Control and Instrumentation Engineering: Sensors

• Control and Instrumentation Engineering 3: Ultimate Exam Preparation study notes for Dimitris Thodis, April 27, 2025

Fundamentals

• Sensors and Actuators are examples of transducers.
• A transducer transforms one kind of energy into another.
• Sensors convert physical inputs to electrical outputs.
• Actuators take signals and convert them into another form of output energy.
• Ideal sensors don't disturb the system they operate within.
• They don't draw any energy from the system.
• They have perfectly monotonic and linear input-output relationship.
• Ideally, they should have zero offset and infinite resolution so they can respond to infinitesimally small inputs.
• Their operation ideally doesn't introduce noise and should only be sensitive to the measured variable.

Sensor Terminology

• Sensitivity: the minimum input of a physical parameter for a detectable output change.
• Expressed as △Output/AInput
• Range: the span of input values a sensors can measure.
• Computed by subtracting the max and min values of the applied parameter that can be measured (Rdyn = Ymax - Ymin).
• Precision consists of Repeatability and Reproducibility.
• Repeatability refers to getting the same results for the same sample under the same conditions over multiple measurements.
• Reproducibility refers to either multiple samples or a single sample being unplugged/broken down and set up again - how consistent the results are.
• Resolution: Smallest detectable incremental change of input parameter that can be detected in the output signal.
• Accuracy: Maximum deviation from true value and the indicated value at the output.
• Time is used to measure error.
• Offset: Output when input is zero under the same particular set of conditions.
• Common in strain gauges and pressure sensors.
• Causes include manufacturing defects, temperature changes, and improper calibration.
• Linearity: Measured as the difference in output for the same input depending on the approach path (direction).
• Hysteresis: Output depends on the direction of input change.
• Response time: Time to settle after an input step.
• Examples: rise time, decay time.
• Depends on material, signal conditioning lag, and thermal inertia where applicable.
• RID: 0.5 - 1s.
• Thermocouple: 100-200ms.
• Thermistor: < 100ms.

Displacement Sensors

• Potentiometer: Sliding contact over a resistive track with constant voltage output.
• V= (R12/R) Vₛ
• Where: Vₒ is the output, Vₛ is the supply, R₁₂ is the resistance between terminal 1 and the slider, and R is the total resistance.
• Simple and linear.
• Resolution depends on the number of turns and material smoothness.
• Errors: wear, noise, nonlinearity at the end, and temperature drift.
• Strain Gauge: Usually part of Wheatstone bridge config.
• Under tension, resistance increases as area narrows, and under compression, area thickens so resistance decreases.
• Expressed as AR/R = Ge
• Where: AR is the change in resistance due to strain, R is unstrained resistance, and G is the gauge factor (approx 2 for metals).
• Applications involve displacement sensing, force, pressure, and acceleration.
• Capacitive Sensor: C = Εᵣε₀A/d
• Where: Er is the relative permittivity of dielectric, e, is the vacuum permittivity, A is the area of overlap, and d is the distance between plates.
• Types: vary distance (common for linear position sensors), vary overlap type (used for sliding plate designs), vary dielectric (used mostly for liquid level sensing) and the push-pull configuration.
• Computed as Ctotal = C₁ * C₂/C₁ + C₂
• LVDT (Linear Variable Differential Transformer): AC output; zero-centered; phase indicates direction Primary (middle) coil excited with AC.
• Core is magnetic and position affects coupling.
• Centered core: V1 = V2, Vout = 0.
• Off-centered: Vout = V1 - V2.
• AC output required demodulator to extract magnitude as well as sign and a low pass filter is needed for DC output.
• Incremental Encoders: Incremental has a disc with 2 layers of slits (slightly off-centre to track direction of rotation) that rotates.
• Third layer of one singular slit acts as the reference point.
• Light passes through slits and is measured by photoencoders.
• Each pulse represents fixed angular movement.
• Capable of giving distance from a reference or previous position (hence "incremental") speed and direction of rotation.
• Potential flaw: requires movement to work and is susceptible to wear and fatigue.
• Resolution is defined by the number of pulses per full rotation: 0 = Npulses/Pulses Per Rotation * 360
• Absolute Encoders: Use Gray Code - One bit changes per position, which avoids transition errors.
• Single change per position also gives clearer indication of when the system is not working properly (we get more than 1 change per position).
• Resolution is 360/2ⁿ where, n is the number of bits (LED/PD pairs).

