1.0INTRODUCTION

In control system, time behaviour of a system is important. When designing a system, the time behaviour may well be the most important aspect of its' behaviour. Points which might be affecting us in first order system are as follows.

How quickly a system responds is important. For example, a control system that's controlling a temperature, how long it takes the temperature to reach a new steady state is important. Say to control a temperature, and we want the temperature to be 200oC. If the temperature goes to 250oC before it settles out, we will want to know that. Control systems designers worry aboutovershoot and how close a system comes to instability. If we try to control speed of an automobile at 55mph and the speed keeps varying between 50mph and 60mph, your design isn't very good.Oscillations in a system are not usually desirable. If we try to control any variable,we want to control it accurately, so we will need to be able to predict the steady state in a system.

These examples are intended to show that the ability to predict details of how a system responds is important when designing systems. These are but a few of many different aspects of time behaviour of a system that are important in control system design. The examples above really are talking about aspects like:

Speed of response Relative stability of the system Stability of the system

When designing systems or circuits we often need to worry about these aspects of the system's time behaviour. Before building a system, we want to know how it will perform. Predictions are vital.

Source: [Franklin et al. (2002), Feedback Control of Dynamic Systems, Retrieved from http://www.facstaff.bucknell.edu/mastascu/econtrolhtml/SysDyn/SysDyn1.html]

1.1Feedback in furnace

The aim of feedback is to provide predictive control of furnace zone temperatures. This is achieved by use of a mathematical model to calculate and download suitable zone temperature set points to dedicated plant controllers such that material is heated to its required discharge temperature, with an acceptable temperature level and distribution across and through the stock, whilst utilising the minimum amount of energy. Pacing of the furnace and mill can be incorporated as part of the closed loop control. An important feature of predictive control is the handling of system delays, generally accounting for a high proportion of overall energy savings. Furnace temperatures are automatically reduced by the predictive controller to lowest possible levels at the onset of a delay and returned to rolling levels prior to termination of the delay, whilst ensuring that stock discharged will achieve required discharge temperature conditions.

Source: [Online Brochure, Retrieved from http://www.tatasteelservices.com/file_ source/StaticFiles/Business_Units/Consulting/38%20Reheaating%2 Furnace%20OnLine%20Basic%20Control%20Systems.pdf]

1.2Goals of this experiment

There are a number of goals for us in this experiment.

First, if we have a first order system, we need to be able to predict and understand how it responds to an input, so we need to be able to do this.

Given a first order system Determine the impulse and step response of the system.

Secondly, we go into a lab and measure a system, and if it is first order, you need to be able to do this.

Given the step response of a first order system, Determine the parameters - DC gain and time constant of the system.

This second goal is considerably different from the first. In the first goal, we are given information about the system and the input to the system, and have to determine how the system responded. In the second goal, we are given information about the input and output of a system and have to determine what the system is. That's a completely different kind of problem, but in both cases we will need to learn the material in the rest of this experiment.

Source: [Franklin et al. (2002). Feedback Control of Dynamic Systems, Retrieved from http://www.facstaff.bucknell.edu/mastascu/econtrolhtml/SysDyn/SysDyn1.html]

Figure 1.2.1: Typical Process of Furnace fuelled by Natural GasSource: [http://www.alternative-heating.com/heating-equipment.html]

Figure 1.2.2: Mesquite Furnace fuelled by propaneSource: http://mesquiteheatingandair.com/mesquite-furnace-repair/

Figure 1.2.3: High Efficiency FurnaceSource: [http://caviereswines.com/smf/tp/high%20efficiency%20lp%20gas%20furnace.html]

1.3Literature Review

The unit operation in this module represents a furnace fuelled by natural gas which is used to preheat a high molecular weight hydrocarbon feed (C16 C26) to a cracking unit at a petroleum refinery. The furnace model consists of energy and component mass balances which result in coupled nonlinear differential equations. The furnace model has seven inputs and four outputs as listed below:InputsOutputs

Hydrocarbon Flow RateHydrocarbon Outlet Temperature

Hydrocarbon Inlet TemperatureFurnace Temperature

Air Flow RateExhaust Gas Flow Rate

Air TemperatureOxygen Exit Concentration

Fuel Gas Flow Rate

Fuel Gas Temperature

Fuel Gas Purity

The combustion of the fuel is assumed to occur via the following reaction mechanism:

There are two major objectives for operation of the furnace. First, in order to minimize fuel costs, the furnace must be operated with proper oxygen composition to ensure complete combustion of the fuel (carbon monoxide is an undesired product). Second, the hydrocarbon feed stream must be delivered to the cracking unit at the desired temperature.

