Control & Instrumentation Engineering Exam Prep PDF

Control and Instrumentation Engineering 3: ULTIMATE EXAM PREPARATION Dimitris Thodis April 27, 2025 1 1 Examinable Material Can you answer each of these points? 1. Fundamentals Define: Transducer, Sensor, Actuator. Sensors and Actu...

Control and Instrumentation Engineering 3: ULTIMATE EXAM PREPARATION Dimitris Thodis April 27, 2025 1 1 Examinable Material Can you answer each of these points? 1. Fundamentals Define: Transducer, Sensor, Actuator. Sensors and Actuators are examples of transducer. A transducer transforms one kind od energy into another. Sensors convert physical inputs to electrical outputs. Actuators take signals and convert them into another form of output energy. IDEAL SENSORS: Do not disturb the system within which they operate, they do not draw any energy from the system and have perfectly monotonic and linear input – output relationship. Ideally they should have zero offset and have infinite resolution (so they can respond to infinites- imally small inputs). Their operation ideally does not introduce noise. They should only be sensitive to the measured variable. 2. Sensor Terminology Sensitivity: The minimum input of physical parameter that will create a detectable output change. ∆Output/∆Input Range: Span of input values a sensor can measure - max and min values of applied parameter that can actually be measured. Rdyn = ymax − ymin Precision: Repeatability and Reproducibility. Repeatability refers to 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 unpluged/broken down and set up again - how consistent are the results. But these terms are often used interchangeably. 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. Error = measured - time Offset: Output when input is zero under the same particular set of conditions. This is common in strain gauges and pressure sensors. Causes include manufacturing defects, temperature changes, improper calibration. Linearity: Measured as the difference in output for the same input depending on the approach path (direction). Hysteresis: Output depends on direction of input change. Response time: Time to settle after an input step. Examples include rise time, decay time. Depends on material, signal conditioning lag, thermal inertia where applicable. RID : 0.5 − 1s T hermocouple : 100 − 200ms T hermistor : < 100ms 2 3. Displacement Sensors Potentiometer: Sliding contact over resistive track. Constant voltage output.   R12 Vo = Vs R Vo is output, Vs is supply, R12 is resistance between terminal 1 and slider, and R is the total resistance. Simple and linear. Resolution depends on number of turns, material smoothness, etc. Errors due to wear, noise, nonlinearity at end, temperature drift. Strain Gauge: Usually a part of wheatstone bridge config. Under tension resistance increases as area narrows, under compression area thickens so resistance decreases. ∆R/R = Gε ∆R change in resistance due to strain. R unstrained resistance. G is the gauge factor (approx 2 for metals). Applications involve displacement sensing, force, pressure, and acceleration. Capacitive Sensor: εr ε0 A C= d ϵr is the relative permittivity of dielectric. ϵo is the vacuum of permittivity, A is the area of overlap and d is the distance between plates. Types include 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. C1 ∗ C2 Ctotal = C1 + C2 LVDT Linear Variable Differential Transformer: AC output; zero-centered; phase indicates di- rection Primary (middle) coil excited with AC. Core is magnetic and position affects coupling. Centred core: V 1 = V 2, Vout = 0 Off-centred: Vout = V1 − V2 AC output required demodulator to extract magnitude as well as sign. Low pass filter needed for DC output. Incremental Encoders: Incremental has disc with 2 layers of slits (slightly off-centre to track direction of rotation) that rotates. 3rd layer of one singular slits to act as reference point. Light passes through slits and is measured by photoencoders. Each pulse represents fixed angular movement. Capable of giving distance from reference or previous position (hence ”incremental”) speed and direction of rotation. Potential flaw - requires movement to work. susceptible to wear and fatigue. Resolution - Defined by number of pulses per full rotation. Npulses θ= ∗ 360 P ulses P er Rotation Absolute Encoders: Utilize Gray Code - One bit changes per position, which avoids transition errors. This single change per position also gives clearer indication of when the system is not working properly (we get more than 1 change per position). 