Formal Lab Reports

 

Some really important pieces of information to start this out:

 

 

Formal Lab Report Info

 

·      Read the manual

·      Read closely the report production instructions

·      Decide what can be answered without much effort

·      Start taking notes

·      Get an understanding of the laboratory itself

·      Talk to your lab partners

·      Highlight the needs of the report that will be discovered in the laboratory itself

·      Start assembling the required information for the specific sections:

 

Abstract

Nomenclature

Introduction

Lab Observations

Results

Discussion

Conclusion

·      If you do not have all the needed information – ask questions – see your TA

·      Prepare a rough draft and have X number of people read it

·      Make changes where they see the need

·      Make decisions on why it is good or poor communication – change if needed

 

 

Suggestions

 

·    Find readers

·    Read out loud

·    Read to see if it makes sense

·    Read to see if it follows some kind of order

·    Read to see if it is understandable

·    Read as if your job depended upon it

·    Ask for help when you need it



Read Instructions

Follow Instructions

Ask Questions

Clarify everything

Build a readership



REPORT CHECKLIST

 

 

The following items make up the elements that will be evaluated in the formal reports for ME 451 from the composition side.  Teaching assistants will comment on the inadequate elements, and you will have to address those comments.

Examples of all these items can be found in the lab and in the library under Craig Gunn's name in the reserved reading.

If you can’t put these numbers at places within your report, then there are important element missing; and you need to address them.

 

 

TITLE PAGE

 

1.Title of paper 

2.Course 

3.Date due 

4.Section time 

5.Name  

6.DRAFT OR FINAL COPY

 

 

SUMMARY

 

7.Overview of the lab

 

8.Why was the lab performed 

 

9.How was the lab performed 

 

10. What was discovered,achieved, or concluded   

 

11. Recommendations

 

12.Past tense used 

 

13.Reference to experiment not paper  

 

14.No personal reference ( I,We)

 

15. It  is before the Tale of  Contents

 

TABLE OF CONTENTS

 

16.All sections represented 

 

17.Abstract and Table of C not listed 

 

18.Lab Observations as a heading

  Analysis,equip,procedure,

  results - sub headings   

 

19.All columns lined up   

 

MOTIVATION AND OVERVIEW

 

20.Ample motivation for the experiment stated

            20A.yours   

            20B.Whirlwind's 

 

21.Sufficient information to orient reader to the substance of experiment 

 

22.Sections to follow mentioned

 

23.Any terminology that reader will need to understand the text.

 

THEORETICAL BACKGROUND

 

24.Mathematical model used to predict system behavior presented with ample explanation and lead in  

 

  25.equations numbered

  26.punctuation with equations        

            (: with follow/s/ing only)

  27.equations have space 

 

EXPERIMENTAL SETUP AND

PROCEDURE

 

28.Schematic of equipment used

29.Figures/Tables correct

    (Figure 1. Title)

30.Figures oriented correctly

  Clearly labelled and   referenced 

 

31.Highlights of equip. used 

 

32.Highlights of the procedure  (not specific steps)

 

RESULTS AND DISCUSSION

 

33.Data presented with clear   indication of what data applies to  

 

34.Reader will understand what this data refers to   

 

35.Trends in data stated (then to be discussed in the discussion section) 

 

36.Clear indication of what reader should see in the data  

 

37.Complete discussion of the results appears 

 

38.Connection of data and Whirlwind is clearly stated 

 

39.Comparison to similar experiments is shown  

 

40.Strong points of study given 

 

41.Weak points of study given

 

42.Statements are specific

 

43.Logical progression to support

 conclusions that follow  

 

 

CONCLUSIONS AND

RECOMMENDATIONS

 

44."The following conclusions are supported by this study:" 

 

45.Conclusions are numbered 

 

46.Conclusions are concise and highly specific 

 

47.Vague statements do not exist

 

48.Conclusions directly flow from discussion 

 

 

 

REFERENCES

 

49.Initials for first names 

 

50.All information included

 

51.References #d in text [1]

 

 

 

 

Comments appear across your papers and the following give you an idea of what those comments entail. Sometimes our own writing sounds perfectly appropriate until someone else takes a look. See what you think.

