INSTRUMENTATION & CONTROL (ME-402) - Unit 5 Short Notes

1.0 FUNDAMENTALS OF MEASUREMENT SYSTEMS

1.1 Elements of a Generalised Measurement System

A measurement system typically consists of three functional elements:

1. Sensor/Transducer: Senses the physical measurand and converts it into a proportional electrical/mechanical signal.

2. Signal Conditioner: Modifies the sensor output (e.g., amplification, filtering, conversion) to a suitable form for the indicator.

3. Indicator/Recorder: Displays, records, or transmits the final measured value (e.g., digital readout, chart recorder, computer interface).

1.2 Classification of Instruments

• Based on Function:

  • Indicating: Provides instantaneous value (e.g., pressure gauge, thermometer).

  • Recording: Produces a continuous record vs. time (e.g., chart recorder, data logger).

  • Integrating: Totals or integrates the input over time (e.g., totalizer for flow).

• Based on Application: Industrial process, biomedical, automotive, environmental, etc.

1.3 Standards and Calibration

• Role of Standards:

  • Primary Standard: Highest accuracy, maintained by national labs (e.g., NPL, NIST).

  • Secondary Standard: Calibrated against primary, used in calibration labs.

  • Working Standard: Used routinely to calibrate instruments in the field.

• Calibration Procedure: Compare instrument output with a standard of known accuracy under specified conditions, adjust if necessary, and document the relationship.

• Necessity: Compensates for drift, wear, and environmental effects to maintain accuracy and traceability.

• Dead Weight Tester (Pressure): Generates a precisely known pressure $$\displaystyle P = \frac{F}{A} = \frac{mg}{A} $$ using calibrated weights on a precision piston.

  DiagramDead weight tester with piston-cylinder assembly and weight set
  .

1.4 Measurement Errors and Uncertainties

• 1.4.1 Types of Errors:

  • Systematic: Consistent, predictable bias (e.g., zero error, calibration error). Correctable.

  • Random: Unpredictable fluctuations (e.g., electrical noise). Quantified statistically.

  • Gross (Practical): Mistakes or blunders (e.g., reading error, transcription error).

  • Static: Error under steady-state conditions.

  • Dynamic: Error due to instrument's inability to follow rapid input changes.

• 1.4.2 Uncertainty Analysis:

  • Absolute Uncertainty ($\Delta x$): ± value in same units as measurement.

  • Relative Uncertainty: $$\displaystyle \frac{\Delta x}{x} $$.

  • Percentage Uncertainty: $$\displaystyle \frac{\Delta x}{x} \times 100\% $$.

• 1.4.3 Error Specification:

  • % of Full Scale Deflection (FSD): Absolute error = $\pm (\text{\% FSD}) \times \text{Full Scale Value}$. Constant absolute error across range.

  • % of True Value (Reading): Absolute error = $\pm (\text{\% Reading}) \times \text{Actual Reading}$. Error proportional to reading.

  [!TIP] For a gauge with range 0-100 units and ±1% FSD, at a reading of 10 units, the possible error is ±1 unit (10% of reading). If specified as ±1% of reading, error at 10 units is ±0.1 unit.

• 1.4.4 Factors Influencing Errors: Environmental (temp, humidity), instrument (design, wear), observer (parallax), inherent (resolution).

• 1.4.5 Quantification & Management: Uncertainty budgeting (root-sum-square). Mitigation: multiple readings, calibration, environmental control, proper mounting.

• 1.4.6 Resolution: Smallest detectable input change. Limited resolution contributes directly to uncertainty, especially for small signals.

2.0 STATIC PERFORMANCE CHARACTERISTICS (Steady-state input)

2.1 Definition and Importance

Characteristics describing instrument performance for constant or slowly varying inputs. Crucial for selecting the right instrument and understanding its limitations.

2.2 Key Characteristics

2.3 Instrument Specifications

Determined from calibration data (plot of output vs. input). Specifications (e.g., accuracy = ±0.5% FSD) allow comparison and selection based on application requirements (range, precision needed, cost).

2.4 Impact on Measurement Accuracy

Total measurement uncertainty is the combined effect of all relevant static characteristics. For example, a measurement's error may be the sum of nonlinearity error, hysteresis error, and repeatability error (often combined as "accuracy" spec).

3.0 DYNAMIC PERFORMANCE CHARACTERISTICS (Time-varying input)

3.1 Dynamic vs. Static

• Static: For steady-state or very slow inputs. Instrument has time to respond fully.

