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Refrigeration, Air Conditioning, and Heating

Courseware Sample

85055-F0

A

REFRIGERATION, AIR CONDITIONING, AND HEATING

COURSEWARE SAMPLE

bythe Staff

ofLab-Volt Ltd.

Copyright © 2008 Lab-Volt Ltd.

All rights reserved. No part of this publication may be reproduced,in any form or by any means, without the prior written permissionof Lab-Volt Ltd.

Printed in CanadaMay 2008

III

Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V

Courseware Outline

Familiarization with the Air Handling / EnergyManagement Training System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII

Sample Exercise Extracted from Familiarization with the Air Hangling / EnergyManagement Training System

Ex. 6 PID Control of Temperature and Humidity . . . . . . . . . . . . . . . . . . . 3

V

Introduction

The Lab-Volt Model 3403 Air Handling / Energy Management Training System isdesigned to introduce students to the principles and components of air handling andenergy management, and help students develop an appreciation for the method ofcontrol. The trainer is controlled mainly by an Allen-Bradley Programmable LogicController (PLC). Access to the PLC is obtained through a personal computer.Instruction on energy management and optimizing system efficiency is providedthrough the PLC’s programming.

FAMILIARIZATION WITH THE AIR HANDLING / ENERGY MANAGEMENTTRAINING SYSTEM

Courseware Outline

VII

Introduction

Exercise 1 Air Flow Control

Exercise 2 Temperature Control

Exercise 3 Humidity Control

Exercise 4 The Programmable Logic Controller

Exercise 5 Supervisory Control and Data Acquisition (SCADA)

Exercise 6 PID Control of Temperature and Humidity

Appendices A Setting up the Air Handling / Energy Management TrainingSystem

B MaintenanceC Controls, Indicators, and ConnectorsD PLC Inputs, Outputs, Addresses, and SymbolsE Control of Duct ElementsF Fault SwitchesG Temperature ConversionH Boolean Algebra and Digital LogicI The Refrigeration CycleJ Glossary of Terms

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Sample Exercise

Extracted from

Familiarization with the

Air Handling / Energy

Management Training System

3

Exercise 6

PID Control of Temperature and Humidity

OBJECTIVE

• Become familiar with PID control of temperature and humidity in a zone using aPLC.

DISCUSSION

In an on-off control system, a controller (thermostat, humidistat, etc.) is used tomaintain the process variable (temperature, humidity, etc.) near the desired setpoint.The controller switches its output when the process variable crosses the setpoint.Since the controlled element is either on or off, the process variable cyclescontinually, going from below the setpoint to above and below again.

PID Controller

A PID (Proportional, Integral, Derivative) controller offers much more precise controlof the process variable. A PID control loop functions in three steps:

1. Measurement of the process variable (PV) by a sensor;2. Calculations in a controller element;3. Action through a controlled variable (CV) such as a damper opening.

With this type of controller, the output, or controlled variable (CV), is an analog valuedetermined using the PID equation. The general form of this equation is

Output = Proportional term + Integral term + Derivative term

The control loop of a typical PID controller is presented in the diagram block ofFigure 6-1. In this loop, the controller subtracts the sensor measurement from thesetpoint to determine the error (E). The error is then used in the proportional,integral, and derivative terms of the PID equation to obtain a correction to thecontrolled variable. Each term (P, I, or D) serves a specific purpose:

• Proportional (P): determines the reaction to the current error. Note thatproportional control alone will never reach the setpoint. A steady-state errorremains that is a function of the proportional gain.

• Integral (I): determines the reaction to recent errors. This term provides anoutput that is function of the accumulated error over time. It forces the signalto reach the setpoint quicker than proportional controller alone and eliminatesthe steady-state error. However, the process tends to overshoot the setpoint.

• Derivative (D): determines the reaction to the rate by which the errorchanges. As the process variable approaches the setpoint, the error willdiminish more slowly. This braking effect is used to reduce the magnitude of


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the overshoot produced by the integral component, but the process variablebecomes slower to reach the setpoint.

Note: PI, PD, P, or I controllers can be obtained from a PID controller bysetting the undesired control gains to zero.

Figure 6-1. PID Controller Diagram.

