### Assignment on Proportional Integral Derivative

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Table of ContentsIntroduction.................................................................................................................................................2Calculating a Transfer function................................................................................................................2SciLab.......................................................................................................................................................2Main Elements.........................................................................................................................................3Examination of Performance...................................................................................................................5Open-Loop System..............................................................................................................................5Closed-Loop System.............................................................................................................................6Improvements.........................................................................................................................................7Different Input Functions.........................................................................................................................8Summary.................................................................................................................................................9References.................................................................................................................................................101

Unit 45 Industrial Systems: - Assignment 1IntroductionSystems 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 ondesired inputs and outputs, the process that is carried out through the system can also bemodified to run a more effective chain which can in turn effect both the inputs and outputs tothe system, such as; a Proportional Integral Derivative (PID) controller can be used to maintaina constant speed on a motor which produces a steady flow rate meaning the input voltage willnot have to be switched, only maintained; thus, saving electricity.Calculating a Transfer functionUsing the Laplace transform a formula can be converted from a real variable, represented as t,into a complex variable, represented as s.d2y(t)dt2+6dy(t)dt+8y(t)=x(t)s2y(s)+6sy(s)+8y(s)=x(s)y(s2+6s+8)=xyx=1s2+6s+8SciLabScilab is open-source, free to obtain software that can be used for statistical analysis andnumerical optimisation through circuit simulation. Circuits can be made with the variouscomponents available on the software’s palette browser to simulate a system which involvesinput – process – output. Using a PID controller a variety of systems can be created, the twomade within this report include an open-loop and closed-loop system. An open loop system willhave an input which in the real world could be some form of transducer. The signal receivedfrom this sensor will be processed and calculated into a digitised reading by the programming ina controller unit. When parameters are set on the controller there may then be an output suchas a relay on the unit changing state which then can trigger more functions in the system;2

alternatively, this could start and run a motor. The output from this system has no effect on theinput.The second most common type of system, closed-loop, works on the same principle but with asecondary feedback signal to the controller. In this case an ultrasonic transducer reads thelevel, the pump is signalled to run but the process in which it pumps into can only take a certainrate of flow meaning there is a feedback signal input into the PID from a flowmeter, this willthen change the analogue output signal for the speed of the pump to maintain the requiredamount of flow. In this system the value from the output will have a direct effect on the inputto achieve a more desirable output to suit the system. This can be useful for a variety ofreasons such as improved precision and running of systems producing a higher quality andmeasurable final output from the process.After using the solution to the above equation as a transfer function in the system designed onScilabs; with a step function input into the PID, a graph can be displayed which can project howthe circuit would behave in a real environment.Main ElementsAs discussed above the circuits are small and simple with only a few components. The input forthe given system is from a step-function. A step function is simply a digital input that has twostates, 0 for off and a second, positive figure (typically 1) which will represent the circuit beingon or energised.In the closed loop system there is a data receiver function that also feeds into the PIDcontroller, this is a summation unit which will calculate the difference between the output andstepped input and vary the actual input to the controller to reduce the difference between thedesired and achieved output.The process of the system is carried out in the PID controller. Each part, Proportional, Integraland Derivative all have a different effect on the output depending on how they are set up.3

The (P) control ensures that the output of the controller is always proportional to the errorsignal received from the feedback loop. This means that the input will continually changeaccording to the input to the controller, for example; if a flow rate setpoint was 70l/s but thepump was achieving 65l/s the frequency would be increased in accordance with achieving theextra 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 outputsignal to be manipulated in accordance with the input for example if the feedback signal was away off the desired level then there would be a rapid increase in speed, on the other hand if thedifference 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 helpprevent system ‘hunting’ where the system will continually overshoot its target until it reachesthe desired setpoint. You can see this more clearly displayed in the graph below. The PI controlhas a greater number of steeper curves before the desired setpoint is reached whereas the PIDcontroller achieves its target much sooner and with a much lower degree of error overall.Figure1– Graph to show output effects generated by PID controlThe output of the system is generated on a graph built in to the circuit. This will display boththe input and the output as per the connections which will allow users to view the performanceof the controller and adjust the settings to achieve a desired result through simulation beforethe system is installed in a real situation. The accuracy of the graphs and calculations in thesimulation are extremely high and as such can be relied upon for genuine applications.4

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