• Dynamic: For rapidly changing inputs. Instrument's inertia and damping cause a lag, leading to amplitude and phase errors. Critical for high-frequency or transient measurements.

3.2 Dynamic Response of Instrument Systems

Generalized Second-Order System: $$\displaystyle \frac{d^2y}{dt^2} + 2\zeta\omega_n \frac{dy}{dt} + \omega_n^2 y = K \omega_n^2 x(t) $$

• $$\displaystyle \omega_n $$: Natural frequency (rad/s).

• $\zeta$: Damping ratio (dimensionless).

• $K$: Static sensitivity.

3.2.1 First-Order Systems

• Transfer Function: $$\displaystyle H(s) = \frac{K}{\tau s + 1} $$

• Time Constant ($\tau$): Time to reach 63.2% of final value for step input.

• Step Response: $$\displaystyle y(t) = K(1 - e^{-t/\tau}) $$

• Examples: RTD, thermistor, many pressure transducers.

• Ramp Response: Tracking error = $\tau \cdot \text{ramp slope}$.

3.2.2 Second-Order Systems

• Transfer Function: $$\displaystyle H(s) = \frac{K \omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2} $$

• Key Parameters:

  • Overshoot ($$\displaystyle M_p $$): $$\displaystyle \% M_p = 100 \cdot e^{\frac{-\zeta\pi}{\sqrt{1-\zeta^2}}} $$ (for $$\displaystyle \zeta < 0.707 $$).

  • Settling Time ($$\displaystyle t_s $$): Time to stay within a tolerance band (e.g., ±2%). $$\displaystyle t_s \approx \frac{4}{\zeta\omega_n} $$ (2% criterion).

  • Rise Time ($$\displaystyle t_r $$): Time to go from 10% to 90% of final value.

• Examples: Accelerometer, LVDT (if core dynamics considered), galvanometer.

3.2.3 Higher-Order Systems

Often approximated by dominant lower-order poles if other poles are much faster.

3.3 Dynamic Response Parameters

• Speed of Response: How quickly instrument reaches final value (rise time, settling time).

• Measuring Lag: Delay between input change and output initiation.

• Fidelity (Dynamic): Ability to reproduce input signal waveform accurately (low distortion). Measured by frequency response.

3.4 Input Signal Types

• Periodic Signals: Repeats after fixed interval (e.g., sine, square). Harmonic signal is a single-frequency sine wave.

• Non-Harmonic Periodic: Complex waveforms (e.g., square, triangular) - contain multiple harmonics.

• Transients: Short-duration, non-repetitive signals (e.g., shock, step).

• Noise: Unwanted random or periodic signals.

• Random Signals: Described statistically (mean, variance, PSD). Instrument response characterized by noise equivalent power or noise bandwidth.

• Impulse Function (Dirac Delta): $\delta(t)$: Infinite amplitude, zero width, unit area. Idealized shock input. Response is the system's impulse response $h(t)$.

3.5 Frequency Domain Analysis

• Fourier Transform (FT): Decomposes a time-domain signal $x(t)$ into its constituent frequencies $X(f)$.

$$X(f) = \int_{-\infty}^{\infty} x(t) e^{-j2\pi ft} dt$$

**Significance:** Reveals frequency content, essential for analyzing system response to complex signals and designing filters.

• Linear Property of FT:

  Statement: FT of a linear combination is the same linear combination of FTs.

$$ \mathcal{F}\{a x_1(t) + b x_2(t)\} = a X_1(f) + b X_2(f) $$

**Proof Sketch:** Follows directly from the linearity of the integral operator.

• Transfer Function & Frequency Response: $$\displaystyle H(j\omega) = H(s)|_{s=j\omega} $$. Magnitude $|H(j\omega)|$ and phase $\angle H(j\omega)$ vs. $\omega$ plotted on Bode plots (log scale). Shows how system attenuates/amplifies different frequencies and introduces phase shift.

4.0 SENSORS AND TRANSDUCERS BY MEASURAND

4.1 Displacement, Position, and Angular Measurements

• Potentiometer:

  • Principle: Resistive voltage divider. Wiper position gives voltage $$\displaystyle V_{out} = V_{in} \cdot \frac{R_2}{R_1+R_2} $$ proportional to displacement.

  • Construction: Resistive element (conductive plastic, wire wound), wiper, terminals.

  • Limitations: Wear (limited life), resolution (wire-wound), loading error (need high-impedance buffer).

  • DiagramPotentiometer with sliding wiper on resistive track
    .

