In this lab, you will construct a temperature control circuit, which will keep an aluminum block at a nearly fixed voltage by controlling a cooling device.

{ ${/download/attachments/205261964/TempControlAll.png?version=4&modificationDate=1557341733000&api=v2}$ The full temperature controller circuit. Don't panic, it can be broken down into 4 basic functional parts.

Figure 1 shows a simplified version of a PID temperature control circuit taken from [1].  The original circuit was designed to allow the user to maintain the temperature of a diode laser at a stable value, either above or below the ambient temperature. Our contains only those elements necessary to investigate the properties of including either proportional or proportional and integral feedback, without a differential component.  

The circuit shown in Figure 1 can be broken down into 4 parts based on function.

• Thermal Monitor: Allows user to monitor the bridge voltage proportional to the thermistor resistance which in turn is proportional to the temperature of the Al block.

• Set Point Monitor:  Allows user to monitor the bridge voltage proportional to the set point resistance. The difference between the Thermal and Set Point Monitor voltages is called the Error Signal.

• Feedback Control: The circuit essentially compares the voltage drop across the thermistor (Thermal Monitor) to the voltage drop across the set point resistance (Set Point Monitor) and generates an output voltage proportional to the difference between the two. This output voltage is used to control the behavior of the next stage of the circuit.  How this output voltage scales with the changing difference between the Thermal and Set Point voltages is determined by the values of { $R_1$ { $R_1$ , { $R_2$ { $R_2$ , and { $C_1$ { $C_1$ . • Thermo Electric Cooler (TEC) Control: Controls the current passing through the TEC using a Field Effect Transistor(FET), based on the signal from the feedback control portion. 

Since this is a multi-part lab, you will not be finishing your circuit in a single period.  The broad expectations of this lab are:

• Day 1: Build and test the temperature sensing, temperature setpoint, and basic feedback control circuits.
• Day 2: Build and test the Thermo Electric Cooler Control circuit, begin to test complete system behavior.
• Day 3:  Finish characterizing the circuit's behavior with different kinds of feedback.

Since you'll have to share power supplies and test equipment with other lab sections, you will _need _to document how your circuit is connected to the power supplies to be able to continue smoothly on subsequent days.

We are using a TL074 op-amp chip for this lab, which contains 4 separate op-amps in a single chip, as shown below:

The Tuesday/Thursday group will have to use individual LF411 chips; we're short of the 4-in-1 packages.

{ ${/download/attachments/205261964/TL074%20Quad%20Op-amp.png?version=1&modificationDate=1557156402000&api=v2}$

A thermistor (temperature-dependent resistor) has been embedded in the aluminum block to allow its temperature to be monitored. This particular thermistor has a resistance of ~100kΩ at 20°C and approximately 150kΩ at 15°C. Eq. 1 shows the relationship between the thermistor resistance and temperature from 20°C to 0°C.

{ $T = 51.9160 − 0.4376R +1.8229 X 10^{−3} R^{2} − 4.3102 X 10^{−6}R^3 + 4.1807 X 10^{−9}R^4$ { $T = 51.9160 − 0.4376R +1.8229 X 10^{−3} R^{2} − 4.3102 X 10^{−6}R^3 + 4.1807 X 10^{−9}R^4$  (1) Here T is temperature in °C and R is resistance in kΩ.

Q: What would you expect { $V_{sensor}$ { $V_{sensor}$  to be when the thermistor is at room temperature ({ $20^\circ$ { $20^\circ$ )? Q: What would you expect { $V_{sensor}$ { $V_{sensor}$  to be when the thermistor is cooled to { $15^\circ$ { $15^\circ$ ? Build the temperature sensing circuit, taking care to set the variable voltages to { $+10 V$ { $+10 V$  and { $-10 V$ { $-10 V$ .  Record what the actual value of { $V_{sensor}$ { $V_{sensor}$  is at room temperature.  You may also want to verify that the resistance of the thermistor decreases as temperature increases by heating the sensor slightly (e.g., by holding the aluminum block). Q:  What is the purpose of the op-amp in this circuit?  (Hint: without the op-amp, what would happen to the output voltage if some substantial current were drawn from the voltage divider?)

{ ${/download/attachments/205261964/Thermistor.png?version=1&modificationDate=1557153892000&api=v2}$ The thermistor is imbeded in a block of aluminum, as shown

{ ${/download/thumbnails/205261964/TemperatureSensor.png?version=4&modificationDate=1557341733000&api=v2}$ The temperature sensing circuit, which will output a voltage { $V_{sensor}$ { $V_{sensor}$ that is proportional to the temperature of the aluminum block.

The circuit shown in Fig. 3 allows us to create a particular voltage using a potentiometer.

Q: What range of { $V_{setpoint}$ { $V_{setpoint}$  would you expect to be able to achieve with this circuit? Construct your circuit, and record what range of values of { $V_{setpoint}$ { $V_{setpoint}$  can be generated.   Q:  What is the purpose of the op-amp in this circuit? 

