8/19/2019 SIOSFDEG http://slidepdf.com/reader/full/siosfdeg 1/10 Schaums Interactive Outline Series: Feedback and Control Systems Through more than l00 solved problems in control system design and analysis, several major echniques of analysis and design are developed and demonstrated. For students and ducators, this Electronic Book is an excellent tool for exploring and understanding the undamentals of feedback control systems. Professionals get advanced numerical and ymbolic techniques for plotting system behavior and solving for stability and design pecifications. The early chapters develop the theoretical foundations while later sections apply this understanding to designing feedback control systems. Plus the Mathcad Engine s built-in so the math is "live" and interactive. Platform: Windows ncludes the Mathcad Engine; requires 4 MB hard disk space Available for ground shipment Topics include: Differential Equations, Difference Equations and Linear Systems, Stability and Routh- Hurwitz Criteria, Transfer Functions and Characteristics Equations, Block Diagram Algebra Signal Flow Graphs, Nyquist, Bode and Nichols Analysis and Design, and much more. Experiment with graphing techniques for root-locus plots.
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8192019 SIOSFDEG
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Schaums Interactive Outline Series
Feedback and Control Systems
Through more than l00 solved problems in control system design and analysis several majorechniques of analysis and design are developed and demonstrated For students andducators this Electronic Book is an excellent tool for exploring and understanding theundamentals of feedback control systems Professionals get advanced numerical andymbolic techniques for plotting system behavior and solving for stability and designpecifications The early chapters develop the theoretical foundations while later sections
apply this understanding to designing feedback control systems Plus the Mathcad Engines built-in so the math is live and interactive
Platform Windowsncludes the Mathcad Engine requires 4 MB hard disk space
Available for ground shipment
Topics include Differential Equations Difference Equations and Linear Systems Stability and Routh-Hurwitz Criteria Transfer Functions and Characteristics Equations Block Diagram Algebra SignalFlow Graphs Nyquist Bode and Nichols Analysis and Design and much more
Experiment with graphing techniques for root-locus
plots
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Schaums Interactive Outline Series
Feedback and Control Systems
Chapter 1 - Introduction
Understanding Feedback Control Systems (Schaums Solved Problem 111) Understanding Feedback Control Terminology (Schaums Solved Problems 11 17
and 18)
Chapter 2 - Control System Terminology
Block Diagrams and Feedback-Control System Terminology I (Schaums Solved
Problem 22) Block Diagrams and Feedback-Control System Terminology II (Schaums Solved
Problem 27)
Chapter 3 - Differential Equations and their Solutions
The Characteristic Equation (Schaums Solved Problems 312 - 313) Free Response Distinct Roots (Schaums Solved Problem 316b and 320) Free Response Repeated Roots (Schaums Solved Problem 316a) Fundamental Sets (Schaums Solved Problem 317)
Forced Response the Weighting Function (Schaums Solved Problems 321 - 322)Chapter 4 - The Laplace Transform and the z-Transform
Solving a Differential Equation by the Laplace Transform Method I (SchaumsExample 417 and Solved Problem 427)
Inverse Laplace Transform by Partial Fractions (Schaums Example 424) Solving a Difference Equation by the z-Transform Method (Schaums Example 441) Solving a Differential Equation by the Laplace Transform Method II(Schaums
Solved Problems 420-423) Pole-Zero Maps (Schaums Solved Problems 432 - 433) Second-Order Systems (Schaums Solved Problem 435) Approximation by a Second-Order System (Schaums Solved Problem 436)
TABLE OF CONTENTS (page 1 of 6)
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Chapter 5 - Stability
Impulse Responses (Schaums Solved Problem 51) The w-Transform (Schaums Example 58) Stability of Discrete-Time Systems (Schaums Solved Problem 522) Approximate vs Exact Solutions for Roots (Schaums Solved Problem 523) Stability of Continuous Systems (Schaums Solved Problem 530a)
Chapter 6 - Transfer Functions
Continuous System Frequency Response Plots (Schaums Examples 68 - 69) Lag Compensators (Schaums Solved Problem 613 and 616) Lag-Lead Compensators (Schaums Solved Problem 614) Unit Step Response Given Poles and Zeros (Schaums Solved Problems 611
and 619) DC Gain (Schaums Solved Problem 621) Frequency-Dependent Gain and Phase (Schaums Solved Problems 622 - 623) Discrete-Time System Frequency Response (Schaums Solved Problem 627)
Chapter 7 - Block Diagrams and Transfer Functions
Unity Feedback System (Schaums Solved Problem 715) Superposition of Multiple Input Systems (Schaums Solved Problem 716) Reduction of Complicated Block Diagrams (Schaums Solved Problems 719)
Chapter 8 - Signal Flow Graphs