• Linear Variable Differential Transformer (LVDT):

  • Principle: AC-excited primary induces voltages in two secondary windings. Core displacement changes coupling, producing a differential output voltage $$\displaystyle V_{out} \propto $$ displacement. Phase indicates direction.

  • Construction: Primary coil, two secondary coils (series-opposite), movable ferromagnetic core.

  • Advantages: No electrical contact (infinite resolution), linear over range, bidirectional, robust.

  • Applications: Position feedback in servos, displacement monitoring.

  • DiagramLVDT cross-section showing coils and core position
    .

• Rotary Variable Differential Transformer (RVDT): Same principle for angular displacement.

4.2 Pressure Measurements

• Fluid Column Manometers:

  • U-tube: $$\displaystyle P = \rho g h $$. Simple, no calibration needed.

    DiagramU-tube manometer with two legs
    .

  • Inclined/Micromanometer: Inclined tube amplifies $h$ for better resolution.

• Mechanical Pressure Gauges:

  • Bourdon Tube: Curved tube straightens under pressure, motion transferred to pointer.

  • Bellows/Diaphragm: Pressure causes expansion/deflection, mechanically linked to indicator.

• Atmospheric Pressure - Barometers:

  • Mercury Barometer: Height of Hg column ($\approx$ 760 mm at sea level).

  • Aneroid Barometer: Sealed bellows expands/contracts with pressure, drives mechanical indicator.

• Elastic Pressure Transducers:

  • Strain Gauge Based: Strain gauges on diaphragm measure deflection.

  • Piezoelectric: Quartz/PZT crystal generates charge $$\displaystyle Q = d \cdot F $$ under stress. AC only, high-frequency response.

• Calibration Standard - Dead Weight Tester: See 1.3.

4.3 Temperature Measurements

• Liquid-in-Glass: Liquid (Hg, alcohol) expands in capillary. Simple, no power. Fragile, limited range.

• Bimetallic Thermometer:

  • Principle: Two metals with different $\alpha$ bonded; differential expansion causes bending.

  • Construction: Strip, helix, or spiral. Helix/spiral amplify motion.

  • Applications: Thermostats, dial thermometers.

• Electrical Resistance Thermometry:

  • RTD (Resistance Temperature Detector): Metal (Pt, Ni, Cu) resistance increases with $T$. Pt100 ($$\displaystyle R=100\Omega $$ at 0°C) is standard. Advantages: High accuracy, stability, linear (Pt). Limitations: Self-heating, cost.

  • Thermistor: Semiconductor (NTC: resistance ↓ with $T$; PTC: resistance ↑). Advantages: High sensitivity, small size. Disadvantages: Non-linear, limited range, self-heating.

• Thermocouple:

  • Principle: Seebeck Effect - Two dissimilar metals joined at junctions generate voltage $$\displaystyle V = \alpha \Delta T $$.

  • Need for Two Metals: Single metal produces no net voltage; junction of two different metals creates the thermoelectric EMF.

  • Construction: Two insulated wires welded at measurement junction.

  • Cold Junction Compensation: Reference junction must be at known temp (ice bath or electronic compensation) because output depends on difference between measurement and reference junctions.

  • DiagramThermocouple with measurement and reference junctions
    .

• Radiation Pyrometers:

  • Optical Pyrometer: Compares brightness of filament (tungsten) with target. "Disappearing filament" technique. Non-contact, high temp.

• Ionisation Transducer: Measures ionisation current in a gas-filled chamber; current changes with temperature. Used for very high temperatures (e.g., furnace).

4.4 Strain, Force, and Load Measurements

• Electrical Resistance Strain Gauge:

  • Principle: Piezoresistive Effect - strain $\varepsilon$ changes resistance $R$.

  • Gauge Factor (GF): $$\displaystyle GF = \frac{\Delta R / R}{\varepsilon} $$

  • Construction: Foil (most common), wire, or semiconductor. Bonded to surface with adhesive.

  • Mounting Procedure (with paper backing): 1. Surface preparation (clean, smooth). 2. Apply adhesive, place gauge with backing paper. 3. Apply pressure, cure. 4. Remove backing paper, lead wires.

  • Application for Bending: Top surface in tension ($+\varepsilon$, $+\Delta R$), bottom in compression ($-\varepsilon$, $-\Delta R$). Rosette gauges measure strain in multiple directions.