{ ${/download/thumbnails/205261964/Trimpot.png?version=1&modificationDate=1557155244000&api=v2}$ Our 50k potentiometers.

{ ${/download/thumbnails/205261964/Setpoint.png?version=4&modificationDate=1557341733000&api=v2}$ The setpoint circuit, which will output a voltage { $V_{setpoint}$ { $V_{setpoint}$ that we can adjust to control how hot we want our aluminum block.

To begin with, consider a control circuit without any feedback at all, shown in Fig. 4.

Q: What do you predict { $V_{feedback}$ { $V_{feedback}$  will be when { $V_{sensor} > V_{setpoint}$ { $V_{sensor} > V_{setpoint}$ ?  What about when { $V_{sensor} < V_{setpoint}$ { $V_{sensor} < V_{setpoint}$ ? Q:  What would happen if you switched the setpoint and sensor connections?

Build the circuit from Fig. 4 and test your predictions.  In this instance it may be useful to use a function generator for one input and ground for the other. 

Q:  What kind of circuit is this?  Briefly explain how you know.

{ ${/download/thumbnails/205261964/NoFeedback.png?version=2&modificationDate=1557154361000&api=v2}$ A control circuit with no feedback whatsoever.

The temperature control circuit will be used to control the current flowing through a Thermo Electric Cooler (TEC) so as to maintain the temperature of an Al block at about 15°C. The TEC uses the Peltier effect to transfer heat from the cold side to the hot side. The rate of heat transfer is governed by the magnitude of the current passing through the TEC. The TEC is a semiconductor device (related to diodes), so polarity of the current flow through the device is important.

As shown at right, the hot side of the TEC is attached with thermal paste to a heat sink while the cold side is attached to the Al block we wish to cool. The thermal paste is sticky enough that it will hold the parts in contact with one another so long as you do not apply too much force to them. Make sure that the hot side of the TEC does not separate from the heat sink as this could result in destruction of the TEC. 

To control the current through the TEC, we will be using a Field Effect Transistor (FET), depicted below.  We haven't used FETs yet in this course, but essentially the resistance between the Source (S) and Drain (D) may vary between infinite and a few ohms, depending on the Gate (G) voltage.  

{ ${/download/thumbnails/205261964/FET.png?version=2&modificationDate=1557341740000&api=v2}$ Our Field Effect Transistor (FET). Note that the Source is named for being the “source” of electrons into the FET and the “drain” is the terminal electrons exit the FET from. Thus, conventional current will be from the drain to the source.

Both the TEC and the Power Transistor need to be able to dissipate heat at they operate, up to 25W. If either device draws too much current without adequate heat sinking they can be destroyed. Although both devices are attached to heat sinks, additional protection against overheating can be had by limiting the current that can be drawn. Both devices should operate fine at currents up to 1.5A.

Q: If the minimum resistance across the transistor's drain and source terminals (effectively in series with the TEC and 2 1{ $\Omega$ { $\Omega$  resistor) is approximately 3.3{ $\Omega$ { $\Omega$ , should our components be safe from over-currents?  Briefly explain.  (For simplification you can assume that there's no resistance across the TEC to find an upper limit for the current.) Construct the circuit, taking care that the TEC's white lead is connected to the benchtop power supply and that the black lead is connected to the FET's drain.

To test your circuit, you should try a variety of input voltages { $V_{in}$ { $V_{in}$  between 0V and 5V.  (You may want to construct a voltage divider for this, your variable power supply is needed for the op-amps.)  For each test voltage, record the Thermal Monitor voltage { $V_{sensor}$ { $V_{sensor}$  after the Al block reaches equilibrium.  At each voltage you will have to wait a few minutes for the temperature of the block to reach equilibrium. 

Q: Make a plot of the transistor gate voltage vs. temperature.  At what input voltage does the cooler begin working?

Q: From your data, estimate how much you have to change the transistor gate voltage to produce about a 1°C temperature change in the block.

Now that you know how the temperature of the Al block varies with the voltage applied to the transistor gate, set the voltage to bring the block to about 5°C below room temperature.

Turn off the 5V supply to the TEC for now to let the aluminum block warm up for the next part of the lab.

The LabQuest Mini (LQM) interface and Logger Pro software will be be used to record voltages as a function of time on the computer. We will record the voltages from the clips which are plugged into CH1 on the LQM, which you'll connect to to record { $V_{sensor}$ { $V_{sensor}$ . Double click on the Temp_V2 icon on your computer's desktop. The software is setup to collect data for 120 seconds. You can change this run length, if necessary, from the menu.

To begin collecting data, click on the Collect button which is located under the menu bar at the right side of the screen. By selecting Analyze → Examine the cursor can be used to read data values from the graph.

The Meters window in the bottom right part of the screen shows, in real time, the voltages being read by the two probes.

Start the software, and turn on the 5V supply so that you can observe how the temperature of the block changes over time.

Q: Draw a sketch of the Thermal Monitor voltage vs. time in your notebook. Include relevant information such as the starting and ending voltages and times.

