Introduction to Signal Processing, Instrumentation, and Control

The following sections are included:

• Dedication
• Preface
• Contents

The following sections are included:

• Introduction
• Process Description-Continuous Casting of Steel
  • Production unit description: mold oscillation system at Nucor Decatur
• Project Approach and Problem Characterization
  • Project approach and workscope
  • Problem characterization
  • Development of highly simplified experimental mockup - hardware testbed
• System Representation
  • Hardware testbed
  • Hardware testbed schematics, negative feedback, and the loop closure under proportional control (P-control)
  • Hardware testbed: instrumentation and data acquisition
  • Validation of hardware testbed: experimental data exhibits resonance problem
• Mathematical System Modeling and Analysis
  • Software testbed
  • Problem investigation: identifying the sources of the distortion
  • Problem definition
• Problem Resolution
  • Solving the problem through controller design
  • Controller implementation and testing on the testbeds and the production unit
• Problem Solving Capability Buildup
  • Stage I – introduction to signals, basic filtering, loading and system integration, sensing and actuation, instrumentation, data acquisition, system identification, and spectral computation
  • Stage II – introduction to spectral analysis and system identification for system modeling, diagnostics, and decision making; basics of analog and digital filter design and implementation
  • Stage III – introduction to controller design and system integration
  • Appendices
  • Homework, project, laboratory, and examination assignments
• Homework 1: Assignment and Solution Guide
• References

The following sections are included:

• Signal Classification and Signal Measures
  • Types of signals
  • Energy-type signal size measures: integrability and summability
• Basic Operations on Signals, Signal Representation
  • Signal representation
  • Basic operations on signals
  • Signal representation
• Delta-function and its Use, Signal Representations, Energy and Power Signals
  • Delta-function
  • Signal energy, power, RMS
• Homework 2: Solved Examples and Solution Guide
• Basic characteristics of a CT sinusoidal signal
  • Period and frequency of sinusoid:
  • Sums of sinusoids
  • Phase of sinusoid
  • Magnitude of sinusoid
• Real Harmonics, Discrete and Continuous Spectra, Frequency Response, Signal Test Instrumentation
  • Fundamental frequency of a sum of sinusoids. Real harmonics
  • Discrete real spectra
  • Continuous spectra and their application to system analysis: continuous frequency response
  • Instrumentation for signal measurement and visualization
• Homework 3: Solved Examples and Solution Guide

The following sections are included:

• Aggregating LTI System Representations for Carrying out Design, Filtering, and Control Tasks
  • Integrative linear time invariant (LTI) system portrait
  • Mechanical systems - a filtering, or input/output viewpoint
  • MS2D system force balance
  • Implicit input/output operator: state-space representation. State-variable filter implementation
  • Impulse response as system representation
  • Explicit input/output operator – convolution integral
  • Pole-zero map: a look inside the dynamic system behavior
  • Frequency response: calculation and use.
  • Bode plots
  • Resonance in the second order systems
  • What each representation is good for
• Review of Parametric System Modeling, Subsystem Commutativity, Firsts Look at System Integration-Subsystem Loading, Output-Dependent System Properties
  • Passive electrical circuits
  • System integration problems
• First Look at Filtering: Basic Instrumentation Techniques-AC versus DC Coupling. Active (Op Amp) Circuits, Loading Mitigation
  • Basic filtering: AC versus DC coupling
  • Op amp based active circuits
  • Other types of signal isolators
  • Voltage dividers and potentiometers
• Basic Motion Sensing: Strain Gauge, Basic Instrumentation Techniques: Bridge Circuit, Instrumentation Amplifier, and Common Mode Rejection Ratio (CMRR)
  • Strain Gauge
  • Ideal instrumentation amplifier
  • Real instrumentation amplifier
• Homework 4: Solved Examples and Solution Guide

The following sections are included:

