John Kuehn
Shirley Hong
Peter Tam
Controlling a Temperature Controlling Device
Abstract:
This experiment enabled us to perform a digital-to-analog (D/A) operation using
the National Instruments DAQ board within our computer. Ultimately, we constructed a
feedback based system that controlled the temperature of an aluminum block with great
precision. Upon many trials, we obtained coefficients with the values A=5.0, B=0.0008,
and C=3.0 which provided the best temperature control and temperature measurements.
These coefficients enabled us to record temperatures with utmost precision of 0.2
degrees Celsius for set temperatures within the range of 15º to 40º degrees Celsius.
Introduction:
The motivation for creating a PID controller was to create a system that could
automatically monitor and control a device or system of devices. This controller can be
used to replace a human operator that would otherwise have to constantly monitor and
adjust the system manually. The PID controller allows us to automatically adjust some
set measurement, and the controller takes care of keeping that device in range of the
specified measurement. We created a PID controller that controls the temperature of an
Aluminum Block.
The PID stands for Proportional, Integral, Derivative. ‘P’ is the proportional gain
parameter. This is the first parameter of the PID control algorithm and has a coefficient
‘A’ attached to it. This output value is proportional to the difference between the set
value and the current value (The Error). In this case the error was the difference in Set
temperature v. Current temperature. ‘I’ is the integral parameter. This output is
proportional to the time integrated with the error signals. This parameter is helpful
because it tends to stabilize right above or below the set point, and provides additional
output to counteract energy losses to the system. This is the second parameter of the PID
control algorithm and has a coefficient ‘B’ attached to it. In this case, the integral
parameter provided a voltage to counteract heat dissipation or absorption from the air in
the room. Lastly, ‘D’ is the derivative function or the rate which the problem overshoots
or undershoots the range of the set point. This is the third parameter of the PID control
algorithm and has a coefficient ‘C’ attached to it. By taking a derivative in the change
error (temperature) small fluctuations are eliminated In this case, the derivative
parameter provided for a more stabile temperature.
By manipulating the variables, the PID controller will change in response to
any change in the measurement or the set point. In our case, it will either raise the
temperature of the aluminum plate or lower the temperature of the plate.
The theoretical concept behind the PID temperature controller is that when the
temperature is measured, this temperature value is used to control the error signal that is
determined by this simple algorithm.
Vin = AE + B t  (m=0 to n) Em + C/t * [ En – En-1 ]
Vin is the voltage applied, A is the gain, En = temperature set point, En-1 is the
previous set point; delta t is the integration time. Thus, this algorithm takes an input
temperature and finds the correct output voltage necessary to heat the aluminum block
and maintain it at the set temperature.
The Thermo Electric device used to cool and heat the block in the PID
temperature controller is also known as the Peltier Thermo-Electric device. We shall
refer to this as a TE Device from now on. The TE Device has an array of thermocouple
junctions and are arranged in such a way as to provide a heating side and a cooling side.
Therefore, heat can be dissipated through this thermoelectric module or it can be
absorbed depending on the direction of current flow through the thermocouplers, which
then can be measured by watts/cm which is I = V^2 /R.
Experimental Setup & Procedure:
1. Build a Vi that instructs your DAQ board to perform a D/A operation named
Simple Write-Easy I/O.
2. Attach a voltmeter between your DAQ board’s Digital-to-Analog Channel 0
Output (DAC0OUT) and Analog Output Ground(AOGND), then verify that you
can use Simple Write-Easy I/O to output voltages.
3. Build a digital temperature controller that can control the temperature of an
aluminum block to within less than 0.05º degrees Celsius of a given set-point
temperature.
A. The algorithm for the controller includes:
i. Reading from the block’s temperature Tsample using a thermistor as the
temperature sensor.
ii. Comparing Tsample with the desired set-point temperature Tset-point
iii. Decide what value of Vin will command the TE device to provide the
heating or cooling needed to bring Tsample closer to Tset-point
iv. Applying this voltage at the Vin input of the voltage-controlled current
driver circuit.
v. Repeating this process continuously to obtain the desired temperature
control of the aluminum block.
First, sample readings of temperature were taken. To average out random
fluctuations when reading the thermistor voltage we determined the mean of the data.
Then, Ohm’s Law and Steinhart-Hart Equation was used to convert the voltage to the
temperature Tsample. The Discrete Sampling PID Control algorithm was then implemented
n
in software: Vin  AE  Bt  Em 
m 0
C
En  En  1. The error E was determined every
t
t seconds and the summation in the right hand side term is over all the error-values
determined since the program started running. (Since our set-up is similar to the one
described in Appendix I of Essick, we originally used constants with the values A=7,
B=1, C=0.5. However, the measurements taken were not at its optimum. Consequently,
we ran many trials of different constants until the optimum values were acquired.) The
Simple Write-Easy I/O was used as a subVI in the block diagram to output of the PID
value for Vin to the input of the TE device’s voltage-controlled current driver circuit.
