Analysis and Simulation of Industrial Systems: Unit 45 Report

This report provides a comprehensive analysis of industrial systems, focusing on the application of PID controllers within both open-loop and closed-loop configurations. The report begins with an introduction to industrial systems and their role in improving efficiency, followed by an explanation of transfer functions and the utilization of Scilab for system simulation. The core of the report details the main elements of the simulated circuits, including step-function inputs and the functionality of the PID controller's proportional, integral, and derivative components. Performance evaluations are presented for both open-loop and closed-loop systems, highlighting the impact of different PID settings. Improvements in system performance are demonstrated through adjusted PID parameters and the analysis of various input functions, such as sine waves and pulsed inputs. The report concludes with a summary of the simulation software's importance in designing and testing electrical systems, along with references to support the findings.

Table of Contents
Introduction................................................................................................................ 2
Calculating a Transfer function............................................................................... 2
SciLab...................................................................................................................... 2
Main Elements......................................................................................................... 3
Examination of Performance................................................................................... 5
Open-Loop System............................................................................................... 5
Closed-Loop System............................................................................................. 6
Improvements......................................................................................................... 7
Different Input Functions......................................................................................... 8
Summary................................................................................................................. 9
References............................................................................................................... 10
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Unit 45 Industrial Systems: - Assignment 1
Introduction
Systems used in industry help to improve efficiency in repetitive work
patterns and standards. They can be analysed, improved and manipulated to
obtain varying results depending on desired inputs and outputs, the process
that is carried out through the system can also be modified to run a more
effective chain which can in turn effect both the inputs and outputs to the
system, such as; a Proportional Integral Derivative (PID) controller can be
used to maintain a constant speed on a motor which produces a steady flow
rate meaning the input voltage will not have to be switched, only
maintained; thus, saving electricity.
Calculating a Transfer function
Using the Laplace transform a formula can be converted from a real variable,
represented as t, into a complex variable, represented as s.
d2 y ( t )
dt2 +6 dy ( t )
dt +8 y ( t ) =x ( t )
s2 y ( s ) +6 sy ( s ) +8 y ( s )=x ( s )
y ( s2 +6 s +8 ) =x
y
x = 1
s2 +6 s+8
SciLab
Scilab is open-source, free to obtain software that can be used for statistical
analysis and numerical optimisation through circuit simulation. Circuits can
be made with the various components available on the software’s palette
browser to simulate a system which involves input – process – output. Using
a PID controller a variety of systems can be created, the two made within
this report include an open-loop and closed-loop system. An open loop
system will have an input which in the real world could be some form of
transducer. The signal received from this sensor will be processed and
calculated into a digitised reading by the programming in a controller unit.
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When parameters are set on the controller there may then be an output such
as a relay on the unit changing state which then can trigger more functions
in the system; alternatively, this could start and run a motor. The output
from this system has no effect on the input.
The second most common type of system, closed-loop, works on the same
principle but with a secondary feedback signal to the controller. In this case
an ultrasonic transducer reads the level, the pump is signalled to run but the
process in which it pumps into can only take a certain rate of flow meaning
there is a feedback signal input into the PID from a flowmeter, this will then
change the analogue output signal for the speed of the pump to maintain the
required amount of flow. In this system the value from the output will have a
direct effect on the input to achieve a more desirable output to suit the
system. This can be useful for a variety of reasons such as improved
precision and running of systems producing a higher quality and measurable
final output from the process.
After using the solution to the above equation as a transfer function in the
system designed on Scilabs; with a step function input into the PID, a graph
can be displayed which can project how the circuit would behave in a real
environment.
Main Elements
As discussed above the circuits are small and simple with only a few
components. The input for the given system is from a step-function. A step
function is simply a digital input that has two states, 0 for off and a second,
positive figure (typically 1) which will represent the circuit being on or
energised.
In the closed loop system there is a data receiver function that also feeds
into the PID controller, this is a summation unit which will calculate the
difference between the output and stepped input and vary the actual input
to the controller to reduce the difference between the desired and achieved
output.
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The process of the system is carried out in the PID controller. Each part,
Proportional, Integral and Derivative all have a different effect on the output
depending on how they are set up.