 

 

 

 


Awkward Wordings – Making No Sense

 

The Marshall test is used to determine the maximum density of bituminous mixtures in the field as well as in the lavatory.

 

Place jumper between sockets A and B; none between X and Y

 

The Women’s Advisory Group is comprised of representatives from four broad areas:

 

When you smell an odorless gas, it is probably carbon monoxide.

 

I had a great internship with Whirl poop.

 

Blood  flows down one leg and up the other.

 

Three kinds of blood vessels are arteries, vanes, and caterpillars.

 

To remove dust from the eye, pull the eye down over the nose.

 

If we don’t succeed , we run the risk of failure.

 

 

Poor Wording – etc.

 

I was recently on a tour of Latin America, and the only regret  I have was that I didn’t study Latin harder in school so I could converse with those people.

 

Mars is essentially in the same orbit....Mars is somewhat the same distance from the Sun, which is very important. We have seen pictures where there are canals, we believe, and water. If there is water, that means there is oxygen. If oxygen, that means we can breathe.

 

i souport publik edukashun.

 

The device must be able to withstand a certain amount of heat

 

Iraqi Head Seeks Arms

 

Queen Mary Having Bottom Scraped

 

Lawmen from Mexico Barbecue Guests

 

Two Soviet Ships Collide – One Dies

 

Enraged Cow Injures Farmer with Ax

 

Man is Fatally Slain

 

 

 

 

Commas, semicolons, colons

 

Take a look at thses examples and see if you can figure why the punctuation is approapriate or not.

 

In the experiment, the results were conclusive.

 

I found it easy to examine the magnesium, cordite and byrillium, and lead.

 

Mary, Bob and I shared the inheritance.

 

You were not to be found using the devices, and I will have to report you for the failure to follow the rules.

 

The last conclusion was correct; the first was slightly wrong.

 

The job was enjoyable; comforting, relaxing, and worthwhile; and long.

 

We need to understand the following:

        Ethics

        Morality

        Price of Lunch

        Vacations

 

We need to understand Ethics, Morality, Price of Lunch, and Vacations.

 

I gave you:

        money

        good looks

        talent

 

 

 

 

 

Some suggestions from the reports that have been turned in over the course of the semesters:

 

Put the laboratory TA’s name on the memo – he/she gives you the grade and should be recognized.

 

It’s means it is

Its is the possessive.

 

Comma in a series   - better to use John, Mary, and Bill – use comma before and

Do not use commas where the sentence is simply showing two items connected by and

  • I bought the equipment and the schematics.
  • I bought the equipment, and the schematics. (delete the comma)

 

When you have an adverb at the beginning of the sentence, place a comma after it to separate it from the rest of the sentence.

  • Therefore, you will need to ready the Bunsen burner.
  • Interestingly, the lab didn’t burn when we spilled the acid on the floor.

 

Avoid prepositions at end of a sentence .

  • Finding the time constant allowed for confirmation of  the lumped capacitance model which this experiment is based upon. (don’t have the preposition at the end of the sentence)

 

  • Finding the time constant allowed for confirmation of  the lumped capacitance model upon which this experiment is based.

 

Don’t put a comma before BUT if no subject and verb follow it.

  • The lab was difficult but valuable
  • The lab was difficult, but it was valuable.

 

Use a colon to designate a list to follow.

  • There were two types of thermocouples: Type E and Type J.  (this has list)
  • I used the Type E and Type J thermocouples.  (This is a flowing sentence with no hesitation)

 

When using a sentence that has two independent clauses connected by a coordinating conjunction use a comma to show the reader that you have two separate sentence ideas contained in the one sentence.

  • The soldered ends of the thermocouple were blistered,  and the problems escalated exponentially

 

 

Tables and Figures

 

  • Put Table #. Title on top of the table.
  • Put Figure #.Title under the figure
  • Don’t call Figures with #’s GRAPHS or PLOTS.

 

SUGGESTION:

  • Write out and capitalize Figure and Table when used with #’s throughout the text. It adds to the look and continuity of the document.
  • Use a consistent form when labeling figures and tables  -  Table 1. Title / Figure 1. Title

 

DATA – This is a plural word so requires a plural verb.

