Sensors, Actuators and Data Acquisition

Introduction

A cyber-physical system (CPS) links computation, communication, and physical processes. Sensors convert physical variables into signals that a computational controller can interpret; actuators convert controller commands into physical action; and a data-acquisition system connects these devices to embedded processors, industrial networks, and supervisory software. The quality of this interface strongly influences the safety, stability, efficiency, and diagnosability of the complete CPS.

A sensor system is not adequately specified by asking only, “What sensor measures this variable?” Engineering decisions must also address range, resolution, sensitivity, bandwidth, loading, environmental conditions, calibration, uncertainty, electrical compatibility, sampling, latency, and failure behavior. Similarly, an actuator must be selected according to force or torque, speed, stroke, power, controllability, thermal limits, efficiency, and safe failure modes.

This chapter develops an integrated approach to sensing, actuation, signal conditioning, sampling, filtering, calibration, and data acquisition. The emphasis is on practical design decisions supported by quantitative analysis.

Learning Objectives

By the end of this chapter, a student should be able to:

1. Explain the roles and operating principles of common sensors and actuators in CPS applications.
2. Select sensors and actuators using range, accuracy, bandwidth, loading, environmental, and interface requirements.
3. Design basic signal-conditioning and data-acquisition chains.
4. Apply sampling theory and filtering principles while recognizing aliasing and phase delay.
5. Calibrate measurement systems and quantify uncertainty using appropriate models.
6. Evaluate a complete sensing-and-actuation solution, including safety, cybersecurity, maintainability, and lifecycle considerations.

1. The Measurement and Control Chain

A typical CPS interface follows the sequence:

Figure: A measurement, computation, and actuation chain in a feedback CPS.

The physical variable is first transduced into an electrical quantity such as voltage, current, resistance, frequency, or digital code. Conditioning may provide excitation, amplification, impedance transformation, isolation, linearization, and anti-alias filtering. An analog-to-digital converter (ADC) samples the signal, after which software estimates state and computes a control command. A driver supplies the voltage and current required by the actuator. The resulting physical action changes the process and is measured again.

The chain contains both energy and information flows. A sensor may consume energy while measuring, and an actuator may inject substantial energy into the plant. The signal path can therefore be electrically correct but physically unsafe—for example, if a valve position sensor is wired correctly while the valve itself can move unexpectedly during commissioning.

2. Sensors: Principles and Selection

2.1 Transduction and sensor characteristics

A sensor transforms a measurand into a usable output. Important characteristics include:

• Range: minimum to maximum measurable input.
• Sensitivity: change in output per unit change in input.
• Resolution: smallest distinguishable input change.
• Accuracy: closeness of a result to the accepted reference value.
• Precision: closeness among repeated results.
• Repeatability: precision under the same conditions.
• Hysteresis: different outputs for increasing and decreasing input at the same input value.
• Linearity: degree to which the input-output relation follows a specified straight-line model.
• Bandwidth: frequency range over which the sensor responds acceptably.
• Drift: change in output over time, temperature, humidity, or other conditions.
• Loading: alteration of the measured system caused by the sensor.

A useful static model is

where x is the measurand, y is the observed output, b is sensitivity, a is offset, and ε represents random and unmodeled effects. This model is appropriate over a limited operating range; nonlinear sensors require additional terms or a calibration map.

Sensitivity is formally

where S has units of output per input. For a temperature sensor producing 10 mV per °C, a 5 °C change produces approximately 50 mV, provided the stated sensitivity is valid over that range.

Accuracy and precision must not be confused. A sensor can have small random variation but a large calibration offset, giving high precision and poor accuracy. Conversely, a sensor can have an unbiased average value but considerable noise, giving acceptable accuracy after averaging but poor instantaneous precision.

2.2 Common sensor families

Resistive sensors include resistance temperature detectors, thermistors, strain gauges, and potentiometers. They require excitation and are vulnerable to lead resistance, self-heating, and electrical noise. A Wheatstone bridge is often used for small resistance changes, especially in strain measurement.

Thermoelectric sensors, such as thermocouples, generate a voltage related to temperature difference. They have wide temperature ranges and rugged construction, but their outputs are small and require reference-junction compensation and careful low-noise amplification.

Capacitive sensors detect changes in capacitance caused by displacement, pressure, humidity, or proximity. They can provide high resolution but are sensitive to parasitic capacitance, contamination, and cable arrangement.