The (P) control ensures that the output of the controller is always
proportional to the error signal received from the feedback loop. This means
that the input will continually change according to the input to the controller,
for example; if a flow rate setpoint was 70l/s but the pump was achieving
65l/s the frequency would be increased in accordance with achieving the
extra 5l/s but this will be constantly monitored and adjusted.
The (I) function is the integration of the error feedback signal. This is what
allows the output signal to be manipulated in accordance with the input for
example if the feedback signal was a way off the desired level then there
would be a rapid increase in speed, on the other hand if the difference was
only minor then the increase to the output signal would also only be minor.
The (D) function is used to monitor and reduce the rate of change of the
output. This is to help prevent system ‘hunting’ where the system will
continually overshoot its target until it reaches the desired setpoint. You can
see this more clearly displayed in the graph below. The PI control has a
greater number of steeper curves before the desired setpoint is reached
whereas the PID controller achieves its target much sooner and with a much
lower degree of error overall.
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Figure 1 – Graph to show output effects generated by PID control
The output of the system is generated on a graph built in to the circuit. This
will display both the input and the output as per the connections which will
allow users to view the performance of the controller and adjust the settings
to achieve a desired result through simulation before the system is installed
in a real situation. The accuracy of the graphs and calculations in the
simulation are extremely high and as such can be relied upon for genuine
applications.
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Examination of Performance
Open-Loop System
Proprtional 5
Integral 10
Derivative 1
In this open loop system, the output can be clearly seen to continually rise
upwards until it reaches its maximum with no fluctuation at all. These are
controlled by the PID settings input as shown above, the high integral
setting means that it will rapidly increase and with no feedback this
increase will be maintained until a fault or maximum is reached.
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Closed-Loop System
Proprtional 0.55
Integral 10
Derivative 10
In this closed loop system, it can be seen that the desired output of 1 has
actually been achieved but this was over the 10 second time frame in the
graph. There is also a slow ramp up time, large overshoot which then in
turn also goes below the desired set point again, this is a great
improvement on the open loop system but is still inefficient.
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Improvements
Open-Loop
Proportional 10
Integral 0.001
Derivative (-)1
As can be seen the changes on the PID controller have had a massively
positive effect, the output reached its maximum target shortly after the
step function and has managed to level out and maintain this point for the
duration of the simulation. Reaching the peak much sooner will benefit the
system as it will use less electricity and resources once it gets there.
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Closed-Loop
Proportional 10
Integral 0.001
Derivative (-)1
The closed loops system has equally been improved in that it reaches the
setpoint before 2.5 seconds, this is only 1.5 seconds after the step function
was activated. There was a slight overshoot of the setpoint but this was
soon corrected and the level was maintained for the duration of the
simulation from then on. Comparing to the last measurement, the newer
one has significantly improved.
Different Input Functions
Using these parameters for the PID controller will also help in getting
accurate readings when using different input sources. Used below was a sine
wave input in an open-loop system, the output can be seen to follow the
trend of the input almost exactly from positive through back down to the
negative cycle also.
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In the setup below a pulsed input was used in the closed-loop system, the
PID settings had to be changed to suit to allow for the output to pulse on and
off to match the input. This is much more difficult in a shorter space of time
and as such the copy of the waveform is not as synchronous. There is a very
close similarity and the PID can be seen to be working with an overshoot,
recalculation and then drop off when it tries to correct once the input is lost.
Summary
Simulation software can play a huge role in designing, creating and testing
electrical systems before they are built. Their electrical philosophy can be
tried, tested and manipulated to ensure the product made works sufficiently.
The output produced can be changed by altering the settings programmed
into the PID controller but some input types are much harder to control than
others as can be seen from the last design.
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References
Figure 1 - Sheble, N. (2019). Automation Basics: P, I, and D together,
separately control the process - ISA. [online] Isa.org. Available at:
https://www.isa.org/standards-and-publications/isa-publications/intech-
magazine/2009/june/automation-basics-pi-and-d-together-separately-control-
the-process/ [Accessed 12 Dec. 2019].
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