A Tutorial Overview Proportional Integral Derivative

PID Applications Typical Examples Automotive Cruise Control Temperature Control Room Ovens Glue Applicators Flow Control Air Delivery Liquids Chemicals Level Control in Tanks VFD and Motor Speed Control

What does the PID do? A PID loop Automates what an Operator with a gauge and a control adjustment knob would do. He would; Read the gauge to determine the current state of the process Adjust the knob to bring the process state to the correct condition Continue to monitor and adjust the knob to maintain the condition

PID Terms Common terms used for both methods. The desired value to where the gauge is adjusted to by the knob is the “Set Point” Any difference between where the gauges needle is and the desired value is referred to as “Error” Manipulated Variable or the output level adjusted to drive the process variable to the correct set point. The position of the needle on the gauge is the “Process Variable” The amount of time used to collect data from the system is the “Sampling Period”. The duration of the control output that is turned on and off according to the manipulated variable is the “Control Period”.

Typical PID Application Temperature Control is a common example of how a controller is used to automatically Adjust a variable to meet a set temperature point Hold the variable at that set point Respond to changes in the set point Respond to changes in the variable Respond to changes in the environment A Control Loop consist of three parts Measurement by a sensor connected to the process (Thermocouple) Decisions made in a Computerized controller with set conditions (PLC) Action through an output device (such as a gas control value)

ON/OFF Temperature Control When the input value is lower than the setting, the output is OFF If the input value is higher than the setting, the output is ON Overshoot, Undershoot and Hunting are present

MicroSmart PID Control FC4A has manual PID control FC5A has New Auto Tuning FC5A has New Tuning Formula

P = Proportional Band To handle the present The Basic Formula is The error is multiplied by a negative value Then its added to the controlled quantity (subtracting the error) The controller output is proportional to the error or a change in measurement (depending on the controller) Sometimes referred to as the GAIN of the feed back loop The Basic Formula is (control output) = (error) X 100 / (proportional gain)

Typical Proportional Operation The outputs Manipulated Variable is in proportion to the deviation between the input value and the setting value in the band Usually the output is turned on until process temperature reaches Point “A” Once it is inside the band it will operate quite like the ON/OFF action but is restricted to the band

Proportional Gain When proportional Band or Gain is widened large process swings Offset from set point is larger Overshooting Undershooting Error grows faster Unstable, hunting is more pronounced When proportional band or Gain is Narrowed The controlled output is turned ON and OFF very close to the set point Drift away from the set point is easily noticeable Setting a proportional Gain that minimizes all of the above issues gives the most stable operation.

Integral A simple proportional system oscillates, moving back and forth around the set point There is nothing to remove the error when it overshoots, it just keeps accumulating The error shows as a drift up or down of the proportional oscillation This error is Integrated (added up over time) and then averaged and then subtracted from the Process variable This corrective action, may best described, as a reset like function Similar to a person pressing a reset button to a predetermined time cycle

What does Integral do ? The chart below shows an easy to understand representation of the ERROR corrected by the Integral function

Integral PI Formula t = Time e = Error d = delta (change in time) PI or (Proportional + Integral) Integral action automatically corrects the OFFSET caused in the Proportional action. The control is performed at, or very near the setting value. The mathematical formula for the Integral is below CONTROLLER OUTPUT = (1 / INTEGRAL) [INTEGRAL of e (t) d (t)] t = Time e = Error d = delta (change in time)

Limitations of PI Control It may take some time for the controlled output to stabilize if there is a disturbance in the process variable or the set point If the integral action time is to shortened, correction becomes strong and the OFFSET is corrected for in a shorter time but hunting is likely to occur If Integral action time is to long, correction becomes weaker, and it will take more time to correct for the OFFSET PI correction is best suited for control, in which slow change is required

PID TUNING Manual Tuning, operator performed & calculated Closed versus Open Loop Tuning Controller tuning techniques are classified as closed or open. Closed loops are more often used and typically give the advantage of giving more realistic results, because the process and controller operate together normally. Open loops are very seldom used for other then Batch process systems. Auto Tuning or a shelf tuning calculation Samples are taken by the control device for a short period just after start-up, which are then processed through a tuning formula and applied to the process

THE IDEAL PID TUNING When the PID is tuned properly the result should look like this As the process variable settles in around the Set point, it should oscillate as shown Each subsequent hump in the oscillation should be ¼ the size of the previous one

MANUAL PID TUNING The Ziegler-Nichols Closed-Loop Method: This manual tuning method is used for best results Remove both the reset (Integral) and error reduction (derivative) actions. Set the controller to PID and place the set point at the most often used level. Generate an upset in the loop and adjust the gain (proportional) until the loop cycles with a constant amplitude to both sides of the set point. Typically gain settings are between 60 to 80% of process. Use of a chart recorder may be helpful. An upset in the process can be produced by increasing or decreasing the set point by some arbitrary amount (about 10 to 20%), waiting until the process begins to respond, then returning the set point to its previous value. Record this Proportional value as Ku

MANUAL PID TUNING Record the period of the oscillations (Pu) Determine the settings from the equations on the next slide Program the settings into the controller thru the WindLDR software.

