REAL-TIME SYSTEMS
Real-time systems (RTS) are systems, intended for the interaction (in the
first turn, for control) with real physical objects and this interaction must run
at a real physical time, in those temporary scales, in which live these objects.
If we speak about control of fast running processes (for instance, when
controlling flying apparatus having speed of the order 600 km/hour and
altitude of 50 m then temporary scales for making and fulfilling decisions
must have order of 0.01 sec).
RTS are usual computing systems (CS), but intended for functioning in
terms of hard temporary restrictions and which must have developed
facilities of the interactions with the external world for the reception of
information on objects of control and for the transferring them worked out
control influences
Real-time system
RTS
Control stimuli
information
external
stimuli
CO
Controlled object
Such systems must possess increased reliability.
There are distinguished soft RTS (violation of timing restrictions in some
range does not lead to the system failure), hard RTS (violation of timing
restrictions leads to the system failure) and firm RTS (violation of timing
restrictions in some range does not lead to the system failure with certain
probability).
EXAMPLE OF REAL-TIME SYSTEM
Let’s consider an analog single-input/single-output PID (Proportional,
Integral and Derivative) controller. 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
Actuator
The output u(t) of the controller consists of 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
b
right rectangular rule of numerical integration (  f ( x)dx  f (b)(b  a) )to
a
transform a continuous integral into a discrete form.
EXAMPLE OF REAL-TIME SYSTEM (CONT 1)
The result is the
kT
k
0
i 1
u k  ek   (ek  ek 1 ) / T    e(t )dt  ek   (ek  ek 1 ) / T    ei
Considering uk-1, we get
k 1
u k 1  ek 1   (ek 1  ek  2 ) / T    ei
i 1
From two last equations, we get
u k  u k 1  aek 2  bek 1  cek
(1)
where 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).
From (1), we can see that during any sampling period (say k-th), the control
output uk depends on the current and past values yi, i<=k. The future
measured values yi for i>k in turn depend on uk. Such a system is called a
(feedback) control loop or simply a loop. CONTROLLER’S
ALGORITHM
We can implement it as an infinite timed loop:
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
ABOUT 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.
We want a sampling period T that achieves a good compromise.
In making this selection we are to consider two factors. The first is the
perceived responsiveness of the overall system (i.e., the plant and the
controller). Oftentimes, the system is operated by a person (driver, pilot).
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).
EXAMPLE OF FLIGHT CONTROLLER
Let’s consider software control structure of the flight controller:
Do the following in the 1/180 –second cycle:
Validate sensor data and select data source; in the presence of failures,
reconfigure the
system
Do the following 30-Hz avionics tasks, each once every six cycles:
keyboard input and mode selection
data normalization and coordinate transformation
tracking reference update
Do the following 30-Hz computations, each once every six cycles:
control laws of the outer pitch-control loop
control laws of the outer roll-control loop
control laws of the outer yaw- and collective control loop
Do each of the following 90-Hz computations once every two cycles, using
outputs
produced by 30-Hz computations and avionics tasks as input:
control laws of the inner pitch-control loop
control laws of the inner roll- and collective-control loop
Compute the control laws of the inner yaw-control loop, using outputs
produced by 90-Hz control-law computations as input
Output commands
Carry out built-in test
Wait until the beginning of the next cycle
EXPLANATION OF PHYSICAL VALUES
Three velocities along axes are called collective velocities, rotational
velocities around axes are illustrated below:
GENERAL CASE CONTROLLERS ALGORITMS
This multirate controller controls only flight dynamics. The control system
on board an aircraft contains many other equally critical subsystems. In
many cases, sensor gives not the value of the state variable, but some
observable attributes of the plant, and state variables should be computed on
their basis. In such more complicated cases controllers may be represented
by the following schema
Set timer to interrupt periodically with period T;
At each clock interrupt, do
Sample and digitize sensor readings to get measured values
Compute control output from measured and state-variable values
Convert control output to analog form
Compute and update plant parameters and state variables
End do
HIERARCHICAL CONTROL
Usually, control is made in many levels, hierarchically.
Figure above shows example of hierarchy of flight control, flight
management and air traffic control systems.
AIR TRAFFIC/FLIGHT CONTROL
The Air Traffic Control (ATC) system is at the highest level. It regulates the
flow of flights to each destination airport. It does so by assigning to each
aircraft an arrival time at each metering fix (known geographical point,
adjacent points are 40-60 miles apart) in the route to destination. The aircraft
is supposed to arrive at the metering fix at the assigned time. At any time
while in flight, the assigned arrival time to the next metering fix is a
reference input to the on-board flight management system. The flight
management system chooses a time-referenced flight path that brings the
aircraft to the next metering fix at the assigned arrival time. The cruise
speed, turn radius, descend/ascend rates and so for required to the chosen
time-referenced flight path are the reference inputs to the flight controller at
the lowest level of hierarchy.
