Автор - Bob Connell, язык - английский.
Описание: A practical tutorial on the mathematics essential to the process control field, written by an experienced process control engineer for practicing engineers and students.
This essential work includes chapters on frequency response analysis, transfer functions and block diagrams, and the Z-N approximation. A handy desk reference for process control engineers - a helpful aid to students in mathematics courses.
Preface
Table of Contents
Trigonometry and Cyclic Functions
Units of Measurement
Functions of Angles
Definitions
Quadrants
Frequency of Cycling
Sine of the Sum of Two Angles
Cosine of a Sum
Sine of a Difference between Two Angles
Cosine of a Difference
Potentially Useful Relationships
Example 1: Tan (X + Y)
Example 2: sin 2X - sin 2Y
Example 3: Radius of the Earth
Example 4: The Third Side
Example 5: Gain and Phase Lag
Differential Calculus
Concept of Approaching a Limit
Example 1: f(t) = t2
Procedure for Determining a Derivative
Derivative of a Sum or Difference
Derivative of a Product
Derivative of a Quotient
Dimensions and Units
Derivative of a Sine Function
Binomial Theorem
Derivative of a Power
Derivative of an Exponential
A Function within a Function
Example 2: Detecting a Maximum or Minimum
Example 3: Watering the Lawn
Integral Calculus Text
Problem Areas
Practical Uses of Integration
Example 1: Powers and Constants
Example 2: sin3 x
Example 3: cos 2x
Example 4: Substitution of Variables
Example 5: Fractions
Example 6: Using Partial Fractions
Example 7: Numerator Higher Order than Denominator
Example 8: Changing to an Angular Mode
Example 9: sin2 x
Example 10: Square Root of (a2 - x2)
Integration over a Specified Range
Example 11: Tank Filling Case
Example 12: Area of a Circle
Example 13: Surface Area of a Sphere
Example 14: Volume of a Sphere
Example 15: The Escape Velocity
Example 16: Area of a Segment of a Circle
Table of Basic Integrals
Infinite Series
Power Series
The nth Term
Test for Convergence
Example 1: Convergence Test 1
Example 2: Convergence Test 2
Example 3: Convergence Test 3
Example 4: The (n+1)th Term
Maclaurin's Series
Example 5: e?t
Practical Disadvantage of Maclaurin's Series
Taylor's Series
Example 6: Value of a Sine Function Using Taylor's Series
Complex Quantities
Background
Graphical Representation
The Complex Variable
Trigonometric and Exponential Functions
Separating the Real and Imaginary Parts
Differential Equations
Introduction
Philosophy
Definitions
Application
Differential Equations of the First Order and First Degree
Category 1: Exact Differentials
Category 2: Variables Separable
Category 3: Homogeneous Equations
Category 4: Linear Differential Equations
Example 1: Time Constant
Linear Differential Equations with Constant Coefficients
Second Order Linear Differential Equation with Constant Coefficients
The Oscillatory Case
The Constant of Integration
Commentary on the Result
Example 2: The Spring/Mass System
Units
Partial Differential Equations
Laplace Transforms
History
Example 1: Step Change
Transforms of Derivatives
Example 2: Time Constant
Example 3: Pendulum
Example 4: Second Order Linear Differential Equations with Constant Coefficients
The Oscillatory Case
Consistency of Results
Table of Laplace Transforms
Frequency Response Analysis
Background
The Bode Diagram
Frequency Response of a Time Constant Element
Frequency Response of a Dead Time Element
Combinations of Components
Period of Oscillation
Summary
Transfer Functions and Block Diagrams
Background
Transfer Functions
The Step Input Function
Time Constants
Dead Time
The Value of the Transfer Function
Example 1: Time Constant
Example 2: Dead Time
Block Diagrams
Conditions for Continuous Oscillation
The Transfer Function of a Closed Loop
Evaluating the Closed Loop Transfer Function
The Z-N Approximation
Historical
The Z-N Approximation
Estimating the Frequency of Oscillation
Values for the Dead Time and Time Constant
Just How Good Is the Approximation?
Making a Process Reaction Curve
Example 1: Reaction of a Real Process
Units, Best Values, Formulas, and Other Good Stuff
True Value
Errors
Errors in Combinations of Quantities
Correction Factor
Significant Figures
Conversion of Units
Converting Formulas to New Units
Example 1: Reynolds Number
Example 2: Pressure of a Column of Liquid
The Most Representative Value (MRV)
Predicting Future Values
How Much Confidence in the Most Representative Value?
