Control Theory Control System Objectives Establish a final condition Provide safe operation ...

Control TheoryControl Theory

Control System ObjectivesControl System Objectives Establish a final conditionEstablish a final condition Provide safe operationProvide safe operation Eliminate the human Eliminate the human elementelement

Assure economical Assure economical operationoperation


SensorSensor ControllerController ControlledControlledDeviceDevice

HVACHVACProcessProcess

System FeedbackSystem Feedback





SensorsSensors

TemperatureTemperature

PressurePressure

HumidityHumidity





SensorsSensorsSensors are approximately linear Sensors are approximately linear indicators of process conditions. indicators of process conditions.

Sensors also have a response time. Sensors also have a response time. DDC controllers can linearize sensor DDC controllers can linearize sensor values and derive calculated values values and derive calculated values

(i.e. flow from (i.e. flow from P).P).





ControllersControllers

Two Position ControlTwo Position Control

Analog ControlAnalog Control

Direct Digital ControlDirect Digital Control


Two Position ControlTwo Position ControlTypically a mechanical device such as Typically a mechanical device such as

a thermostat or pressure switcha thermostat or pressure switch

Picture of A70


Two Position ControlTwo Position ControlA mechanical thermostat opens or A mechanical thermostat opens or

closes a relay based on the closes a relay based on the temperature. this applies a voltage temperature. this applies a voltage

to a two position fan coil valve which to a two position fan coil valve which goes full open or full closed.goes full open or full closed.

DifferentialDifferentialTemperatureTemperatureIncreasingIncreasing

Cut inCut intemperaturetemperature

Full flow to FCUFull flow to FCU

Cut outCut outtemperaturetemperature

No flow to FCUNo flow to FCU


Two Position ControlTwo Position ControlLow CostLow Cost

Inaccurate ControlInaccurate Control

Inflexible StrategiesInflexible Strategies

Cannot be NetworkedCannot be Networked

Used for Simple On / Off Control suchUsed for Simple On / Off Control suchas FCU in Hotel Guest Roomsas FCU in Hotel Guest Rooms

Used for Safety ControlsUsed for Safety Controls


Analog ControlAnalog ControlUses analog electronics but no Uses analog electronics but no

microprocessor.microprocessor.

Picture of System 350


Analog ControlAnalog ControlA temperature sensor located in the A temperature sensor located in the return air of a CAV AHU controls the return air of a CAV AHU controls the

chilled water valve using a chilled water valve using a proportional algorithm.proportional algorithm.


Analog ControlAnalog ControlLow-Medium CostLow-Medium Cost

Reasonably Accurate ControlReasonably Accurate Control

Inflexible StrategiesInflexible Strategies

Cannot be NetworkedCannot be Networked

Used for AHU without BASUsed for AHU without BAS


Direct Digital ControlDirect Digital ControlUses microprocessor to do Uses microprocessor to do

calculations and can be networked calculations and can be networked with BASwith BAS

Picture of DDC Controller


Direct Digital ControlDirect Digital Control1. Convert input signal from analog to 1. Convert input signal from analog to

digital formatdigital format

2. Use computer program to calculate 2. Use computer program to calculate the value to be sent to the outputthe value to be sent to the output

3. Generate output signal from 3. Generate output signal from calculated valuecalculated value


Direct Digital ControlDirect Digital ControlMedium CostMedium Cost

Accurate ControlAccurate Control

Flexible StrategiesFlexible Strategies

Can be NetworkedCan be Networked

Used for AHU with BASUsed for AHU with BAS


Direct Digital ControlDirect Digital ControlCurrent DDC technology implements Current DDC technology implements

analog control algorithms using analog control algorithms using microprocessor.microprocessor.

Next generation DDC technology will Next generation DDC technology will add adaptive tuning, mechanical add adaptive tuning, mechanical

system diagnostics and system diagnostics and characterization of the controlled characterization of the controlled

device. device.





Controlled DeviceControlled Device

VAV Box Actuator

VSD





Controlled DeviceControlled DeviceControlled devices are almost never Controlled devices are almost never

linear and also demonstrate linear and also demonstrate hysteresis. Controlled devices are hysteresis. Controlled devices are typically oversized and this makes typically oversized and this makes proper control even more difficult.proper control even more difficult.





HVAC ProcessHVAC ProcessIt is critical to understand the It is critical to understand the

characteristics of the HVAC process characteristics of the HVAC process when applying controls. when applying controls.