Encoders

• Incremental Encoder
• Output: Pulses (HIGH/LOW).
• Position Tracking: Relative (counts pulses from reference).
• After Power Loss: Loses position and needs re-homing.
• Complexity: Simpler design using 1 track and LED/detector.
• Cheaper cost.
• Resolution: Determined by number of slots (PPR).
• Wiring/Signals: Few wires (A, B, optional Z).
• Installation: Needs homing sequence at start-up.
• Failure Risk: Can lose count if signal missed (vibration, noise).
• Common Use: Motor control, conveyor belts, simple motion tracking.
• Absolute Encoder
• Output: Digital code (binary or Gray code).
• Position Tracking: Absolute (direct position from code).
• After Power Loss: Retains exact position instantly.
• Complexity: Complex using multiple tracks and LEDs/detectors.
• More expensive cost.
• Resolution: Determined by number of bits (tracks).
• Wiring/Signals: More wires (parallel binary or serial outputs).
• Installation: No homing needed.
• Failure Risk: Safer: Reads position directly.
• Common Use: Robotics, CNC machines, aerospace, safety-critical systems.
• Incremental Encoder Benefits: Cheap, simple integration, fast counting, and easy controller interface.
• Incremental Encoder Disadvantages: Needs homing after shutdown and can lose position if pulses are missed.
• Absolute Encoder Benefits: Instant position knowledge, survives power loss, safer in critical systems.
• Absolute Encoder Disadvantages: More expensive, larger, and needs more wiring and decoding electronics.
• Use Incremental encoders if you want a low-cost solution for speed or relative movement measurement.
• Use Absolute Encoders if you need reliable, power-failure-proof, and exact shaft position at all times.
• Hall Effect: VH = IB/ned where B is the magnetic field strength, d is the thickness of the conductive plate, n is the charge carrier density, and e is the elementary charge (electron charge).
• Hall effect is the generation of a voltage across a conductor plate when a magnetic field is applied perpendicular to the current flowing through the plate.
• Due to electrons drifting sideways due to Lorentz force, the magnet moves.
• It changes the value of the measured hall voltage while still applying a perpendicular field.
• See slides: the effects of the magnet being moved parallel (axially) to the field, magnet being moved perpendicular to the direction of the applied field.
• IR Optical Proximity Sensors: IR LED emission reaches a target, is reflected, and then received by a photodiode.
• Output Voltage ∝ Amount of Reflected IR
• Results are nonlinear.
• Need digital post-processing for linearization.
• Have short ranges.
• Can be affected by target colour, surface, and ambient light.
• Not ideal for a single voltage signal, we have two possible distances.

