Measurement and Control Principles

Measurement and Control Principles

Chapter Introduction

This chapter covers the fundamental principles of measurement and control that every instrumentation and control technician must master for the Red Seal exam. You will find essential definitions, applicable physical laws, calculation procedures, and references to relevant Canadian standards. Mastery of these concepts is indispensable, as they form the basis of nearly all exam questions on control loops, transmitters, actuators, and safety systems.

Physical Quantities and Units of Measurement

International System of Units (SI)

Canada officially uses the International System of Units. You must know the seven base units and their symbols:

The most common derived units in instrumentation include the pascal (Pa) for pressure, the volt (V) for voltage, the ohm (Ω) for resistance, and the degree Celsius (°C) for temperature. Remember that the kelvin and degree Celsius share the same graduation scale: a difference of 1 K equals a difference of 1 °C. The conversion is performed as follows: °C = K − 273.15.

Multiples and Sub-multiples

The following SI prefixes are frequently used in instrumentation:

Exam trap: do not confuse the symbol M (mega, 10⁶) with m (milli, 10⁻³). An error of factor 10⁹ can have disastrous consequences in a transmitter span calculation.

Industrial Measurement Scales

In Canadian industrial settings, certain non-SI units remain common. psi (pounds per square inch) for pressure, °F (degrees Fahrenheit) for temperature, and the imperial gallon for volume are still encountered in existing installations. You must be able to perform the following conversions:

Fundamental Laws of Electricity Applied to Instrumentation

Ohm's Law

Ohm's Law establishes the relationship between voltage (V), current (I), and resistance (R):

V = I × R

This law is omnipresent in 4-20 mA loop calculations. For example, to determine the minimum supply voltage required for a loop with a total resistance of 500 Ω and a maximum current of 20 mA:

V = 0.020 A × 500 Ω = 10 V

Loop calculation procedure: add all resistances in the loop (transmitter resistance, wire resistance, receiver input resistance), then multiply by the maximum current of 20 mA to obtain the minimum required voltage. Add a safety margin of 10 to 15% to account for supply voltage variations.

Kirchhoff's Laws

The node law (first law) states that the sum of currents entering a node equals the sum of currents leaving it. The loop law (second law) states that the algebraic sum of voltages in a closed loop is zero.

These laws apply directly to measurement circuits with multiple instruments. For example, in a circuit with a transmitter and two receivers in series, the same current flows through all elements. In a circuit with receivers in parallel, the voltage is common but the currents divide according to the resistances.

Electric Power

The power dissipated in a circuit is calculated as:

P = V × I = I² × R = V² / R

This calculation is essential for sizing precision resistors and verifying that they do not exceed their power rating. For example, a 250 Ω resistor carrying 20 mA dissipates:

P = (0.020)² × 250 = 0.1 W

A 1/8 W (0.125 W) resistor would therefore be adequate, but a larger safety margin is recommended in practice.

Standardized Measurement Signals

4-20 mA Signal

The 4-20 mA signal is the industrial standard for analog transmission of measurements. The 4 mA current represents the zero scale (minimum value) and 20 mA represents the full scale (maximum value). The 4 mA current, rather than 0 mA, allows you to:

Percentage of scale calculation: for a measurement expressed as a percentage of span (0 to 100%), the current is calculated as:

I (mA) = 4 + (0.16 × %)

Conversely, to convert a current to a percentage:

% = (I − 4) / 0.16

Example: a pressure transmitter with a span of 0 to 1000 kPa transmits 12 mA. What is the measured pressure?

% = (12 − 4) / 0.16 = 50%

Pressure = 0 + (50/100) × 1000 = 500 kPa

Other Standardized Signals

The 3-15 psi pneumatic signal remains in use in environments where electricity presents an explosion risk. The zero scale corresponds to 3 psi, allowing detection of line rupture (zero pressure).

HART Protocol

The HART (Highway Addressable Remote Transducer) protocol superimposes a digital communication signal on the analog 4-20 mA signal. Frequency Shift Keying (FSK) modulation uses two frequencies: 1200 Hz for logical "1" and 2200 Hz for logical "0". Since the average value of the digital signal is zero, the analog signal is not affected.

