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Design of feedback control systems / Raymond T. Stefani [and others].

By: Material type: TextTextSeries: Oxford series in electrical and computer engineeringPublisher: New York : Oxford University Press, 2002Edition: Fourth editionDescription: xvi, 848 pages : illustrations ; 24 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 0195142497
  • 9780195142495
Subject(s): DDC classification:
  • 629.83
LOC classification:
  • TJ216. D417 2001
Contents:
1. Continuous-Time System Description -- 1.1. Preview -- 1.2. Basic Concepts -- 1.2.1. Control System Terminology -- 1.2.2. The Feedback Concept -- 1.3. Modeling -- 1.4. System Dynamics -- 1.5. Electrical Components -- 1.5.1. Mesh Analysis -- 1.5.2. State Variables -- 1.5.3. Node Analysis -- 1.5.4. Analyzing Operational Amplifier Circuits -- 1.5.5. Operational Amplifier Applications -- 1.6. Translational Mechanical Components -- 1.6.1. Free Body Diagrams -- 1.6.2. State Variables -- 1.7. Rotational Mechanical Components -- 1.7.1. Free Body Diagrams -- 1.7.2. Analogies -- 1.7.3. Gear Trains and Transformers -- 1.8. Electromechanical Components -- 1.9. Aerodynamics -- 1.9.1. Nomenclature -- 1.9.2. Dynamics -- 1.9.3. Lateral and Longitudinal Motion -- 1.10. Thermal Systems -- 1.11. Hydraulics -- 1.12. Transfer Functions and Stability -- 1.12.1. Transfer Functions -- 1.12.2. Response Terms -- 1.12.3. Multiple Inputs and Outputs -- 1.12.4. Stability -- 1.13. Block Diagrams -- 1.13.1. Block Diagram Elements -- 1.13.2. Block Diagram Reductions -- 1.13.3. Multiple Inputs and Outputs -- 1.14. Signal Flow Graphs -- 1.14.1. Comparison and Block Diagrams -- 1.14.2. Mason's Rule -- 1.15. A Positioning Servo Example -- 1.16. Controller Model of a Thyroid Gland -- 1.17. Stick-Slip Response of an Oil Well Drill -- 1.18. Summary -- 2. Continuous-Time System Response -- 2.1. Preview -- 2.2. Response of First-Order Systems -- 2.3. Response of Second-Order Systems -- 2.3.1. Time Response -- 2.3.2. Overdamped Response -- 2.3.3. Critically Damped Response -- 2.3.4. Underdamped Response -- 2.3.5. Undamped Natural Frequency and Damping Ratio -- 2.3.6. Rise Time, Overshoot and Settling Time -- 2.4. Higher-Order System Response -- 2.5. Stability Testing -- 2.5.1. Coefficient Tests -- 2.5.2. Routh-Hurwitz Testing -- 2.5.3. Significance of the Array Coefficients -- 2.5.4. Left-Column Zeros -- 2.5.5. Row of Zeros -- 2.5.6. Eliminating a Possible Odd Divisor -- 2.5.7. Multiple Roots -- 2.6. Parameter Shifting -- 2.6.1. Adjustable Systems -- 2.6.2. Khartinov's Theorem -- 2.7. An Insulin Delivery System -- 2.8. Analysis of an Aircraft Wing -- 2.9. Summary -- 3. Performance Specifications -- 3.1. Preview -- 3.2. Analyzing Tracking Systems -- 3.2.1. Importance of Tracking Systems -- 3.2.2. Natural Response, Relative Stability and Damping -- 3.3. Forced Response -- 3.3.1. Steady State Error -- 3.3.2. Initial and Final Values -- 3.3.3. Steady State Errors to Power-of-Time Inputs -- 3.4. Power-of-Time Error Performance -- 3.4.1. System Type Number -- 3.4.2. Achieving a Given Type Number -- 3.4.3. Unity Feedback Systems -- 3.4.4. Unity Feedback Error Coefficients -- 3.5. Performance Indices and Optimal Systems -- 3.6. System Sensitivity -- 3.6.1. Calculating the Effects of Changes in Parameters -- 3.6.2. Sensitivity Functions -- 3.6.3. Sensitivity to Disturbance Signals -- 3.7. Time Domain Design -- 3.7.1. Process Control -- 3.7.2. Ziegler-Nichols Compensation -- 3.7.3. Chien-Hrones-Reswick Compensation -- 3.8. An Electric Rail Transportation System -- 3.9. Phase-Locked Loop for a CB Receiver -- 3.10. Bionic Eye -- 3.11. Summary -- 4. Root Locus Analysis -- 4.1. Preview -- 4.2. Pole-Zero Plots -- 4.2.1. Poles and Zeros -- 4.2.2. Graphical Evaluation -- 4.3. Root Locus for Feedback Systems -- 4.3.1. Angle Criterion -- 4.3.2. High and Low Gains -- 4.3.3. Root Locus Properties -- 4.4. Root Locus Construction -- 4.5. More About Root Locus -- 4.5.1. Root Locus Calibration -- 4.5.2. Computer-Aided