Motion Sensors

• Tachometer: Configuration: rotating coil in magnetic field, produces voltage, directly proportional to angular velocity.
• Vo = κω
• Applications: rotational speed measurement.
• Output: analogue, sensitive to noise and load changes.
• Incremental Encoder: counting pulses per second to obtain speed.
• ⍵ = 2π * PPS/PPR
• PPR comes from sensor spec, represents pulses per revolution.
• PPS is measured and is pulses per second
• Accelerometer: Uses a Spring mass damper setup
• F = mx + bx + kx
• Use integration to find v.
• Types include Resistive measures strain vs variable resistance.
• Capacitive measures displacement via plate separation.
• Piezoelectric generates charge under acceleration used for dynamic measurements.
• Applications: vibration sensing, mobile phones screen rotation, vehicle crash detection.
• Note: high natural frequency needed to prevent resonance, output must be filtered from noise.
• Gyroscope: Measures angular velocity using conservation of angular momentum.
• Types: MEMS vibrating elements - coriolis force, mechcanical rotating mass, optical type ring lazer, fibre optic.
• MEMS gyros detect phase shift or coriolis force acting on vibrating elements due to rotation. Applications: inertial measurements in aerospace applications, phones for motion tracking.
• Require initial calibration, and may drift over time additive measurement noise.
• ~ω = ω + b + η
• 3 DOF system, w is the true angular velocity, b is the bias which is temperature dependant and may change over time (but approximated as a constant), and η is additive measurement noise.
• GPS: Satellite Positioning from time-of-flight of signals. Provides position, velocity and time.
• Each satellite sends a signal that includes its position in space (x,y.z) and the time (t) the signal was transmitted, which tells us x,y,z,t.
• The receiver on Earth notes the time it receives the signal ti.
• To find the true received time ti we subtract b what which is the receiver's clock bias versus GPS satellite clocks.
• di = (ti - si)c gives the pseudorange to each satellite. Where ti is the true time we receive the signal and si is the time that the satellite i sent the signal (radio waves).
• We typically need 4 satellites (3 for x,y,z and 1 for clock bias b). We imagine each satellite provides an equation in the form:
• (x – xin)2 + (y – Yın)2 + (z − Z₁n)2 = (dın)2
• Equation solvable for 4 unknowns.
• More than 4 satellites means that the system is overdetermined - which is a good thing.
• Weighted least squares method is used to drastically reduce measurement error.
• Applications: navigation and positioning, mapping and surveying, etc. Worth noting clock bias is a time element which makes this problem 4D. Pseudorange is not the exact distance - essentially a time-of-flight method but with radio waves.
• Time-of-Flight (ToF) Sensors: d = vt/2
• Types incluce
• Ultrasonic: High frequency sound pulse sent out. Measured delay in reflected signal. Good for close-range detection. Good for measuring liquid levels and typically used in proximity sensors in robots. Disadvantages include it being affected by temperature, humidity, and air pressure which can cause surfaces may even absorb heat or deflect sound and muddling the signal.
• LIDAR: Laser (light) pulses instead of sound, is much faster and has higher resolution. Good for terrain mappin. obstacle avoidance in autonomous vehicles, and human gesture sensing in scanners. Disadvantages include being affected by smoke and rain, and target surface reflectivity.
• RADAR: Radio waves which are muchLarger distances. Can detect velocity via doppler shift. Used in aerospace altimeters, traffic speed monitoring, weather monitoring.
• Pressure difference deflects a circular diaphragm:
• Diaphragm-based type.
• Types include straing gauges.
• Capacitive sensors.
• LVDTs
• Has either a flat diaphragm (which has limited movement) or corrugated diaphragms (greater sensitivity and range).
• Expressed as € = AL/L → AR/R = Ge
• Integrated silicon diaphragms with on-chip signal processing:
• sensitivity ≈ 0.6mV/kPa
• Range is 0-100 kPa
• Response time ≈ 1ms
• Applications: HVAC, automotive, and industrial process control.
• Bourdon Tube: a curved/spiral metal tube that straightens slightly under internal pressure.
• tube deforms, that deformation is converted to mechanical pointer movement using linkages.
• Types:
• GEARED - where the tube connects to gears that amplify and transfer motion to a pointer.
• SPIRAL - tube wound into a spiral shape for larger displacement for better sensitivity and resolution.
• Applications: steam boilers, hydraulic systems, gas cylinders. Special features include the fact that Bourdon Tubes are 100% mechanical.
• Piezoelectric Sensors: Only for dynamic pressure measurements.

Flow Sensors

• Differential Flow Metres: Q = CA√2ΔΡ/ρ
• Use flow through a restriction (orifice, nozzle, venturi, etc.) which causes a pressure drop. The drop is measured and used to decipher flowrate from Bernoulli.
• Turbine Flowmeter: Q ∝ f
• Type: Flow spins multi-blade rotor placed in the stream.
• Counts the number of blade passes/rotations using magnetic pickup or optical sensor.
• Limits involve sensitivity due to viscosity and is not ideal for unclean/multi-phase fluids.
• Ultrasound Time of Flight: 2 transducers placed in channel for flow at angles facing each other (not perpendicular).
• Pulses emitted and time is measured between each transducer, if the flow direction is accelerated it is decelerated in other direction.
• Where clearly t₁ is smaller, since it is the time the mediumisflowing.
• u = c² * (Δt)/2Lcosθ
• Vortex Flowmeter: Body is placed in the stream, Vortices are shed alternately from each side and shedding frequency is measured.
• f = Stv/d where St is the Strouhal number and d is the width of the bluff body.
• Good because no moving parts and very durable: uniquely well suited to gasses, steam, and in some cases liquids.
• Coriolis Flowmeter: Fluid moves through vibrating tubes and coriolis force causes tube deformation. Phase shift between inlet and outlet ends of vibrating tubes are measured.
• Fₒ = 2mow
• Highly accurate but very expensive.