Inductive and magnetic sensors include variable-reluctance sensors, linear variable differential transformers, Hall-effect sensors, and magnetoresistive devices. They are useful for position, speed, and current measurement and often tolerate harsh environments.

Optical sensors measure interruption, reflection, intensity, time of flight, or image features. They can be noncontact and fast, but dust, ambient light, alignment, and surface reflectivity affect performance.

Inertial sensors use microelectromechanical systems to measure acceleration and angular rate. Their principal limitations include bias instability, scale-factor error, vibration sensitivity, and integration drift. Position obtained by integrating acceleration is especially vulnerable to accumulated error.

Pressure and flow sensors commonly use diaphragms, strain elements, thermal effects, or differential-pressure principles. Installation geometry, fluid density, pulsation, and blockage must be considered.

The correct choice depends on the application, not simply the nominal accuracy. A high-resolution sensor with inadequate bandwidth or poor environmental protection may be inferior to a less precise but robust alternative.

2.3 Sensor loading and excitation

A voltage-output sensor connected to a low-resistance input can be loaded, changing its output. If a source has Thévenin voltage V_s and resistance R_s, connected to an input resistance R_i, the measured voltage is

This divider relationship assumes linear resistances and negligible input reactance. When R_i is much larger than R_s, loading is small. A buffer amplifier can increase effective input resistance, but it introduces offset, bias-current, noise, power, and saturation considerations.

Excitation circuits must also be evaluated. A constant-current excitation for a resistive sensor reduces some wiring effects, whereas constant-voltage excitation may be simpler. Self-heating occurs when power dissipated in the sensor changes the measurand. For a resistance R carrying current I, electrical power is

where P is in watts. The resulting temperature rise depends on the sensor’s thermal resistance and mounting conditions.

3. Actuators and Power Interfaces

An actuator converts a command into force, torque, displacement, flow, heat, or another physical effect. Common classes are:

Selection begins with the load. For translational motion, required force may include acceleration, friction, gravity, and process resistance:

Here m is mass, a is acceleration, F_friction is friction force, F_process is external resistance, and m g_component is the component of weight along the motion axis. The equation is a simplified force balance; rotating mechanisms, compliance, impacts, and safety factors may require a dynamic model.

For rotary motion, the corresponding ideal balance is

where τ is torque, J is rotational inertia, α is angular acceleration, and τ_load is external load torque. Mechanical power is

where v is linear velocity and ω is angular velocity in radians per second. Electrical input power exceeds mechanical output because of losses. Continuous ratings and peak ratings must be distinguished, and thermal limits often determine continuous capability.

The actuator driver must match logic levels, voltage, current, switching frequency, isolation, and protection requirements. A microcontroller pin generally cannot drive a motor directly. A transistor, H-bridge, relay, valve driver, or servo amplifier may be necessary. Flyback suppression is required for many inductive loads. Emergency stopping should remove hazardous energy in a controlled and independently evaluated manner rather than relying only on software.

4. Signal Conditioning

Signal conditioning prepares a sensor signal for conversion and interpretation. Typical functions include:

1. Amplification: increases a small signal while preserving relevant information.
2. Attenuation: reduces a signal that exceeds ADC input range.
3. Buffering: prevents loading between stages.
4. Differential measurement: rejects common-mode interference when implemented with an appropriate amplifier and layout.
5. Isolation: limits hazardous voltage transfer and ground-loop currents.
6. Excitation: supplies a controlled current or voltage to passive sensors.
7. Linearization: compensates for a known nonlinear response.
8. Filtering: reduces unwanted frequency components.
9. Protection: limits transients, overvoltage, electrostatic discharge, and reverse polarity.

For an ADC with input range 0 to V_ref and an ideal N-bit code, the nominal code width is

where q is in volts per code. The ideal conversion code for an input within range is approximately

The exact endpoint convention depends on the ADC architecture and data sheet. Quantization is not the only error: offset, gain, differential nonlinearity, integral nonlinearity, reference error, noise, and input settling also matter.

An instrumentation amplifier is often suitable for bridge sensors because it provides high input impedance and adjustable gain. However, its common-mode input range and output swing must remain within specified limits. A circuit that has adequate differential gain can still saturate if the common-mode voltage is too high.