  • Data are collected to ensure quality. ( If it sounds bad, reword the sentence!)
  • These data were flawed.

 

##

  • If you have regular numbers, don’t attach the # sign to them
  • I have #2

 

Verb Tense

 

  • Use the past tense to talk about things that you have finished.

You can use the present and the past tenses, but make sure that the reader knows when these things are happening.

 

  • I will do the lab. It was a great experience to finish it on time. I am able to move things around on the computer with ease. I will keep doing this yesterday. (A little confusing.)

 

Appendices

 

  • Appendices are information that you may not readily need for your report but may be interesting or needed by a more diligent reader.
  • Label tables and figures in order from the beginning Table A1, A2, A3 / Figure A1, A2, A3.
  • If you have a number of sections in your appendices label as B1, B2, / C1, C2, etc.

 

Avoid:

 

  • Using First, second, third in you r writing – sounds like a story. Just move through the points. The reader should be able to figure out what comes first then second…

 

Hyphens

 

  • These drive me crazy. If they bother you, look up definitions for hyphen in a grammar book and copy the definition and keep it close by as I do.
  • RULE: Use a hyphen to connect two or more words functioning together as an adjective.
    1. We used a time-based orthoscope.

 

 

 

  

 

  • Avoid putting Quotation marks “   “ around words. This draws unneeded attention to the word.

 

This is

 

  • Avoid  This is beginnings to sentences. Sound is not good and relays a message to the reader that you are simply telling a story.

 

Broken up

 

  • Use divided or other better word.

 

Effects/affects

 

  • Effect is the noun / affect is the verb
  • The effect of the lab was affected by Bill’s snoring.

 

FLOW

 

  • Make an effort to look closely at your text and see if you can easily find the ways in which the text moves smoothly. If it is easy to read, it flows

 

  • The laboratory was developed to provide easy access to the equipment used in industry. This equipment was donated by four companies in the greater Lansing area. Ambotech, one of the donators, felt strongly about the importance of giving students a chance to work with “real world” equipment.

 

Figures and Tables

 

 

 

 

 

 


s

p

e

e

d

 

 

 

 

               action

 

Figure 1. The Cascading Harmonics of F=W+2

 

Figure 1 The Cascading Harmonics of F=W+2

 

Figure 1 The Cascading Harmonics of F=W+2. Applications enhanced by J.Tomlinson, MIT.

 

 

Table 1. Number of Trial Runs in Relation to Temperature

 

 

Trial Runs

 

 

 

Temperature

 

 

 

 

 

 

 

 

 

 

 

Notice the different acceptable formats for the figures.

Figures designated under the figure. Tables with headings on top.

 

 

By Spelling out and capitalizing Figure and Table, your entire document is uniform. Consistency is vital in any document that you create.

 

 

 

 

 

Making the text work

 

Paragraphing:

               topic sentences

          supporting ideas

          no more

 

Transitions:

Word, phrase, sentence, paragraph, or even a longer passage that ties information together

 

               usually

                              however

                        on the other hand

                        in spite of

 moreover

also

as a result of

therefore

for example

next

then

and

but

in the first place

 

 

1. To start out – be mechanical

         This concludes the discussion. Next I will tell about the conclusions. The conclusions are now over.

 

2. When done with a first draft read it out loud and look for places where a good transition would help the text to     flow more smoothly.

 

 

Remember – Don’t let your reader get lost. Transitions help the reader to connect thoughts together. Without the connections, it is easy to lose track of the message.

 

 

Pronouns and Antecedents

 

 

Make sure that nouns and pronouns agree with each other. Also make sure that the reader knows exactly what you are referring to when you use a pronoun. First paragraph has many unclear pronouns. Paragraph two is much better.

 

 

The magnesium became much lighter after the tube was filled and greater heat was gained in the process, which it didn’t account for. It was difficult to handle. This might not have caused any problems, but it could have created some difficulty in measuring the results, which they were not accounted for in.