Level Sensors

• Float-Based Sensors: Buoyant float rises/falls with liquid surface. Float movement mechanically linked to either a potentiometer, magnetic switch, read relay, or rotary encoded.
• Application: fuel tanks, water tanks, point level output as well as constant output since it's always floating.
• Differential Pressure: Pressure /h = p/pg
• Differential pressure gauge is used to measure pressure, used to find height.
• Load Cell Method: W = pghA, good because it doesn't require contact with the fluid andit is suitable for corrosive, toxic, or slurry fluids.
• Limitation: Sensitivity to vibrations or irregular tank sizes, since we need constant cross-sectional area.
• Capacitive Sensors: Liquid changes dielectric constant shifting upwards or downwards between capacitor plates.
• Requires calibration. and is used for non-conductive fluids.
• C = ΕrεoA / d
• Ultrasonic Level Sensors: Time of flight sensor, calculating distance from echo time.

Temperature Sensors

• Liquid-in-Glass Thermometers: Classic thermal expansion. Slow response time and good accuracy for stable systems.

• Hg Range: -35-600C

• Alchohol Range: -80 - 70C

• Pentane Range: -200 - 130C

• Bimetallic Strips: Two bonded metals with different coefficients of thermal expansion. Curvature with temperature change used to make/break electrical contacts and are robust and cheap with an Accuracy of ± 1C and they are robust and cheap.

• Resistance Temperature Detectors RTD (e.g., Pt100):

• Rt = Ro( * αt)

• With being resistance at OC and at a being the temperature coefficient of resistance. Principle: Metal resistance increases linearly with temperature.

• Platinum RTD Range: -20-800C

• Accuracy: ±0.1C

• Sensitivity: 0.4 w/C for 1000

• Thermistors: R(T) = Roeß(Δ/Δ-Δ)

• Semiconductors drop exponentially with increasing temperatures.

• Include PTC and NTC: extremely non-linear and sensitive.

• Thermocouples: Thermoelectric effect - when conductor subjected to thermal gradient, and it generates voltage.

• Thermocouple: two conductors of different metal alloys that produce a voltage at the point where the two conductors are in contact. Predicted voltage depends on the difference of temperature at the junction to other parts of the conductor (this relation is not necessarily linear):

• E = aT + bT²

• Where E is the EMF (V) and a and b are constants for the metal pair with Different alloys used for different temperature ranges.

• Thermocouple Cold Junction Compensation: Voltmeter is connected across the thermocouple. Add extra thermocouple on purpose, and seep its temperature constant to track voltage and reference temperature.

• V ∝ (T; - Tref) where Tref is determined by an IC compensator.

• Semiconductor IC Temp Transducers:

• PN junction where voltage drop changes with temperature, packed as ICs with built-in amplification.

• Output - 10mV/C

• Supply = 5V Can operate from 4 – 30V

• Accuracy = ±0.4C

• Range- 55C to 150C

• Interface (analogue output), cheap, compact as ICs, and limited to semiconductor operation temperatures (< 150C).

• Pyrometers: non-contact infrared temperature measurement of radiation by hot bodies.

• Types include optical pyrometer (disappearing filament) which matches filament brightness with hot object by summing IR radiation over all wavelengths emitted.

• ∝ T* for radiation Good for ranges of 600C - 3000C with a ±0.5°C accuracy.

Carbon Monoxide (CO) Sensors

• CO causes symptoms at 10 parts per million and causes death at 2000ppm.
• Sensor resistance (approx):

1ΜΩ in clean air 800ΚΩ at 10ppm 10ΚΩ at 100ppm 2 - 5ΚΩ at 1000ppm Plotting R against CO concentration yields an extremely steep decay curve. Instead use I = V/R, I is directly proportional with concentration of CO, so measuring current will directly find CO concentration.