Grounding and shielding are part of conditioning. Shielding does not automatically eliminate noise; a shield connected at inappropriate points can create ground-loop currents. Differential signaling, twisted pairs, star or carefully planned ground structures, galvanic isolation, physical separation from switching conductors, and suitable cable termination are commonly combined.

5. Sampling, Aliasing, and Filtering

A continuous signal becomes a sequence of samples at sampling frequency f_s. The sampling interval is

If a signal contains no frequency components above f_max, ideal uniform sampling permits reconstruction when

This is the Nyquist condition for band-limited signals. Equality is not a safe engineering design because components exactly at the boundary and practical filter transition bands create ambiguity. Real systems therefore sample faster than the theoretical minimum and use an analog anti-alias filter before the ADC.

Aliasing occurs when higher-frequency content appears as lower-frequency content after sampling. For a sinusoid at frequency f, the apparent alias frequency can be described by folding the frequency around integer multiples of f_s. For example, a 700 Hz interference component sampled at 1,000 samples/s appears at 300 Hz. Digital filtering after the ADC cannot remove this false 300 Hz component because the original distinction has already been lost.

A first-order low-pass filter has transfer function

where R is resistance, C is capacitance, and s is the complex frequency variable. Its cutoff frequency is

This model assumes ideal components and a sufficiently high input impedance. At frequencies much greater than f_c, attenuation increases at approximately 20 dB per decade. A low cutoff reduces noise but also reduces speed and introduces phase lag.

Digital filters include moving averages, finite impulse response filters, infinite impulse response filters, and state estimators. A length-M moving average is

where x[k] is the input sample and y[k] is the filtered output. It is simple and reduces uncorrelated noise, but it delays changes and can obscure short faults. Filtering in a control loop must be evaluated together with loop stability and timing latency.

Sampling rate is also a systems issue. The designer must account for sensor bandwidth, filter settling, ADC conversion time, communication delay, computation time, actuator response, and control-loop frequency. A nominally fast ADC does not guarantee a fast closed-loop system.

6. Calibration and Uncertainty

Calibration compares an instrument with a reference and establishes a relationship between indicated output and a known input. A basic two-point calibration assumes a linear model:

where y is the measured output, a is offset, b is sensitivity, and x_estimated is the estimated measurand. If two reference points are (x₁,y₁) and (x₂,y₂), then

and

The calibration interval must be chosen according to drift, use severity, manufacturer guidance, regulatory requirements, and consequences of failure. Calibration is not the same as adjustment: calibration measures deviation, whereas adjustment changes the instrument to reduce deviation.

Uncertainty expresses incomplete knowledge of the measurand. Common components include reference uncertainty, repeatability, resolution, environmental effects, drift, hysteresis, and model error. If independent standard uncertainties u₁, u₂, …, u_n contribute to a result, a common first-order combination is

This root-sum-square form assumes approximate independence and sensitivity coefficients equal to one. More generally, if a result y depends on quantities x_i,

with covariance terms added when inputs are correlated. The expanded uncertainty is often reported as

where k is a coverage factor selected according to the reporting convention and statistical basis. A statement such as “measured temperature = 42.0 ± 0.6 °C, coverage factor 2” is more informative than a long decimal without uncertainty.

Uncertainty budgets should distinguish random variation from systematic effects. Repeated measurements estimate repeatability but do not reveal an unrecognized calibration bias. Traceability requires a documented connection to stated references through an unbroken chain of calibrations, each contributing to uncertainty.

7. Data-Acquisition Interfaces

Data-acquisition systems may use analog voltage, current loops, frequency, pulse width, serial buses, or network protocols. Common interfaces include:

• 0–10 V: simple analog signaling, but susceptible to voltage drop and ground differences.
• 4–20 mA: robust industrial current signaling; the live zero allows detection of an open circuit in many systems.
• Frequency or pulse signals: useful for speed, flow, and event counting.
• I²C and SPI: short-distance board-level digital buses.
• UART, RS-485, CAN, and industrial Ethernet: communication over progressively more capable physical and network layers.

Interface selection should consider distance, electromagnetic environment, number of nodes, synchronization, deterministic timing, diagnostic capability, isolation, and cybersecurity. A protocol is not automatically safe because it is digital. Authentication, message integrity, access control, secure configuration, and network segmentation may be required when sensor or actuator data can affect safety or production.