While recording the Thermal Monitor voltage on the computer, quickly change the transistor gate voltage by the amount you determined was needed to produce a { $1^\circ$ { $1^\circ$  temperature change. Observe how the Al block approaches its new equilibrium temperature. Q: What is the characteristic time for the Al block to reach the new equilibrium temperature with no feedback control?

{ ${/download/thumbnails/205261964/TEC.png?version=1&modificationDate=1557155363000&api=v2}$ { ${/download/thumbnails/205261964/Cooler.png?version=1&modificationDate=1557236130000&api=v2}$ The thermo electric cooler, shown in place with aluminum block and heat skink.

{ ${/download/thumbnails/205261964/HeaterControl.png?version=3&modificationDate=1557154442000&api=v2}$ The heater control circuit, which will cause the TEC to heat up when { $V_{feedback}$ { $V_{feedback}$ is sufficiently high. { ${/download/thumbnails/205261964/Test%20voltage%20gen.png?version=1&modificationDate=1557336414000&api=v2}$ A potentiometer-based circuit for generating a 0-5V test voltage

Now that you've verified that each individual portion of the circuit is functioning, you can begin to test how well the overall circuit controls the aluminum block's temperature.

Connect your four sub-circuits together as shown in Fig. 1., leaving the 5V supply to the TEC turned off for now.

With the BK Precision power supply ({ $+5 V$ { $+5 V$ ) turned off, adjust the set point resistance to produce about a 5°C drop in temperature of the Al block. Start the data collection on the computer and then turn on the BK Precision power supply. Observe how the temperature of the block approaches the setpoint temperature.

Sketch the Thermal and Set Point Monitor voltages in your notebook.

Q: Does the Al block settle on the set point temperature with this circuit?  If so, how long does it take?  If now, what does it do instead?

Now that you've got a roughly functioning circuit, it is time to improve how well it controls the temperature; this can be done by modifying the control circuitry.

Q:  What do you predict { $V_{feedback}$ { $V_{feedback}$  will be in terms of { $V_{sensor}$ { $V_{sensor}$ , { $V_{setpoint}$ { $V_{setpoint}$ , { $R_1$ { $R_1$ , and { $R_2$ { $R_2$ ? Q: Why is this called proportional control?  What is the thing that is proportional to what?

Modify your control circuit as shown in Fig 6.  We suggest starting with a 10:1 ratio of { $R_2$ { $R_2$  to { $R_1$ { $R_1$ .  You may want to disconnect the sensor, setpoint, and feedback connections in order to test this circuit with a known signal; otherwise it may be difficult to tell if the modified circuit is behaving as intended. After you are satisfied that your control circuit is functioning, re-connect it to the other sub-circuits.  Once again, prepare to record both { $V_{sensor}$ { $V_{sensor}$  and { $V_{setpoint}$ { $V_{setpoint}$  with the computer.  With the BK Precision power supply ({ $+5 V$ { $+5 V$ ) turned off, adjust the set point resistance to produce about a 5°C drop in temperature of the Al block. Start the data collection on the computer and then turn on the BK Precision power supply. Observe how the temperature of the block approaches the setpoint temperature. Sketch the Thermal and Set Point Monitor voltages in your notebook. Q: Does the Al block reach the set point temperature?

Q: What is the characteristic time with which the block reaches equilibrium?

Repeat the measurement for different values of the proportional gain.

Q: How does the characteristic response time of the TEC change as a function of gain?

Find the gain at which the temperature oscillates about the equilibrium value, and keep { $R_1$ { $R_1$  and { $R_2$ { $R_2$  constant when moving on the the next part.

Finally, consider the control circuit shown in Fig. 7.

Q:  What do you predict { $V_{feedback}$ { $V_{feedback}$  will be in terms of { $V_{sensor}$ { $V_{sensor}$ , { $V_{setpoint}$ { $V_{setpoint}$ , { $R_1$ { $R_1$ , { $R_2$ { $R_2$ , and { $C_1$ { $C_1$ ?  (Note: your prediction should reduce to your previous circuit as { $C_1 \rightarrow \infty$ { $C_1 \rightarrow \infty$ ) Modify your control circuit as shown in Fig 7.  Choose a capacitor which, when combined with { $R_1$ { $R_1$ , produces an RC time constant about a factor of 3 shorter than the response time you measured using only proportional feedback. Use the computer to record { $V_{sensor}$ { $V_{sensor}$  and { $V_{setpoint}$ { $V_{setpoint}$  again, using the same procedure as before. Q: How does the addition of the capacitor change the network's behavior? 

{ ${/download/thumbnails/205261964/PFeedback.png?version=3&modificationDate=1557154586000&api=v2}$ A control circuit with only proportional feedback, which will output a voltage { $V_{feedback}$ { $V_{feedback}$ that depends on differences in the setpoint and sensor voltages. { ${/download/thumbnails/205261964/PIFeedback.png?version=3&modificationDate=1557154693000&api=v2}$ A control circuit with both proportional and integral feedback, which will output a voltage { $V_{feedback}$ { $V_{feedback}$ that depends on differences in the setpoint and sensor voltages.