360 Resolution = 2n n is the number of bits (LED/PD pairs). 3  Feature Incremental Encoder Absolute Encoder Output Pulses (HIGH/LOW) Digital code (binary or Gray code) Position Tracking Relative (counts pulses from refer- Absolute (direct position from code) ence) After Power Loss Loses position; needs re-homing Retains exact position instantly Complexity Simpler design (1 track, 1 Complex (multiple tracks, multiple LED/detector) LEDs/detectors) Cost Cheaper More expensive Resolution Determined by number of slots Determined by number of bits (PPR) (tracks) Wiring/Signals Few wires (A, B, optional Z) More wires (parallel binary or serial outputs) Installation Needs homing sequence at start-up No homing needed Failure Risk Can lose count if signal missed (vi- Safer: reads position directly bration, noise) Common Use Motor control, conveyor belts, sim- Robotics, CNC machines, ple motion tracking aerospace, safety-critical sys- tems Type Benefits Incremental Cheap, simple integration, fast counting, easy controller interface. Absolute Instant position knowledge, survives power loss, safer in critical systems. Type Disadvantages Incremental Needs homing after shutdown, can lose position if pulses are missed. Absolute More expensive, larger, needs more wiring and decoding electronics. Decision Guide – Use Incremental Encoder if you want a low-cost solution for speed or relative movement measurement. – Use Absolute Encoder if you need reliable, power-failure-proof, exact shaft position at all times. Hall Effect: IB VH = ned 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). The 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. This is due to electrons drifting sideways due to lorentz force. The magnetic moves (while still applying a perpendicular field) and thus changes the value of the measured hall voltage. See the slides for the effects of the magnet being moved parallel (axially) to the field and the magnet being moved perpendicular to the direction of the applied field. 4  IR Optical Proximity Sensors: IR LED emission reaches target, reflected, received by photodiode. Output V oltage ∝ Amount of Ref lected IR Not an ideal sensor bc for a single voltage signal, we have 2 possible distances (see fig, in the slides). So we must choose our IR distances carefully. The results are nonlinear, and need digital post-processing for linearization. They have short ranges. IR sensors can be affected by target colour, surface, and ambient light :/ 4. Motion Sensors Tachometer: Rotating coil configuration in a magnetic field which produces voltage. Output voltage is directly proportional to angular velocity. Vo = kω Applications include any rotational speed measurement. Output is analogue - it is sensitive to noise and load changes. Incremental Encoder: In this case we count puses per second to obtain speed. 2π · PPS ω= PPR PPR comes from sensor spec, represents spulses per revolution. PPS is measured and is pulses per second. Accelerometer: Spring mass damper setup F = mẍ + bẋ + kx To find v we integrate. Accelerometer types include: Resistive (measures strain vs variable resis- tance), capacitive (measures displacement via plate separation), piezoelectric (generates charge under acceleration - used for dynamic measurements). Applications involve vibration sensing, mobile phones for screen rotation, vehicle crash detection. Worth noting we need a high natural frequency to prevent resonance, output must be filtered from noise. Gyroscope: Measures angular velocity using conservation of angular momentum. Types include MEMS (vibrating elements - coriolis force), mechanical rotating mass, and optical type (ring lazer, fibre optic). MEMS gyros detect phase shift or coriolis force acting on vibrating elements due to rotation. Applications include inertial measurements in aerospace applications, phones for motion tracking. It is worth noting they require initial calibration, and may drift over time (additive measurement noise). ˜ω = ω + b + η 3 DOF system. ω is the true angular velocity, b is the bias which is temperature dependant and may change over time (but approximated as a constant), η is additive measurement noise. GPS: Satellite Positioning from time-of-flight of signals. Provides position, velocity and time. How it functions: 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 which is the receiver’s clock bias versus GPS satellite clocks. This gives the pseudorange to each satellite: di = (ti − si )c where ti is the true time we receive the signal and si is the time that the satellite i sent the signal (radio waves). This is not the exact geometric distance, however, due to clock offset. 