A DAQ specification should state channel count, input type, range, resolution, sampling rate, simultaneous or multiplexed sampling, accuracy, isolation, trigger capability, timestamp quality, storage, and maintenance provisions. Multiplexed ADCs sample channels at different times; this matters when signals change quickly or phase relationships are important.

Time synchronization is essential in distributed CPS. A sensor value without a trustworthy timestamp can produce incorrect velocity, phase, or causal conclusions. Designers should distinguish sensor time, acquisition time, transmission time, and processing time, and should record data quality flags such as overrange, stale data, communication loss, and calibration status.

8. Worked Example: Temperature Acquisition

A temperature transmitter produces 4–20 mA over a range of −20 °C to 180 °C. It is connected to a 250 Ω precision resistor, producing a voltage for a 0–5 V ADC. Determine the voltage at 70 °C and the ideal 12-bit ADC code, assuming the ADC reference is exactly 5.000 V and no other errors.

The temperature span is 200 °C and the current span is 16 mA. At 70 °C, the fraction of span is

The current is

Using V = IR,

For a 12-bit ADC, the ideal code is approximately

Thus the nearest integer code is approximately 2293. The result is idealized: transmitter accuracy, resistor tolerance, reference error, ADC gain and offset error, wiring resistance, temperature effects, and current-loop faults would contribute to the actual uncertainty.

9. Illustrative Case: Conveyor-Based Sorting Cell

Background

A small manufacturing cell sorts packages by height and mass. A photoelectric sensor detects package arrival, a laser displacement sensor estimates height, a load cell estimates mass, and a servo-driven diverter sends each package to one of three bins.

Problem

Initial trials produced false classifications. The laser signal was noisy near reflective packaging, the load-cell reading changed when the conveyor motor started, and packages occasionally arrived at the diverter before the controller had completed classification.

Analysis

The system review identified three interacting problems. First, the laser sensor had adequate static resolution but insufficient optical robustness for all package surfaces. Second, the load-cell amplifier shared a noisy supply return with the motor driver. Third, the acquisition software treated sensor values as if they were instantaneous, ignoring conversion time and transport delay.

The team defined requirements: package speed up to 0.5 m/s, height resolution of 1 mm, mass uncertainty below 20 g, classification decision at least 0.3 s before diversion, and safe stopping if a sensor becomes invalid.

Approach and Solution

The laser sensor was mounted at a controlled angle and supplemented with a diffuse optical sensor for presence confirmation. The load cell used a differential instrumentation amplifier, shielded cable, separate regulated excitation, and a low-pass analog filter before a 16-bit ADC. The motor driver and measurement electronics were given controlled grounding and galvanic isolation where needed.

The sampling plan used a rate substantially above the bandwidth required for package motion, with an analog anti-alias filter. A digital moving average was applied only after checking its delay against the available classification time. Calibration used certified masses at several points rather than only zero and full scale. The software stored raw values, filtered values, timestamps, calibration version, and validity flags.

A state machine was implemented: Idle, Package detected, Acquire, Classify, Await diverter, Divert, and Fault. A watchdog and timeout transferred the system to a safe state if the expected measurement or actuator acknowledgment did not arrive.

Outcome

False classifications were reduced because optical confirmation rejected invalid laser readings and the load-cell signal was isolated from motor noise. The state machine prevented premature diversion and made timing faults visible. The system also became easier to maintain because calibration records and sensor-health diagnostics were retained with production data.

Learning Points

The case demonstrates that sensor performance is a property of the complete measurement chain, not of a sensor data sheet alone. Grounding, sampling, latency, mechanics, calibration, software state, and actuator timing must be designed together. It also illustrates why “more filtering” is not a universal solution: excessive filtering can make a measurement arrive too late.

10. Safety, Ethics, and Contemporary Developments

Sensor and actuator failures can injure people, damage equipment, or create environmental harm. A safety-related design should identify hazardous energy, foreseeable misuse, single-point failures, diagnostic coverage, safe states, and independent protective measures. A software estimate should not be treated as a safety-rated replacement for a properly designed guard, interlock, emergency stop, or redundant sensor when the risk assessment requires those measures.

Data from sensors may reveal worker behavior, production rates, location, or health-related information. Collection should be limited to legitimate purposes, protected against unauthorized access, retained only as necessary, and communicated transparently. Calibration records and audit trails support accountability, while access controls and signed firmware help protect the integrity of measurements and commands.

