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Transfer Function Analysis

Transfer Function Analysis

An extremely important topic in engineering is that of transfer functions. Simply defined, a transfer function…


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Problem-solving by Simplification

Problem-solving by Simplification

A whole class of problem-solving techniques focuses on altering the given problem into a simpler form that is…


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The s Variable: Euler’s Relation and Phasor Expressions of Waveforms

The s Variable: Euler’s Relation and Phasor Expressions of Waveforms

A powerful mathematical concept useful for analyzing practically any physical system – electrical…


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Formulae for Common Chemical Compounds

Formulae for Common Chemical Compounds

Most of these formulae appear in molecular chemical form rather than structural form. For example, ethanol…


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Phasors, Phase Shift and Phasor Algebra

Phasors, Phase Shift and Phasor Algebra

Phasors are to AC circuit quantities as polarity is to DC circuit quantities: a way to express the…


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Fiber Optic Data Communication

Fiber Optic Data Communication

Light has long been used as a long-range signaling medium. While communication by light through open air is…


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Control Valve Sizing

Control Valve Sizing

When control valves operate between fully open and fully shut, they serve much the same purpose in process…


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Transformer Basics and Principles of Operation

Transformer Basics and Principles of Operation

The transformer is one of the most important components in all of AC circuitry. Principally used to…


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Radio-energy Pulse in Guided-wave Radar Level Measurement

Radio-energy Pulse in Guided-wave Radar Level Measurement

The following animation shows how a radio-energy pulse travels down and then up the waveguide of a guided-wave…


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Pneumatic Actuator Response

Pneumatic Actuator Response

A limitation inherent to pneumatic valve actuators is the amount of air flow required to or from the actuator…


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Digital Multimeter (DMM) Tips and Tricks

Digital Multimeter (DMM) Tips and Tricks

The digital multimeter (DMM) is quite possibly the most useful tool in the instrument technician’s…


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Equivalent Series and Parallel Circuits

Equivalent Series and Parallel Circuits

Impedance in a series circuit is the orthogonal sum of resistance and reactance: \[Z = \sqrt{R^2 + (X_L -…


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Understanding Electrical Power Grids

Understanding Electrical Power Grids

The term “grid” refers to the conductors and equipment interconnecting power sources to power…


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What are Simple Machines?

What are Simple Machines?

A machine in the broad sense of the word is any device designed to translate some form of energy into useful…


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Digital Representation of Text

Digital Representation of Text

Binary patterns are not just able to represent numerical values. Given a standardized code, they may represent…


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How to Teach Yourself PLC Programming

How to Teach Yourself PLC Programming

Learning PLC programming is a very important skill. If your job involves programming, then you will likely…


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Function Block Diagram (FBD) Programming

Function Block Diagram (FBD) Programming

(Will be addressed in future versions of this book)


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VSD and VFD Motor Drive Features

VSD and VFD Motor Drive Features

Modern DC and AC motor drives provide features useful when using electric motors as final control elements.…


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Common Diagnostic Mistakes in Control Systems

Common Diagnostic Mistakes in Control Systems

Volumes could be written about poor diagnostic technique. The following mistakes are not intended to comprise…


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Symbolic Versus Numerical Calculus

Symbolic Versus Numerical Calculus

Calculus has a reputation for being difficult to learn, and with good reason. The traditional approach to…


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Numerical Differentiation

Numerical Differentiation

As we have seen, the concept of differentiation is finding the rate-of-change of one variable compared to…


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PID Control Terminology

PID Control Terminology

PID control can be a confusing concept to understand. Here, a brief summary of each term within PID (P. I, and…


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Classified Areas and Electrical Safety Measures

Classified Areas and Electrical Safety Measures

Any physical location in an industrial facility harboring the potential of explosion due to the presence of…


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Understanding the Calculus Concepts of Differentiation and Integration

Understanding the Calculus Concepts of Differentiation and Integration

The following animation shows the calculus concepts of differentiation and integration (with respect to time)…


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Proportional-only Offset

Proportional-only Offset

A fundamental limitation of proportional control has to do with its response to changes in setpoint and…


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Legal Code

Legal Code

Creative Commons Attribution 4.0 International Public License By exercising the Licensed Rights (defined…


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Stoichiometry and the Law of Mass Conservation

Stoichiometry and the Law of Mass Conservation

Stoichiometry is the accounting of atoms before and after a chemical reaction. It is an expression of the Law…


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the Negative Consequences of Poor PID Controller Tuning

the Negative Consequences of Poor PID Controller Tuning

Much has been written about the benefits of robust PID control. Increased productivity, decreased equipment…


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How to Teach Yourself PLC Programming

How to Teach Yourself PLC Programming

Learning PLC programming is a very important skill. If your job involves programming, then you will likely…


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Digital PID Controllers

Digital PID Controllers

The vast majority of PID controllers in service today are digital in nature. Microprocessors executing PID…


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Concepts and Laws of Probability

Concepts and Laws of Probability

While the term “probability” may evoke images of imprecision, probability is in fact an exact…


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Feedforward with Dynamic Compensation

Feedforward with Dynamic Compensation

As we have seen, feedforward control is a way to improve the stability of a feedback control system in the…


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Mechanical Vibration Switches

Mechanical Vibration Switches

A much simpler alternative to continuous vibration sensors (displacement or acceleration) and monitoring…


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Relation Control

Relation Control

A control strategy similar to ratio control is relation control. This is similar to ratio control in that a…


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Electrical Sources and Electronic Load

Electrical Sources and Electronic Load

By definition, a source is a device delivering energy into a system, while a load is a device extracting…


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National Institute of Standards and Technology (NIST) Traceability

National Institute of Standards and Technology (NIST) Traceability

As defined previously, calibration means the comparison and adjustment (if necessary) of an instrument’s…


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On/off Control (Bang-bang Control)

On/off Control (Bang-bang Control)

Once while working as an instrument technician in an aluminum foundry, a mechanic asked me what it was that I…


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Overpressure Protection Devices

Overpressure Protection Devices

Fluid pressure exerts force on any surface area it contacts, as described by the formula \(F = PA\). One…


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Transformer Basics and Principles of Operation

Transformer Basics and Principles of Operation

The transformer is one of the most important components in all of AC circuitry. Principally used to…


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Applications of Spectroscopy for Analytical Measurement

Applications of Spectroscopy for Analytical Measurement

Much of our knowledge about atomic structure comes from experimental data relating the interaction between…


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