Computations made by controllers of low levels may be simple and
deterministic while high-level controller interacting with operator is more
complex and variable (for example, expert system). Period of low-level
controller ranges from milliseconds to seconds, the periods of high-level
controllers may be minutes and even hours.
AIR TRAFFIC CONTROL SYSTEM
The ATC system monitors the aircraft in its coverage area and generates and
presents information needed by the operators. Outputs from the ATC system
include the assigned arrival times to metering fixes for individual aircraft.
These outputs are reference inputs to on-board flight management systems.
Thus, the ATC system indirectly controls the embedded components in low
levels of hierarchy. In addition, the ATC system provides voice and
telemetry links to on-board avionics. The ATC system gathers information
on the state of each aircraft via one or more active radars. Such radar
interrogates each aircraft periodically.
AIR TRAFFIC CONTROL SYSTEM (CONT 1)
When interrogated, an aircraft responds by sending the ATC system its state
variables: identifier, position, altitude, heading and so on (these variables in
the figure are referred to collectively as a track record, and the current
trajectory of the aircraft is a track). The ATC system processes messages
from aircraft and stores state information in the database. This information is
picked up and processed by display processors. At the same time, the
surveillance system continuously analyses the scenario and alerts the
operators whenever it detects any potential hazard (e.g., a possible collision).
Again, the rates at which human interfaces operate (keyboards and displays)
must be at least 10 Hz.
From this example, we can see that a command and control system bears
little resemblance to low-level controllers. In contrast to low-level controller
whose workload is either purely or mostly periodic, a command and control
system computes and communicates in response to sporadic events and
operator’s commands. It may process images and speech, query and update
databases, simulate various scenarios, and the like. The resource and
processing times demands can be large and varied.
CRITERIA USED FOR RTS DESIGN
When designing RTS, as well as for the comparison of existing
systems are used different criteria of their quality, the most
important of them are the following:
 Performance - an amount of executed operations in the unit of
the time. If, for instance, there must be solved batch of tasks
z i ir1 with computational complexities (total amount of
operations) Qi then performance may be calculated as
r
Р=
Q
i 1
T
i
,
where Т is the time of execution of all the batch tasks.
To evaluate current performance at the time moment t there may be used
P(t)= lim
 0
Q (t , t   )
,

where Q(t1,t2) is complexity of tasks executed by system in the time
interval [t1,t2).
 System cost С, which must include not only cost of its creation
or purchase price but also cost of maintaining it in the working
state
 Cost of performance unit (1 operation/sec), calculated as С/Р,
or inverse value Р/С, characterizing performance obtained per
dollar of expenditure.
 System
volume,
system
mass,
energy
consumption,
intensiveness of system radiation, working temperature
CRITERIA USED FOR RTS DESIGN (CONT 1)
RTS are intended to solve definite sets of tasks, for example,
simulate moving of flying apparatus, finding out optimal trajectory
of flying, making and transfer of control stimuli to corresponding
mechanical devices. These tasks are to be solved in minimal
possible time or in the time not greater than predefined. In
connection with that there may be considered the following
criteria:
 Minimization of the total execution time То of the batch having
L tasks. If fi is a moment of the time of termination of i-th task,
then total execution time
То= max f i ,
i 1, L
and it is necessary to find
min max f i .
i 1, L
This criterion corresponds to maximization of performance of the
system when solving given batch of tasks, because computational
complexity is constant, and denominator is minimized in the
expression for performance.
CRITERIA USED FOR RTS DESIGN (CONT 2)
 Each task of the batch may have its deadline di – time moment
before which it must be solved. There may be used the
following criteria:
L
min
( f
i 1
i
 di ) ,
i
 di | ,
L
min
| f
i 1
L
min
 max( 0, f
i 1
i
 di )
min max  f i  d i 
i 1, L
min max | f i  d i |
i 1, L
min max | 0, f i  d i | .
i 1, L
The first 3 criterions use mean deviations from deadline terms, and last 3 use
maximal deviations. In the first criterion an excess of deadline term for one
task can be compensated by earlier solution of other tasks, in the second
variant are fined both an excess of deadline term, and early solution, in the
third variant is fined only excess of deadline term. For last three criterions
important is maximum deviation. Besides, there can be introduced weights,
characterizing importance of tasks and, accordingly, violations of deadline
terms for the given task.