Contemporary CPS designs increasingly use edge analytics, sensor fusion, wireless sensing, time-sensitive networking, and machine-learning models. These technologies are useful when they address a defined requirement. Sensor fusion can combine complementary measurements, but correlated errors must not be treated as independent evidence. Machine learning may detect anomalies, yet it requires representative data, monitoring for drift, explainable alarms where appropriate, and a deterministic fallback for safety-critical action. Wireless sensors reduce cabling but introduce battery constraints, interference, latency, and cybersecurity exposure.

11. Design Best Practices and Limitations

A disciplined design workflow is:

1. Define the physical variable, range, dynamics, accuracy, uncertainty, and consequences of error.
2. Specify the actuator load, motion profile, energy, duty cycle, and safe state.
3. Select transducers and interfaces using environmental and lifecycle requirements.
4. Design excitation, protection, grounding, isolation, and conditioning.
5. Establish the analog bandwidth and anti-alias filter before selecting sample rate.
6. Quantify ADC resolution and all significant error sources.
7. Calibrate using traceable references and maintain uncertainty budgets.
8. Validate timing, synchronization, communication loss, saturation, and fault behavior.
9. Document wiring, scaling, units, calibration coefficients, diagnostic flags, and maintenance intervals.
10. Test normal operation, boundary conditions, faults, recovery, and safe shutdown.

Important limitations remain. Data-sheet accuracy may apply only under specified temperature, supply, mounting, and calibration conditions. A model based on independent errors can understate uncertainty when errors are correlated. A digital filter can reduce visible noise while hiding a developing fault. Redundancy does not guarantee safety if redundant sensors share the same power supply, mounting error, software defect, or environmental disturbance. Finally, high data volume does not compensate for poor observability or poorly defined requirements.

Chapter Summary

Sensors transduce physical variables into signals, while actuators transform commands into physical effects. Their successful integration requires consideration of static characteristics such as range, sensitivity, accuracy, precision, hysteresis, and drift, as well as dynamic characteristics such as bandwidth, latency, and phase delay. Loading and excitation can alter the measured system, and actuator selection must account for force, torque, power, duty cycle, thermal behavior, and driver compatibility.

Signal conditioning provides amplification, buffering, isolation, filtering, protection, and linearization. ADC resolution is only one part of acquisition quality; reference, gain, offset, noise, nonlinearity, timing, and grounding also matter. Sampling must satisfy the bandwidth requirement and must be preceded by anti-alias filtering. Digital filtering can improve estimates but introduces delay and cannot repair aliasing that occurred before conversion.

Calibration establishes the relationship between indication and measurand. Uncertainty budgets combine relevant sources and communicate the limits of knowledge. A complete DAQ design includes interface selection, synchronization, validity flags, diagnostics, cybersecurity, safety, and maintenance. The conveyor case demonstrates that reliable CPS behavior emerges from coordinated mechanical, electrical, computational, and organizational design rather than from isolated component specifications.

Key Terms

Sensor: Device or system that transduces a physical measurand into an output signal.

Measurand: Quantity intended to be measured.

Actuator: Device that converts a command into physical force, motion, flow, heat, or another effect.

Sensitivity: Change in output per unit change in input.

Accuracy: Closeness of a measurement result to an accepted reference value.

Precision: Closeness among repeated measurement results.

Resolution: Smallest distinguishable change in the measured quantity.

Hysteresis: Dependence of output on the direction or history of input change.

Drift: Change in indication or sensitivity over time or environmental conditions.

Loading: Alteration of a measured system caused by connection of the measurement device.

Signal conditioning: Processing that prepares a sensor signal for conversion or interpretation.

ADC: Analog-to-digital converter that represents an analog input as a digital code.

Quantization: Mapping of a continuous amplitude to discrete digital levels.

Aliasing: Misrepresentation of higher-frequency content as lower-frequency content after sampling.

Anti-alias filter: Analog filter used before sampling to attenuate unwanted high-frequency content.

Calibration: Comparison with references to establish measurement relationship and deviation.

Uncertainty: Quantified expression of incomplete knowledge about a measurement result.

Data acquisition: Collection, conditioning, conversion, timing, and storage or transmission of measurement data.