Key points for the exam:

Pressure Measurement Principles

Definitions

Pressure is defined as the force exerted per unit area: P = F/A. In instrumentation, we distinguish:

The relationship between these pressures is expressed as:

P_absolute = P_gauge + P_atmospheric

Exam trap: a gauge pressure transmitter indicates 0 psi when the applied pressure equals atmospheric pressure. An absolute pressure transmitter indicates approximately 14.7 psi (101.325 kPa) under the same conditions at sea level.

Pressure Measurement Elements

Hydrostatic Pressure Calculation

The pressure exerted by a liquid column is calculated as:

P = ρ × g × h

Where ρ is the density of the liquid (kg/m³), g is gravitational acceleration (9.81 m/s²), and h is the column height (m).

Example: what is the pressure at the bottom of a tank containing 5 m of water?

P = 1000 kg/m³ × 9.81 m/s² × 5 m = 49 050 Pa = 49.05 kPa

This calculation is fundamental for level measurement by hydrostatic pressure and for wet leg compensation in differential pressure transmitters.

Temperature Measurement Principles

Temperature Scales

Types of Temperature Sensors

Thermocouples: two different metals joined at one end produce a voltage proportional to the temperature difference between the measuring junction and the reference junction. Standardized types according to ASTM E230 / IEC 60584 include:

Exam trap: the voltage generated by a thermocouple is non-linear. Reference tables must be used for voltage-temperature conversion. Cold junction compensation is mandatory when the reference junction is not maintained at 0 °C.

RTD (Resistance Temperature Detector): the resistance of a pure metal varies with temperature. Platinum is the most commonly used (PT100: 100 Ω at 0 °C). The approximate relationship is:

R(T) = R₀ × (1 + α × T)

Where α = 0.00385 Ω/Ω/°C for platinum according to IEC 60751. Measurement is typically performed in a 3-wire or 4-wire configuration to eliminate lead wire resistance.

Thermistor: semiconductor resistance with a very high negative temperature coefficient (NTC). The useful range is limited (−50 to 300 °C) but the sensitivity is excellent.

Sensor Comparison

Flow Measurement Principles

Continuity Equation

For an incompressible fluid in steady flow through a conduit of variable cross-section:

Q = A₁ × v₁ = A₂ × v₂

Where Q is the volumetric flow rate (m³/s), A is the cross-sectional area (m²), and v is the velocity (m/s).

Types of Flowmeters

Differential pressure flowmeters: based on Bernoulli's equation, they create a restriction in the conduit (orifice plate, Venturi tube, nozzle). Flow is proportional to the square root of the differential pressure:

Q = K × √(ΔP)

This quadratic relationship is essential: a 1% error in ΔP measurement results in a 0.5% error in flow. The useful measurement range is limited to approximately 3:1 due to non-linearity.

Electromagnetic flowmeters: based on Faraday's law. The voltage induced in a conductive fluid passing through a magnetic field is proportional to velocity:

E = B × L × v

Where E is the induced voltage (V), B is the magnetic induction (T), L is the distance between electrodes (m), and v is the velocity (m/s). These flowmeters require a conductive fluid (minimum conductivity of approximately 5 µS/cm) and are not suitable for gases.

Vortex flowmeters: an obstacle (bluff body) placed in the flow generates alternating vortices whose frequency is proportional to fluid velocity. The frequency f is given by:

f = St × v / d

Where St is the Strouhal number (≈0.2 for standard geometries), v is the velocity, and d is the width of the obstacle.

Coriolis mass flowmeters: directly measure mass flow rate through the deformation of a vibrating tube subjected to flow. The phase difference between two measurement points is proportional to the mass flow rate. These instruments offer the best accuracy (0.1% of reading) but present significant pressure drop.