• Sampling Basics
  • Discrete time sinusoid and digital frequency
• Frequency of DT Sinusoid, Principal Range, Aliasing as Folding, Sampling Theorem
  • Frequency of DT sinusoid
  • Digital frequency folding
• Sampling Basics: Analog-to-Digital (A/D) and Digital-to-Analog (D/A) Conversion. Harmonic Signals: Review of Complex Numbers, Complex Variables, and Complex Functions
  • Signal conversion
  • Harmonic signals
  • Review of complex numbers, variables, and functions
• Homework 5: Solved Examples and Solution Guide
• Complex Harmonic Signals. Discrete Double-Sided Spectrum of CT and DT Periodic Signals. First Look at the Exponential Fourier Series.
  • From real harmonics to complex ones. Discrete double-sided spectrum of periodic signals
  • DT complex harmonic signals
  • Adding harmonics after folding and overlap
• Homework 6: Solved Examples and Solution Guide
• Use of Spectrum for Diagnostics and System Identification. Ideal and Real Signal Reconstruction. The Need for Oversampling.
  • Use of spectrum for diagnostics
  • Signal reconstruction
  • DT spectrum plots
• Homework 7, Part A: Solved Examples and Solution Guide

The following sections are included:

• Projection of Signal, Continuous Time and Discrete Time Harmonic Bases, Continuous Time Fourier Series
  • Continuous time harmonic basis
  • Continuous time Exponential Fourier series
• Discrete Fourier Series, Power of Periodic CT and DT Signals - Parseval's Relationship.
  • Discrete Fourier Series (DFS)
  • Power of periodic signals: Parseval's relationship
• Homework 7, Part B: Solved Examples and Solution Guide
• Analytical CT Fourier Series and Spectra Calculation for Square Wave
  • Square wave Exponential Fourier series representation
  • Plotting square wave spectra: Fourier coefficients as functions of frequency
• Signal Speed and Bandwidth, Gibbs Phenomenon, Windowing, Filtering as Complex Windowing
  • Link between time and frequency domains: signal speed
  • Convergence of Fourier series: building abruptly changing (infinite speed) signals through smooth basis functions
  • Spectral windowing
  • What are we getting through bandwidth, i.e. means for handling almost abruptly changing (very high speed) signals
• Sampling Continuous Signal Spectra: Computation of H(jω) from Fourier Series
• Computing System Frequency Response from Finite Duration Sampled Data Record: Discrete Fourier Transform (DFT)
  • Sampling CF spectra: computation of H(jω) from Fourier series - summary
  • Sampling CF spectra: computation of H(jω) from Fourier series using DT data
  • Discrete Fourier Transform
• DFS and DFT as Diagnostic Tools for Catching Low Magnitude Harmonics. Fast Fourier Transform and its Use
  • Fast Fourier Transform (FFT)
  • Developing DFT-based magnifying glass
• Homework 8: Solved Examples and Solution Guide

The following sections are included:

• Linear Systems: Parametric versus Nonparametric Models, Remaining Objectives and Key Relations, Impulse Response of DT System
  • Parametric system models based on physical laws
  • Working with noisy data and poorly parametrizable systems: key objectives
• Discrete Time Fourier Transform (DTFT), Fourier Transform: Theory and Practice.
  • Key relations: frequency response of DT system and its relation to frequency response of CT system
  • Discrete Time Fourier transform (DTFT) from DFS
  • Key time domain/frequency domain relations for processing test data
• Introduction to Nonparametric System Modeling: Convolution as Both Impulse and Frequency Response Based Filtering of CT and DT Signals
  • Working with field test data: linearity and time-invariance admit standard response-based signal processing techniques for finding nonparametric models
  • Building a noncausal convolution integral
  • CT: impulse response
  • CT and DT system response
• Ideal and Real Filters: Continuous and Discrete Time
  • Continuous time ideal filters
  • Continuous time real filters
  • Discrete time filters
• Project 1: Solved Examples and Solution Guide
• Exam 1: Solved Examples and Solution Guide