The proportional, integral, and derivative terms must be individually adjusted, or"tuned" to the system being controlled. This is usually done using a trial and errormethod. When properly tuned, the controller should maintain much more accurateand stable control of the process variable than an on-off type controller, and shouldrespond rapidly to changes in setpoint and load without excessive cycling of theprocess variable about the setpoint.

PID Instruction in a Ladder Program

In RSLogix 5 ladder programs, a PID instruction exists that can be used for PIDprocess control. The process and controlled variables are identified directly in theinstruction box, as shown in Figure 6-2. The setpoint and the three constants arestored in the control block, a file reserved for controlling the PID instruction.


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Figure 6-2. PID Instruction Box.

The PID instruction samples the process variable at regular intervals. For eachsample, it determines the error, or difference between the setpoint and the processvariable. The error is used in the PID equation to calculate the controlled variable.

PID control of both temperature and humidity is performed in this exercise using theindependent gains form of the PID equation. For temperature control, the processvariable is the ZONE 1 THERMOCOUPLE level (Z1_TC) and the controlled variableis the REHEATER analog output (REHEAT_AN). The equations used are then:

where E(t) is the error;SP is the setpoint;

PV(t) is the process variable;CV(t) is the controlled variable (output);

Kp is the proportional gain constant;Ki is the integral gain constant;

Kd is the derivative gain constant;dt is the time between samples.

For humidity control, the process variable is the ZONE 1 relative humidity (Z1_HUM)and the controlled variable is the HUMIDITY DAMPER (HUMID_DMP). Because thedamper uses reverse control, (0% = OPEN, 100% = CLOSED), the error is obtainedby subtracting the process variable from the setpoint. A bias is added so that thedamper is closed by default. The equations used are then:

Scaled and Unscaled Data

The PID instruction must use "unscaled" data from the analog input modules. In thePLC Programming Software, unscaled data is defined as data that ranges from 0 to4095. In contrast, data from the thermocouples is "scaled" because it can range from-200 to 1200°C. Humidity data is also scaled because it can range from 0 to 100%.


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The descaling calculations are performed using FAL (File Arithmetic and Logic)instructions. These calculations make use of the scaled minimum and maximumvalues of the input data, Smin and Smax, as defined below.

To descale the thermocouple inputs, the following calculation is performed:

where TCU is the unscaled thermocouple value (range: 0 to 4095);TCS is the scaled thermocouple value (range: -200 to 1200);Smin is the scaled minimum value (-200);Smax is the scaled maximum value (1200).

To descale the relative humidities, the following calculation is performed:

where HUMU is the unscaled relative humidity (range: 0 to 4095);HUMS is the scaled relative humidity (range: 0 to 100);

Smin is the scaled minimum value (0);Smax is the scaled maximum value (100).

PROCEDURE

Setup

G 1. Make the following adjustments:

POWER PANEL:POWER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OFFEXTERIOR AIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . WINTERPOWER CONSUMPTION recorder POWER . . . . . . . . . . . . . ONPOWER CONSUMPTION recorder CHART . . . . . . . . mid. pos.

PLC-5:POWER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ONKEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REM


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THERMOSTATS:SUMMER (back) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80°F (27°C)WINTER (back) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50°F (10°C)

MANUAL DAMPERS:INLET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OPEN

CONTROL PANEL

DUCT ELEMENTS:PREHEATER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REMOTEHUMIDIFIER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REMOTECOOLER/DEHUMIDIFIER . . . . . . . . . . . . . . . . . . . . . . REMOTEREHEATER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REMOTE

AIR FLOW:BLOWER SPEED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MANUALHUMIDIFIER DAMPER . . . . . . . . . . . . . . . MANUAL (CLOSED)ZONE 1 DAMPER . . . . . . . . . . . . . . . . . . . . . MANUAL (OPEN)ZONE 2 DAMPER . . . . . . . . . . . . . . . . . . . . . MANUAL (OPEN)RECIRC. DAMPER . . . . . . . . . . . . . . . . . . MANUAL (mid. pos.)

ZONE 1 AND ZONE 2:THERMOSTAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REMOTEHUMIDISTAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REMOTEHEAT SOURCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OFF

G 2. Place the POWER switch in the I (ON) position.