5  We cannot use the distance to a single satellite, we typically need 4. 3 for x,y,z and another for b, the clock bias. We imagine each satellite provides an equation in the form: (x = xin )2 + (y − yin )2 + (z − zin )2 = (din )2 Equation solvable for 4 unknowns. More than 4 satellites means the system is overdetermined - which is a good thing. We can use techniques like the weighted least squares method to drastically reduce measurement error. Applications include 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, and this is essentially a time-of-flight method but with radio waves. Time-of-Flight (ToF) Sensors: vt d= 2 Types include: (1) Ultrasonic. High frequency sound pulse sent out. Measured delay in reflected signal. Good for close-range detection. Good for measuring liquid levels. Typically used in proximity sensors in things like robots. Disadvantages include it being affected by temperature, humidity, and air pressure. Surfaces may even absorb heat or deflect sound, muddling the signal. (2) LIDAR: Laser (light) pulses instead of sound. Much faster and higher resolution. Good for terrain mapping, obstacle avoidance in autonomous vehicles, and human gesture sensing in scanners. Disadvantages include being affected by smoke and rain, and target surface reflectivity. (3) RADAR: Radio waves. Much larger distances. Can detect velocity via doppler shift. Used in aerospace altimeters, traffic speed monitoring, weather monitoring. 5. Pressure Sensors Diaphragm-based: Pressure difference deflects a circular diaphragm. Types include strain gauges, capacitive sensors, LVDTs. Key forms come either as a flat diaphragm (which has limited movement) and corrugated diaphragms (greater sensitivity and range). Note - deflection-based strain: ∆L ∆R ϵ= → = Gϵ L R TEXTBOOK SUPPLEMENTARY MOTIVATION: Integrated silicon diaphragms with on-chip signal processing: sensitivity ≈ 0.6mV /kP a range ≈ 0 − 100 kP a response time ≈ 1ms Applications involve HVAC, automotive, industrial process control. Bourdon Tube: Working principle involves a curved/spiral metal tube that straightens slightly under internal pressure. The tube deforms, and that deformation is converted into mechanical pointer movement using linkages. Types involve GEARED - where the tube connects to gears that amplify and transfer motion to a pointer. SPIRAL - tube wound into spiral shape for larger displacement for better sensitivity and resolution. Applications involve steam boilers (obviously), hydraulic systems, and gas cylinders. Special features include the fact that Bourdon Tubes are 100% mechanical. Piezoelectric Sensors: Only for dynamic pressure measurements. 6 6. Flow Sensors Differential Flow Metres: s 2∆P Q = CA ρ The working principle involves 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 Flow spins a multi-blade rotor placed in the stream. Magnetic pickup or optical sensor counts the number of blade passes/rotations. Limits involve sensitivity due to viscosity. It is also 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 between the two, and time is measured for both pulses. Since they are off-centred, the pulse in flow direction is accelerated and the pulse against the flow is decelerated. L t1 = (c + vcosθ) L t2 = (c − vcosθ) Where clearly t1 is smaller, since it is the time in the direction of flow. Overall equation: c2 (∆t) v= 2Lcosθ Vortex Flowmeter: Here, a bluff body is placed in the stream. Vortices are shed alternately from each side. Shedding frequency is measured. St · v f= 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 defor- mation. Phase shift between inlet and outlet ends of vibrating tubes are measured. Fc = 2mωv Highly accurate but very expensive. 