The General Input-Output Gain Formula (Schaums Solved Problems 88 and 811) Transfer Function Computation of Cascaded Components and Block Diagram
Reduction Using Signal Flow Graphs (Schaums Solved Problem 814)
Chapter 9 - Sensitivity of Feedback Systems
The Sensitivity of the Transfer Function (Schaums Examples 92 and 94) Comparing Sensitivity of Transfer Functions (Schaums Solved
Problem 93) Open-Loop vs Closed-Loop Systems (Schaums Example 96) Sensitivity with Respect to |G| (Schaums Examples 97 - 98)
TABLE OF CONTENTS (page 2 of 6)
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Feedback and Control Systems
Chapter 10 - Analysis and Design of Feedback Control Systems
Gain and Phase Margin (Schaums Solved Problems 102 - 103) Average Delay Time (Schaums Solved Problem 104) Bandwidth of a Lowpass System (Schaums Solved Problem 105) Bandwidth of a Resonant System (Schaums Solved Problem 1015) Octaves (Schaums Solved Problem 106) Resonant Frequency (Schaums Solved Problem 107)
Delay Time and Rise Time (Schaums Solved Problems 108 - 109) Rise Time for a Discrete-Time System (Schaums Solved Problem 1010) Frequency vs Time-Domain Specifications (Schaums Examples 102 - 103) A Deadbeat System (Schaums Example 107)
Chapter 11 - Nyquist Analysis
Nyquist Stability for a Discrete-Time System (Schaums Examples 1111 and 1114) Nyquist Stability for a Continuous System (Schaums Solved Problems 1143
and 1155) Relative Stability (Schaums Solved Problem 1159) Nyquist Stability for a Discrete-Time System II (Schaums Solved Problem 1167) Nyquist Analysis of Time-Delayed Systems (Schaums Supplementary Problem
1180)
Chapter 12 - Nyquist Design
Gain Factor Compensation (Schaums Solved Problems 121 - 123) Continuous System Lead Compensation (Schaums Example 124) Digital Lag Compensator (Schaums Solved Problem 1212) Digital Compensation Networks (Schaums Example 127 and Solved Problem 1216)
Continuous System Lag Compensation (Schaums Example 125) General Compensation Issues (Schaums Solved Problem 1210)
TABLE OF CONTENTS (page 3 of 6)
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Chapter 13 - Root-Locus Analysis
Angle and Magnitude Criteria (Schaums Example 131 and Solved Problem 134) Gain Margin from the Root-Locus Plot (Schaums Example 138 and Solved
Problem 1335) Departure Angles (Schaums Solved Problems 1324 and 1326) Root-Locus with Poles and Zeros (Schaums Example 139) Root-Locus for a Discrete System (Schaums Solved Problem 1331)
Root-Locus for Positive and Negative Gain (Schaums Solved Problem 1328)
Chapter 14 - Root-Locus Design
Gain Factor Compensation (Schaums Solved Problem 141) Dominant Pole-Zero Approximation (Schaums Solved Problem 1412) Feedback Compensation (Schaums Solved Problem 1417) Point Design (Schaums Solved Problem 1414) Feedback Compensation and Point Design (Schaums Solved Problem 1416) Digital Compensation (Schaums Example Problem 145) Lead Compensation on the Root-Locus (Schaums Example Problem 142) Lag Compensation on the Root-Locus (Schaums Example Problem 143)
Chapter 15 - Bode Analysis
The Bode Form and the Bode Gain (Schaums Solved Problem 152) Constructing Bode Plots (Schaums Solved Problems 157 and 1510) Relative Stability (Schaums Solved Problems 158 and 1511) Discrete-Time Frequency Response (Schaums Solved Problem 1513) Second Order System Peak Frequency Response (Schaums Solved Problem 155
and Section 154)
Chapter 16 - Bode Design
Gain Factor Compensation (Schaums Solved Problem 162) Lead and Lag Parameters (Schaums Sections 163 and 164) Lead and Gain Compensation (Schaums Solved Problem 165) Lag and Gain Compensation (Schaums Solved Problem 168) Lag-Lead Compensation (Schaums Solved Problem 1610) Digital System Compensation (Schaums Example 166)
TABLE OF CONTENTS (page 4 of 6)
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Chapter 17 - Nichols Chart Analysis
Magnitude-Phase Plots and Relative Stability - Type 1 System (SchaumsSolved Problems 172 and 176)
Magnitude-Phase Plots and Relative Stability - Type 2 System (SchaumsSolved Problems 174 and 177)
Discrete-Time Gain Phase Plots (Schaums Solved Problems 175 and 179) Closed-Loop Frequency Response Functions (Schaums Solved Problem 1714) Nichols Charts (Schaums Solved Problem 1715)
Chapter 18 - Nichols Chart Design
Gain Factor Compensation (Schaums Solved Problem 181) Closed-Loop Gain Factor Compensation (Schaums Solved Problem 184) Lead and Lag Compensator Magnitude-Phase Plots (Schaums Sections 184
and 185) Lead and Gain Network Compensation (Schaums Solved Problem 187) Lag and Gain Network Compensation (Schaums Example Problem 184)
Chapter 19 - Introduction to Nonlinear Control Systems
Taylor Series Expansion (Schaums Solved Problem 194) Phase Plane Methods (Schaums Solved Problem 199) Frequency Response Methods (Schaums Solved Problem 1919)
Chapter 20 - Introduction to Advanced Topics in Control SystemAnalysis and Design
Appendix A - Some Laplace Transform Pairs and Properties Useful forControl Systems Analysis
Appendix B - Some z-Transform Pairs and Properties Useful for ControlSystems Analysis
TABLE OF CONTENTS (page 5 of 6)
