Instrumentation

Chapter One: Applications of Electronic Instrument Systems

1. Introduction to Electronic Instrumentation Systems

  • Objective: To introduce electronic instrumentation systems that enable accurate measurement of mechanical and thermal quantities.
    • Mechanical Quantities Include:
    • Strain
    • Force
    • Pressure
    • Moment
    • Torque
    • Displacement
    • Velocity
    • Acceleration
    • Flow Velocity
    • Mass Flow Rate
    • Volume Flow Rate
    • Frequency
    • Time
    • Thermal Quantities Include:
    • Temperature
    • Heat Flux
    • Specific Heat
    • Thermal Conductivity

2. Advantages of Electronic Instrumentation Systems over Mechanical Measurement Systems

  • Focus on electronic instrumentation due to the following reasons:
    1. Electronic systems usually provide data that more accurately and completely characterize the design or process being evaluated.
    2. Electronic systems provide an electrical output signal which can either:
    • Be used directly for analog control of processes.
    • Be digitized for automatic data reduction.
    1. Mechanical measurement systems typically have slower response times and are less capable of responding rapidly to changes in physical quantity.

3. Mechanical vs. Electrical Instruments

  • Comparison:
    • Example: Mechanical pressure gauge vs. electrical pressure gauge
    • Mechanical pressure gauge: Slow response, less accurate
    • Electrical pressure gauge: Fast response, more accurate

4. Components of an Electronic Instrumentation System

  • A complete electronics instrument system usually consists of at least six of the eight subsystems:
    1. Transducer
    • Converts changes in mechanical or thermal quantities into changes of electrical quantities.
    • Example: Strain gauge sensor converts strain into changes in electrical resistance, which can further be converted into voltage.
    1. Power Supply
    • Provides energy to drive the transducer (can be AC or DC).
    • Example: DPS-2303DF Multiple Output DC Power Supply with outputs such as 0-30V/0-3A, 2.5V, 3.3V.
    1. Signal Conditioner
    • Converts transducer output into a more usable electrical signal.
    • Employs components like Wheatstone bridge, filters (low-pass, high-pass), integrators, differentiators, and notch filters.
    1. Amplifiers
    • Amplify small voltage outputs from transducers or signal conditioners.
    • Example: 1 mV signal amplified to 1 V.
    1. Recorders
    • Devices that display measurements in readable formats; can be analog or digital (e.g., oscilloscopes).
    1. Data Processor
    • Incorporates analog-to-digital conversion. Example setup depicted in circuit form.
    1. Command Generator
    • Provides control voltage representing variations in critical process parameters.
    • Example: Controlling the time-temperature profile in an oven.
    1. Process Control
    • Monitors or adjusts quantities that must be maintained at specific values.
    • Example: Cruise control in cars or altitude control in aircraft.

5. Engineering Analysis

  • Conducted to evaluate new or modified designs to ensure efficient and reliable performance when prototypes are operational.
  • Approaches:
    1. Theoretical Approach:
    • Develop analytical models with assumptions regarding operating conditions, loads, materials, etc.
    • Derive equations to describe system behavior and solve for validation.
    • Possible uncertainties due to model accuracy and numerical procedures.
    1. Experimental Approach:
    • Fabrics a prototype to test performance directly by measuring significant quantities.
    • Benefits: Reduces uncertainties, no analytical model required.
    • Drawbacks: High costs, potential errors from placement of transducers.
    • Optimal strategy involves combining both techniques for comprehensive evaluation.

6. Process Control

  • Types of Control:
    1. Open-Loop Control:
    • Sensors display data continuously; operators adjust process inputs manually.
    • Example: Old air conditioning systems, manual speed control in vehicles.
    1. Closed-Loop Control:
    • Systems without manual intervention.
    • Example: Car cruise control, autopilot systems.

7. Process Control Devices

  • Types of devices used in process control adjustment include:
    • Motors:
      • DC motors and stepping motors.
    • Solenoids:
      • Produce magnetic forces to open/close valves.
    • Servo Control Valves:
      • Quicker response versus motorized valves.
    • Positioning Devices:
      • Rotational (motors), Linear (powerscrews, piezoelectric actuators).
    • Resistance Heating Devices.

8. Experimental Error

  • Defined as the difference between true and measured values (e.g., displacement, pressure).
  • Errors cannot be entirely avoided but can be minimized.
  • Sources of error include:
    1. Accumulation of Accepted Error:
    • Each instrumentation system element has manufacturer-specified accuracy limits.
    • Example: Recorder error as ±2% of full-scale values, resulting in accumulated error formula: ext{Accumulated Error} ( ext{ε}a) = ext{ε}^2{ ext{T}} + ext{ε}^2{ ext{SC}} + ext{ε}^2{ ext{A}} + ext{ε}^2_{ ext{R}}
      • Individual elements’ errors affect overall system accuracy.
    1. Improper Functioning of Instruments:
    • Issues like calibration errors, zero-offset, and range errors due to maintenance defects.
      • Sensitivity (S) defined as:
        S = rac{ riangle Qo}{ riangle Qi}
      • The relationship between output and input:
        Qo = S imes Qi + Z_0
      • Removal of Z0 indicates linear output behavior, which might not hold at extreme values.
    1. Calibration Errors:
    • Includes zero-offset and range errors affecting accuracy.
    1. Effect of Transducer on Process:
    • Transducer must not significantly affect the process; its size should be minimal.
    • Example: The placement of transducer impacts accuracy on structural elements like beams.
    1. Dual Sensitivity Errors:
    • Transducers may be sensitive to unintended quantities, introducing errors.
    1. Other Sources of Error:
    • Lead-wire effects leading to resistance variation, electronic noise from magnetic fields, and human operator error.

9. Minimizing Experimental Error

  • Strategies include:
    • Carefully selecting transducers;
    • Ensuring accuracy and checking for accumulated errors;
    • Calibration of each system component;
    • Assessing operational environment;
    • Using shielded lead wires and addressing electronic noise;
    • Performing complete system calibration.

10. Example Analysis: Pressure Sensor

  • Operation Features:
    • Input range: 0-1000 cm $H_2O$
    • Excitation: ±15 V DC; Output range: 0-5 V DC; Temperature range: 0 − 50°C.
  • Performance Metrics:
    • Reading: 500 cm $H_2O$ at 7°C.
    • Linearity error: ±0.5% FSO.
    • Hysteresis error: < ±0.15% FSO.
    • Sensitivity error: ±0.25% of reading;
    • Thermal sensitivity error: ±0.02%/°C of reading;
    • Thermal zero drift: ±0.02%/°C of FSO.
  • Calculating Overall Instrument Error:
    1. In cm $H_2O$:
      • Linearity error = ±0.005 × 1000 = ±5 cm $H_2O$;
      • Hysteresis error = ±0.0015 × 1000 = ±1.5 cm $H_2O$;
      • Sensitivity error = ±0.0025 × 500 = ±1.25 cm $H_2O$;
      • Thermal sensitivity error = ±0.0002 × 500 × 7 = ±0.7 cm $H_2O$;
      • Thermal zero drift = ±0.0002 × 1000 × 7 = ±1.4 cm $H_2O$;
      • Overall instrument error (cm $H2O$) = ext{Error} ext{total} = ext{√}(5^2 + 1.5^2 + 1.25^2 + 0.7^2 + 1.4^2) ext{cm} H_2O
    2. In Volts:
      • Calculated error contributions yield an overall instrument error of $±0.0278 V$.

11. Suggested Problems from the Textbook

  • Problems: 19, 23, 27, 28, 30, 33, 34