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Execution Time Validation of the Mathematical

Models of a Electric Motor inSoft Real Time Simulation

M.T.A. Jorge Salvador Valdez Martnez

Dr. Pedro Guevara Lpez

Dr. Juan Carlos Garca Infante


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Correct

Answers

Temporal

Constraints

Real

Process

STR

1.1 Real Time System

Classification (Time Constraints)

Hard Real Time System

In Real-time systems, the response times are always in synchrony with the dynamics of

the environment in all ranges of evolution, and the data set is always stable and

converges at every point to appropriate values [GMC07]. In these systems, it is absolutelyimperative that responses occur strictly within the time periods specified, otherwise there

is risk of causing a disaster or system instability. And they have the following

characteristics [GM03]:

Strict response deadline

Temporal behavior determined by the environment

Predictable behavior OverloadCritical security requirements

Active redundancy

Reduced data volume.


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Soft Real Time Systems

Response times are in synchrony with the dynamic environment in intervals of evolution in

any sense of probability. The output is an interval bounded by minimum and maximum

range and the data set can be marginally stable and converges (probabilistically) toappropriate values. They work correctly if a restriction is lost, the performance is degraded

but not destroyed the system because of failure in the delivery time information [GMC07].

These systems have the following characteristics [GM03]:

Flexible response deadline

Temporal behavior determined by computer

Degraded performance against overloadsNon-critical security requirements

Fail recovery

Large volume of data



Correct

Answers

Temporal

Constraints

Real

Process

STR


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Firm Real Time Systems

Systems where high response times are not acceptable in any sense of probability in the

intervals of evolution, although the data set is always stable and have convergence at all

points to appropriate values when the environment gets steady [GMC07].If do not respect the time constraint does not help the service it provides, and therefore

the real-time system is not functional.



Correct

Answers

Temporal

Constraints

Real

Process

STR


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1.2 Real Time Simulation

Minimal CharacteristicsA simulator can be considered to work in real-time, if it has the following characteristics

[BK08]:

Deterministic response to disruptions

Communication between processes

High-precision timers

Interrupt Handling

A real-time system provides to the user:

Synchronization services (The external real time with the Operative system time)

Capture and interruption treatment (it is a mechanism that is responsible for capturing

interrupts when occur, and advise models or tasks that interest them such disruption is

already present)File management(It is required because of depending on the systems behavior,

sometimes is needed to get data or view data)

Measurement of real time: Because in the Mathematical models, should know the actual

time to do certain actions (Task).


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1.3 Real Time Simulation

SIMULINKIn SIMULINK, the Synchronization services is possible with the asynchronousinterruptions services (Warnings) to the Operating System with Async IRQ Source block.

To the deterministic response to disruptions, in SIMULINK there are blocks that help

to get information from external data (as well as interruptions), and there are blocks that

help to give certain response to the outside, using data acquisition cards.

To manage files, SIMULINK has a number of blocks that allows observe the systems

behavior (with a Digital Oscilloscope) and is possible to save digital information obtainedin Digital SINKS.

With Measurement of real time, is possible to obtain it (using MATLAB command line).

For the physical system modeled and simulated must have minimal time constraints, for

its simulation:

1) Ability to express recursively using models obtained from discretization methods (eg

finite differences, Z transform)

2) The value of convergence is bounded within a finite interval on which it is oscillating

3) The mathematical model simulated permits the extraction and release of information

observable and synchronized with the time evolution of the process by considering the

sampling criteria [Nyq28]. And it needs to give the correct answers and bounded in time

according to the time constraints of the dynamic system..


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2.1 Physical Models Simulation:

DC motor Fundamentals [Gue99]

LJ

eatkit

LJ

tikRbt

LJ

RJLbt

)()(

)()()(

22

(1)

L

eati

L

tkRti

aa

)(

)()(

(2)

RJ

eatkit

RJ

tikRbt

)()(

)()(

22

(3)

)(

)(tkR

eati

a

(4)

Second Order Model First Order Model

Figure 1. Series wound DC Motor:Electromechanical circuit

if

ia

Rf Lf

Ra La

ARMOR

ea

J

b

t

t

Varmor

CONSTANT INDUCED

FIELD

MOTOR

t


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2.2 Physical Models Simulation:

Simulation graphics (Angular Speed and Electric Current)

Figure 2. Angular Speed Figure 3. Armor Electric Current

1) Ability to express recursively

2) The value of convergence is bounded

3) The mathematical model simulated permits the extraction and release of

information observable and synchronized with the time evolution of the process byconsidering the sampling criteria [Nyq28]..