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Appendix C - Block Diagram Transformation Theorems
Appendix D - Solving Polynomials Using the Companion Matrix
References and Bibliography
Index
TABLE OF CONTENTS (page 6 of 6)
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Feedback and Control Systems
Constructing Bode Plots
Statement
Construct the Bode plot for the frequency response function given below Also determinethe gain and phase margins for the system
System Parameters
Solution
To create the Bode plot for this function plot the magnitude in decibels and the phaseusing the phase function shown in Chapter 15
SAMPLE PAGE (page 1 of 3)
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SAMPLE PAGE (page 2 of 3)
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Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)
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Feedback and Control Systems
Chapter 1 - Introduction
Understanding Feedback Control Systems (Schaums Solved Problem 111) Understanding Feedback Control Terminology (Schaums Solved Problems 11 17
and 18)
Chapter 2 - Control System Terminology
Block Diagrams and Feedback-Control System Terminology I (Schaums Solved
Problem 22) Block Diagrams and Feedback-Control System Terminology II (Schaums Solved
Problem 27)
Chapter 3 - Differential Equations and their Solutions
The Characteristic Equation (Schaums Solved Problems 312 - 313) Free Response Distinct Roots (Schaums Solved Problem 316b and 320) Free Response Repeated Roots (Schaums Solved Problem 316a) Fundamental Sets (Schaums Solved Problem 317)
Forced Response the Weighting Function (Schaums Solved Problems 321 - 322)Chapter 4 - The Laplace Transform and the z-Transform
Solving a Differential Equation by the Laplace Transform Method I (SchaumsExample 417 and Solved Problem 427)
Inverse Laplace Transform by Partial Fractions (Schaums Example 424) Solving a Difference Equation by the z-Transform Method (Schaums Example 441) Solving a Differential Equation by the Laplace Transform Method II(Schaums
Solved Problems 420-423) Pole-Zero Maps (Schaums Solved Problems 432 - 433) Second-Order Systems (Schaums Solved Problem 435) Approximation by a Second-Order System (Schaums Solved Problem 436)
TABLE OF CONTENTS (page 1 of 6)
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Chapter 5 - Stability
Impulse Responses (Schaums Solved Problem 51) The w-Transform (Schaums Example 58) Stability of Discrete-Time Systems (Schaums Solved Problem 522) Approximate vs Exact Solutions for Roots (Schaums Solved Problem 523) Stability of Continuous Systems (Schaums Solved Problem 530a)
Chapter 6 - Transfer Functions
Continuous System Frequency Response Plots (Schaums Examples 68 - 69) Lag Compensators (Schaums Solved Problem 613 and 616) Lag-Lead Compensators (Schaums Solved Problem 614) Unit Step Response Given Poles and Zeros (Schaums Solved Problems 611
and 619) DC Gain (Schaums Solved Problem 621) Frequency-Dependent Gain and Phase (Schaums Solved Problems 622 - 623) Discrete-Time System Frequency Response (Schaums Solved Problem 627)
Chapter 7 - Block Diagrams and Transfer Functions
Unity Feedback System (Schaums Solved Problem 715) Superposition of Multiple Input Systems (Schaums Solved Problem 716) Reduction of Complicated Block Diagrams (Schaums Solved Problems 719)
Chapter 8 - Signal Flow Graphs
The General Input-Output Gain Formula (Schaums Solved Problems 88 and 811) Transfer Function Computation of Cascaded Components and Block Diagram
Reduction Using Signal Flow Graphs (Schaums Solved Problem 814)
Chapter 9 - Sensitivity of Feedback Systems
The Sensitivity of the Transfer Function (Schaums Examples 92 and 94) Comparing Sensitivity of Transfer Functions (Schaums Solved
Problem 93) Open-Loop vs Closed-Loop Systems (Schaums Example 96) Sensitivity with Respect to |G| (Schaums Examples 97 - 98)
TABLE OF CONTENTS (page 2 of 6)
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Feedback and Control Systems
Chapter 10 - Analysis and Design of Feedback Control Systems
Gain and Phase Margin (Schaums Solved Problems 102 - 103) Average Delay Time (Schaums Solved Problem 104) Bandwidth of a Lowpass System (Schaums Solved Problem 105) Bandwidth of a Resonant System (Schaums Solved Problem 1015) Octaves (Schaums Solved Problem 106) Resonant Frequency (Schaums Solved Problem 107)
Delay Time and Rise Time (Schaums Solved Problems 108 - 109) Rise Time for a Discrete-Time System (Schaums Solved Problem 1010) Frequency vs Time-Domain Specifications (Schaums Examples 102 - 103) A Deadbeat System (Schaums Example 107)
Chapter 11 - Nyquist Analysis
Nyquist Stability for a Discrete-Time System (Schaums Examples 1111 and 1114) Nyquist Stability for a Continuous System (Schaums Solved Problems 1143
and 1155) Relative Stability (Schaums Solved Problem 1159) Nyquist Stability for a Discrete-Time System II (Schaums Solved Problem 1167) Nyquist Analysis of Time-Delayed Systems (Schaums Supplementary Problem
1180)
Chapter 12 - Nyquist Design