Filtering is extraction of useful content from noisy measurements. In its simplest form, considered in the present book, is attenuates the signals outside of the frequency range of interest, as exemplified by the antialiasing filter. In its more complicated form, necessary for functioning of many modern systems and represented, for example, by Kalman filtering, it estimates system state on the basis of the system model and statistical noise properties…

The following sections are included:

• Working with Real Signals: Introduction to Discrete-Continuous (Mixed) Spectral analysis. Correlation and Spectral Density for Energy Signals
  • Motivation: a) capturing and tracking periodic signals hidden in noise, b) system model building using random signals
  • Real signals
  • Correlation for energy signals: CT
• Correlation and Spectral Density for Power Signals
  • From energy to power
  • Power spectral density
  • Calculating the PSD using pre-limit approximation
  • Calculating PSD using periodic extension
• Correlation and Spectral Density of Ideal Mixed Signals.
  • Building a power spectral density graph
  • PSD of a mixed ideal signal
• Discrete-Continuous (Mixed) Spectral Analysis of a Sampled Signal. Spectral Analysis Applications: Diagnostics, System Identification
  • Spectral analysis of sampled data
  • Detecting CT sinusoids in noise
• Applications of PSD and FFT
  • Diagnostics
  • FFT-based detection of hidden CT sinusoids – DFT ⇒ DFS ⇒ FS : summary
  • System identification using PSD: from signal processing to control
  • Filtering action of physical system
• Project 2: Solved Examples and Solution Guide
• Exam 2: Solved Examples and Solution Guide

The following sections are included:

• Control Objectives, System Layout, Open-Loop and Closed-Loop Systems, Block Diagrams, System Performance Assessment: Tracking, Disturbance Rejection, Robustness, Position and Velocity Servomechanisms
  • Control system examples
  • Plant, and closed-loop and open-loop control systems layouts and objectives
  • Block diagrams
• Closed-Loop System Topology, Negative and Positive Feedback. Block Diagram Reduction. Closed-Loop Tracking. Disturbance Rejection, Robustness, Response Shaping (Stabilization), and Output Error
  • General closed-loop system
  • Closed-loop transfer function: unity feedback (perfect sensing)
• Basic Control Action
  • Basic control actions
  • Second-order systems
• Homework 10: Solved Examples and Solution Guide
• Basic Controller Design: Shaping the Second Order System Step Response with P and PD Controllers. Steady State Error for Unit Step and Unit Ramp Inputs. Closed-Loop Stability and Closed-Loop Poles
  • Closed-loop position and velocity servos with P-controller under unity feedback
  • Response shaping using PD controller
• Basic Controller Design: Disturbance Rejection Using Internal Model Principle, Measurement Noise Rejection through Loop Frequency Response Shaping
  • Controller gain over the entire frequency range
  • Closed-loop transfer function for infinite controller gain at zero frequency: I-controller
  • Internal Model Principle (IMP) controller
  • Measurement noise rejection. 2DOF controller topology. RST structure
• Mold Oscillator Problem Solution through Feedback Testbed. PID Gain Tuning, Integrator Anti-Windup
  • Mold oscillator problem
  • Solution of the mold velocity distortion problem
  • PID gain tuning
  • Anti-windup
• Project 3: Solved Examples and Solution Guide
• Exam 3: Solved Examples and Solution Guide

The following sections are included:

• Appendix A: Useful Mathematical Formulas
• Appendix B: System Classification
• Appendix C: Fourier Series
• Appendix D: Fourier Transform
• Appendix E: Laplace Transform
• Appendix F: Basic Types of Sensors and Actuators
• Appendix G: Euler-Bernoulli and Timoshenko Beam Models and Their Use in Software Testbed Development
• Appendix H: Software Testbed Matlab Programs

The following sections are included:

• Bibliography
• Index