 

 

 

The magnesium became much lighter after the tube was filled and after greater heat was gained in the process. A lightness that was not accounted for in the process. The magnesium at this point in the process was difficult to handle because of its temperature and its lack of weight. These problems might not have caused any problems, but they could have created some difficulty in measuring the results, results that were not accounted for in the original expectations of the experiment.

 

 
 
Subject/ Verb Placement

 

Notice how the placement of the subject to the verb affects the understanding of the text – if the verb and subject are close, it is easier to understand. If further apart, the meaning is less clear.

 

The magnesium after filling the tube and gaining greater heat in the process which was not a bad thing but might have created some difficulty became much lighter.

 

 

The magnesium became much lighter after the tube was filled and greater heat was gained in the process, which was not a bad thing but might have created some difficulty

 

The magnesium became much lighter after the tube was filled and greater heat was gained in the process. This might not have caused any problems, but could have created some difficulty in measuring the results.

 

 

Guidelines for writing the ME 451 Lab Report

 

While we state and approximate page length, It is vital that you get your message across and stop. Repetition does not get you a better grade. A short succinct report speaks volumes.

 

 

The Abstract (approximately 200-250 words)

 

The experiments were conducted to (don’t mention anything about people – only the lab) ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________

 

 

 

The laboratories were conducted by using the following tools, materials, laws, theories

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________

 

 

The conclusions drawn from the laboratories were

________________________________________________________________________

________________________________________________________________________

 

 

 

Nomenclature (all the symbols used in the paper)

 

All symbols contained in the equations ( no abbreviations) in alphabetical order

 

Arabic

 

f       = frequency

H(t)  = heat in the mixing tank

h      =  heater core temperature

T(t)   = mixing tank temperature

T      = Time (seconds)

 

Greek

 

t = V/Q = time constant (sec)

r = density (gm/cc)

 

Introduction (approximately ½ page)

 

            In industry, processes often require control of the temperature of a fluid in a holding tank.  Therefore, two experiments were performed which investigated the issues related to this control process.  The first was a simulation, utilizing Matlab scripts to simulate a physical system; the second was an actual temperature control experiment involving a holding tank of water with hot and cold water inputs.  The primary objective of performing this experiment was to gain an understanding of the response of a first-order system.  This response was characterized by a time constant and a time delay, which were functions of the system parameters.

 

Some important background material that may be of importance to the reader is

__________________________________________________________________________________________________________________

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________

 

            The system’s behavior was predicted (see Analysis) using mathematical models and then tested (see Experimental Procedure) to see how favorably the system’s actual response followed the predicted response (see Results and Discussion).  Conclusions based on data acquired are presented along with practical applications for utilizing the lessons learned in the laboratory.

 

 

Equipments and Procedures (don’t COPY lab manual -approximately 2 pages –

 

A pump is used to inject water of temperature Tinp into a mixing tank.  The input water’s temperature is controlled by selecting fluid from tank 1 at T1 or tank 2 at T2.  The changing temperature in the mixing tank is sensed by a thermocouple.  If the temperature in the tank is too high, the high temperature valve is closed (valve 2) and the low temperature valve is opened (valve 1).  If the temperature in the tank is too low, the low temperature valve is closed and the high temperature valve is opened.

And any other equipment or computer programs used

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________

It is perfectly okay to bullet the equipment used and then explain why it was used

·       A mixing bowl

·       Two ice cubes

·       Three tongs

 

The above list of equipment was used to ……The ice cubes were of particular importance because…..

 

Results (approximately 1 page)

 

It is important to note the following information that can be learned/shown from the data collected in the three experiments _________________________________________________________________

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

(do not explain just tell what data were collected)

 

 

         Table 1. Title

 


           

 

 

 

 

 

 

 

 


        Figure 1. Title

Spend time making sure that yours readers understand what you want them to see. What are the specific things that everyone must be clear on before you present your interpretations of those happenings.

The section should show a unified set of results that do not come from each experiment but reflect a total picture of what you have discovered and what you will tell the reader.