Common-mode signal: Component present similarly on two measurement conductors.

Traceability: Documented connection of a measurement result to stated references through calibration chains.

Review Questions

Short Answer Questions

1. Distinguish accuracy from precision and give an example of a measurement that is precise but inaccurate.
2. Why can a sensor with high resolution still be unsuitable for a control application?
3. State two purposes of signal conditioning and explain why each is needed.
4. What is aliasing, and why must anti-alias filtering occur before the ADC?
5. What is the difference between calibration and adjustment?

Long Answer Questions

1. Explain how a sensor should be selected for a CPS application, including static, dynamic, environmental, electrical, and maintenance requirements.
2. Describe the complete signal path from a physical process through sensing, conditioning, ADC conversion, computation, actuator driving, and physical response.
3. Compare voltage, 4–20 mA, and digital communication interfaces for an industrial installation.
4. Explain how grounding, shielding, isolation, and filtering influence measurement integrity in a motor-driven system.
5. Discuss the construction and use of an uncertainty budget for a calibrated temperature or force measurement.

Analytical / Application Questions

1. An 8-bit ADC has a 0–5 V input range. Calculate its ideal code width and explain whether it can resolve a 10 mV change. State the assumptions behind your conclusion.
2. A motor must accelerate a 4 kg load at 1.5 m/s² against 8 N of process resistance and 3 N of friction. Calculate the ideal required force before applying a safety factor, and identify additional mechanical effects that may need consideration.
3. A sensor signal contains useful content to 80 Hz and significant interference at 600 Hz. Propose a sampling and filtering strategy, explaining the trade-off between attenuation, delay, and computational cost.

Multiple Choice Questions with Answers

Question 1

Which characteristic describes the closeness of repeated measurements to one another?

A. Accuracy

B. Precision

C. Sensitivity

D. Range

Correct Answer: B. Precision

Question 2

A 4–20 mA transmitter spans −20 °C to 180 °C. What current corresponds ideally to 80 °C?

A. 8.0 mA

B. 10.4 mA

C. 12.0 mA

D. 14.4 mA

Correct Answer: C. 12.0 mA

Question 3

What is the principal purpose of an analog anti-alias filter?

A. Increase ADC resolution

B. Remove false components after sampling

C. Attenuate frequency content above the usable sampled bandwidth before conversion

D. Convert current into torque

Correct Answer: C. Attenuate frequency content above the usable sampled bandwidth before conversion

Question 4

A 12-bit ideal ADC uses a 0–4.096 V reference. What is its nominal code width?

A. 0.001 V

B. 0.01 V

C. 1 mV

D. 12 mV

Correct Answer: C. 1 mV

Question 5

Which actuator is most directly associated with very high force-to-mass ratio and compressed-air operation?

A. Pneumatic cylinder

B. Piezoelectric stack

C. Thermocouple

D. Potentiometer

Correct Answer: A. Pneumatic cylinder

Question 6

If a sensor source resistance is 1 kΩ and its input resistance is 9 kΩ, what fraction of the ideal source voltage appears at the input under the divider model?

A. 0.10

B. 0.50

C. 0.90

D. 1.10

Correct Answer: C. 0.90

Question 7

Which statement about a moving-average filter is correct?

A. It can remove aliasing that occurred before ADC conversion

B. It reduces some noise but introduces response delay

C. It always increases control-loop bandwidth

D. It eliminates calibration error

Correct Answer: B. It reduces some noise but introduces response delay

Question 8

For a rotating actuator, which equation represents the ideal inertial torque component?

A. τ = Jα

B. τ = V/I

C. τ = m/a

D. τ = RC

Correct Answer: A. τ = Jα

Question 9

Why is a live zero commonly used in a 4–20 mA loop?

A. It makes the signal wireless

B. It allows some open-circuit or zero-value faults to be distinguished from a valid zero measurement

C. It eliminates the need for calibration

D. It guarantees zero noise

Correct Answer: B. It allows some open-circuit or zero-value faults to be distinguished from a valid zero measurement

Question 10

Which statement best describes measurement uncertainty?

A. It is identical to sensor resolution

B. It is a quantified expression of incomplete knowledge about the measurement result

C. It is only the random error observed in one reading

D. It is the actuator’s maximum power

Correct Answer: B. It is a quantified expression of incomplete knowledge about the measurement result