Control Theory Control System Objectives  Establish a final condition  Provide safe operation  Eliminate the human element  Assure economical operation

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback SensorsTemperaturePressureHumidity

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback Sensors Sensors are approximately linear indicators of process conditions. Sensors also have a response time. DDC controllers can linearize sensor values and derive calculated values (i.e. flow from  P).

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback Controllers Two Position Control Analog Control Direct Digital Control

Control Theory Two Position Control Typically a mechanical device such as a thermostat or pressure switch Picture of A70

Control Theory Two Position Control A mechanical thermostat opens or closes a relay based on the temperature. this applies a voltage to a two position fan coil valve which goes full open or full closed. Differential TemperatureIncreasing Cut in temperature Full flow to FCU Cut out temperature No flow to FCU

Control Theory Two Position Control Low Cost Inaccurate Control Inflexible Strategies Cannot be Networked Used for Simple On / Off Control such as FCU in Hotel Guest Rooms Used for Safety Controls

Control Theory Analog Control Uses analog electronics but no microprocessor. Picture of System 350

Control Theory Analog Control A temperature sensor located in the return air of a CAV AHU controls the chilled water valve using a proportional algorithm.

Control Theory Analog Control Low-Medium Cost Reasonably Accurate Control Inflexible Strategies Cannot be Networked Used for AHU without BAS

Control Theory Direct Digital Control Uses microprocessor to do calculations and can be networked with BAS Picture of DDC Controller

Control Theory Direct Digital Control 1. Convert input signal from analog to digital format 2. Use computer program to calculate the value to be sent to the output 3. Generate output signal from calculated value

Control Theory Direct Digital Control Medium Cost Accurate Control Flexible Strategies Can be Networked Used for AHU with BAS

Control Theory Direct Digital Control Current DDC technology implements analog control algorithms using microprocessor. Next generation DDC technology will add adaptive tuning, mechanical system diagnostics and characterization of the controlled device.

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback Controlled Device VAV Box Actuator VSD

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback Controlled Device Controlled devices are almost never linear and also demonstrate hysteresis. Controlled devices are typically oversized and this makes proper control even more difficult.

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback HVAC Process It is critical to understand the characteristics of the HVAC process when applying controls.

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback HVAC Process The HVAC process will limit the range of possible control. For example, the mechanical system will not allow a room setpoint of 5°C to be achieved.

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback The system feedback will introduce delays. For example, it may take a few minutes for a change in valve position to cause a change in room temperature.

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback The system feedback will introduce “noise”. For example, turbulence and stratification make accurate measure of pressure and temperature difficult.

Control Theory Examples of VAV Control Loops SensorControllerControlledDeviceHVACProcess System Feedback

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback Temperature sensor located after cooling coil DDCController Valve actuator and chilled water valve Cooling coil extracts heat from air stream Air stream after cooling coil affects temperature sensor Off-Coil Temperature Control in VAV AHU

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback Static pressure sensor located in ductwork DDCController Variable speed drive controller connected to fan motor Fan controls airflow into ductwork VAV boxes open and close varying duct static pressure Static Pressure Control in VAV AHU

Control Theory SensorControllerControlledDeviceHVACProcess System Feedback Velocity pressure sensor located in VAV box DDCController (flow setpoint calculated from room temperature) Damper actuator and VAV box damper Damper controls air flow through VAV box Air flow through box affects velocity pressure across sensor Flow Control in VAV Box

Control Theory Control Loop Calculations

Control Theory + Setpoint Input - Error CalculateProportionalTermCalculateIntegralTerm Deadband Proportional band Integral time Output = P Term + I Term + Error* + CalculateError*

Control Theory Control Loop Calculations The first step is to calculate the difference between the controlled variable (input) and the setpoint. This difference is called “Error”. Error = Input - Setpoint

Control Theory Control Loop Calculations If Error is less than the Deadband, then Error* = 0 If Error is greater than the Deadband, then Error* = Error - Deadband If Input is close to Setpoint (± Deadband), then assume Error is zero. The use of a Deadband eliminates minor output adjustments and stabilizes control.

Control Theory Control Loop Calculations Next, calculate the Proportional Term: For Proportional-Only control: Output = Proportional Term

Control Theory Control Loop Calculations Proportional-Only Control Output 100% 0% Setpoint ProportionalBand Deadband Input

Control Theory Control Loop Calculations Proportional-Only Control Example Setpoint = 12°C Deadband = 0.3°C Proportional Band = 4°C InputOutput

Control Theory Control Loop Calculations In the DDC Controller, the control loop calculations are repeated every 1.5 seconds. A new sample of the input and a new output command is calculated every 1.5 seconds. The Proportional Term is not time dependent. The Proportional Term is calculated each 1.5 seconds and the calculation does not depend on previous calculations.

Control Theory Control Loop Calculations Proportional-Only Control results in a continuous error. Setpoint Deadband Time Input Time Output Proportional Only Output

Control Theory Control Loop Calculations The Integral Term is time dependent: Integral Term as calculated at this sample time Integral Term as calculated at the previous sample time Proportional Term as calculated at this sample time

Control Theory Control Loop Calculations The Integral Term will be calculated as long as the output is between 0% and 100%. Once the output is 0% or 100%, the Integral Term will stop calculating. This feature is called “anti-windup”. Anti-windup allows the loop to change from saturation to control as quickly as possible.

Control Theory Control Loop Calculations Integral Term calculations 0 sec Example Setpoint = 12°C Deadband = 0.3°C Proportional Band = 4°C Input = 14.3°C Integral Time = 15.0 Integral Term (0) = 0.0 TimeOutput 1.5 sec sec sec sec. 70.0

Control Theory Control Loop Calculations As long as Error* is positive, the Integral Term continues to grow. Setpoint Deadband Time Input Time Proportional Term Integral Term

Control Theory Control Loop Calculations The Integral Term shrinks when Error* goes negative. Setpoint Time Input Time Proportional Term Integral Term

Control Theory Control Loop Calculations The output of a proportional plus integral control loop will force the error to zero over time. Most HVAC applications use proportional plus integral control loops. Time Proportional Term Integral Term Output

Control Theory The proportional term affects the sensitivity of the control loop. (STRENGTH) The integral term affects the responsiveness of the control loop. (SPEED) Control Loop Calculations

Control Theory Control Loop Calculations DDC Controllers are equipped to provide Proportional + Integral + Derivative control but the derivative term is almost never used. The derivative term is proportional to the rate of change of the input. The derivative term “amplifies” any naturally occurring “noise” in the input resulting in unstable control.