Gain Factor Compensation (Schaums Solved Problems 121 - 123) Continuous System Lead Compensation (Schaums Example 124) Digital Lag Compensator (Schaums Solved Problem 1212) Digital Compensation Networks (Schaums Example 127 and Solved Problem 1216)
Continuous System Lag Compensation (Schaums Example 125) General Compensation Issues (Schaums Solved Problem 1210)
TABLE OF CONTENTS (page 3 of 6)
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Chapter 13 - Root-Locus Analysis
Angle and Magnitude Criteria (Schaums Example 131 and Solved Problem 134) Gain Margin from the Root-Locus Plot (Schaums Example 138 and Solved
Problem 1335) Departure Angles (Schaums Solved Problems 1324 and 1326) Root-Locus with Poles and Zeros (Schaums Example 139) Root-Locus for a Discrete System (Schaums Solved Problem 1331)
Root-Locus for Positive and Negative Gain (Schaums Solved Problem 1328)
Chapter 14 - Root-Locus Design
Gain Factor Compensation (Schaums Solved Problem 141) Dominant Pole-Zero Approximation (Schaums Solved Problem 1412) Feedback Compensation (Schaums Solved Problem 1417) Point Design (Schaums Solved Problem 1414) Feedback Compensation and Point Design (Schaums Solved Problem 1416) Digital Compensation (Schaums Example Problem 145) Lead Compensation on the Root-Locus (Schaums Example Problem 142) Lag Compensation on the Root-Locus (Schaums Example Problem 143)
Chapter 15 - Bode Analysis
The Bode Form and the Bode Gain (Schaums Solved Problem 152) Constructing Bode Plots (Schaums Solved Problems 157 and 1510) Relative Stability (Schaums Solved Problems 158 and 1511) Discrete-Time Frequency Response (Schaums Solved Problem 1513) Second Order System Peak Frequency Response (Schaums Solved Problem 155
and Section 154)
Chapter 16 - Bode Design
Gain Factor Compensation (Schaums Solved Problem 162) Lead and Lag Parameters (Schaums Sections 163 and 164) Lead and Gain Compensation (Schaums Solved Problem 165) Lag and Gain Compensation (Schaums Solved Problem 168) Lag-Lead Compensation (Schaums Solved Problem 1610) Digital System Compensation (Schaums Example 166)
TABLE OF CONTENTS (page 4 of 6)
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Chapter 17 - Nichols Chart Analysis
Magnitude-Phase Plots and Relative Stability - Type 1 System (SchaumsSolved Problems 172 and 176)
Magnitude-Phase Plots and Relative Stability - Type 2 System (SchaumsSolved Problems 174 and 177)
Discrete-Time Gain Phase Plots (Schaums Solved Problems 175 and 179) Closed-Loop Frequency Response Functions (Schaums Solved Problem 1714) Nichols Charts (Schaums Solved Problem 1715)
Chapter 18 - Nichols Chart Design
Gain Factor Compensation (Schaums Solved Problem 181) Closed-Loop Gain Factor Compensation (Schaums Solved Problem 184) Lead and Lag Compensator Magnitude-Phase Plots (Schaums Sections 184
and 185) Lead and Gain Network Compensation (Schaums Solved Problem 187) Lag and Gain Network Compensation (Schaums Example Problem 184)
Chapter 19 - Introduction to Nonlinear Control Systems
Taylor Series Expansion (Schaums Solved Problem 194) Phase Plane Methods (Schaums Solved Problem 199) Frequency Response Methods (Schaums Solved Problem 1919)
Chapter 20 - Introduction to Advanced Topics in Control SystemAnalysis and Design
Appendix A - Some Laplace Transform Pairs and Properties Useful forControl Systems Analysis
Appendix B - Some z-Transform Pairs and Properties Useful for ControlSystems Analysis
TABLE OF CONTENTS (page 5 of 6)
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Appendix C - Block Diagram Transformation Theorems
Appendix D - Solving Polynomials Using the Companion Matrix
References and Bibliography
Index
TABLE OF CONTENTS (page 6 of 6)
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Feedback and Control Systems
Constructing Bode Plots
Statement
Construct the Bode plot for the frequency response function given below Also determinethe gain and phase margins for the system
System Parameters
Solution
To create the Bode plot for this function plot the magnitude in decibels and the phaseusing the phase function shown in Chapter 15
SAMPLE PAGE (page 1 of 3)
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Feedback and Control Systems
SAMPLE PAGE (page 2 of 3)
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Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)
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Feedback and Control Systems
Chapter 5 - Stability
Impulse Responses (Schaums Solved Problem 51) The w-Transform (Schaums Example 58) Stability of Discrete-Time Systems (Schaums Solved Problem 522) Approximate vs Exact Solutions for Roots (Schaums Solved Problem 523) Stability of Continuous Systems (Schaums Solved Problem 530a)
Chapter 6 - Transfer Functions
Continuous System Frequency Response Plots (Schaums Examples 68 - 69) Lag Compensators (Schaums Solved Problem 613 and 616) Lag-Lead Compensators (Schaums Solved Problem 614) Unit Step Response Given Poles and Zeros (Schaums Solved Problems 611
and 619) DC Gain (Schaums Solved Problem 621) Frequency-Dependent Gain and Phase (Schaums Solved Problems 622 - 623) Discrete-Time System Frequency Response (Schaums Solved Problem 627)
Chapter 7 - Block Diagrams and Transfer Functions
