Dynamics and Control

Standard pneumatic transmitter outputs are 3-15 psig and standard electrical signals are 4-20 mA. Current is favored over voltage for industrial use electrical signals because it is less susceptible to transmission line signal corruption. Analog electrical signals for micro-controllers (e.g. Arduino) or micro-processors (e.g. Raspberry Pi) are typically 0-5 VDC or 0-3.3 VDC. Some transmitters provide a Modbus interface to allow digital TCP/IP or Serial communication.

For each transmitter, develop a linear mathematical expression that relates the measured quantity (flow, pressure, level, temperature, concentration) with the corresponding transmitter analog result (psig, mA, VDC).

Problem 1 - Pressure

A pressure gauge produces a signal of 20 mA at an upper pressure of 500 psig and a signal of 4 mA at a lower pressure limit of 0 psig.

• Develop an expression for the pressure to current relationship.
• What is the gain, zero, and span of the transmitter?
• What signal is expected at 200 psig?
• What signal is expected at 600 psig?

Problem 2 - Flow rate

An old flow rate meter converts gallons per second into a guage pressure. At 250 gal/sec (upper saturation limit), the flow meter produces a 15 psig signal. At 0 gal/sec, the flow meter returns a signal of 3 psig.

• Develop an expression for the flow to pressure relationship.
• What is the gain, zero, and span of the transmitter?
• What is the expected signal at 100 gal/sec?
• What is the expected signal with -10 gal/sec (reverse flow)?

Problem 3 - Level

An ultrasonic level sensor produces 1 VDC at 80 cm tank level and 5 VDC at 0 cm tank level.

• Develop an expression for the level to voltage relationship.
• What is the gain, zero, and span of the transmitter?
• What is the expected signal at a level of 30 cm?
• The voltage signal from the sensor is transmitted to a nearby signal conditioning rack that is 10 m away. Every time a large motor in the room is used, the reported level in the tank has more random variation (noise). What is one possible cause and a possible remedy?

Problem 4 - Temperature

A fluid temperature is measured with a type-K thermocouple. A thermocouple produces a change in voltage because of the junction of two dissimilar metals at the probe tip.

• Find information online for the typical range in temperature and associated voltage signals for a type-K thermocouple.
• How can a low voltage signal source be transmitted without becoming corrupted? Search for information on thermocouple signal conditioners and report the output specification of at least one.
• A researcher would like to measure up to 2000 K. What type of thermocouple would be able to measure higher temperatures? Type-K thermocouples are typically able to measure up to 1500 K.

Problem 5 - Concentration

A gas chromatograph measures concentration of the gas in a fluidized bed polyethylene reactor with reported values for C₂H₄ (ethylene), C₂H₆ (ethane), H₂ (hydrogen), N₂ (nitrogen), and C₅H₁₂ (isopentane). The values are transmitted with Modbus TCP/IP as integers because only a single register (16 bits) is available for each signal. An unsigned integer requires 16 bits and can transmit an integer between 0 and 2¹⁶-1 (65,535).

• How can concentration values in the range of 0.00-100.00 mol% be transmitted over Modbus TCP/IP as an unsigned integer between 0 and 65,535 without losing the two significant decimal places?
• What scaling factor is applied before transmission on the 16-bit register and after transmission on the receiving side to recover the original number.
• Using those scaling factors, what is the integer value transmitted at 32.23 mol% C₅H₁₂?

Another way to remedy the integer resolution issue is to use two registers (32 bits) to store and transmit the values as floating point numbers or to use OLE for Process Control (OPC) to transmit floating point numbers.