• Wheatstone Bridge:

  • Configuration: Four arms (R1-R4). Balanced when $$\displaystyle \frac{R1}{R2} = \frac{R3}{R4} $$. Output $$\displaystyle V_o = V_{ex} \left( \frac{R3}{R3+R4} - \frac{R2}{R1+R2} \right) $$.

  • For Strain Gauges:

    • Quarter Bridge: One active gauge. $$\displaystyle V_o \approx \frac{V_{ex}}{4} \cdot \frac{\Delta R}{R} $$.

    • Half Bridge: Two active gauges (e.g., tension/compression). $$\displaystyle V_o \approx \frac{V_{ex}}{2} \cdot \frac{\Delta R}{R} $$.

    • Full Bridge: Four active gauges. $$\displaystyle V_o \approx V_{ex} \cdot \frac{\Delta R}{R} $$. Maximum sensitivity, temperature compensation (adjacent arms opposite strain).

  • DiagramWheatstone bridge with strain gauges in various configurations
    .

• Load Cell: Principle: Strain gauges mounted on a mechanical structure (beam, canister) that deforms under load. Output from bridge proportional to force/weight. Used in scales, industrial weighing.

• Piezoelectric Transducers:

  • Principle: Certain crystals (quartz, PZT) generate electric charge $$\displaystyle Q = d \cdot F $$ when stressed.

  • Characteristics: High-frequency response, generates AC signal only (charge leaks away for static loads), very high output impedance (needs charge amplifier).

  • Applications: Force, pressure, acceleration measurement (vibration).

4.5 Flow Measurements

• Differential Pressure Flowmeters (Bernoulli's Principle):

  • Venturi Meter:

    • Construction: Converging section, constant throat, diverging section.

    • Working: Velocity increases, pressure drops at throat. $$\displaystyle Q = C_d A_t \sqrt{\frac{2(P_1-P_2)}{\rho(1-\beta^4)}} $$, where $$\displaystyle \beta = d/D $$.

    • Advantages: Low permanent pressure loss, no sharp edges, good for dirty fluids.

    • DiagramVenturi meter with pressure taps
      .

  • Orifice Meter:

    • Construction: Orifice plate (sharp-edged hole) in pipe. Pressure taps upstream/downstream.

    • Disadvantages: Higher permanent loss, plate wears, sensitive to installation.

• Positive Displacement Flowmeters: Measure volume directly (e.g., oval gear, nutating disc). Good for viscous fluids.

• Electromagnetic Flowmeters:

  • Principle: Faraday's Law - conductor (fluid) moving in magnetic field $B$ generates voltage $$\displaystyle V = BLDv $$, where $L$ = electrode spacing, $D$ = pipe diameter, $v$ = velocity.

  • Construction: Non-magnetic pipe, magnetic coils, electrodes.

  • Advantages: No obstruction, bidirectional, measures volumetric flow directly, for conductive fluids only.

  • DiagramElectromagnetic flowmeter with magnetic coils and electrodes
    .

4.6 Velocity and Rotational Speed Measurements

• Stroboscope:

  • Principle: Produces high-frequency light flashes. If flash rate $$\displaystyle f_{flash} $$ equals object speed $$\displaystyle f_{obj} $$ (or integer multiple), object appears stationary.

  • Use: Visualize and measure speed of rotating/oscillating objects. $$\displaystyle f_{obj} = n \cdot f_{flash} $$ for $n$ blades/features.

  • DiagramStroboscope flashing on rotating fan
    .

• Electromagnetic Techniques:

  • Tachogenerator: DC/AC generator; output voltage $\propto$ rotational speed.

  • Eddy Current Tachometer: Proximity probe; rotating toothed wheel modulates magnetic field, inducing AC voltage frequency $\propto$ speed.

• Mechanical Tachometers: Centrifugal (weights fly out), vibrometer. Low accuracy, largely obsolete.

5.0 CONTROL SYSTEMS

5.1 Basic Definitions

• Control System: Arrangement to cause a plant (process) to attain a desired output (controlled variable).

• Plant: The physical system being controlled.

• Input (Command/Reference): Desired output value.

• Output (Controlled Variable): Measured quantity (e.g., temperature, level).

• Disturbance: Unwanted input affecting the output.

• Feedback: Measuring output and feeding it back to compare with input.

5.2 Open-Loop Control System

• Block Diagram: Controller → Plant → Output (No feedback path).

• Principle: Output is not measured or compared to input. Control action is predetermined.

• Examples: Washing machine timer, traffic light (fixed timing), toaster.

• Advantages: Simple, cheap, stable (no stability issues).