Root Locus -- 4.6. Root Locus for Other Systems -- 4.6.1. Systems with Other Forms -- 4.6.2. Negative Parameter Ranges -- 4.6.3. Delay Effects -- 4.7. Design Concepts (Adding Poles and Zeros) -- 4.8. A Light-Source Tracking System -- 4.9. An Artificial Limb -- 4.10. Control of a Flexible Spacecraft -- 4.11. Bionic Eye -- 4.12. Summary -- 5. Root Locus Design -- 5.1. Preview -- 5.2. Shaping a Root Locus -- 5.3. Adding and Canceling Poles and Zeros -- 5.3.1. Adding a Pole or Zero -- 5.3.2. Canceling a Pole or Zero -- 5.4. Second-Order Plant Models -- 5.5. An Uncompensated Example -- 5.6. Cascade Proportional Plus Integral (PI) Compensation -- 5.6.1. General Approach to Compensator Design -- 5.6.2. Cascade PI Compensation -- 5.7. Cascade Lag Compensation -- 5.8. Cascade Lead Compensation -- 5.9. Cascade Lag-Lead Compensation -- 5.10. Rate Feedback Compensation (PD) -- 5.11. Proportional-Integral-Derivative Compensation (PID) -- 5.12. Pole Placement -- 5.12.1. Algebraic Compensation -- 5.12.2. Selecting the Transfer Function -- 5.12.3. Incorrect Plant Transmittance -- 5.12.4. Robust Algebraic Compensation -- 5.12.5. Fixed-Structure Compensation -- 5.13. An Unstable High-Performance Aircraft -- 5.14. Control of a Flexible Space Station -- 5.15. Control of a Solar Furnace -- 5.16. Summary --
6. Frequency Response Analysis -- 6.1. Preview -- 6.2. Frequency Response -- 6.2.1. Forced Sinusoidal Response -- 6.2.2. Frequency Response Measurement -- 6.2.3. Response at Low and High Frequencies -- 6.2.4. Graphical Frequency Response Methods -- 6.3. Bode Plots -- 6.3.1. Amplitude Plots in Decibels -- 6.3.2. Real Axis Roots -- 6.3.3. Products of Transmittance Terms -- 6.3.4. Complex Roots -- 6.4. Using Experimental Data -- 6.4.1. Finding Models -- 6.4.2. Irrational Transmittances -- 6.5. Nyquist Methods -- 6.5.1. Generating the Nyquist (Polar) Plot -- 6.5.2. Interpreting the Nyquist Plot -- 6.6. Gain Margin -- 6.7. Phase Margin -- 6.8. Relation between Closed Loop and Open Loop Frequency Response -- 6.9. Frequency Response of a Flexible Spacecraft -- 6.10. Summary -- 7. Frequency Response Design -- 7.1. Preview -- 7.2. Relationship between Root Locus, Time Domain and Frequency Domain -- 7.3. Compensation Using Bode Plots -- 7.4. Uncompensated System -- 7.5. Cascade Proportional Plus Integral (PI) and Cascade Lag Compensation -- 7.6. Cascade Lead Compensation -- 7.7. Cascade Lag-Lead Compensation -- 7.8. Rate Feedback Compensation (PD) -- 7.9. Proportional-Integral-Derivative Compensation -- 7.10. An Automobile Driver as a Compensator -- 7.11. Summary -- 8. State Space Analysis -- 8.1. Preview -- 8.2. State Space Representation -- 8.2.1. Phase-Variable Form -- 8.2.2. Dual Phase-Variable Form -- 8.2.3. Multiple Inputs and Outputs -- 8.2.4. Physical State Variables -- 8.2.5. Transfer Functions -- 8.3. State Transformations and Diagonalization -- 8.3.1. Diagonal Forms -- 8.3.2. Diagonalization Using Partial-Fraction Expansion -- 8.3.3. Complex Conjugate Characteristic Roots -- 8.3.4. Repeated Characteristic Roots -- 8.4. Time Response From State Equations -- 8.4.1. Laplace Transform Solution -- 8.4.2. Time-Domain Response of First-Order Systems -- 8.4.3. Time-Domain Response of Higher-Order Systems -- 8.4.4. System Response Computation -- 8.5. Stability -- 8.5.1. Asymptotic Stability -- 8.5.2. BIBO Stability -- 8.5.3. Internal Stability -- 8.6. Controllability and Observability -- 8.6.1. The Controllability Matrix -- 8.6.2. The Observability Matrix -- 8.6.3. Controllability, Observability and Pole-Zero Cancellation -- 8.6.4. Causes of Uncontrollability -- 8.7. Inverted Pendulum Problems -- 8.8. Summary -- 9. State Space Design -- 9.1. Preview -- 9.2. State Feedback and Pole Placement -- 9.2.1. Stabilizability -- 9.2.2. Choosing Pole Locations -- 9.2.3. Limitations of State Feedback -- 9.3. Tracking Problems -- 9.3.1. Integral Control -- 9.4. Observer Design -- 9.4.1. Control Using Observers -- 9.4.2. Separation Property -- 9.4.3. Observer Transfer Function -- 9.5. Reduced-Order