7. Level Sensors Float-based Sensors: Bouyant float rises/falls with liquid surface. Float movement is mechani- cally linked to either a potentiometer, magnetic switch, read relay, or rotary encoded. Application in fuel tanks, water tanks, can give point level output as well as continuous output (constant monitoring since it’s always floating). Differential Pressure: P h= ρg A differential pressure gauge is used to measure pressure - used to find height. 7  Load Cell Method: W = ρghA Good because it doesn’t require contact with the fluid. Suitable for corrosive, toxic, or slurry fluids. Limitation is its high sensitivity to vibrations or irregular tank sizes, since we need a constant cross-sectional area. Capacitive Sensors: Liquid changes dielectric constant since it shifts upwards or downwards between the capacitor plates. Requires calibration and is used for non-conductive fluids. ϵr ϵo A C= d Ultrasonic Level Sensors: Time of flight sensor. Distance from echo time. 8. Temperature Sensors Liquid-in-Glass Thermometers: Classic thermal expansion. Slow response time, good accuracy for stable systems. Range: Hg: -35 - 600C Alchohol: -80 - 70C Pentane: -200 - 130C Bimetallic Strips: Two bonded metals with different coefficients of thermal expansion. Curvature with temperature change used to make/break electrical contacts. They are robust and cheap. Accuracy of ± 1C. Resistance Temperature Detectors RTD (e.g., Pt100): Rt = R0 (1 + αt) With o being resistance at 0C and a being the temperature coefficient of resistance. Principle: Metal resistance increases linearly with temperature. For a Platinum RTD: Range: -20 - -800C Accuracy: ±0.1C Sensitivity: 0.4 ω/C for 100Ω Thermistors: R(T ) = R0 eβ(1/T −1/T0 ) These are semiconductors. Resistanec drops exponentially with increasing temperature. Types include PTC and NTC (positive and negative temp coeff). They are extremely non-linear and sensitive. Thermocouples: Working principle is the Thermoelectric effect - when a conductor is subjected to a thermal gradient, it will generate a voltage. A thermocouple consists of two conductors of different metal alloys that produce a voltage at the point where the two conductors are in contact. This predicted voltage is dependent on the difference of temperature at the junction to other parts of the conductor (this relation is not necessarily linear): E = aT + bT 2 Where E is the EMF (V) and a and b are constants for the metal pair. This relationship is almost linear. Different alloys are used for different temperature ranges. 8  Thermocouple Cold Junction Compensation: If we try to connect a voltmeter across the ther- mocouple, an issue arises. We get at least one more thermocouple in the system, since dissimilar metals of the thermocouple connections and the voltmeter connections meet. However, this will not occur if the materials are the same - but keeping the materials the same may impact perfor- mance. What do we do? We introduce this extra thermocouple on purpose, and sleep its temperature constant. We may now track this reference temp and keep this relation for voltage: V ∝ (Tj − Tref ) Tref is determined by an IC compensator. Semiconductor IC Temp Transducers: The working principle here is a PN junction where volt- age drop changes with temperature. These are simply packaged as ICs with built-in amplification. MOTIVATION: LM35 Output − 10mV /C Supply = 5V (Can operate f rom 4 − 30V ) Accuracy = ±0.4C Range = −55C to 150C These are good because they are easy to interface (since it is an analogue output). They are also very cheap and compact since they are ICs, but are limited to semiconductor operation temperatures (< 150C). Pyrometers: Non-contact infrared temperature measurement of radiation emitted by hot bodies. Types include optical pyrometer (disappearing filament) which matches filament brightness with hot object. Total radiation pyrometer - sums IR radiation over all wavelengths emitted. P ∝ T 4 f or radiation Good for ranges of 600C - 3000C with a ±0.5o C accuracy 9. Carbon Monoxide (CO) Sensors CO causes symptoms at 10 parts per million. It causes death at 2000ppm. See graphs on slides. Sensor resistance (approx): > 1MΩ in clean air 800KΩ at 10ppm 10KΩ at 100ppm 2 − 5KΩ at 1000ppm As can be seen in the graphs on the slides, plotting R against CO concentration yields an 6 extremely steep decay curve. This is not usable, so instead we plot 10 R against concentration instead. This means due to Ohm’s law I = V/R, I is directly proportional with concentration of CO, so by measuring current we can directly find CO concentration. 9