Unity Feedback System (Schaums Solved Problem 715) Superposition of Multiple Input Systems (Schaums Solved Problem 716) Reduction of Complicated Block Diagrams (Schaums Solved Problems 719)
Chapter 8 - Signal Flow Graphs
The General Input-Output Gain Formula (Schaums Solved Problems 88 and 811) Transfer Function Computation of Cascaded Components and Block Diagram
Reduction Using Signal Flow Graphs (Schaums Solved Problem 814)
Chapter 9 - Sensitivity of Feedback Systems
The Sensitivity of the Transfer Function (Schaums Examples 92 and 94) Comparing Sensitivity of Transfer Functions (Schaums Solved
Problem 93) Open-Loop vs Closed-Loop Systems (Schaums Example 96) Sensitivity with Respect to |G| (Schaums Examples 97 - 98)
TABLE OF CONTENTS (page 2 of 6)
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Schaums Interactive Outline Series
Feedback and Control Systems
Chapter 10 - Analysis and Design of Feedback Control Systems
Gain and Phase Margin (Schaums Solved Problems 102 - 103) Average Delay Time (Schaums Solved Problem 104) Bandwidth of a Lowpass System (Schaums Solved Problem 105) Bandwidth of a Resonant System (Schaums Solved Problem 1015) Octaves (Schaums Solved Problem 106) Resonant Frequency (Schaums Solved Problem 107)
Delay Time and Rise Time (Schaums Solved Problems 108 - 109) Rise Time for a Discrete-Time System (Schaums Solved Problem 1010) Frequency vs Time-Domain Specifications (Schaums Examples 102 - 103) A Deadbeat System (Schaums Example 107)
Chapter 11 - Nyquist Analysis
Nyquist Stability for a Discrete-Time System (Schaums Examples 1111 and 1114) Nyquist Stability for a Continuous System (Schaums Solved Problems 1143
and 1155) Relative Stability (Schaums Solved Problem 1159) Nyquist Stability for a Discrete-Time System II (Schaums Solved Problem 1167) Nyquist Analysis of Time-Delayed Systems (Schaums Supplementary Problem
1180)
Chapter 12 - Nyquist Design
Gain Factor Compensation (Schaums Solved Problems 121 - 123) Continuous System Lead Compensation (Schaums Example 124) Digital Lag Compensator (Schaums Solved Problem 1212) Digital Compensation Networks (Schaums Example 127 and Solved Problem 1216)
Continuous System Lag Compensation (Schaums Example 125) General Compensation Issues (Schaums Solved Problem 1210)
TABLE OF CONTENTS (page 3 of 6)
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Feedback and Control Systems
Chapter 13 - Root-Locus Analysis
Angle and Magnitude Criteria (Schaums Example 131 and Solved Problem 134) Gain Margin from the Root-Locus Plot (Schaums Example 138 and Solved
Problem 1335) Departure Angles (Schaums Solved Problems 1324 and 1326) Root-Locus with Poles and Zeros (Schaums Example 139) Root-Locus for a Discrete System (Schaums Solved Problem 1331)
Root-Locus for Positive and Negative Gain (Schaums Solved Problem 1328)
Chapter 14 - Root-Locus Design
Gain Factor Compensation (Schaums Solved Problem 141) Dominant Pole-Zero Approximation (Schaums Solved Problem 1412) Feedback Compensation (Schaums Solved Problem 1417) Point Design (Schaums Solved Problem 1414) Feedback Compensation and Point Design (Schaums Solved Problem 1416) Digital Compensation (Schaums Example Problem 145) Lead Compensation on the Root-Locus (Schaums Example Problem 142) Lag Compensation on the Root-Locus (Schaums Example Problem 143)
Chapter 15 - Bode Analysis
The Bode Form and the Bode Gain (Schaums Solved Problem 152) Constructing Bode Plots (Schaums Solved Problems 157 and 1510) Relative Stability (Schaums Solved Problems 158 and 1511) Discrete-Time Frequency Response (Schaums Solved Problem 1513) Second Order System Peak Frequency Response (Schaums Solved Problem 155
and Section 154)
Chapter 16 - Bode Design
Gain Factor Compensation (Schaums Solved Problem 162) Lead and Lag Parameters (Schaums Sections 163 and 164) Lead and Gain Compensation (Schaums Solved Problem 165) Lag and Gain Compensation (Schaums Solved Problem 168) Lag-Lead Compensation (Schaums Solved Problem 1610) Digital System Compensation (Schaums Example 166)
TABLE OF CONTENTS (page 4 of 6)
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Feedback and Control Systems
Chapter 17 - Nichols Chart Analysis
Magnitude-Phase Plots and Relative Stability - Type 1 System (SchaumsSolved Problems 172 and 176)
Magnitude-Phase Plots and Relative Stability - Type 2 System (SchaumsSolved Problems 174 and 177)
Discrete-Time Gain Phase Plots (Schaums Solved Problems 175 and 179) Closed-Loop Frequency Response Functions (Schaums Solved Problem 1714) Nichols Charts (Schaums Solved Problem 1715)
Chapter 18 - Nichols Chart Design
Gain Factor Compensation (Schaums Solved Problem 181) Closed-Loop Gain Factor Compensation (Schaums Solved Problem 184) Lead and Lag Compensator Magnitude-Phase Plots (Schaums Sections 184
and 185) Lead and Gain Network Compensation (Schaums Solved Problem 187) Lag and Gain Network Compensation (Schaums Example Problem 184)
Chapter 19 - Introduction to Nonlinear Control Systems
Taylor Series Expansion (Schaums Solved Problem 194) Phase Plane Methods (Schaums Solved Problem 199) Frequency Response Methods (Schaums Solved Problem 1919)