 

Discussion/Interpretations of Results  (approximately 1/2 – 1 page)

 

 

            The time constant of the system was in agreement with its theoretical calculated value for all the experiments performed.  The same is true for all the time delays, except the tdly for the long process delay loop.  The actual delay time was 25 sec.; the predicted delay time was 60 sec.  ( notice how the results are explained) This is probably due to the fact that the water in the delay tube was hot water from the previous experiment, not cold water as the equation assumed.  Since the water temperature in the tube was higher than predicted, its effect on the mixing tank water was quicker and more profound (Figure 12).

Conclusions (use 1.2.3.form to indicate your conclusions from the experiments)

 

The following conclusions are supported by the results of these experiments:

1. The time constant of a physical system is independent of the time delay for said system and vice-versa.

 

Recommended  Applications (where can what you have learned be used in the real world)

 

1. The system should be designed such that the delay time is neither too short nor too long.  Too short, and the valves are continually being open and shut to regulate temperature.  Too long, and the system’s temperature fluctuates too much to be in equilibrium.

 

 

 

 

A Sample Paper (no figures and tables shown at this time – just headings)

 

 

 

 

 

 

Water Temperature Control

 

ME 451 : Control Systems

 

Section 7B

 

YOUR NAME

 

TA’s NAME

 

 

 

 

 

Abstract

            Many industrial processes require the control of the temperature of a fluid in a holding tank.  To gain insight into the actual process of fluid temperature control, several experiments were performed.  Matlab scripts were used to simulate the response of the physical system used later:  A mixing tank containing water was connected to a cold water holding tank and a hot water holding tank.  Water was pumped from each of these tanks, and the effects of time delay and the time constant of the response of the physical control apparatus were examined.  The virtual instrument “Tank Temperature Control” was used to control the operation of the system which utilized thermocouples to monitor the tank temperature.

Several important conclusions were supported by the experiments performed.  The time constant of a system is independent of the time delay, and vice-versa.  Also, the system should be designed for a delay time that is neither too long or too short.  With a short time delay, the valves are continually being opened and closed to regulate temperature.  This is known as hunting.  Too long, and the tank temperature fluctuates too much to be in equilibrium.  Finally, the system should utilize valves that can be opened and closed incrementally, rather than valves which have only 2 states: fully open or fully closed.  Multi-stage valves would allow the system temperature to approach the desired equilibrium point with more precision and accuracy and reduce the percent overshoot.
Nomenclature

Arabic

Cp = specific heat of water (cal/C*gm)

 

H(t) = heat in mixing tank

           

Hinp(t) = heat added to tank

           

Hs(t) = heat spilled from the tank

           

H(0) = initial heat in tank

           

Qinp(t) = input flow rate (cc/min)

           

Qs(t) = spill flow rate (cc/min)

           

Tinp(t) = input temperature (C)

           

T(t) = mixing tank temperature (C)

           

V = mixing tank volume (cc)

 

            Greek

t = V/Q = time constant (sec)

           

r = density (gm/cc)


Contents

            Nomenclature…………………………………… 3

            Introduction……………………………………... 5

            Analysis…………………………………………. 5

            Experimental Procedure………………………… 12

            Results…………………………………………... 23

            Discussion………………………………………. 24

            Conclusions………………………………...…… 25
Introduction

            In industry, processes often require control of the temperature of a fluid in a holding tank.  Therefore, two experiments were performed which investigated the issues related to this control process.  The first was a simulation, utilizing Matlab scripts to simulate a physical system; the second was an actual temperature control experiment involving a holding tank of water with hot and cold water inputs.  The primary objective of performing this experiment was to gain an understanding of the response of a first-order system.  This response was characterized by a time constant and a time delay, which were functions of the system parameters.

            The system’s behavior was predicted (see Analysis) using mathematical models and then tested (see Experimental Procedure) to see how favorably the system’s actual response followed the predicted response (see Results and Discussion).  Conclusions based on data acquired were recorded.