G 3. Adjust the BLOWER SPEED to obtain a velocity pressure of 1" onMANOMETER 3. Balance the system to ensure equal air flow in the twozones (as in Exercise 1) and do the following adjustments:

AIR FLOW:ZONE 2 DAMPER . . . . . . . . . . . . . . . . . . . MANUAL (CLOSED)

G 4. Turn on the computer, the monitor, and the printer. Start the RSLogix 5Programming Software.

Ladder Program for PID Control

G 5. Open the program PID_Z1.RSP, download it in the PLC memory, and putthe PLC in REMOTE PROG mode. This program provides PID control oftemperature and humidity in ZONE 1.


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Examine the listing to understand how the program operates. This programhas two PID instructions: one for temperature and one for humidity (rungs13 and 14). FAL instructions are used to descale input data (rungs 9, 10,and 11).

Note: Those three FAL instructions descale more than one wordat a time. For instance, N:10:11 (Z1_TC) becomes N17:9 whendescaled, because the FAL instruction is applied to sixconsecutive words.

G 6. Make sure that all addresses in the PID boxes are set correctly:

Zone1 Temperature PID

Control Block N22:0Process Variable N17:9Tieback 0Control Variable N13:7

Zone 1 Humidity PID

Control Block N21:0Process Variable N17:12Tieback 0Control Variable N13:6

G 7. Double-click "Setup Screen" in the first PID instruction box (rung 13). ThisPID instruction controls the temperature in ZONE 1. Figure 6-3 shows whatthis window should look like.

Figure 6-3. Setup Screen of the Temperature PID Instruction.


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Note: Values on the Setup Screen can also be found in the fileidentified as "Control Block". File N22, for instance, storesinformation about the ZONE 1 temperature PID instruction.

Double-click "Setup Screen" in the second PID instruction box (rung 14).This PID instruction controls the humidity in ZONE 1. Figure 6-4 shows whatthis window should look like.

Figure 6-4. Setup Screen of the Humidity PID Instruction.

G 8. On the Air Handling / Energy Management Training System, set theHUMIDIFIER DAMPER to REMOTE and put the PLC in REMOTE RUNmode.

G 9. On the computer screen, reopen the first PID setup screen(temperature).Change the temperature (scaled) setpoint to 30. Since error is set to 0(SP-PV) the following relation should hold:

ES = SPS - PVS

where ES is the scaled error;SPS is the scaled setpoint (displayed as "(Scaled) Setpoint");PVS is the scaled process variable (displayed as "Scaled PV Value").


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This relationship also holds for the unscaled values, although these are notdisplayed in the setup screen:

EU = SPU - PVU

where EU is the unscaled error;SPU is the unscaled setpoint;PVU is the unscaled process variable.

G 10. Change the proportional gain Kp to 10.00. (Since the multiplier, in squarebrackets, is .01, you must enter 1000.)

Note the current controlled variable expressed in percent:

Current CV % =

Knowing the scaled error value (ES), verify that your measure is correct. Usethe following calculations:

EU = SPU - PVU= [(SPS + 200) x 2.925] - [(PVS + 200) x 2.925]= 2.925 x (SPS - PVS)= 2.925 x ES

Since Kp = 10 and Ki = Kd = 0,

CVU = Kp x EU= 10.00 x EU

Finally,

CV % = CVU / 4095 x 100%

For example, if the scaled error is equal to 8 and Kp = 10.00, then

EU = 2.925 x 8 = 23.4CVU = Kp x Eu = 234CV % = (234 / 4095) x 100% . 6%

What value of CV % do you calculate?

CV % =

Is this value equal to the displayed value of CV %?

G Yes G No

G 11. Increase the proportional gain Kp to 50.00 (enter 5000). Once the processvariable has stabilized, the error should be less than with Kp = 10.00.


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Increase Kp to 100.00. Note that with proportional control only (Ki = Kd = 0),increasing the gain Kp decreases the error but does not eliminate it.

Note: As the CV % increases, the REHEATER pilot lamp flasheson for a longer portion of its cycle.