The furnace has the following manipulated and controlled variables:

Manipulated VariablesControlled Variables

Air Flow RateHydrocarbon Outlet Temperature

Fuel Gas Flow RateOxygen Exit Concentration

The system also has the following load (or disturbance) variables:

Load Variables

Hydrocarbon Flow Rate

Fuel Gas Purity

1.4Objectives

The purpose of this module is to demonstrate the properties of a first order system for various values of the system gain and time constant. This module also illustrates the dynamic response of a first order to different input signals.

2.0 METHODOLOGY

2.1Procedure

i. The Furnace was selected from the Main Menu. This is done by clicking the left mouse button once on the Furnace button. This opens the menu window for the furnace modules. The left mouse button was clicked on the Furnace button. Two additional windows will opened, one for the input and output graphs and one for the furnace process flow sheet.ii. Under the Simulation menu, Start was selected. This command should be executed once during a lab session. It is the simulated equivalent to a perfect process startup. The process output graphs are located on the window labelled Furnace Pro ess Monitor. Then we can noticed how the outputs remain unchanged with time.iii. Next, the fuel gas purity was being decreased. This will act as a disturbance to the system. By double clicking on the Fuel Gas Purity box, the value was changed from 1.0 to 0.95 by clicking on the value box and using the backspace key to erase the old value. When we have entered a new value, the Close button was clicked on. Again, we noticed how the outputs on the process monitor are changing with time. Then the Fuel Gas Purity was returned to 1.0 by double clicking on Fuel Gas Purity box and the value was adjusted as done before.iv. The furnace then starts. The initial steady state values for each of the inputs and outputs of the furnace were recorded in a table.v. The following sequence of increases in the air flow rate was done by double clicking the left mouse button on the Air Flow Rate box. The remaining inputs (the six other inputs) will be kept at their initial steady state values. After each change in the air flow rate, the system allowed to reach a new steady state (approximately 40 simulation minutes) and then the values of the output variables obtained using the pointers on the output graphs was recorded in table. After that, the Air Flow Rate was returned to its initial value allows the furnace to reach steady state.vi. The following sequence of increases in the fuel gas flow rate was done by double clicking the left mouse button on the Fuel Gas Flow Rate box. The remaining inputs (the six other inputs) will be kept at their initial steady state values. After each change in the fuel gas flow rate, the system was allowed to reach a new steady state (approximately 40 simulation minutes) and then the values of the output variables obtained using the pointers on the output graphs was recorded in table. The Fuel Gas Flow Rate then was returned to its initial value allows the furnace to reach steady state.vii. The following sequence of increases in the hydrocarbon flow rate was done by double clicking the left mouse button on the Hydrocarbon Flow Rate box. The remaining inputs (the six other inputs) being kept at their initial steady state values. After each change in the hydrocarbon flow rate, the system was allowed to reach a new steady state (approximately 40 simulation minutes) and then the values of the output variables obtained using the pointers on the output graphs was recorded in table. The Hydrocarbon Flow Rate was returned to its initial value allows the furnace to reach steady state.viii. The following sequence of increases in the fuel gas purity was done by double clicking the left mouse button on the Fuel Gas Purity box. The remaining inputs (the six other inputs) being kept at their initial steady state values. After each change in the fuel gas purity, the system was allowed to reach a new steady state (approximately 40 simulation minutes) and then the values of the output variables obtained using the pointers on the output graphs was recorded in table. The Fuel Gas Purity was returned to its initial value allows the furnace to reach steady state.ix. The nominal Air Flow Rate was increased by 20% and Procedure 4-8 was repeated.x. To end the session, the simulation was stopped by selecting Stop under the Simulation menu, Yes were selected under the Quit menu from the Main Menu window. This will return you to the MATLAB prompt. At this prompt, type quit to exit MATLAB.

