analog PID control of VTI He vapor pressure


As written, my draft abstract is too long, but it focuses on the key points of this article (and significantly narrows the scope of the article). Some of the material should move into the main body of the article.

We present an improved method for temperature control of an ICE-Oxford Variable Temperature Insert (VTI) at temperatures below 4.2 K (down to a base temperature of 1.3 K for our system). The closed cycle VTI is part of a liquid-cryogen-free ICE-OXford cryostat; the sample probe is thermally linked to the VTI through the use of a small amount of He exchange gas, allowing the temperature of the sample probe to be raised above that of the VTI.

In both the original (ICE-Oxford) and our improved design, the temperature of the VTI is controlled by measuring and controlling the vapor pressure of the VTI 4He bath. A sealed pump continually pumps on the VTI helium space; the liquid helium fill rate for the VTI is adjusted through analog control of an motor-controlled needle valve. A 10 V input to the servo motor controller causes the needle valve to fully open, while a 0 V input causes the needle value to fully close.

Using the as supplied method, we were able to control the pressure with a precision of \(\pm 0.2\) mbar but with an absolute accuracy of only 2 mbar. With better choice of PID settings, it might be possible to reduce the systematic offset in the pressure stepping, but not overall precision. This is because the as supplied method uses a computer to directly read the low-resolution (\(\pm 0.1\) mbar) digital output of the pressure gauge. The speed with which the software-based PID controller can update the output of the computer D to A board (or, originally, on of the additional analog outputs of a Lake Shore temperature controller) is further limited by the update rate of the digital display.

Our improved method of temperature control improves the precision and absolute accuracy of the pressure control by an order of magnitude: \(\pm 0.02\) mbar or better in precision and \(\pm 0.2\) mbar in absolute accuracy (compared to the setpoint). To do this, we make two changes the nature of the PID control of the needle valve servo-motor and the manner in which the He vapor pressure is read by the PID controller. First, instead of using a computer to read the and then a low speed software PID control loop to produce the analog voltage input needed by the motor controller, we indirectly measure the higher resolution (\(\pm 0.005\) mbar) analog voltage output of the pressure gauge and, in addition, use an analog PID controller to hold that voltage at the desired setpoint.


We are collecting energy and entropy data of the superconductivity of organic synthesized molecular superconductors. with the effects of magnetic fields up to 9 Tesla and temperature from 1.5 to 5 Kelvin in order to gain a greater understanding of the materials and their properties.

Experiment Process

The experiment will be conducted in a closed system, where the sample will be placed into the Innovatative Cryogenic Engineering (ICE) machine containing liquid helium. Inside the ICE machine, it will be exposed to low temperatures. Ultimately, we are trying to control and maintain the temperature within the Innovatative Cryogenic Engineering (ICE) machine; however, we are unable to measure the temperature directly. As a result, we are measuring the pressure through a pressure sensor in the chamber instead, since we know that there is a direct relationship between pressure and temperature because of the co-existing liquid and gas phases within the chamber. The pressure inside the chamber will be read through the pressure sensor on top of the ICE machine. Any changes in pressure will be noted via the gauge, and will be read either manually or digitally. We will control the internal pressure of the VTI Helium through the amount of voltage we send to the needle valve which controls the inward flow of helium gas: 10V opens the valve fully, increasing the pressure, and 0V closes the valve fully, decreasing the pressure. The pump pumps away helium gas, at a constant rate, into a condenser until we need to pump helium back into the system.


Installation of the PID controller

The PID controller system was installed to digitally analyze and control the pressure instead of the computer program we were using. The implementation of the PID controller remedied two flaws of the previous system. First, we were able to gain more precision and accuracy in pressure value reading with the digital analog output than the computer output reading. Second, with carefully determined PID settings, the pressure in the VTI chamber is much better controlled in both reaction time and precision.

Analog Output Reading in relation to the Computer Output Reading Resolution Improvement

Using an analog output reading improved the precision of the reading of the pressure from +/-0.1 mbar to +/- 0.01 mbar. Orginally a computer system was controlling the temperature of the system, by monitoring the pressure; however, the digital signal the computer reading had limited precision, because it only detected variation of 0.1 mbar or larger. The large margin of error for the pressure gave us little control of the temperature inside of the sample chamber. On the other hand, the analog PID receives a continuous reading, thus increasing the response time of the changing pressures inside the ICD machine and its sensitive to pressure changes. This transition from digital to analog allowed us to gain greater precision up to +/-0.01 mbar, which means we have more control of the temperature ranges the sample experiences.

pressure gauge –> pressure analog digital displayer –> black box(amplifies the current so it can be seen by the motor to control the servo) –> PID(set V0,PID finds difference between set and measured V, use P/I/D settings) –> V that goes to needle valve.

Setpoint Accuracy and Stability

Because we are studying the effects of temperature on inorganic materials, the system has to be able to react quickly when we change the temperature via pressure from one to other, as well remain relatively stable at the chosen temperature with minimal noise. We will pick a voltage setpoint for where we want the system to oscillate at and whenever we change the setpoint, we want the the smallest amount of error between the measured voltage and the setpoint voltage. This stability is achieved by finding the three best suited parallel control paths:

The proportional path, P
The integral path with a gain of I
The derivative path gain D

Thus, we have to determine a PID setting that fulfills both of these requirements.

Gaining Setpoint Accuracy After Implementation of PID analog controller

Implementing the PID analog controller improved the setpoint accuracy. Before the computer system used a formula to convert voltage into a pressure; however we were unable to check the certainty of this conversion because only two significant figures were displayed. The PID analog controller was able to display values to five significant figures, so we could verify the formula conversion and get more information (?? phasing sounds awkward). Furthermore, with the PID, we were to monitor the accuracy of the system by looking at the error between the measured voltage and setpoint voltage, as well as monitor how well the pressure is being controlled by the PID settings.

Determining the PID settings

The PID cannot respond well to drastic changes, so we implemented small changes in the setpoint and using different PID settings, we observed how well the measured voltage was able to quickly respond to the changing setpoint. We derived the best suited PID settings with the one of the Zeigler-Nicols tuning methods: the closed loop tuning method. First we switched to manual control and started working only with the P setting, disabling the I and D. We started at a low setting for the P and slowly increased it until the process starts to oscillate. The point is where P started to oscillate was recorded as Ku, the “ultimate” gain. Afterwards we zoom into the graph and count the period of the oscillations, Tu. Using Ziegler-Nichols tuning parameter we then determined the PI setting and if the system had a quick response time, we would continue and find the PID setting.

smaller changes in setpoint offered better stability

varying gain (PID), varying how big of reaction to the motor controller offset - prevent the valve from fully close when there is no change in voltage - open a little bit at the voltage we want to -how much it should be open when the pressure is how you want

increase gain - oscillate small gain - never approach

Voltage PID output = adjustable amount + average amount step change looking at period of oscillations

the PID also give us a error of the setpoint and the value the PID is controlling to so we can determine how far off we are.

Photo: another picture with overshooting and no stability showing control to the 0.01 mB

However, occasionally noise gets bigger despite controlling pretty well