RTS Introduction
Terminology
Real-Time
System Design Issues
Example RTS
Common Misconceptions
Brief History
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Terminology
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System
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Real-Time Definitions
Deadlines come from the underlying physical phenomena of the
system under control. For example, in animated displays, images must
be updated at approximately 30 frames/second to provide continuous
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motion
2009)
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Events and Determinism
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Determinism
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CPU Utilization
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Real-Time System Design
Issues
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Example Real-Time Systems
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Single-input single-output PID
controller

PID (Proportional, Integral and Derivative). The
analog sensor reading y(t) gives the measured state
of the plant at time t. Let e(t)=r(t)-y(t) denote the
difference between the desired state r(t) and the
measured state y(t) at time t.
Reference input
r(t)
uk
rk
Control-law
computation
A/D
D/A
yk
A/D
u(t)
y(t)
Sensor
Plant
CMPE-443 Real-Time System Design (Spring
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Actuator
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PID Controller
The output u(t) of the controller depends on three terms: a term that
is proportional to e(t), to the integral of e(t) and to the derivative of
e(t). In the sampled data version, the inputs to the control-law
computation are the sampled values yk and rk, k=0,1,2,.., which
analog-to-digital converters produce by sampling and digitizing y(t)
and r(t) periodically every T units of time. ek=rk-yk is the k-th sample
value of e(t). There are many ways to discretize the derivative and
integral of e(t). For example, we can approximate derivative of e(t)
for (k-1)T<=t<=kT by (ek-ek-1)/T and use the right rectangular rule of
numerical integration to transform a continuous integral into a
b
discrete form:
 f ( x)dx  f (b)(b  a)
a
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PID Controller
a,b,c are some constants; they are chosen at the design time.
During the k-th sampling period, the RTS computes the output
of the controller according to this expression. Different
discretization methods may lead to different expressions for uk,
but they all are simple to compute (10-20 machine instructions).
kT
k
0
i 1
u k  ek   (ek  ek 1 ) / T    e(t )dt  ek   (ek  ek 1 ) / T    ei T
k 1
u k 1  ek 1   (ek 1  ek 2 ) / T    ei T
i 1
uk  uk 1  aek 2  bek 1  cek
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Controller algorithm
Set timer to interrupt periodically with period T;
At each timer interrupt, do
Do analog-to-digital conversion to get y
Compute control output u
Make digital-to-analog conversion and output
u
End do
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Time sampling
The length T of time between any two consecutive instants at which y(t) and r(t)
are sampled is called the sampling period. T is a key design choice. The
behavior of the resultant digital controller critically depends on this parameter.
Ideally, we want the sampled data version behave like the analog version. This
can be done by making T small. However, this will lead to more frequent
control-law computation and higher processor-time demand.
The operator may issue a command at any time, say at t. The consequent
change in the reference input is read and reacted to by the digital controller at
the next sampling instant. This instant can be as late as t+T. Thus, sampling
introduces a delay in a system response. The operator will feel the system
sluggish when the delay exceeds a tenth of a second. Therefore, the sampling
period should be under this limit.
The second factor is the dynamic behavior of the plant (considered earlier).
It is recommended to use sampling frequency twice as highest possible
frequency occurring in the system to be able to reproduce such signals
(Nyquist-Kotelnikov theorem).
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Common Misconceptions
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Brief History
http://en.wikipedia.org/wiki/Whirlwind_(computer)
http://en.wikipedia.org/wiki/Semi_Automatic_Ground_Environment
http://en.wikipedia.org/wiki/Sabre_Airline_Reservations_System
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