HVAC ProcessHVAC ProcessThe HVAC process will limit the range The HVAC process will limit the range of possible control. For example, the of possible control. For example, the mechanical system will not allow a mechanical system will not allow a

room setpoint of 5°C to be achieved.room setpoint of 5°C to be achieved.





System FeedbackSystem FeedbackThe system feedback will introduce The system feedback will introduce delays. For example, it may take a delays. For example, it may take a few minutes for a change in valve few minutes for a change in valve position to cause a change in room position to cause a change in room

temperature.temperature.





System FeedbackSystem FeedbackThe system feedback will introduce The system feedback will introduce

“noise”. For example, turbulence “noise”. For example, turbulence and stratification make accurate and stratification make accurate

measure of pressure and measure of pressure and temperature difficult.temperature difficult.


Examples of VAV Control LoopsExamples of VAV Control Loops








TemperatureTemperaturesensor locatedsensor located

after cooling coilafter cooling coil

DDCDDCControllerController

Valve actuatorValve actuatorand chilledand chilledwater valvewater valve

Cooling coilCooling coilextracts heatextracts heat

from air streamfrom air stream

Air stream after cooling coilAir stream after cooling coilaffects temperature sensoraffects temperature sensor

Off-Coil Temperature Control in VAV AHUOff-Coil Temperature Control in VAV AHU





Static pressureStatic pressuresensor locatedsensor located

in ductworkin ductwork


Variable speedVariable speeddrive controllerdrive controllerconnected toconnected to

fan motorfan motor

Fan controlsFan controlsairflow intoairflow intoductworkductwork

VAV boxes open and closeVAV boxes open and closevarying duct static pressurevarying duct static pressure

Static Pressure Control in VAV AHUStatic Pressure Control in VAV AHU





Velocity pressureVelocity pressuresensor locatedsensor located

in VAV boxin VAV box


(flow setpoint(flow setpointcalculated fromcalculated from

room temperature)room temperature)

Damper actuatorDamper actuatorand VAV boxand VAV box

damperdamper

Damper controlsDamper controlsair flow throughair flow through

VAV boxVAV box

Air flow through box affectsAir flow through box affectsvelocity pressure across sensorvelocity pressure across sensor

Flow Control in VAV BoxFlow Control in VAV Box


Control Loop CalculationsControl Loop Calculations


++

SetpointSetpoint

InputInput --ErrorError

CalculateCalculateProportionalProportional

TermTerm

CalculateCalculateIntegralIntegral

TermTerm

DeadbandDeadband Proportional bandProportional bandIntegral timeIntegral time

Output = P Term + I TermOutput = P Term + I Term

++

Error*Error*

++

CalculateCalculateError*Error*


Control Loop CalculationsControl Loop CalculationsThe first step is to calculate the The first step is to calculate the difference between the controlled difference between the controlled variable (input) and the setpoint. variable (input) and the setpoint. This difference is called “Error”.This difference is called “Error”.

Error = Input - SetpointError = Input - Setpoint


Control Loop CalculationsControl Loop CalculationsIf Error is less than the Deadband,If Error is less than the Deadband,

then Error* = 0then Error* = 0

If Error is greater than the Deadband,If Error is greater than the Deadband,then Error* = Error - Deadbandthen Error* = Error - Deadband

If Input is close to Setpoint (± If Input is close to Setpoint (± Deadband), then assume Error is Deadband), then assume Error is

zero. The use of a Deadband zero. The use of a Deadband eliminates minor output adjustments eliminates minor output adjustments

and stabilizes control.and stabilizes control.


Control Loop CalculationsControl Loop CalculationsNext, calculate the Proportional Term:Next, calculate the Proportional Term:

For Proportional-Only control:For Proportional-Only control:

Output = Proportional TermOutput = Proportional Term

Proportional Term 100Error*

Proportional Band


Control Loop CalculationsControl Loop CalculationsProportional-Only ControlProportional-Only Control

OutputOutput100%100%

0%0%

SetpointSetpoint

ProportionalProportionalBandBand

DeadbandDeadband

InputInput

11.011.0 0.00.0


Control Loop CalculationsControl Loop CalculationsProportional-Only ControlProportional-Only Control

ExampleExampleSetpoint = 12°CSetpoint = 12°C

Deadband = 0.3°CDeadband = 0.3°CProportional Band = 4°CProportional Band = 4°C

InputInput OutputOutput

12.312.3 0.00.0

14.314.3 50.050.0

16.316.3 100.0100.0

17.017.0 100.0100.0


Control Loop CalculationsControl Loop CalculationsIn the DDC Controller, the control loop In the DDC Controller, the control loop

calculations are repeated every 1.5 calculations are repeated every 1.5 seconds. A new sample of the input seconds. A new sample of the input

and a new output command is and a new output command is calculated every 1.5 seconds.calculated every 1.5 seconds.