Using the SCADA Program for Proportional Control

G 12. Start RSView32 software. Open the file 3403.RSV and run the project.

On the main window, click "PID Control". The window of Figure 6-5 shouldappear. In this window, you can modify the temperature and the humiditysetpoints, as well as the proportional, integral, and derivative gain constants.

Figure 6-5. PID Control Window in RSView32.

Study the display to understand how the temperature control loop operates.The proportional, integral, and derivative gain constants for this loop are


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identified as TEMP_KP, TEMP_KI, and TEMP_KD, respectively. These areentered as whole numbers, which are multiplied by the indicated factors toobtain the actual constants:

TEMP_KP: 0.01TEMP_KI: 0.001 / secsTEMP_KD: 0.01 secs

HUM_KP: 0.01HUM_KI: 0.001 / secsHUM_KD: 0.01 secs

G 13. Set all gain constants to 0. The temperature process variable, setpoint, andoutput (control variable) are identified as TEMP_PV, TEMP_SP, andTEMP_OUT, respectively.

– The process variable is equal to the ZONE 1 thermocouple reading(Z1_TC).

– The setpoint should presently be equal to 30.

– The output should be zero, since the gains are all zero.

G 14. Enter 10000 for TEMP_KP (equivalent to Kp = 100.00). Note that theREHEATER begins heating. The process variable TEMP_PV will begin toincrease slowly.

Go to the "Trend" window, adjust the Y-Axis, and note near what value theZone 1 Thermocouple stabilizes.

Observe that, as the process variable approaches the setpoint, the output(control variable) decreases. This is because the control equation for thesystem is presently

CV = Kp x E = Kp(SP-PV)

where CV is the output (control variable);Kp is the proportional gain;E is the error;

SP is the setpoint;PV is the process variable.

When the system is stable, observe that there is a gap (error) between theprocess variable and the setpoint.

Change TEMP_KP back to 0 and wait until the process variable is stable.

G 15. Go back to the PID Control window and change the proportional gainconstant TEMP_KP to 150.00 (enter 15000).


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Return to the trend window and observe near what value the Zone 1Thermocouple stabilizes.

Note: Increasing the proportional gain should decrease but noteliminate the error.

Change TEMP_KP back to 0 and wait until the process variable is stable.

Integral Control

G 16. Change the integral gain to 1.000 (enter 1000), and go to the trend window.

Observe the trend until the process variable is stable. Note that the processvariable first overshoots the setpoint, then decreases. Note also that it takesa long time for the system to stabilize, but when it does, there is practicallyno error.

Return to the PID Control window. Change the integral gain to 0 and waituntil the process variable is stable.

Change the integral gain to 5.000 (enter 5000), and return to the trendwindow. Observe that the stabilization time is shorter with a higher gain, butthe overshoot is greater. There may also be an undershoot before theprocess variable stabilizes.

G 17. Experiment with various combinations of proportional, integral, andderivative gains. Try to obtain the combination that provides the most rapidstabilization with the least overshoot.

Note: The maximum value you can enter for the proportional,integral, or derivative gain is 32767.

Humidity Control

G 18. In the PID Control window, set all six proportional, integral, and derivativegains to 0.

G 19. Observe the display to understand the operation of the humidity loop. Sincethe damper uses reverse control (0% = OPEN, 100% = CLOSED), the erroris obtained by subtracting the process variable from the setpoint. A bias isadded at the output of the PID instruction to close the damper by default.

Note: The bias is identified as "Feed Forward" in the humiditySetup Screen of the ladder program.

Set the humidity setpoint to slightly higher that the present value of theprocess variable. Then experiment with different gains. You can use theTrend window to observe the evolution of the ZONE 1 humidity.


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Temperature and Humidity Control

G 20. Set the gains in both loops to control temperature and humiditysimultaneously. Experiment with different gains, using theTrend window tomonitor the system behavior.

G 21. Place the POWER switch in the 0 (off) position. Turn off the computer andthe printer.

CONCLUSION

In this exercise, you learned how to use a PID instruction in a ladder diagram forproportional, integral, and derivative control of a process variable. You also used theSCADA program to tune the proportional, integral, and derivative gain constants fortemperature and humidity control.

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