Lab Observations

Analysis

            A pump is used to inject water of temperature Tinp into a mixing tank.  The input water’s temperature is controlled by selecting fluid from tank 1 at T1 or tank 2 at T2.  The changing temperature in the mixing tank is sensed by a thermocouple.  If the temperature in the tank is too high, the high temperature valve is closed (valve 2) and the low temperature valve is opened (valve 1).  If the temperature in the tank is too low, the low temperature valve is closed and the high temperature valve is opened.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.  System Diagram

The mixing system consisted of the plant (the apparatus required to perform the operations) and the associated control system.  To model the plant, consider the heat in the mixing tank as a function of time, which was given by

H(t) = H(0) + Hinp(t) + Hs(t)

(1)

The heat added to the tank from time 0 to time t was

Hinp(t) =   rcpTinp(t)Qinp(t)dt

(2)

while the total heat spilled from the mixing tank was

Hs(t) =   rcpT(t)Qs(t)dt

(3)

where cp and r were assumed to be constants.

            Substituting eq. (2) and eq. (3) into eq. (1) gave

H(t) = H(0) +   rcpTinp(t)Qinp(t)dt -  rcpT(t)Qs(t)dt

(4)

However, since

H(t) = rcpVT

(5)

we can rearrange eq. (4) using eq. (5) to get

T(t) = T(0) + 1/V  Tinp(t)Qinp(t)dt - 1/V  T(t)Qs(t)dt

(6)

            In the experiment performed, as in normal operating situations, the spill volume equaled the input volume (Qs = Qinp = Q).  Taking the derivative of eq. (6) with respect to time gave

T(t) = -(Q/V)T(t) + (Q/V)Tinp(t)

(7)

which was the system state equation.  Tinp(t) was the system input and T(t), the mixing tank temperature, was the system output.  The plant transfer function, which relates output to input, was placed in the “s” domain by taking the Laplace Transform of eq. (5) and rearranging terms, giving

Output = Transfer Function * Input

or

T(s) = Gp(s)Tinp(s)

where

Gp = (Q/V)/(s + Q/V)

(8)

            There exists two distinctly different ways of controlling the output of a given plant: open-loop control and closed-loop feedback control.

            An open-loop control system uses the desired output and the plant model to determine an input function that will give the desired output.  An open-loop control system assumes the desired output is reached upon execution of the input (see Figure 2).

           

 

 

 

 

 

 

Figure 2.  An Open-Loop Control

A closed-loop feedback control system monitors the output in order to make changes to the input.  With the addition of a feedback loop, the output becomes a function of the input (see Figure 3).

 

 

 

 

 

 

 

Figure 3.  A Closed-Loop Feedback Control

 

Once the control system has been selected, the state equation can be solved.  The input function can be written as a step function

Tinp(t) = Tinph(t-tdly)

(9)

where

h(t-tdly) = 1 if t ³ tdly

                0 if t £ tdly

            The step function above represents the on-off condition of the input function and Tinp represents the magnitude of the input function (either T1, high temperature, or T2, low temperature).  Solving eq. (7), the state equation, for the above input temperature gives

T(t) = A*exp(-Q/V)t + Tinp

(10)

where

(Q/V) = 1/t  and  A = (T0 – Tinp)

with T0 as the initial mixing tank temperature.

            This is a decaying exponential that starts at T0 and approaches the input temperature Tinp at a speed determined by the time constant t.  Large values of t yield a system with slow response time while small values of t yield a system with a quicker response time (see Figure 4).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.  Plant Response for a Small and Large Time Constant

            The mixing tank temperature is regulated in iterated steps when implementing a closed-loop feedback control system.  If the mixing tank temperature is too hot, cold water is added by opening the appropriate valve.  If the tank temperature is too cold, hot water is added.  During these operations, the mixing tank responds according to eq. (8) with initial condition given by tank temperature at the moment the mixing tank input switches from hot to cold or cold to hot.

            How fast the control can change the input temperature T0 is determined by the time delay, which is the time between when the control changes input flow and the time that flow reaches the mixing tank.  Figure 5 shows a typical response with a time delay.  The figure shows the response of the system for a desired temperature Td when the tank starts at a temperature of T0.  The time from t0 to t2 represents the time high temperature water is withdrawn from the hot water tank.  The system responds after the delay time, tdly, which equals the time required for hot (or cold) water to travel from its holding tank through hoses to the mixing tank.  The delay is seen in the time difference from t1 to t0 and t3 to t2.  At t1, the system starts responding according to eq. (10).  At t2, the control measures the mixing tank temperature as too high, and switches from hot to cold water input.  The mixing tank temperature continues to rise because hot water is still present in the hose system until enough water has been pumped from the cold water tank to force cold water into the mixing tank.