Chapter 20 - Introduction to Advanced Topics in Control SystemAnalysis and Design
Appendix A - Some Laplace Transform Pairs and Properties Useful forControl Systems Analysis
Appendix B - Some z-Transform Pairs and Properties Useful for ControlSystems Analysis
TABLE OF CONTENTS (page 5 of 6)
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Feedback and Control Systems
Appendix C - Block Diagram Transformation Theorems
Appendix D - Solving Polynomials Using the Companion Matrix
References and Bibliography
Index
TABLE OF CONTENTS (page 6 of 6)
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Schaums Interactive Outline Series
Feedback and Control Systems
Constructing Bode Plots
Statement
Construct the Bode plot for the frequency response function given below Also determinethe gain and phase margins for the system
System Parameters
Solution
To create the Bode plot for this function plot the magnitude in decibels and the phaseusing the phase function shown in Chapter 15
SAMPLE PAGE (page 1 of 3)
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Feedback and Control Systems
SAMPLE PAGE (page 2 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Chapter 10 - Analysis and Design of Feedback Control Systems
Gain and Phase Margin (Schaums Solved Problems 102 - 103) Average Delay Time (Schaums Solved Problem 104) Bandwidth of a Lowpass System (Schaums Solved Problem 105) Bandwidth of a Resonant System (Schaums Solved Problem 1015) Octaves (Schaums Solved Problem 106) Resonant Frequency (Schaums Solved Problem 107)
Delay Time and Rise Time (Schaums Solved Problems 108 - 109) Rise Time for a Discrete-Time System (Schaums Solved Problem 1010) Frequency vs Time-Domain Specifications (Schaums Examples 102 - 103) A Deadbeat System (Schaums Example 107)
Chapter 11 - Nyquist Analysis
Nyquist Stability for a Discrete-Time System (Schaums Examples 1111 and 1114) Nyquist Stability for a Continuous System (Schaums Solved Problems 1143
and 1155) Relative Stability (Schaums Solved Problem 1159) Nyquist Stability for a Discrete-Time System II (Schaums Solved Problem 1167) Nyquist Analysis of Time-Delayed Systems (Schaums Supplementary Problem
1180)
Chapter 12 - Nyquist Design
Gain Factor Compensation (Schaums Solved Problems 121 - 123) Continuous System Lead Compensation (Schaums Example 124) Digital Lag Compensator (Schaums Solved Problem 1212) Digital Compensation Networks (Schaums Example 127 and Solved Problem 1216)
Continuous System Lag Compensation (Schaums Example 125) General Compensation Issues (Schaums Solved Problem 1210)
TABLE OF CONTENTS (page 3 of 6)
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Feedback and Control Systems
Chapter 13 - Root-Locus Analysis
Angle and Magnitude Criteria (Schaums Example 131 and Solved Problem 134) Gain Margin from the Root-Locus Plot (Schaums Example 138 and Solved
Problem 1335) Departure Angles (Schaums Solved Problems 1324 and 1326) Root-Locus with Poles and Zeros (Schaums Example 139) Root-Locus for a Discrete System (Schaums Solved Problem 1331)
Root-Locus for Positive and Negative Gain (Schaums Solved Problem 1328)
Chapter 14 - Root-Locus Design
Gain Factor Compensation (Schaums Solved Problem 141) Dominant Pole-Zero Approximation (Schaums Solved Problem 1412) Feedback Compensation (Schaums Solved Problem 1417) Point Design (Schaums Solved Problem 1414) Feedback Compensation and Point Design (Schaums Solved Problem 1416) Digital Compensation (Schaums Example Problem 145) Lead Compensation on the Root-Locus (Schaums Example Problem 142) Lag Compensation on the Root-Locus (Schaums Example Problem 143)
Chapter 15 - Bode Analysis
The Bode Form and the Bode Gain (Schaums Solved Problem 152) Constructing Bode Plots (Schaums Solved Problems 157 and 1510) Relative Stability (Schaums Solved Problems 158 and 1511) Discrete-Time Frequency Response (Schaums Solved Problem 1513) Second Order System Peak Frequency Response (Schaums Solved Problem 155
and Section 154)
Chapter 16 - Bode Design
Gain Factor Compensation (Schaums Solved Problem 162) Lead and Lag Parameters (Schaums Sections 163 and 164) Lead and Gain Compensation (Schaums Solved Problem 165) Lag and Gain Compensation (Schaums Solved Problem 168) Lag-Lead Compensation (Schaums Solved Problem 1610) Digital System Compensation (Schaums Example 166)
TABLE OF CONTENTS (page 4 of 6)
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Feedback and Control Systems
Chapter 17 - Nichols Chart Analysis
Magnitude-Phase Plots and Relative Stability - Type 1 System (SchaumsSolved Problems 172 and 176)
Magnitude-Phase Plots and Relative Stability - Type 2 System (SchaumsSolved Problems 174 and 177)
Discrete-Time Gain Phase Plots (Schaums Solved Problems 175 and 179) Closed-Loop Frequency Response Functions (Schaums Solved Problem 1714) Nichols Charts (Schaums Solved Problem 1715)
Chapter 18 - Nichols Chart Design
Gain Factor Compensation (Schaums Solved Problem 181) Closed-Loop Gain Factor Compensation (Schaums Solved Problem 184) Lead and Lag Compensator Magnitude-Phase Plots (Schaums Sections 184