The Standard Deviation
Curve Fitting
Index
Описание: A practical tutorial on the mathematics essential to the process control field, written by an experienced process control engineer for practicing engineers and students.
This essential work includes chapters on frequency response analysis, transfer functions and block diagrams, and the Z-N approximation. A handy desk reference for process control engineers - a helpful aid to students in mathematics courses.
Preface
Table of Contents
Trigonometry and Cyclic Functions
Units of Measurement
Functions of Angles
Definitions
Quadrants
Frequency of Cycling
Sine of the Sum of Two Angles
Cosine of a Sum
Sine of a Difference between Two Angles
Cosine of a Difference
Potentially Useful Relationships
Example 1: Tan (X + Y)
Example 2: sin 2X - sin 2Y
Example 3: Radius of the Earth
Example 4: The Third Side
Example 5: Gain and Phase Lag
Differential Calculus
Concept of Approaching a Limit
Example 1: f(t) = t2
Procedure for Determining a Derivative
Derivative of a Sum or Difference
Derivative of a Product
Derivative of a Quotient
Dimensions and Units
Derivative of a Sine Function
Binomial Theorem
Derivative of a Power
Derivative of an Exponential
A Function within a Function
Example 2: Detecting a Maximum or Minimum
Example 3: Watering the Lawn
Integral Calculus Text
Problem Areas
Practical Uses of Integration
Example 1: Powers and Constants
Example 2: sin3 x
Example 3: cos 2x
Example 4: Substitution of Variables
Example 5: Fractions
Example 6: Using Partial Fractions
Example 7: Numerator Higher Order than Denominator
Example 8: Changing to an Angular Mode
Example 9: sin2 x
Example 10: Square Root of (a2 - x2)
Integration over a Specified Range
Example 11: Tank Filling Case
Example 12: Area of a Circle
Example 13: Surface Area of a Sphere
Example 14: Volume of a Sphere
Example 15: The Escape Velocity
Example 16: Area of a Segment of a Circle
Table of Basic Integrals
Infinite Series
Power Series
The nth Term
Test for Convergence
Example 1: Convergence Test 1
Example 2: Convergence Test 2
Example 3: Convergence Test 3
Example 4: The (n+1)th Term
Maclaurin's Series
Example 5: e?t
Practical Disadvantage of Maclaurin's Series
Taylor's Series
Example 6: Value of a Sine Function Using Taylor's Series
Complex Quantities
Background
Graphical Representation
The Complex Variable
Trigonometric and Exponential Functions
Separating the Real and Imaginary Parts
Differential Equations
Introduction
Philosophy
Definitions
Application
Differential Equations of the First Order and First Degree
Category 1: Exact Differentials
Category 2: Variables Separable
Category 3: Homogeneous Equations
Category 4: Linear Differential Equations
Example 1: Time Constant
Linear Differential Equations with Constant Coefficients
Second Order Linear Differential Equation with Constant Coefficients
The Oscillatory Case
The Constant of Integration
Commentary on the Result
Example 2: The Spring/Mass System
Units
Partial Differential Equations
Laplace Transforms
History
Example 1: Step Change
Transforms of Derivatives
Example 2: Time Constant
Example 3: Pendulum
Example 4: Second Order Linear Differential Equations with Constant Coefficients
The Oscillatory Case
Consistency of Results
Table of Laplace Transforms
Frequency Response Analysis
Background
The Bode Diagram
Frequency Response of a Time Constant Element
Frequency Response of a Dead Time Element
Combinations of Components
Period of Oscillation
Summary
Transfer Functions and Block Diagrams
Background
Transfer Functions
The Step Input Function
Time Constants
Dead Time
The Value of the Transfer Function
Example 1: Time Constant
Example 2: Dead Time
Block Diagrams
Conditions for Continuous Oscillation
The Transfer Function of a Closed Loop
Evaluating the Closed Loop Transfer Function
The Z-N Approximation
Historical
The Z-N Approximation
Estimating the Frequency of Oscillation
Values for the Dead Time and Time Constant
Just How Good Is the Approximation?
Making a Process Reaction Curve
Example 1: Reaction of a Real Process
Units, Best Values, Formulas, and Other Good Stuff
True Value
Errors
Errors in Combinations of Quantities
Correction Factor
Significant Figures
Conversion of Units
Converting Formulas to New Units
Example 1: Reynolds Number
Example 2: Pressure of a Column of Liquid
The Most Representative Value (MRV)
Predicting Future Values
How Much Confidence in the Most Representative Value?
The Standard Deviation
Curve Fitting
Index