In order to construct the digital temperature-control system, the thermistor-based
digital thermometer from Chapter 10 is rebuilt. The thermistor is now used to monitor
Tsample. An 1F capacitor is added to shunt high-frequency noise signals to ground. The
unity-gain buffer is not included in the circuit due to unstable and inconsistent results.
Vout and GND is connected to the inputs of the A/D channel of our LabVIEW system.
(The software was wired as shown in the attached pages.)
Results:
Many tests were run on the PID temperature controller. The controller was tested
for range, stability, speed, and accuracy. Before any of these tests could be run, it was
first necessary to find the proper coefficients for the control algorithm. Starting with the
book’s suggestion: A=7.0, B=1.0, C=0.5 and testing various other configurations, trial
and experimentation led us to believe the coefficients A=5.0, B=0.0008, and C=3.0 were
best suited for our setup. Starting at room temperature (around 23º Celsius) and climbing
to a set temperature of 32º Celsius was the standard for testing coefficients. One can see
by the graph on the following page why we chose the coefficients that we did. Since only
one Thermo- Electric device was available for use in this experiment, and there were no
secondary devices or backups, much care had to be taken to prevent damage to the unit.
TE Device specifications were somewhat of a mystery since its data sheet was in a
different language, therefore operating values of 2.0 ± 0.1 amps where used instead of the
alleged 8.0 amps the specifications seemed to suggest. When positive voltage was
applied to the circuit, positive amperage flowed though the TE device causing heating of
the aluminum block, and when negative voltage was applied, the current flowed the
opposite direction and caused for cooling of the block.
To find the range of the temperature controller we simply ran it at the maximum
input and output voltage for extended periods until the temperature of the aluminum
block reached its maximums and minimums respectively. We found that the block could
reach temperatures as low as 5.2º Celsius and temperatures as high as 75.4º Celsius.
The testing of the controller’s stability went hand in hand with finding the best
coefficients for the PID algorithm. We chose the values A, B, and C based on which
looked the most stable. We noted that stability increased with an increase in the C term
which correlates to the damping factor in the PID algorithm. This makes sense, but this
term was also responsible for the situations in which aluminum block temperatures would
not quite reach the desired set temperatures, especially when the set temperatures were
below room temperature.
The speed of this temperature control unit depended on many factors. Some
limiting factors include: The power supply driving the TE Device, the Room
Temperature, and the heat transfer properties of the aluminum block. These factors were
assumed to be constant for all tests. The one factor we did control (as stated earlier) was
the voltage supplied to the controlling circuit and thus controlling how much current was
applied to the TE device. Granted, we limited the current source to 2.0 amps, the PID
control algorithm could be modified to reduce the rate of temperature change of the
aluminum block. The ‘A’ coefficient was in charge of the proportional part of the PID
control algorithm. When testing for the best coefficients to use, A was changed slightly
in the range from 5.0-7.0. The results of changing these constants were small, but the
results imply that smaller values of ‘A’ caused for faster divergence to the desired set
temperature. This goes against our assumptions that higher values of ‘A’ increase the
proportional rate of change.
The accuracy of our digital temperature controller was highly dependent on a
rather inaccurate temperature reader. Reasons for the inaccurate temperature reader will
be discussed later, but it is important to verify that the PID controller is accurate. To test
this, we actually did not read a “real” temperature. Instead we faked temperatures by
providing the “temperature read” input of the PID algorithm with an array of input
temperatures. With this being the case we could watch a non-fluctuating output voltage
supplied to the control circuit. We believe that this voltage would regulate the control
circuit to maintain a very accurate and stable temperature.
Discussion and Conclusion:
The book wanted a digital temperature controller that could adjust the temperature
of an aluminum block to within .05º Celsius of a given set temperature. We were able to
maintain the aluminum block at a temperature accurate to 0.2º Celsius in the range
between 15º and 40º Celsius. It is not possible to get any better accuracy without having
a stable temperature reader. The temperature reader ranged ± 0.3º C in very short time
spans, and therefore caused the output voltage to fluctuate similarly. We were able to
achieve accuracy of 0.2º C by reading in an average of multiple temperatures, and
increasing the ‘C’ term (differential term) in the PID control algorithm to help stabilize
fluctuations. Aside from the temperature-reading problem, all other aspects of the PID
control algorithm coincided with PID control theory. The automatic temperature
controller was fast, efficient, stable, and simple to operate. To keep a cup of tea warm, or
keep a can of beer cool, this would be an overly accurate and involved method, but one
could not be unhappy with the results.
References:
Essick, John, Advanced LabView Labs.
Upper Saddle River, NJ: Prentice Hall, 1999.
Pellet, Professor David E., Room 337, UC Davis Physics Department. 2002
Mouer, William. PID Basics. 1999. PID Controller Basics.
1999, Stanford University. http://bigben.stanford.edu/Labsuite/pid_basics.htm
* Special Note * Some aspects of this report may be somewhat repetitive, and this is the
result of multiple people working on different parts. The outline for the Physics 122 Lab
write-up is somewhat redundant already, so we apologize if we are the same.
* Other Note * Have a Good Summer, and if you publish this in a world renown Physics
Journal let us know. –JAK, Pete, Shirley