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5.  System Response

 
Experimental Procedure

            Equipment includes:

·       Matlab scripts to simulate response of a physical system

·       Physical system seen in Figure 1

·       Virtual instrument “Tank Temperature Control”

 

Simulation

For the simulation part of the experiment, it was assumed that Q = 30 cc/sec and V = 2000 cc.  The differential equation governing the system is, therefore

x = -(3/200)x + (3/200)u

(11)

and the plant transfer function is

Gp = [(3/200)/(s + 3/200)]

(12)

        The solution to eq. (9) is therefore given by

T(t) = [T(0) – Tinp]exp[-(Q/V)t] + Tinp

(13)

            Open-Loop Mode

            Using Matlab commands, a physical control system was simulated.  The flow rate was set to 30 cc/sec; the mixing tank volume, 2000 cc.  A time vector from 0 to 400 seconds was then created.

 

 

 

The first experiment simulated heating a mixing tank from 15 °C to 40 °C using a hot water input of 40 °C.  The result was then plotted (see Figure 6).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6.  System Response for T0 = 15 °C and Tinp = 40 °C

The second experiment simulated cooling the mixing tank from 45 °C to 16 °C using cold water at 16 °C as the input.  The result was then plotted (see Figure 7).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 7.  System Response for T0 = 45 °C and Tinp = 16 °C

The third experiment simulated heating the mixing tank from 21° C to 45 °C using 45 °C water as the input.  The result is plotted in Figure 8.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 8.  System Response for T0 = 21 °C and Tinp = 45 °C

 

        Closed-Loop Mode

            Using Matlab, a simulation of a feedback control system was established.  In this simulation, the valve is opened from the cold water tank when the measured water temperature in the mixing tank goes above the desired value.  Similarly, when the holding tank temperature is below the desired value, the valve from the hot water tank is opened.

            Using the script “lab2_sim” available in the laboratory, several experiments were performed, keeping t equal to the value set earlier, and setting the hot water tank to a temperature of 45 °C and the cold water tank to 15 °C.

            Experiment 4:  (see Figure 9)

delay time = 0 sec., initial temperature = 30 °C, desired temperature = 38 °C

           

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 9.  System Response for tdly = 0 sec., T0 = 30 °C and Tdesired = 38 °C

 

Experiment 5: (see Figure 10)

delay time = 16 sec., initial temperature = 30 °C, desired temperature = 38 °C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 10.  System Response for tdly = 16 sec., T0 = 30 °C, and Tdesired = 38 °C

            Experiment 6: (see Figure 11)

            delay time = 32 sec., initial temperature = 30 °C, desired temperature = 38 °C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 11.  System Response for tdly = 32 sec., T0 = 30 °C, and Tdesired = 38 °C

Physical System

            The effects of time delay and the time constant on the response of the water temperature control apparatus were examined using the system seen in Figure 1 and the Virtual Instrument (VI) “Water Temperature Control” available on the computers in the laboratory.  The lengths of the tubes connecting tanks 1 and 2 to the mixing tank were measured without the process delay loop: L1 = L2 = 1.308 m.  The lengths of the long process delay tubes were then measured: Ldly = 7.84 m.  The cross-sectional area of the tubes connecting the holding tanks to the mixing tanks were also measured: A = 1.572E-4 m2.  The volume of the mixing tank up to the height of the primary overflow tube was also measured: V = 1.966E-3 m3.  The flow rates (Q) into the mixing tank were measured by catching the overflow for 150 seconds, weighing the total amount of water that overflowed the tank (equal to amount of water which flowed into the mixing tank), dividing the weight by the density of water (1000 kg/m3), and finally dividing by the elapsed time (150 sec.):  Qavg. = 23.81 cc/sec.