and 185) Lead and Gain Network Compensation (Schaums Solved Problem 187) Lag and Gain Network Compensation (Schaums Example Problem 184)
Chapter 19 - Introduction to Nonlinear Control Systems
Taylor Series Expansion (Schaums Solved Problem 194) Phase Plane Methods (Schaums Solved Problem 199) Frequency Response Methods (Schaums Solved Problem 1919)
Chapter 20 - Introduction to Advanced Topics in Control SystemAnalysis and Design
Appendix A - Some Laplace Transform Pairs and Properties Useful forControl Systems Analysis
Appendix B - Some z-Transform Pairs and Properties Useful for ControlSystems Analysis
TABLE OF CONTENTS (page 5 of 6)
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Schaums Interactive Outline Series
Feedback and Control Systems
Appendix C - Block Diagram Transformation Theorems
Appendix D - Solving Polynomials Using the Companion Matrix
References and Bibliography
Index
TABLE OF CONTENTS (page 6 of 6)
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Schaums Interactive Outline Series
Feedback and Control Systems
Constructing Bode Plots
Statement
Construct the Bode plot for the frequency response function given below Also determinethe gain and phase margins for the system
System Parameters
Solution
To create the Bode plot for this function plot the magnitude in decibels and the phaseusing the phase function shown in Chapter 15
SAMPLE PAGE (page 1 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
SAMPLE PAGE (page 2 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Chapter 13 - Root-Locus Analysis
Angle and Magnitude Criteria (Schaums Example 131 and Solved Problem 134) Gain Margin from the Root-Locus Plot (Schaums Example 138 and Solved
Problem 1335) Departure Angles (Schaums Solved Problems 1324 and 1326) Root-Locus with Poles and Zeros (Schaums Example 139) Root-Locus for a Discrete System (Schaums Solved Problem 1331)
Root-Locus for Positive and Negative Gain (Schaums Solved Problem 1328)
Chapter 14 - Root-Locus Design
Gain Factor Compensation (Schaums Solved Problem 141) Dominant Pole-Zero Approximation (Schaums Solved Problem 1412) Feedback Compensation (Schaums Solved Problem 1417) Point Design (Schaums Solved Problem 1414) Feedback Compensation and Point Design (Schaums Solved Problem 1416) Digital Compensation (Schaums Example Problem 145) Lead Compensation on the Root-Locus (Schaums Example Problem 142) Lag Compensation on the Root-Locus (Schaums Example Problem 143)
Chapter 15 - Bode Analysis
The Bode Form and the Bode Gain (Schaums Solved Problem 152) Constructing Bode Plots (Schaums Solved Problems 157 and 1510) Relative Stability (Schaums Solved Problems 158 and 1511) Discrete-Time Frequency Response (Schaums Solved Problem 1513) Second Order System Peak Frequency Response (Schaums Solved Problem 155
and Section 154)
Chapter 16 - Bode Design
Gain Factor Compensation (Schaums Solved Problem 162) Lead and Lag Parameters (Schaums Sections 163 and 164) Lead and Gain Compensation (Schaums Solved Problem 165) Lag and Gain Compensation (Schaums Solved Problem 168) Lag-Lead Compensation (Schaums Solved Problem 1610) Digital System Compensation (Schaums Example 166)
TABLE OF CONTENTS (page 4 of 6)
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Schaums Interactive Outline Series
Feedback and Control Systems
Chapter 17 - Nichols Chart Analysis
Magnitude-Phase Plots and Relative Stability - Type 1 System (SchaumsSolved Problems 172 and 176)
Magnitude-Phase Plots and Relative Stability - Type 2 System (SchaumsSolved Problems 174 and 177)
Discrete-Time Gain Phase Plots (Schaums Solved Problems 175 and 179) Closed-Loop Frequency Response Functions (Schaums Solved Problem 1714) Nichols Charts (Schaums Solved Problem 1715)
Chapter 18 - Nichols Chart Design
Gain Factor Compensation (Schaums Solved Problem 181) Closed-Loop Gain Factor Compensation (Schaums Solved Problem 184) Lead and Lag Compensator Magnitude-Phase Plots (Schaums Sections 184
and 185) Lead and Gain Network Compensation (Schaums Solved Problem 187) Lag and Gain Network Compensation (Schaums Example Problem 184)
Chapter 19 - Introduction to Nonlinear Control Systems
Taylor Series Expansion (Schaums Solved Problem 194) Phase Plane Methods (Schaums Solved Problem 199) Frequency Response Methods (Schaums Solved Problem 1919)
Chapter 20 - Introduction to Advanced Topics in Control SystemAnalysis and Design
Appendix A - Some Laplace Transform Pairs and Properties Useful forControl Systems Analysis
Appendix B - Some z-Transform Pairs and Properties Useful for ControlSystems Analysis
TABLE OF CONTENTS (page 5 of 6)
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Schaums Interactive Outline Series
Feedback and Control Systems
Appendix C - Block Diagram Transformation Theorems
Appendix D - Solving Polynomials Using the Companion Matrix
References and Bibliography
Index
TABLE OF CONTENTS (page 6 of 6)
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Schaums Interactive Outline Series
Feedback and Control Systems
Constructing Bode Plots
Statement