• Limitations: No error correction, high sensitivity to disturbances and parameter variations, low accuracy.

5.3 Closed-Loop (Feedback) Control System

• Block Diagram:

  
  Setpoint → [Comparator] → [Controller] → [Plant] → Output
  
                    ↑                           ↓
  
                    └────── [Sensor] ←──────────┘
  
  

• Principle: Output is measured by a sensor, fed back to comparator. Error $$\displaystyle e = r - y $$ drives controller to reduce error to zero.

• 5.3.1 Advantages:

  • High accuracy (error correction).

  • Rejects disturbances.

  • Reduced sensitivity to parameter changes (e.g., plant gain variations).

• 5.3.2 Limitations:

  • Stability issues (can oscillate if poorly designed).

  • More complex, expensive (needs sensor, controller).

  • May have slower response if tuned conservatively.

5.4 Specific Control System Examples

• Boiler Water Level Control System:

  • Components: Level sensor (differential pressure transmitter), controller (PID), control valve (feedwater).

  • Working: Setpoint level compared with measured level. Error signal adjusts feedwater valve to maintain level despite steam demand changes.

  • DiagramBlock diagram of boiler level control
    .

• Temperature Control System: Heater, temperature sensor (thermocouple/RTD), controller, power controller (SSR).

• Position Control System (Servo): Servo motor, position sensor (potentiometer, encoder), amplifier, controller.

5.5 Servomechanism

• Definition: A closed-loop system where the output is a mechanical position (or its derivatives: velocity, acceleration).

• Components: Power amplifier, servo motor (DC, AC), feedback sensor (pot, resolver, encoder), controller.

• Examples: Antenna positioning, CNC machine axes, radar tracking.

6.0 MATHEMATICAL MODELING AND ANALYSIS OF SYSTEMS

6.1 System Modeling Fundamentals

Purpose: Predict dynamic/steady-state behavior, design controllers. Use lumped parameter models (components represented by ideal elements).

6.2 Modeling of Electrical Systems

• Component Equations:

  • Resistor: $$\displaystyle v = Ri $$

  • Inductor: $$\displaystyle v = L \frac{di}{dt} $$

  • Capacitor: $$\displaystyle i = C \frac{dv}{dt} $$ or $$\displaystyle v = \frac{1}{C} \int i dt $$

• Example (Series RLC): $$\displaystyle L\frac{di}{dt} + Ri + \frac{1}{C}\int i dt = v_{in}(t) $$

  Differential equation: $$\displaystyle L\frac{d^2i}{dt^2} + R\frac{di}{dt} + \frac{1}{C}i = \frac{dv_{in}}{dt} $$

  Transfer function $$\displaystyle I(s)/V_{in}(s) = \frac{1}{Ls^2 + Rs + 1/C} $$.

6.3 Modeling of Mechanical Systems

• Translational:

  • Mass ($m$): $$\displaystyle F = m \frac{d^2x}{dt^2} $$ (Newton's 2nd law).

  • Spring ($k$): $$\displaystyle F = kx $$ (Hooke's law).

  • Damper ($b$): $$\displaystyle F = b \frac{dx}{dt} $$ (viscous friction).

  • Mass-Spring-Damper: $$\displaystyle m\frac{d^2x}{dt^2} + b\frac{dx}{dt} + kx = F(t) $$

  Transfer function $$\displaystyle X(s)/F(s) = \frac{1}{ms^2 + bs + k} $$.

• Rotational:

  • Moment of inertia ($J$): $$\displaystyle T = J \frac{d^2\theta}{dt^2} $$.

  • Torsional spring ($K$): $$\displaystyle T = K\theta $$.

  • Rotary damper ($B$): $$\displaystyle T = B \frac{d\theta}{dt} $$.

  • Equation: $$\displaystyle J\frac{d^2\theta}{dt^2} + B\frac{d\theta}{dt} + K\theta = T(t) $$.

• Analogies (Force-Voltage / Impedance Analogy):

  | Mechanical (Translational) | Electrical | | :--- | :--- | | Force ($F$) | Voltage ($V$) | | Velocity ($$\displaystyle v = dx/dt $$) | Current ($i$) | | Mass ($m$) | Inductance ($L$) | | Damping ($b$) | Resistance ($R$) | | Compliance ($1/k$) | Capacitance ($C$) |

6.4 Formulating System Equations

1. Identify independent energy storage elements (masses, springs, L, C).

2. Apply Newton's laws (mechanical) or Kirchhoff's laws (electrical).

3. Write differential equations in terms of state variables (e.g., displacement, velocity for mechanical; inductor current, capacitor voltage for electrical).

