Proportional Feedback Controller

Transcription

1 Experiment 7 Proportional Feedback Controller Objectives 1. Construct a proportional feedback circuit to control the temperature of a water bath. 2. Observe the effects of gain on the stability of the control temperature. Equipment 1. Proto board Sealed thermistor temperature sensor 3. 1 bipolar high power npn transistor 4. Styrofoam cup with lid and 7.5 or 8 Ω, 5 Watt resistor sealed at the bottom of the cup DIP 741 op amps 6. Appropriate resistors 7. 1 Topward dual power supply 8. Connecting wires 9. 2 multimeters ohm, 50 Watt resistors Introduction Feedback circuitry is a highly useful method for controlling experimental parameters, temperature being just one example. Many other examples of feedback circuitry include antilock braking systems (ABS) on cars to avoid skidding, levitation devices for magnetically levitated trains, and electronic circuitry for scanning tunneling and atomic force microscopes. Suppose you would like to perform measurements on a superconductor precisely at its transition temperature, e. g K. You would perform the experiment in a cryostat, first cooling the sample with liquid helium to 4.2 K, then thermally isolating the sample in a low pressure of helium gas and warming to the desired temperature of 12.0 K. To keep the sample from warming above 12.0 K or cooling back below 12.0 K some means of temperature control is necessary. A feedback circuit would be used that could monitor the temperature, transform the temperature into a voltage signal and feed part of this signal back into a heater placed next to the sample. In the diagram in figure 1, the deviation of the sample temperature from the desired temperature is monitored and this deviation is amplified and fed into the heating resistor. This type of feedback control is known as proportional feedback since the current delivered to the heating resistor is proportional to the temperature deviation between the sample temperature and the desired temperature. 37

2 Heater Feedback Signal Sample X 5 Temperature Sensor Temperature to Voltage (Sample Temp = 8.0 K) Input Transducer Circuit (Desired Temp = 12.0 K) (Sample Voltage = 3.0 V) (Desired Voltage = 4.5 V) V ref = 4.5 V Difference Voltage Amplifier Circuit Gain Amplifier Voltage to Current Output Transducer Circuit Figure 1. Feedback control circuit To construct your feedback controller, you will mostly use a combination of circuits which you have previously built. You will use the same thermistor circuit which you used for last weeks lab, shown in figure 2. 5 volts R i V in R T R 1 R 2 Figure 2. Input Transducer Circuit After the temperature is transformed into a voltage, you will compare this voltage to a specified reference voltage and output the difference voltage between the two. To do this, you will use a differential amplifier, shown in figure 3. For Vin, you will use the desired reference voltage which corresponds to the desired reference temperature. The Vin input will come from the output of the thermistor circuit. 38

3 R 2 V in V in R 1 R' 1 R' 2 Figure 3. Differential amplifier Questions 1. For the differential amplifier, if R1' = R1 and R2' = R2, determine Vout in terms of R1, R2, Vin and Vin (derive Vout from the two op amp rules showing all of your work). Your answer should justify the name differential amplifier. 2. Compute the output for the above amplifier if Vin = Vin = 5 volts and R1' = k, R1 = k, R2' = k and R2 = 99.9 k. This demonstrates the problem of an unwanted output if the resistors are not precisely matched. To amplify the difference voltage, you will use an inverting amplifier, shown in figure 4, with variable gain from 0 to Rmax/Rin. Note the potentiometer as feedback resistor. 0 to R max V in R in Figure 4. Inverting amplifier Question 3. The noninverting amplifier, shown in figure 5, has the same configuration of resistors as for the inverting amplifier, shown above. Determine the range of possible gains for the noninverting amplifier. Can you see the advantage of using the inverting amplifier for this application? 39

4 R in 0 to R max V in Figure 5. Noninverting Amplifier The final segment of the circuit involves transforming the amplified difference voltage into an output current. To do this, we will use a transistor current source, as shown in figure 6. The input voltage will come from the output of the inverting amplifier. The load refers to the resistive heater next to the sample. 15 volts load I V in R Figure 6. Transistor current source Questions 4. For the transistor current source, we will use a high power transistor, a high power 25 Ω resistor for R, and a single high power ~ 8 Ω resistor for the heater (load). Determine the absolute maximum load current for this current source if the maximum input voltage, Vin, is 15 volts. Assume a 0.6 volt drop from base to emitter. Remember that the collector voltage must be more positive than the emitter voltage, even when the transistor is saturated. 5. What should be the minimum wattage of the load resistor? 6. What happens to the load current when the input voltage goes negative (or drops below 0.6 volts)? 40

5 The entire feedback circuit which you will construct is diagrammed in figure 7. The thermistor circuit should be exactly the same as you used last week. This will avoid unnecessary recalibration of the thermistor. 5 V 15 V R T R i _ R 2 _ 2 k 0 8 Ω heater _ R 1 V ref 25 Ω Figure 7. Temperature control feedback circuit Questions 7. Suppose your sample and thermistor are presently at a temperature of 35 o C and the output of your thermistor circuit is presently 6.8 volts. You would like to control at a temperature of 40 o C which will correspond to a thermistor circuit output of 6.0 volts. Therefore, you set the reference voltage to the differential amplifier to 6.0 volts. Assuming a potentiometer resistance of 6 k for the gain amplifier and using all the other parameters shown in figure 7, determine the current through the 8 Ω heater. 8. Determine the current through the 8 Ω heater when the temperature is 45 o C, assuming the same reference voltage as in question 7. Procedure Construct the feedback circuit diagrammed in figure 7. Instead of using a potentiometer for the feedback resistor on the inverting amplifier, we will first use a resistor to simulate maximum gain (50), and later we will use a 20 k resistor to simulate a significantly smaller gain (10). For all 12 V and 12 V op amp connections, and the 5V connection to the thermistor circuit, use the proto board. For the 15 V connection to the transistor, use one of the outputs of the Topward power supply. For the resistors on the differential amplifier, use 1% metal film resistors to obtain good matching. You will control at 30 o C using an appropriate reference voltage, as determined from your results from last weeks lab. You will obtain this voltage from 41

6 the second output of the Topward power supply. During the experiment, you will be monitoring the output voltage of the thermistor circuit and the current through the heater. Draw the entire circuit including the voltmeter and ammeter in the proper locations. Place just enough water in the styrofoam cup to cover the resistor. Place your thermistor in the cup and place the lid on the cup. The first set of data you will take will be for the 50 gain on the inverting amplifier. Record the thermistor circuit output voltage and heater current as a function of time. You may want to record data every half minute. Take data until the thermistor reaches a fairly constant voltage (This should require about 30 minutes). Now replace the feedback resistor of the inverting amplifier with a 20 k resistor (for a gain of 10). Repeat the entire experiment with this new gain value to obtain a second set of data. For each of the two sets of data, graph your results as temperature and current vs time. You should use a double y axis plot with temperature on the left y axis and current on the right y axis. You should first convert your thermistor circuit output voltages into thermistor resistances, then convert these resistances into temperatures using your data from last weeks lab. Comment on the relative feedback stability for the two gain settings. 42