MANUAL TUNING FORMULA Basic Tuning equations for calculating PID settings using the Ziegler-Nichols Closed-Loop method Proportional is 0.6 Ku Integral is 0.5 Pu Derivative is Pu / 8

The PID Function Block The PID Operands S1 = Control Register S2 = Control Relay S3 = Process Set point S4 = Process variable (actual state of the process) D1 = Manipulated variable ( PID correction output)

The PID Function block Double Clicking on the PID Function Block brings up the Set up Dialog Box tool. Fill in the boxes with valid Operands. For help please use the guide lines listed in Chapter 21 of the Users Manual.

The PID Function block The Module type 0 - 4095 for the End refresh type of Analog Card 0 - 50000 for the ladder refresh type of Analog Card The Data type Select Word (W) or Integer (I) when using the Ladder refresh analog module type.

The PIDST Function Block Macro This Dialog Box MACRO makes it easy to set the Operands for the PID Function Control Block. Set the Module type Set the Data Type Set the first three Operands (S1, S2 and S3) for the PID Control Function Block that this MACRO will set up the parameters for. This ties the two Function Blocks together.

For our example it should look like this

Set the PID Parameters Operation Mode Control Action Integral Action Proportional type

PID Action Operation Mode Parameters Set By PID Action User Auto tuning and PID Action User Auto Tuning User Advanced Auto Tuning and PID Action Fully Automatic Advanced Auto Tuning Semi Automatic

Control Action When tuning Manually the Control action must be chosen. Direct Control Action Reverse control Action When Auto Tuning is chosen then this is set for you when it auto Tunes.

Direct Control Action Is used for cooling temperature control

Reverse Control Action Is used for Heating temperature control

Integral Action Disable sets the Integral to start at the beginning of the PID action Enable sets the Integral to start when the process variable gets to a percentage of the proportional term.

Proportional Action Proportional Term Gain: The Output Manipulated Variable is calculated from the deviation between the Set Point and the Process variable. Band: The Output Manipulated Variable is calculated the same way but the Integral action is only on while the process variable is between the set Point and the limit set by the Band.

PID Action Parameters Set Point This must be set by the operator This is the point in the process that you wish the process variable to operate at. The Set point may be changed at any time by entering a new value into S3 of the PID Control Function Block

PID Action Parameters Sampling Period The sampling period determines a time interval between PID executions PID executions are in relation to the beginning of each PLC SCAN. The sampling period may be longer then one SCAN time.

PID Action Parameters Control period The Control Period is the duration of the ON/OFF cycle of the control output. The ON pulse duration is set by the combined product of the control period (S1+13) and the output manipulated variable (S1+1). PID Control Operand is (Control relay S2+6).

PID Action Parameters Proportional Gain This sets the amplitude of the swing of the process variable above and below the set point. Only used during the manual setting of the PID A good starting point would be 60% For maximum performance Gain must be set using a trend chart recorder.

PID Action Parameters Integral time This must be set by the operator during manual PID tuning. This is the time interval in the process that you wish the Integral reset action to operate at.

PID Action Parameters Derivative Time This must be set by the operator during manual PID tuning. This is the time interval in the control period that you wish the derivative ERROR to be removed from the process. Derivative Gain This is a value usually set between 20 to 30 % to help eliminate noise or fluctuations in the process variable.

Input settings Linear conversion Disabled The process variable is stored in the PID Function without Scaling or conversion Enabled When enabled the conversion function is useful for scaling the process variable to an actual engineering value.

Input settings Input Filter Used to smooth out fluctuations in the process variable. Helps stabilize the reading of the process variable, such as temperature readings when the value changes faster then the sampling rate. In effect during Auto Tuning and PID action.

Input settings High Alarm When the process variable is higher then or equal to the set value then the S2+4 control relay will activate Low Alarm When the process variable is lower then or equal to the set value then the S2+5 control relay will activate These settings have nothing to do with Auto Tuning or the PID action and must be set independently

AT Parameters The AT parameters tool box is used for Manually setting The Set point is the point at which the Auto Tuning stops and the PID action starts Usually set to the same value used for the process set point. The sampling period sets the rate at which data is collected from the process during Auto Tuning only. The control period sets the ON/OFF cycle of the control output (S2+6) The AT parameters tool box is used for Manually setting the Auto Tuning by user The output manipulated variable Limits the amount of output during Auto Tuning only

Output settings This is not used for analog output values from the PID PID Control Function Block destination operand (D1) The manipulated variable is displayed as a range from 0 -100 Disabled The range is set to 0 – 100 Enabled The range can be limited to upper and lower limits. Such as 26 and 49 This is not used for analog output values from the PID Use Data register represented by S1+24