Construct the Bode plot for the frequency response function given below Also determinethe gain and phase margins for the system
System Parameters
Solution
To create the Bode plot for this function plot the magnitude in decibels and the phaseusing the phase function shown in Chapter 15
SAMPLE PAGE (page 1 of 3)
8192019 SIOSFDEG
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Schaums Interactive Outline Series
Feedback and Control Systems
SAMPLE PAGE (page 2 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Chapter 17 - Nichols Chart Analysis
Magnitude-Phase Plots and Relative Stability - Type 1 System (SchaumsSolved Problems 172 and 176)
Magnitude-Phase Plots and Relative Stability - Type 2 System (SchaumsSolved Problems 174 and 177)
Discrete-Time Gain Phase Plots (Schaums Solved Problems 175 and 179) Closed-Loop Frequency Response Functions (Schaums Solved Problem 1714) Nichols Charts (Schaums Solved Problem 1715)
Chapter 18 - Nichols Chart Design
Gain Factor Compensation (Schaums Solved Problem 181) Closed-Loop Gain Factor Compensation (Schaums Solved Problem 184) Lead and Lag Compensator Magnitude-Phase Plots (Schaums Sections 184
and 185) Lead and Gain Network Compensation (Schaums Solved Problem 187) Lag and Gain Network Compensation (Schaums Example Problem 184)
Chapter 19 - Introduction to Nonlinear Control Systems
Taylor Series Expansion (Schaums Solved Problem 194) Phase Plane Methods (Schaums Solved Problem 199) Frequency Response Methods (Schaums Solved Problem 1919)
Chapter 20 - Introduction to Advanced Topics in Control SystemAnalysis and Design
Appendix A - Some Laplace Transform Pairs and Properties Useful forControl Systems Analysis
Appendix B - Some z-Transform Pairs and Properties Useful for ControlSystems Analysis
TABLE OF CONTENTS (page 5 of 6)
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Schaums Interactive Outline Series
Feedback and Control Systems
Appendix C - Block Diagram Transformation Theorems
Appendix D - Solving Polynomials Using the Companion Matrix
References and Bibliography
Index
TABLE OF CONTENTS (page 6 of 6)
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Schaums Interactive Outline Series
Feedback and Control Systems
Constructing Bode Plots
Statement
Construct the Bode plot for the frequency response function given below Also determinethe gain and phase margins for the system
System Parameters
Solution
To create the Bode plot for this function plot the magnitude in decibels and the phaseusing the phase function shown in Chapter 15
SAMPLE PAGE (page 1 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
SAMPLE PAGE (page 2 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Appendix C - Block Diagram Transformation Theorems
Appendix D - Solving Polynomials Using the Companion Matrix
References and Bibliography
Index
TABLE OF CONTENTS (page 6 of 6)
8192019 SIOSFDEG
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Schaums Interactive Outline Series
Feedback and Control Systems
Constructing Bode Plots
Statement
Construct the Bode plot for the frequency response function given below Also determinethe gain and phase margins for the system
System Parameters
Solution
To create the Bode plot for this function plot the magnitude in decibels and the phaseusing the phase function shown in Chapter 15
SAMPLE PAGE (page 1 of 3)
8192019 SIOSFDEG
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Schaums Interactive Outline Series
Feedback and Control Systems
SAMPLE PAGE (page 2 of 3)
8192019 SIOSFDEG
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Schaums Interactive Outline Series
Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Constructing Bode Plots
Statement
Construct the Bode plot for the frequency response function given below Also determinethe gain and phase margins for the system
System Parameters
Solution
To create the Bode plot for this function plot the magnitude in decibels and the phaseusing the phase function shown in Chapter 15
SAMPLE PAGE (page 1 of 3)
8192019 SIOSFDEG
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Schaums Interactive Outline Series
Feedback and Control Systems
SAMPLE PAGE (page 2 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
SAMPLE PAGE (page 2 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)
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Schaums Interactive Outline Series
Feedback and Control Systems
Now find the gain and phase crossover frequencies There are two ways to do this Firstfrom the magnitude and phase angle plots we can make a good guess at where w 1 awp are respectively and solve the necessary equations Or we could find where the twocurves plotted on each the magnitude and phase angle plots intersect by setting themequal to each other and solving for w Both ways are shown here Solve for w 1 by using thegraph and for w p by using the equations
Input a guess value for w 1 based on the magnitude plot intersection and change it untilthe answer to the |GH(w)| function is unity
For w p set the phase equation equal to -180 deg (or -p) and use the root function
Guess
Therefore the gain margin is
And the phase margin is
SAMPLE PAGE (page 3 of 3)