL_SYSTEMS.all;
entity stop_r is
generic (
k_stop : stiffness; \*Constante de rigidez de parada do motor*\
damp_stop : damping := 1.0e-9; \*Constante de amortecimento de parada domotor*\
ang_max : angle; \*Valor mximo do ngulo *\
ang_min : angle := 0.0 \*Valor mnimo do ngulo *\ );
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port ( terminal ang1, ang2 : rotational);
end entity stop_r;
architecture ideal of stop_r is
quantity velocity : velocity;
quantity ang across trq through ang1 to ang2;
begin
velocity == ang'dot; \*Define a velocidade angular em funo da derivada da
posio angular no tempo *\
if ang'above(ang_max) use
trq == k_stop * (ang - ang_max) + (damp_stop * velocity);
; \*Calcula trq em funo da velocidade, do amortecimento de parada, da diferena
entre a posio angular mxima e a atual e da rigidez de parada *\
elsif ang'above(ang_min) use
trq == 0.0;
else
trq == k_stop * (ang - ang_min) + (damp_stop * velocity);
\*Calcula trq em funo da velocidade, do amortecimento de parada, da diferena
entre a posio angular mnima e a atual e da rigidez de parada *\
end use;
break on ang'above(ang_min), ang'above(ang_max);
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end architecture ideal;
-------------------------------------------------------------------------------
-- Copyright (c) 2003 Mentor Graphics Corporation
Simulao para velocidade angular.
Substituiu-se o motor cujo controle era feito para posicionamento pelo de controle
de velocidade, e por conseguinte substituiu-se a carga correspondente.
Component--> atuadores e motores motor dc revoluo
Copiar e posicionar sobre a rea de trabalho sem retirar o motor cujo controle foi de
posio.
Figura 09: Circuito modificado para incluir carga dinmica.
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Simulao:
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Figura 10:Velocidade, corrente e sentido de rotao em funo do tempo.
A curva em branco representa a velocidade. As curvas em azul representam o qual
sentido da rotao (direto ou inverso de acordo com conveno ) e a ltima
curva representa a corrente.
Simulao paramtrica
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Figura 11: Representao posio em funo do tempo atravs de simulao
paramtrica.