4. Eliminate intermediate variables to get input-output relationship.

6.5 Transfer Function

• Definition: Laplace transform of the impulse response $h(t)$, or ratio of output Laplace transform to input Laplace transform under zero initial conditions.

$$H(s) = \frac{Y(s)}{X(s)} \bigg|_{IC=0}$$

• Derivation: Take Laplace transform of linear differential equation (with zero IC), solve for $Y(s)/X(s)$.

• Poles: Roots of denominator polynomial. Determine stability and natural response.

• Zeros: Roots of numerator polynomial. Affect forced response.

6.6 Time Domain Analysis

• Standard Inputs:

  • Step: $$\displaystyle x(t) = A \cdot u(t) $$. Tests system's ability to reach a new steady state.

  • Ramp: $$\displaystyle x(t) = At $$. Tests tracking of linearly increasing signals.

  • Impulse: $$\displaystyle x(t) = A\delta(t) $$. Tests system's inherent dynamics (impulse response = inverse TF).

• Example Problem: For $$\displaystyle H(s)=\frac{50}{s(s+10)} $$ and step input $10V$:

  • Input $$\displaystyle X(s) = 10/s $$.

  • Output $$\displaystyle Y(s) = H(s) \cdot \frac{10}{s} = \frac{500}{s^2(s+10)} $$.

  • Time Constant ($\tau$): The non-integrating pole is at $$\displaystyle s=-10 $$, so $$\displaystyle \tau = 1/10 = 0.1 $$ s.

  • Settling Time ($$\displaystyle t_s $$): For the exponential mode, $$\displaystyle t_s \approx \frac{4}{\zeta\omega_n} $$. Here, the second-order part has $$\displaystyle \omega_n^2 = 0 $$? Actually, $H(s)$ is type 1 (pole at origin). The dominant real pole is at -10, so $$\displaystyle t_s \approx 4/10 = 0.4 $$ s for the transient to decay. However, due to the integrator, the output will have a steady-state ramp ($$\displaystyle y_{ss} \approx 5t $$), so it does not "settle" to a constant. The question likely expects the $\tau$ and $$\displaystyle t_s $$ of the fastest stable mode (pole at -10).

6.7 Frequency Domain Analysis

• Fourier Transform (see 3.5.1) is used to analyze steady-state response to periodic inputs.

• For a sinusoidal input $$\displaystyle x(t) = X_0 \sin(\omega t) $$, steady-state output is $$\displaystyle y(t) = Y_0 \sin(\omega t + \phi) $$, where $$\displaystyle Y_0/X_0 = |H(j\omega)| $$ and $$\displaystyle \phi = \angle H(j\omega) $$.

• Bode Plots: Graphical representation of $$\displaystyle |H(j\omega)|_{dB} $$ and $\angle H(j\omega)$ vs. $\log \omega$. Useful for design and stability analysis (gain/phase margins).

7.0 PERFORMANCE ASSESSMENT AND ADDITIONAL INSTRUMENTS

7.1 Types of Tests for System Performance

• Analysis Tests: Use deterministic, known inputs (step, ramp, sine) to fully characterize response.

• Sequential Tests: Apply a series of step changes to assess performance under varying conditions.

• Random Tests: Use random (noise) input to simulate real-world disturbances and measure statistical properties (e.g., noise rejection).

7.2 Psychrometer

• Sling Psychrometer: Two thermometers (dry bulb, wet bulb) mounted on a frame, whirled to evaporate water from wet bulb wick.

• Working: Evaporation cools wet bulb. Dry-bulb and wet-bulb temperatures used with psychrometric chart to determine relative humidity, dew point.

• DiagramSling psychrometer with two thermometers
  .

7.3 Accelerometer Calibration

• Gravitational Method: Tilt accelerometer; known acceleration $$\displaystyle a = g \sin\theta $$.

• Shaker Table: Place accelerometer on electrodynamic shaker with reference accelerometer; apply known sinusoidal acceleration.

• Back-to-Back: Mount test accelerometer alongside calibrated reference on vibration exciter.

7.4 Miscellaneous Instruments (Cross-Referenced)

• Venturimeter & Orifice Meter: 4.5.1

• Load Cell: 4.4.3

• Manometer: 4.2.1

• Stroboscope: 4.6.1

• Barometer: 4.2.3

• Potentiometer: 4.1.1

• Impulse Function: 3.4.4