3.0RESULTS AND DISCUSSIONS

3.1Results

3.1.1Initial Steady State Values of Inputs and OutputsInputsValueUnit

Hydrocarbon Flow Rate0.035m3/min

Hydrocarbon Inlet Temperature310K

Air Flow Rate17.9m3/min

Air Temperature310K

Fuel Gas Flow Rate1.21m3/min

Fuel Gas Temperature310K

Fuel Gas Purity1mol CH4/mol total

OutputsValueUnit

Hydrocarbon Outlet Temperature610.2303K

Furnace Temperature1427.2969K

Exhaust Gas Flow Rate 45.0658m3/min

Oxygen Exit Concentration0.9225mol O2/min

Table 3.1.1.1

3.1.2Air Flow RateAir Flow RateHydrocarbon Outlet Temperature Oxygen Exit Concentration

17.9 (nominal)610.23030.9225

18.1607.66450.9492

18.3605.09870.9758

18.5602.33551.0056

18.7599.96711.0352

Table 3.1.2.13.1.3Fuel Gas Flow RateFuel Gas Flow RateHydrocarbon Outlet TemperatureOxygen Exit Concentration

1.21 (nominal)610.39470.9191

1.22612.76320.8993

1.23614.86840.8783

1.24616.97340.8586

1.25618.99620.8366

Table 3.1.3.1

3.1.4Hydrocarbon Flow RateHydrocarbon Flow RateHydrocarbon Outlet TemperatureOxygen Exit Concentration

0.0350 (nominal)609.78990.9174

0.0355606.00840.9187

0.0360602.73110.9212

0.0365598.94960.9187

0.0370596.17650.9237

Table 3.1.4.1

3.1.5Fuel Gas PurityFuel Gas PurityHydrocarbon Outlet TemperatureOxygen Exit Concentration

1.00 (nominal)609.60530.9217

0.99607.23680.9480

0.98604.34210.9757

0.97601.71051.0032

0.95595.65791.0608

Table 3.1.5.1

3.1.6Initial Steady State Values of Inputs and Outputs (20% Increases of Air Flow Rate)InputsValueUnit

Hydrocarbon Flow Rate0.035m3/min

Hydrocarbon Inlet Temperature310K

Air Flow Rate21.48m3/min

Air Temperature310K

Fuel Gas Flow Rate1.21m3/min

Fuel Gas Temperature310K

Fuel Gas Purity1mol CH4/mol total

OutputsValueUnit

Hydrocarbon Outlet Temperature567.7583K

Furnace Temperature1271.2612K

Exhaust Gas Flow Rate 45.0166m3/min

Oxygen Exit Concentration1.4330mol O2/min

Table 3.1.6.1

3.1.7Air Flow Rate with 20% IncreasesAir Flow RateHydrocarbon Outlet TemperatureOxygen Exit Concentration

21.48569.75831.4330

21.75565.32031.4715

21.69563.48961.5089

22.20560.91351.5386

22.40559.38681.5681

Table 3.1.7.1

3.1.8Fuel Gas Flow Rate with 21.48 m3/min of Air Flow RateFuel Gas Flow RateHydrocarbon Outlet TemperatureOxygen Exit Concentration

1.21 (nominal)568.26751.4379

1.22570.28371.4129

1.23572.19291.3856

1.24574.06501.3592

1.25576.35971.3429

Table 3.1.8.1

3.1.9Hydrocarbon Flow Rate with 21.48 m3/min of Air Flow RateHydrocarbon Flow RateHydrocarbon Outlet TemperatureOxygen Exit Concentration

0.0350 (nominal)562.63651.4435

0.0355565.90581.4359

0.0360563.20201.4284

0.0365557.56501.4208

0.0370553.30351.3906

Table 3.1.9.1

3.1.10Fuel Gas Purity with 21.48 m3/min of Air Flow RateFuel Gas PurityHydrocarbon Outlet Temperature (K)Oxygen Exit Concentration

1.00 (nominal)569.08221.3985

0.99566.19231.4693

0.98562.38211.5058

0.97560.98771.5136

0.95555.42621.6291

Table 3.1.103.2Discussions

a) Using the information from Procedure 5-8, calculate the steady state gain for each of the following input-output pairings. This can be accomplished by graphically by plotting the output versus input values from the tables and calculating the best linear fit to the data.*Hint: There are 8 steady state gain,