Correction Factors

For differential pressure flowmeters, operating conditions often differ from reference conditions. The following corrections apply:

Level Measurement Principles

Measurement Methods

Hydrostatic pressure measurement: the pressure at the bottom of an open tank is proportional to level:

P = ρ × g × h

For a closed tank under pressure, a differential pressure transmitter measures the difference between the bottom pressure and the pressure in the upper part of the tank.

Level transmitter span calculation: for a 3 m high tank containing a liquid with a specific gravity of 0.9:

Span = ρ × g × h = 900 kg/m³ × 9.81 m/s² × 3 m = 26 487 Pa ≈ 26.5 kPa

Float and displacer measurement: the float follows the liquid surface; the displacer (plunger) experiences a buoyancy force proportional to level. The buoyancy force is calculated as:

F = ρ_liquid × V_submerged × g

Radar measurement: the time of flight of an electromagnetic wave reflected by the liquid surface gives the distance. The distance is calculated as:

d = (c × t) / 2

Where c is the speed of light (3 × 10⁸ m/s) and t is the time of flight. The level is obtained by subtracting the measured distance from the total tank height.

Ultrasonic measurement: same principle as radar but with sound waves. The speed of sound in air varies with temperature (approximately 331 m/s at 0 °C, increasing by 0.6 m/s per °C). Temperature compensation is required.

Method Comparison

Control Loops

Elements of a Control Loop

A closed control loop comprises four essential elements:

Control Modes

On/Off control: the output is either 100% or 0%. Hysteresis is necessary to avoid rapid oscillation. Application: level control with a pump.

Proportional control (P): the output is proportional to the error:

Output = Kp × e + Bias

Where Kp is the proportional gain and e is the error (setpoint − measurement). Proportional control always leaves a residual error (offset) in steady state.

Proportional-integral control (PI): the integral action eliminates the residual error by integrating the error over time:

Output = Kp × e + Ki × ∫e dt

Integral action increases the risk of oscillation if the gain is too high. Windup (integrator saturation) occurs when the actuator reaches its limit and the integral continues to accumulate.

Proportional-integral-derivative control (PID): the derivative action anticipates changes in the error:

Output = Kp × e + Ki × ∫e dt + Kd × de/dt

Derivative action improves transient response but amplifies measurement noise. It should never be used on a noisy measurement.

Controller Tuning

The Ziegler-Nichols tuning methods are the most well-known:

Open-loop method: apply a step to the process and record the response curve. Determine the dead time (L) and the time constant (T). The recommended parameters are:

Ultimate gain method (closed-loop): increase the proportional gain until sustained oscillations are obtained. Note the ultimate gain (Ku) and the ultimate period (Pu). The recommended parameters are:

Exam trap: the Ziegler-Nichols methods give aggressive starting points. Fine-tuning is always necessary in practice. Do not confuse dead time (L) with time constant (T) in the open-loop method.

Applicable Canadian Standards

Canadian Electrical Code

The Canadian Electrical Code, Part I (CE Code) governs electrical installations in hazardous locations. The rules relevant to instrumentation include:

Intrinsic safety (Rule 18-150) is a protection method where the electrical energy available in the circuit is limited to a level incapable of igniting the hazardous atmosphere. Intrinsic safety barriers (Zener or galvanic) are certified devices that limit voltage and current.

CSA B149.1

CSA B149.1 (Natural Gas and Propane Installation Code) applies to gas installations. Instrumentation technicians may be called upon to work on burner systems, safety valves, and pressure regulators covered by this standard. Key requirements include:

Other Relevant Standards

Calibration Procedures

Pressure Transmitter Calibration

Typical procedure:

Acceptance criteria: the maximum permissible error is typically ±0.1% of span for a smart transmitter, ±0.5% for an analog transmitter. Hysteresis must not exceed half of the maximum permissible error.

Thermocouple Calibration

Control Valve Calibration

Pitfalls to Avoid

Summary

This chapter covers the fundamental principles you must master to pass the Red Seal exam in instrumentation and control. The concepts presented here are applied in all areas of the trade: oil and gas, pulp and paper, chemical, pharmaceutical, power generation, and water treatment. A thorough understanding of these principles, combined with practice of calculations and procedures, will prepare you effectively for the exam.