Experiment 7: (see Figure 12)

            Tank 1 was filled with cold water (16 °C) and tank 2 with hot water (47 °C).  The VI was set to manual mode and the mixing turned off.  With the initial mixing tank temperature, T0, at 26 °C, and a desired temperature of 41 °C, the hot water valve was manually opened.  The short process delay was used, so when the mixing tank reached 41 °C, the hot water was turned off and the cold water turned on.  There was a short time delay, then the water temperature began to steadily decrease.  Switching to the long process delay, a new desired temperature of 24 °C was established.  When the tank

 

temperature reached 24 °C, the cold water was turned off and the hot water turned on.  There was a longer delay this time, however, since a longer process delay tube was used.

           

           

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 12.  Manually Controlled Feedback System.  T0 = 26 °C, Tdesired = 41 °C

 

Experiment 8: (see Figure 13)

            The VI was switched to automatic mode and a desired temperature of 32 °C was entered.  Using inputs of 16 °C for tank 1 and 44 °C for tank 2, a graph showing the system response was created.  Using Matlab once again, the script “wtemp” was run.  After inputting the system parameters mentioned above, a graph was created, simulating the response of the physical system.  These two graphs were then superimposed for comparison.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 13.  Automatic Control Feedback System.  Comparison of Measured vs. Predicted Values


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 14.  Determining Steady State Condition of Response.  T0 = 16 °C, Tinp = 45 °C

Results

            Finding the time constant, t, of the system can be done two ways:

-1-       t = V/Q = (2000cc)/(30cc/sec) = 66.7 sec.

-2-       Graphically – see Figures 4 and 8: t = time it takes for system to make 63% of the temperature change from T0 to Tinp. t = 65 sec.

            The system is deemed having reached its steady state after 98% of the temperature change has occurred.  This occurs after approximately 4 time constants.  In other words, after 4t seconds, the system is in equilibrium.

                        Using the long process delay loop, the time delay and time constant of the system were determined graphically (see Figure 11).  t = 66 seconds (t is the same value for all experiments).  time delay = 32 seconds.

            The time delay of the control system was determined by the length of the tube that connected each holding tank to the mixing tank.  Longer tube means longer time delay.

            The time constant of the control system was determined by the flow rate (Q) into the mixing tank and the volume (V) of the mixing tank.  large V = large t, large Q = small t.

            For the physical system used, the flow rate was equal to 23.81 cc/sec.  This value was unchanged by the process delay time.  Using the measured values of V and Q, t was calculated for the physical system.  t = 82.57 sec.  The delay time for the system was calculated using tdly = (A*L)/Q.  tdly = 8.64 sec for the short process delay, tdly = 60.4 sec. for the long process delay.

            Using the graph generated from the manual control mode (Figure 12), the time delay and time constants were calculated.

Short process delay loop: t = 86 sec., tdly = 12 sec.

Long process delay loop: t = 88 sec., tdly = 25 sec.

 

Discussion

              

            The time constant of the system was in agreement with its theoretical calculated value for all the experiments performed.  The same is true for all the time delays, except the tdly for the long process delay loop.  The actual delay time was 25 sec.; the predicted delay time was 60 sec.  This is probably due to the fact that the water in the delay tube was hot water from the previous experiment, not cold water as the equation assumed.  Since the water temperature in the tube was higher than predicted, its effect on the mixing tank water was quicker and more profound (Figure 12).

            The actual time delay for the short delay loop was measured as 12 seconds, while the predicted delay time was 8.5 seconds.  Figure 13 shows the discrepancies between these 2 systems.

            The system reached steady-state, or 98% of its final value, in 285 seconds (Figure 14).  This is approximately equal to 4.2 time constants.  The standard determination for steady state is after 4t seconds, where t is a function of system parameters.


Conclusions

            The following conclusions are supported by the results of these experiments:

1.         The time constant of a physical system is independent of the time delay for said system, and vice-versa.

2.         The system should be designed such that the delay time is neither too short nor too long.  Too short, and the valves are continually being open and shut to regulate temperature.  Too long, and the system’s temperature fluctuates too much to be in equilibrium.

3.         Instead of using valves that have only 2 states, open or closed, an optimum system would incorporate valves that can be opened and closed incrementally.  This would allow the system to approach the desired equilibrium point with more precision and accuracy and reduce the percent overshoot.