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Pipe and Pipe Fittings

Pipe and Pipe Fittings

Pipe is a hollow structure designed to provide an enclosed pathway for fluids to flow, usually manufactured…


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Interposing Relays in PLCs

Interposing Relays in PLCs

In addition to directly performing logic functions, electromechanical relays may also be used as interposing…


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Periodic Table of the Ions

Periodic Table of the Ions


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Resistance, Reactance, and Impedance

Resistance, Reactance, and Impedance

Electrical Resistance Resistance (\(R\)) is the dissipative opposition to an electric current, analogous to…


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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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Fluorescence Measurement

Fluorescence Measurement

When a high-energy photon strikes an atom, it may eject one of the lower-level electrons from its shell,…


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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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Human-Machine Interfaces (HMIs)

Human-Machine Interfaces (HMIs)

Human-machine interfaces, or HMIs, are a critical part of nearly all control systems, complementing the…


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Single-line Electrical Diagrams

Single-line Electrical Diagrams

Electrical power grids primarily consist of three-phase AC circuits. This means most power lines (transmission…


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On/off Electric Motor Control Circuits

On/off Electric Motor Control Circuits

An electric motor is often used as a discrete control element in a control system if driving a pump, conveyor…


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How Derivatives and Integrals Relate to One Another

How Derivatives and Integrals Relate to One Another

Like many other mathematical operations, the derivative and the integral perform inverse operations from each…


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Introduction to Protective Relaying

Introduction to Protective Relaying

Circuit breakers used in residential, commercial, and light industrial service are self-tripping devices: they…


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Understanding the “Normal” Status of a Process Switch

Understanding the “Normal” Status of a Process Switch

Perhaps the most confusing aspect of discrete sensors is the definition of a sensor’s normal status.…


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Elementary Thermodynamics

Elementary Thermodynamics

Thermodynamics is the study of heat, temperature, and their related effects in physical systems. As a subject,…


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Functional Diagrams: the Flow of Information within a Control System

Functional Diagrams: the Flow of Information within a Control System

A unique form of technical diagram for describing the abstract functions comprising a control system (e.g. PID…


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Ladder Diagram (LD) Programming Contacts and Coils

Ladder Diagram (LD) Programming Contacts and Coils

In the United States, the most common language used to program PLCs is Ladder Diagram (LD), also known as…


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Mathematical Problem-solving Techniques

Mathematical Problem-solving Techniques

Some problem-solving techniques are unique to quantitative problems, involving mathematical calculations. In…


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Electrical Resistance and Ohm’s Law

Electrical Resistance and Ohm’s Law

To review, voltage is the measure of potential energy available to electric charges. Current is the uniform…


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Capacitive Level Measurement

Capacitive Level Measurement

Capacitive level instruments measure electrical capacitance of a conductive rod inserted vertically into a…


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Tuning PID Controllers

Tuning PID Controllers

Learning how to tune PID controllers is a skill born of much practice. Regardless of how thoroughly you may…


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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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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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Molecular Quantities

Molecular Quantities

Sample sizes of chemical substances are often measured in moles. One mole of a substance is defined as a…


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Process and Instrument Diagrams

Process and Instrument Diagrams

The next level of detail is the Process and Instrument Diagram, or P&ID. Here, we see a “zooming…


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Force-balance Pressure Transmitters

Force-balance Pressure Transmitters

An important legacy technology for all kinds of continuous measurement is the self-balancing system. A…


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Valve Failure Modes

Valve Failure Modes

An important design parameter of a control valve is the position it will “fail” to if it loses…


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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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Basics of Electrical Current

Basics of Electrical Current

Current is the name we give to the motion of electric charges from a point of high potential to a point of low…


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Control Valve Characterization

Control Valve Characterization

Control valves are supposed to deliver reliable, repeatable control of process fluid flow rate over a wide…


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Common Control Valve Problems

Common Control Valve Problems

Valves can experience a number of problems, most of them either preventable or repairable. These problems can…


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ANSI/IEEE Function Number Codes

ANSI/IEEE Function Number Codes

In the United States, the ANSI and IEEE organizations have standardized a set of numerical codes referring to…


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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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The Concept of Integration

The Concept of Integration

Suppose we wished to measure the consumption of propane over time for a large propane storage tank supplying a…


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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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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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Continuous Float Level Transmitters

Continuous Float Level Transmitters

Perhaps the simplest form of solid or liquid level measurement is with a float: a device that rides on the…


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Pipe and Pipe Fittings

Pipe and Pipe Fittings

Pipe is a hollow structure designed to provide an enclosed pathway for fluids to flow, usually manufactured…


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Pressure Sensor Accessories

Pressure Sensor Accessories

Multiple accessories exist for pressure-sensing devices to function optimally in challenging process…


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Memory Maps and I/O Addressing

Memory Maps and I/O Addressing

A wise PLC programmer once told me that the first thing any aspiring programmer should learn about the PLC…


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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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