Industrial Control (Students guide, 1999, v1.1 )

IF Sign = 1 THEN DriveDone

Drive = 0

DriveDone:

RETURN

'********* Drive the heater Drive_Heater:

FOR PWMCount = 1 TO PWMTime 'Apply pwm at 220 mSec for each PWMTime repetion PWM Heater,drive * 255/100,220

NEXT

RETURN

'********* Plot Data

Plot_Data:

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DEBUG DEC Temp,CR

'** Nicely formatted message output for reading (4 lines) DEBUG "Set:", DEC SP," Temp:", DEC Temp

DEBUG " %Err:",SDEC Err," %B=", DEC B, " %P=", SDEC P DEBUG " %I=",SDEC I," %D=", SDEC D

DEBUG " %Drive:",SDEC Drive, CR

'** Comma-seperated message output for import into spreadsheet

'DEBUG ",",DEC Temp,",",SDEC Err,",",SDEC P,",",SDEC I,",",SDEC D,",",SDEC Drive,CR RETURN

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RETURN

'********** Set sign of value SetSign:

IF Sign.bit15 = 0 THEN SignPos 'If signbit is 1, then negative Sign = -1

Return SignPos:

Sign = 1 SignDone:

Return

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Figure 6.2: Main Process Flow

Figure 6.2 is a flowchart of the main loop for the PID program. Specifics of each of the processes will be discussed as they arise.

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All microcontrollers have their limitations, as do other systems, such as Programmable Logic Controllers (PLCs). In programming complex operations such as PID, it is important to understand the limitations and finding alternative means.

We’ve been dealing with the restriction of integer values, such as temperature being in tenths of degrees. One other limitation we’ll deal need to deal with is that of negative numbers. While the BASIC Stamp can use negative values, it cannot divide them or use the MIN and MAX instructions to set limits on their size. In this section both of these will be important. The values of drive for PID will be negative or positive depending if drive should be added to the total or subtracted. We will also need to limit the maximum values so that we do not exceed 100% in certain circumstances, such as total drive.

To perform these tasks, a routine called SetSign is used. Several routines call it using a GOSUB. The possibly negative value to be manipulated is saved to a word variable Sign. When SetSign is called, the sign bit (bit15) is examined. If the sign bit is 1, it is a negative value and the variable Sign is set to -1. If the sign bit is 0, it is positive and Sign is set to positive 1. Back in our calling routine, the absolute value of our possibly negative number is manipulated. The result is then multiplied by Sign to return the value back to positive or negative. The range of signed values can be from –32,768 to +32767.

The first part of program to consider is the total drive calculations. Figure 6.3 is a flowchart for these routines. As discussed, the total drive is the sum of 3 different evaluations based on the error. The total drive % will then be applied to the heater using PWM for 5 seconds. This allows a long on-time compared to a relatively short off-time when performing other operations.

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Figure 6.3: Flowchart of Drive Routine

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Exercises

Exercise #1: Bias Drive

As discussed, a system in equilibrium is where the energy gains in a system equal the energy losses. When a system is designed typically the engineers will have determined anticipated average losses on the system. The Bias Drive is the drive needed to compensate for average losses. By designing the system so that a 50% drive is sufficient for average losses, provides the ability to add or subtract up to 50% due to other losses or large disturbances to the system. This affords the maximum amount of control.

%DriveTOTAL = %DriveBIAS + %DrivePROP + %DriveINT + %DriveDERIV

For the eggs in our incubator to hatch healthy chicks, 50% drive on our heater would provide sufficient energy to maintain temperature in the incubator near 101.5F with average losses. Unfortunately, our system is not well engineered. Being a non-insulated plastic canister with a small resistor for a heater, chances are that 50% drive will not be sufficient under most circumstances for our desired setpoint. Some limitations on our experimental incubator are:

•A bias of 50% PWM drive is insufficient to provide a temperature of 101.5F.

•Every incubator will have a different stable temperature for 50% bias drive due to many factors.

•Our incubator is a fragile, steady state system. Factors such as room temperature and vents or fans blowing on the canister will shift the temperature.

•Moving or bumping the incubator will cause air mixing and affect the measured temperature.

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We will deviate from our optimum incubator setpoint in order to operate the system around a 50% bias temperature. Note that this bias temperature may fluctuate due to room conditions. It is recommended that the student read through all of the Chapter 6 material first and then try to perform as many hands-on portions consecutively as possible.

Copid = B

%DriveTOTAL = %DriveBIAS

Determining the Bias Temperature:

1)De-energize your system and allow it to cool to room temperature.

2)Verify that the Drive Control Setting matches the following:

Note that Kp, Ki and Kd are all 0 providing 0 drive from these evaluations allowing only bias drive of 50% to the heater.

3)Energize your system and download the program to the BASIC Stamp 2.

4)Close the debug window and connect on StampPlot Lite.

5)Reset your BASIC Stamp 2 by pressing “reset” on the Board of Education.

6)Allow the incubator temperature to stabilize to the find the 50% bias temperature.

7)Round your stabilized temperature to the nearest whole degree and set it as your SP (setpoint) constant (98.8 = 990).

Figure 6.4 is the plot of our test incubator stabilizing.

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Figure 6.4: Bias Temperature at 50% Drive

Note the amount of time it took the temperature to stabilize. In our test, approximately 450 seconds. In a system with a first-order response, such as our incubator, the system requires 5 time-constants (5TCs) to stabilize (or reach 99% of the new value) following a step-change in conditions, in this case going from 0% to 50% drive. 1 time-constant (1TC) for our system would be 450/5 or 90 seconds. The response time of the system is important in tuning a system as you will see later.

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Expercise #2: Proportional Control

Copid = B +(Kp*E)

%DriveTotal = %DriveBIAS +% DrivePROP

The next evaluation in the PID equation is proportional control of the system. The amount of drive from proportional control is a direct relationship to how much error exists in the system. The greater the error the greater the amount of proportional drive.

Let’s say our setpoint is 101.5F, and a bias of 50% PWM is sufficient to maintain this temperature. If the temperature drops to 101.0F, giving a -0.5F error, do we want to drive at 100% PWM, or something lower, to bring the temperature back to the setpoint?

For our incubator example, we want to maintain a temperature of 101.5F. The steadier we maintain this temperature, the healthier our eggs will be. It is allowable, though, to go 0.5F above or below this setpoint. So our setpoint will be 101.5 with an allowable band of +/- 0.5F, or 101.0F to 102.0F degrees.

If any error correction reaches the upper or lower limits, we want to take full action to return temperature back to the setpoint. Any error between the setpoint and the limits will provide a proportional amount of drive action. Figure 6.5 is a graphical representation of the incubator temperature verses the amount of drive needed for the given band.

Figure 6.5: Temperature vs. Drive

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