# Whenever the differential equations and the mathematicalWhenever the differential equations and the mathematical

Whenever a computer simulation of a model of any
physical process or a system is done in parallel to its physical counterpart
can be referred to as the real time simulation. The
virtual representation of physical system i.e. a virtual model runs
simultaneously and also for the same time as the physical system. They may
share common input variables and come out with comparable output. One
good example for a RTS can be operation of the Fuel Injection System of a
modern day computer controlled car engine, the onboard computer (Engine Control
Unit) calculates the duration of operation and the interval between each
operation based upon the throttle input, camshaft position, inputs from Oxygen
Sensors, inputs from NOx sensors etc. all of which are measured in real time.
Another suitable example are the computer games where outcomes are generated
based on user inputs in real time.

A computer does all the computations using an
operating system which eventually does all of its calculations in the form of
0’s and 1’s. All the differential equations, state equations or any mathematical
functions representing a physical system will converted to a discrete system of
0’s and 1’s, these will be solved by the computer simulation software using
their own solvers. The solvers use different numerical methods to do the
computations and each may take different amount of time and produce results
with different accuracy.

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To work with RTS the simulation associated would
be for discrete time with a constant step size. Variable time-steps simulation
is not suitable for RTS and hence the time is incremented in equal step sizes
called Simulation Time Steps and the simulation itself is often called Fixed
Time Simulation.

As mentioned earlier the differential equations
and the mathematical functions representing the model are solved to perform the
i/o operations and to obtain the output of the model. However during a
‘discrete non real time simulation’ the actual time required to solve the
aforementioned equations and functions may be more or less than the simulation
time step. But in case of real time simulation it is necessary that (apart from
the precise modeling of the physical system) all the computations are done
within the simulation time step so that the model under test can accurately
represent the functioning and perform all the I/O operations of its equivalent
real or physical system.

If the computations are not complete within the
simulation time step the real time simulation results are not accurate which is
also referred to as ‘overrun’. Moreover if the computations are done before the
simulation time step is complete then the remaining time, called the
‘idle-time’ is simply lost, which is in contrast to the accelerated
simulations where the remaining time would be used to perform the computations
of the subsequent time step.