The Proportional Term is not time The Proportional Term is not time dependent. The Proportional Term is dependent. The Proportional Term is calculated each 1.5 seconds and the calculated each 1.5 seconds and the

calculation does not depend on calculation does not depend on previous calculations.previous calculations.


Control Loop CalculationsControl Loop CalculationsProportional-Only Control results in a Proportional-Only Control results in a

continuous error. continuous error.

SetpointSetpointDeadbandDeadband

TimeTime

InputInput

TimeTime

OutputOutput

Proportional Only Output Proportional Only Output


Control Loop CalculationsControl Loop CalculationsThe Integral Term is time dependent:The Integral Term is time dependent:

IntegralTerm(t)=1.5secondsIntegralTime

Proportional Term(t) IntegralTerm(t 1)

Integral TermIntegral Termas calculatedas calculatedat this sampleat this sample

timetime

Integral TermIntegral Termas calculatedas calculated

at the previousat the previoussample timesample time

Proportional TermProportional Termas calculatedas calculatedat this sampleat this sample

timetime


Control Loop CalculationsControl Loop CalculationsThe Integral Term will be calculated as The Integral Term will be calculated as

long as the output is between 0% long as the output is between 0% and 100%.and 100%.

Once the output is 0% or 100%, the Once the output is 0% or 100%, the Integral Term will stop calculating. Integral Term will stop calculating.

This feature is called “anti-windup”.This feature is called “anti-windup”.

Anti-windup allows the loop to change Anti-windup allows the loop to change from saturation to control as quickly from saturation to control as quickly

as possible.as possible.


Control Loop CalculationsControl Loop CalculationsIntegral Term calculationsIntegral Term calculations

0 sec.0 sec. 50.050.0

ExampleExampleSetpoint = 12°CSetpoint = 12°C

Deadband = 0.3°CDeadband = 0.3°CProportional Band = 4°CProportional Band = 4°C

Input = 14.3°CInput = 14.3°CIntegral Time = 15.0Integral Time = 15.0

Integral Term (0) = 0.0Integral Term (0) = 0.0

TimeTime OutputOutput

1.5 sec.1.5 sec. 55.055.0

3.0 sec.3.0 sec. 60.060.0

4.5 sec.4.5 sec. 65.065.0

6.0 sec.6.0 sec. 70.070.0


Control Loop CalculationsControl Loop CalculationsAs long as Error* is positive, the As long as Error* is positive, the Integral Term continues to grow. Integral Term continues to grow.

SetpointSetpointDeadbandDeadband

TimeTime

InputInput

TimeTime

Proportional Term Proportional Term

Integral Term Integral Term


Control Loop CalculationsControl Loop CalculationsThe Integral Term shrinks when Error* The Integral Term shrinks when Error*

goes negative.goes negative.

SetpointSetpoint

TimeTime

InputInput

TimeTime

Proportional Term Proportional Term

Integral Term Integral Term


Control Loop CalculationsControl Loop CalculationsThe output of a proportional plus The output of a proportional plus integral control loop will force the integral control loop will force the

error to zero over time.error to zero over time.

Most HVAC applications use Most HVAC applications use proportional plus integral control proportional plus integral control

loops.loops.

TimeTimeProportional Term Proportional Term

Integral Term Integral Term Output Output


The proportional term The proportional term affects the sensitivityaffects the sensitivity

of the control loop. of the control loop. (STRENGTH)(STRENGTH)

The integral term The integral term affects the affects the

responsiveness of the responsiveness of the control loop. (SPEED)control loop. (SPEED)

Control Loop CalculationsControl Loop Calculations


Control Loop CalculationsControl Loop CalculationsDDC Controllers are equipped to DDC Controllers are equipped to provide Proportional + Integral + provide Proportional + Integral +

Derivative control but the derivative Derivative control but the derivative term is almost never used.term is almost never used.

The derivative term is proportional to The derivative term is proportional to the rate of change of the input. The the rate of change of the input. The

derivative term “amplifies” any derivative term “amplifies” any naturally occurring “noise” in the naturally occurring “noise” in the

input resulting in unstable control. input resulting in unstable control.

Control Theory Control System Objectives Establish a final condition Provide safe operation ...

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