CRITERIA USED FOR RTS DESIGN (CONT 3)
 For server type systems, for instance, phone stations,
communication nodes, headquarters may be important criterion
defining mean number of tasks (users) served in the time unit,
i.e. throughput of the system. Here is important not
computational complexity of executed tasks but number of
served users standing beyond these tasks, number of made
decisions. Throughput is maximized when mean time of staying
tasks in the system is minimized. Let number of tasks be – L,
time moment of i-th task arriving to the system is si, time
moment of i-th task execution finishing is fi, i=1,..,L. Then
mean time of staying tasks in the system is Тс =
L
( f
i 1
i
 si ) / L .
If time staying in the system of i-th task is f i  si , i  1, L , then
we may say that for i-th task each unit of time 1/( f i  si ), i  1, L ,
part of task leaves the system and in whole the following
L
number of tasks L /  ( f i  si ) leave system per time unit, i.e.
i 1
throughput is value inverse to mean time of staying tasks in the
system. Thus, to maximize throughput it is necessary to
minimize mean time of staying tasks in the system, and for
maximization of performance we need in minimization of
maximal time of staying tasks in the system.
APPROACHES TO OPTIMIZATION TASKS
Let’s note that minimization of То is NP-hard task.
For solution of such tasks usually are applied polynomial-hard
heuristic algorithms giving not optimal but rather good solutions.
So, to optimize То there may be used algorithm LPT (Largest
Processing Time task – first) with time complexity О(LlogL+Ln).
Essence of that algorithm is to sort tasks in the descending order of
execution times and assigning them in such order to freeing
processors.
It was proved that when allocating any batch П of independent
tasks (order of assigning may be arbitrary, there is no precedence
relation on the tasks set)
То(П,LPT)/То(П,ОPТ)<(4/3-1/(3n)),
where То(П, ОPТ) – is optimal execution time of batch П.
Task of optimization of Тс is optimally solved by algorithm SPT
(Shortest Processing Time task – first) of the same time complexity
as LPT.
In SPT algorithm tasks with less execution time are
pushed forward.
EXAMPLES OF APPLICATION OF LPT AND SPT
Let tasks of the batch П have the following execution times:
(3,3,2,2,2).
Then in the case of 2-processor system (n=2)
P1
P2
1
3
Tо(ОPТ)
=6
2
3
3
P1
3
P2
3
a)
2
3
1
To(SPT)
=7
Tc(SPT)=
4
c)
P1
1
3
P2
2
3
3
To(LPT)
=7
Tc(LPT)
=4.6
Tasks are represented by
their numbers
b)
MULTIPLE CRITERIA OPTIMIZATION
When designing RTS we are to take into account many different
criteria, often contradicting each other (performance – cost, performance –
size, etc.). It’s obvious that optimal solution of this task is extremely hard,
because it is necessary to solve make multiple criteria optimization. Here, as
a rule, two simplifying approaches are used:
- usage of one general criterion which is obtained by forming one
expression involving all necessary criteria (usually sum, or weighted sum
with weights taken from (0,1), showing importance of corresponding
criterion, sum of weights equal to 1);
- optimization on one criterion using other as restrictions.
So, design of RTS is a complex multiple criteria task in the result of
solving which there must be obtained CS having desired for control of
respective objects features. For achieving such a goal it is necessary to use
existing resources in optimal way. As it is obvious from modification of only
order of tasks serving, without modification of hardware, cost, mass and so
on, we can significantly influence on system characteristics
TOPICS TO BE CONSIDERED FARTHER
Main resources of the system are processors, processor time, RAM,
external memory. These resources are used by processes running program
codes. So, we shall consider problems of control of processes and system
resources.
Usually RTS is to control multiple objects simultaneously; therefore
even in the case of uniprocessor systems they are to support multitasking,
Therefore for RTS it is very important to manage in optimal way parallel
processes responsible for corresponding controlled objects.
For the sake of more rapid response (control outputs) it is widely
used parallelizing of computations between several processors, so we shall
consider issues of parallelizing and related problems.
RTS are dedicated for controlling of real objects and cost of their
failure may be extremely high (for instance, error in controlling of nuclear
reactor on Chernobyl nuclear power station). Therefore there must be used
methods for increasing reliability of software and hardware incorporated in
RTS. We shall consider approaches to this issue starting from design.
RTS are complicated software-hardware products, in which there
must be present model of controlled object, facilities for interaction with
external world with the help of input-output devices. To simplify
development of such systems there were elaborated SCADA systems, which
we shall briefly consider in our course.
Very important for RTS are issues of communication with external
devices, which is usually organized with the help of drivers. We shall also
briefly touch this topic.