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Table 1. Code to obtain The execution time:First Order Mathematical Model

for MC=1:experimentosfor ejec=1:ejecuciones

omega(MC,1)=0;

tic;

for n=1:1000

F(MC,n)=(k*omega(MC,n))/R;

ia(MC,n)=gamma/(1+F(MC,n));

C(MC,n)=(R*b+k*k*ia(MC,n)*ia(MC,n))/(R*J);

beta(MC,n)=(k*ia(MC,n)*eao)/(R*J);

omega(MC,n+1)=(xi*beta(MC,n)+omega(MC,n))/(1+xi*C(MC,n));

end

tiempodeejecucion(MC,ejec)=toc;

end

end

for tt=1:ejecuciones

ejecucionMontecarlo(tt)=sum(tiempodeejecucion

(:,tt))/numel(tiempodeejecucion(:,tt));

end

2.3 Simulation

Results

(Off line)

Figure 4. First Order Finite Differences Execution


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Table 2. Code to obtain The execution time:Second Order Mathematical Model

for MC=1:1for ejec=1:1

omega(MC,1)=0;

ia(MC,1)=eao/R;

ia(MC,2)=eao/R;

omega(MC,2)=0;

tic;

for n=3:1000

D(MC,n)=(R+k*omega(MC,n-xi))/L;

ia(MC,n)=(xi*delta+ia(MC,n-

xi))/(1+xi*D(MC,n));

B(MC,n)=(R*b+k*k*ia(MC,n)*ia(MC,n))/(L*J);alfa(MC,n)=(k*ia(MC,n)*eao)/(L*J);

omega(MC,n)=(xi*alfa(MC,n)+(2+A*xi)*omega(MC,

n-xi)-omega(MC,n-

2*xi))/(1+xi*A+xi*xi*B(MC,n));

end

tiempodeejecucion(MC,ejec)=toc;

end

end

for tt=1:ejecuciones

ejecucionMontecarlo(tt)=sum(tiempodeejecucion(:,tt))/numel(tiempodeejecucion(:,tt));

end

Fi ure 5. . Second Order Finite Differences

2.3 Simulation

Results

(Off line)


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Figure 6. Block Diagram in SIMULINK:First Order Mathematical Model

u(t)

w(t-xi)i(t)

corriente d e Armadura

Primer Orden

-1

Z

Xi

u(t)

i(t)

w(t-x)

w(t)

Velocidad angular

Primer Orden

Velocidad

angular

Step-K-

Gain

Corriente de

Armadura

Analog

Output

Analog Output1

National Instruments

PCI-1200 [auto]

Analog

Output

Analog OutputNational Instruments

PCI-1200 [auto]

93

93

Figure 8. NI PCI 1200 Output:First Order Mathematical model Execution timesec06.2

2.3 Simulation

Results

(Soft real time )


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Figure 7. Block Diagram in SIMULINK:

Second Order Matematical model

u(t)

i(t)

w(t - xi)

w(t - 2xi)

w(t)

Velocidad Angular

Segundo Orden

Velocidad

Angular

Step

-1Z

Integer Delay2

-1Z

Integer Delay1

-1

Z

Integer Delay

u(t)

i(t - xi)

w(t - xi)

i(t)

Corriente de Armadura

Segundo orden

Corriente de

armadura

Analog

Output

Analog Output1


PCI-1200 [auto]

Analog

Output

Analog Output


PCI-1200 [auto]

93

93

-K-

1/(2*pi)

Figure 9. NI PCI 1200 Output:Second Order Mathematical model Execution timesec10.2

2.3 Simulation

Results

(Soft real time)


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3.1 Execution time

Importance

Figure 10. Real Time Simulation Time Line

[Med07]

t Simulation time

T Real time(tn, Tn)

Task

(tn+1, Tn+1)

Communication time

Idle time

Execution time of a task


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The mathematical model simulated permits the extraction and release of information

observable and synchronized with the time evolution of the process by considering thesampling criteria [Nyq28]..


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[Val09]. Valdez Martnez J. S. Modelado discreto, Simulacin, y Control de un Motor de Corriente

Continua Tipo Serie Considerando: Prdidas Mecnicas, Elctricas y Magnticas. Tesis de Maestra,

CICATA Legaria, Mxico.

[MG03] Medel Jurez J. J. y Guevara Lpez P. Introduccin a los sistemas en tiempo real IPN

[MGC07] Medel Jurez J. J. Guevara Lpez P. y Cruz Lpez D. Temas Selectos de Sistemas en tiempo

RealIPN

[GVL09] Guevara Lpez P. Valdez Martnez J. S. y Lpez E. Un Prototipo Virtual para la Enseanza delFuncionamiento del Motor de Corriente Continua Congreso Internacional de Innovacin Educativa,

Mxico

[Gue99] Guevara Lpez P. Controlde motores de corriente continua con capacidad de telecontrol y tele

monitoreo. Tesis de Maestra, CIC IPN Mxico

[Var82] Vargas Prudente P. Problemas Resueltos de mquinas Sincronas: Conversin de Energa II

IPN, 1982

[BK08] Bergero F. y Kofman E. Desarrollo de un simulador de sistemas hbridos en tiempo real.XXI Congreso Argentino de Control Automtico, Argentina

[Gue04] Guevara Lpez P. Filtrado Digital en Tiempo Real: Anlisis Computacional para Estimacin de

Parmetros en Sistemas Estocsticos Lineales Estacionarios. Tesis de Doctorado, CIC IPN Mxico

[Nyq28] Nyquist H. Certain Topics in Telegraph Transmission Theory. AIEE Transactions, EUA.

[Med07] Praveen Medisetti Real Time Simulation and Hardware-in-loop Testing of a hybrid Electric

Vehicle Control System Tesis de DoctoradoFaculty of The University of Akron, EUA, 2007.

4 Bibliography

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