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Introduction to Calculus

Introduction to Calculus

Few areas of mathematics are as powerfully useful in describing and analyzing the physical world as calculus:…


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Logic Programming in PLCs

Logic Programming in PLCs

Although it seems each model of PLC has its own idiosyncratic standard for programming, there does exist an…


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Kirchhoff’s Current and Voltage Laws

Kirchhoff’s Current and Voltage Laws

Two extremely important principles in electric circuits were codified by Gustav Robert Kirchhoff in the year…


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Antennas and Resonant Circuits (Tank Circuits)

Antennas and Resonant Circuits (Tank Circuits)

Capacitors store energy in electric fields, proportional to the square of voltage. Inductors store energy in…


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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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Filled-bulb Temperature Sensors

Filled-bulb Temperature Sensors

Filled-bulb systems exploit the principle of fluid expansion to measure temperature. If a fluid is enclosed in…


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LRV and URV Settings, Digital Trim (Digital Transmitters)

LRV and URV Settings, Digital Trim (Digital Transmitters)

The advent of “smart” field instruments containing microprocessors has been a great advance for…


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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 Difference Between Series and Parallel Circuits

The Difference Between Series and Parallel Circuits

In addition to Ohm’s Law, we have a set of rules describing how voltages, currents, and resistances…


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Vibration Physics

Vibration Physics

One very convenient feature of waves is that their properties are universal. Waves of water in the ocean,…


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Pilot Valves and Pneumatic Amplifying Relays

Pilot Valves and Pneumatic Amplifying Relays

Self-balancing mechanisms consisting solely of a baffle/nozzle detector coupled to a feedback bellows, while…


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Disassembling a Globe Valve

Disassembling a Globe Valve

The following collection of photographs chronicles the complete disassembly of a Fisher E-body globe valve…


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Different PID Equations

Different PID Equations

For better or worse, there are no fewer than three different forms of PID equations implemented in modern PID…


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Valve Positioners

Valve Positioners

The reason why a pneumatic control valve’s stem position corresponds linearly to the amount of air…


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Assessing Student Learning

Assessing Student Learning

As a general rule, high achievement only takes place in an atmosphere of high expectations. Sometimes these…


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Chemical Reactor Temperature Control Example

Chemical Reactor Temperature Control Example

Sometimes we encounter a diversity of instrument signal standards in one control system. Such is the case with…


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Pressure-based Flowmeters

Pressure-based Flowmeters

All masses require force to accelerate (we can also think of this in terms of the mass generating a reaction…


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Calibration Errors and Testing

Calibration Errors and Testing

The efficient identification and correction of instrument calibration errors is an important function for…


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Instantaneous and Time-overcurrent (50/51) Protection

Instantaneous and Time-overcurrent (50/51) Protection

Perhaps the most basic and necessary protective relay function is overcurrent: commanding a circuit breaker to…


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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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