Therefore, steady state gain can be obtained from the graph output versus input values where the slope of the line represents the steady state gain.

i. Figure 3.2.1: A Graph of Hydrocarbon Outlet Temperature versus Air Flow RateAir Flow Rate

Steady State Gain, K = -12.928 K.min/m3

Figure 3.2.2: A Graph of Oxygen Exit Concentration versus Air Flow Rate

Steady State Gain, K = 0.1409 mol O2/m3

ii. Fuel Gas Flow Rate

Figure 3.2.3: A Graph of Hydrocarbon Outlet Temperature versus Air Flow Rate

Steady State Gain, K = 214.13 K.min/m3

Figure 3.2.4: A Graph of Oxygen Exit Concentration versus Air Flow Rate

Steady State Gain, K = -2.057 mol O2/m3

iii. Hydrocarbon Flow Rate

Figure 3.2.5: A Graph of Hydrocarbon Outlet Temperature versus Air Flow Rate

Steady State Gain, K = -6857.1 K.min/m3

Figure 3.2.6: A Graph of Oxygen Exit Concentration versus Air Flow Rate

Steady State Gain, K = 2.52 mol O2/m3

iv. Fuel Gas Purity

Figure 3.2.7: A Graph of Hydrocarbon Outlet Temperature versus Air Flow Rate

Steady State Gain, K = 280.23 K.min/m3

Figure 1: A Graph of Oxygen Exit Concentration versus Air Flow Rate

Steady State Gain, K = -2.7859 mol O2/m3

b) Compared with results from (a), is the nonlinear behaviour of the furnace apparent? How this behaviour manifested?

The nonlinear of the furnace is apparent. As we compare the graphical results, the steady state gain, K varies as the operating points are changed. As we can see, the steady state gain, K for air flow rate based on hydrocarbon outlet temperature is -12.928 K.min/m3. Meanwhile the values for fuel gas flow rate, hydrocarbon flow rate and fuel gas purity are 214.13 K.min/m3, -6857.1 K.min/m3, and 280.23 K.min/m3 respectively. As we can see here clearly that the steady state gain varies significantly when we alter the operating points. The same goes for the flow rate based on oxygen exit concentration. Therefore, the nonlinear behaviour of the furnace is apparent.

c) Using the gains obtained in (1), determine the values of the Air Flow Rate and Fuel Gas Flow Rate that are necessary to increase the Hydrocarbon Outlet Temperature by 7 C and decrease the Oxygen Exit Concentration by 0.05 mol O2/m3 by assuming the load variables remain constant. Calculate the new value of the Fuel Gas Flow Rate and Air Flow Rate.

i. Air Flow Rate

For Hydrocarbon Outlet Temperature,T = 7oC or 7KInitial Temperature = 610.2303KNew Temperature = 617.2303KBased on graph in figure 3.2.1,

For Oxygen Exit Concentration,Initial Concentration = 0.9225 mol O2/m3New Concentration = 0.9225 0.05 = 0.8725 mol O2/m3Based on graph in figure 3.2.2,

ii. Fuel Gas Flow Rate

For Hydrocarbon Outlet Temperature,T = 7oC or 7KInitial Temperature = 610.2303KNew Temperature = 617.2303KBased on graph in figure 3.2.3,

For Oxygen Exit Concentration,Initial Concentration = 0.9225 mol O2/m3New Concentration = 0.9225 0.05 = 0.8725 mol O2/m3Based on graph in figure 3.2.4,

4.0CONCLUSION AND RECOMMENDATION

4.1Conclusion

Based on the experimental results and discussions, we found out that in order to get the desired output of hydrocarbon temperature and oxygen concentration, the inputs including air flow rate, fuel gas flow rate, hydrocarbon flow rate and fuel gas purity should be manipulated. In detail, increase in stated inputs results decrease in hydrocarbon temperature and increase in oxygen concentration. Although we manage to get the expected results, however the value we obtained is inaccurate because the time taken has error about 0.5%. Since the error is not high, therefore, the results we obtained are true. At the end of the experiment, we able to find out the steady state gain and the properties of a first order system for various values of inputs.

4.2Recommendation

In order to perform this experiment in the most excellent way, there are some suggestions from us. This experiment should be done by selecting the time constant by taking some relevant range. Failure to do this, will result in inaccurate result and poor graphically analysis. The data obtained from this stimulation is used to perform backward analysis; hence accuracy is an important factor in this experiment. The result analysis should be done in proper graphical scale and this will result in smooth graph. Overall, this experiment is fun to execute.

5.0REFERENCES

Book of Process Control & Instrumentation, 2nd ed, Seborg D. E., Edgar T. F., Mellichamp D. A Franklin et al. (2002). Feedback Control of Dynamic Systems (4 ed.). New Jersey: Prentice Hall. ISBN 0-13-032393-4. Joseph L. Hellerstein, Dawn M. Tilbury, and Sujay Parekh (2004). Feedback Control of Computing Systems. John Wiley and Sons. ISBN 0-47-126637-X, ISBN 978-0-471-26637-2. Goodwin, Graham (2001). Control System Design. Prentice Hall. ISBN 0-13-958653-9.

6.0APPENDICES

Figure 6.1: Process Control Monitor

23

Figure 6.2: Output Results' Monitor

Figure 6.3: Air Flow Rate at 17.9 m3/min

Figure 6.4: Air Flow Rate at 18.1 m3/min

Figure 6.5: Air Flow Rate at 18.3 m3/min

Figure 6.6: Air Flow Rate 18.5 m3/min

Figure 6.7: Air Flow Rate at 18.7 m3/min

Figure 6.8: Air Flow Rate at 21.48 m3/min

Figure 6.9: Air Flow Rate at 21.72 m3/min

Figure 6.10: Air Flow rate at 21.96 m3/min

Figure 6.11: Air Flow Rate at 22.20 m3/min

Figure 6.12: Air Flow Rate at 22.40 m3/min

Figure 6.13: Fuel Gas Flow Rate at 1.21 m3/min

Figure 6.14: Fuel Gas Flow Rate at 1.22 m3/min

Figure 6.15: Fuel Gas Flow Rate at 1.23 m3/min

Figure 6.16: Fuel Gas Flow Rate at 1.24 m3/min

Figure 6.17: Fuel Gas Flow Rate at 1.25 m3/min

Figure 6.18: Fuel Gas Flow Rate at 1.21 m3/min (B)

Figure 6.19: Fuel Gas Flow Rate at 1.22 m3/min (B)

Figure 6.20: Fuel Gas Flow Rate at 1.23 m3/min (B)

Figure 6.21: Fuel Gas Flow Rate at 1.24 m3/min (B)

Figure 6.22: Fuel Gas Flow Rate at 1.25 m3/min (B)

Figure 6.23: Hydrocarbon Flow Rate 0.0350 m3/min

Figure 6.24: Hydrocarbon Flow Rate at 0.0355 m3/min

Figure 6.25: Hydrocarbon Flow Rate at 0.0360 m3/min

Figure 6.26: Hydrocarbon Flow Rate at 0.0365 m3/min

Figure 6.27: Hydrocarbon Flow Rate at 0.0370 m3/min

Figure 6.28: Hydrocarbon Flow Rate at 0.0350 m3/min (B)

Figure 6.29: Hydrocarbon Flow Rate at 0.0355 m3/min (B)

Figure 6.30: Hydrocarbon Flow Rate at 0.0360 m3/min (B)

Figure 6.31: Hydrocarbon Flow Rate at 0.0365 m3/min (B)

Figure 6.32: Hydrocarbon Flow Rate at 0.0370 m3/min (B)

Figure 6.33: Fuel Gas Purity at 1.00 mol CH4 / mol total

Figure 6.34: Fuel Gas Purity at 0.99 mol CH4 / mol total

Figure 6.35: Fuel Gas Purity at 0.98 mol CH4 / mol total

Figure 6.36: Fuel Gas Purity at 0.97 mol CH4 / mol total

Figure 6.37: Fuel Gas Purity at 0.95 mol CH4 / mol total

Figure 6.38: Fuel Gas Purity at 1.00 mol CH4 / mol total (B)

Figure 6.39: Fuel Gas Purity at 0.99 mol CH4 / mol total (B)

Figure 6.40: Fuel Gas Purity at 0.98 mol CH4 / mol total (B)

Figure 6.41: Fuel Gas Purity at 0.97 mol CH4 / mol total (B)

Figure 6.42: Fuel Gas Purity at 0.95 mol CH4 / mol total (B)