Observer Design -- 9.5.1. Separation Property -- 9.5.2. Reduced-Order Observer Transfer Function -- 9.6. A Magnetic Levitation System -- 9.7. Summary -- 10. Advanced State Space Methods -- 10.1. Preview -- 10.2. The Linear Quadratic Regulator Problem -- 10.2.1. Properties of the LQR Design -- 10.2.2. Return Difference Inequality -- 10.2.3. Optimal Root Locus -- 10.3. Optimal Observers--The Kalman Filter -- 10.4. The Linear Quadratic Gaussian (LQG) Problem -- 10.4.1. Critique of LGQ -- 10.5. Robustness -- 10.5.1. Feedback Properties -- 10.5.2. Uncertainty Modeling -- 10.5.3. Robust Stability -- 10.6. Loop Transfer Recovery (LTR) -- 10.7. H¥ -- 10.7.1. A Brief History -- 10.7.2. Some Preliminaries -- 10.7.3. H¥ -- 10.7.4. Weights in H¥ -- 10.8. Summary -- 11. Digital Control -- 11.1. Preview -- 11.2. Computer Processing -- 11.2.1. Computer History and Trends -- 11.3. A /D and D /A Conversion -- 11.3.1. Analog-to-Digital Conversion -- 11.3.2. Sample and Hold -- 11.3.3. Digital-to-Analog Conversion -- 11.4. Discrete-Time Signals -- 11.4.1. Representing Sequences -- 11.4.2. Z-Transformation and Properties -- 11.4.3. Inverse z-Transform -- 11.5. Sampling -- 11.6. Reconstruction of Signals from Samples -- 11.6.1. Representing Sampled Signals with Impulses -- 11.6.2. Relation between the z-Transform and the Laplace Transform -- 11.6.3. The Sampling Theorem -- 11.7. Discrete-Time Systems -- 11.7.1. Difference Equations Response -- 11.7.2. Z-Transfer Functions -- 11.7.3. Block Diagrams and Signal Flow Graphs -- 11.7.4. Stability and the Bilinear Transformation -- 11.7.5. Computer Software -- 11.8. State Variable Description of Discrete-Time Systems -- 11.8.1. Simulation Diagrams and Equations -- 11.8.2. Response and Stability -- 11.8.3. Controllability and Observability -- 11.9. Digitizing Control Systems -- 11.9.1. Step-Invariant Approximation -- 11.9.2. Z-Transfer Functions of Systems with Analog Measurements -- 11.9.3. A Design Example -- 11.10. Direct Digital Design -- 11.10.1. Steady State Response -- 11.10.2. Deadbeat Systems -- 11.10.3. A Design Example -- 11.11. Summary -- Appendix A. Matrix Algebra -- Appendix B. Laplace Transform.
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Item type Current library Call number Copy number Status Date due Barcode
Book City Campus City Campus Main Collection 629.83 DES (Browse shelf(Opens below)) 1 Available A284471B

Includes bibliographical references.

1. Continuous-Time System Description -- 1.1. Preview -- 1.2. Basic Concepts -- 1.2.1. Control System Terminology -- 1.2.2. The Feedback Concept -- 1.3. Modeling -- 1.4. System Dynamics -- 1.5. Electrical Components -- 1.5.1. Mesh Analysis -- 1.5.2. State Variables -- 1.5.3. Node Analysis -- 1.5.4. Analyzing Operational Amplifier Circuits -- 1.5.5. Operational Amplifier Applications -- 1.6. Translational Mechanical Components -- 1.6.1. Free Body Diagrams -- 1.6.2. State Variables -- 1.7. Rotational Mechanical Components -- 1.7.1. Free Body Diagrams -- 1.7.2. Analogies -- 1.7.3. Gear Trains and Transformers -- 1.8. Electromechanical Components -- 1.9. Aerodynamics -- 1.9.1. Nomenclature -- 1.9.2. Dynamics -- 1.9.3. Lateral and Longitudinal Motion -- 1.10. Thermal Systems -- 1.11. Hydraulics -- 1.12. Transfer Functions and Stability -- 1.12.1. Transfer Functions -- 1.12.2. Response Terms -- 1.12.3. Multiple Inputs and Outputs -- 1.12.4. Stability -- 1.13. Block Diagrams -- 1.13.1. Block Diagram Elements -- 1.13.2. Block Diagram Reductions -- 1.13.3. Multiple Inputs and Outputs -- 1.14. Signal Flow Graphs -- 1.14.1. Comparison and Block Diagrams -- 1.14.2. Mason's Rule -- 1.15. A Positioning Servo Example -- 1.16. Controller Model of a Thyroid Gland -- 1.17. Stick-Slip Response of an Oil Well Drill -- 1.18. Summary -- 2. Continuous-Time System Response -- 2.1. Preview -- 2.2. Response of First-Order Systems -- 2.3. Response of Second-Order Systems -- 2.3.1. Time Response -- 2.3.2. Overdamped Response -- 2.3.3. Critically Damped Response -- 2.3.4. Underdamped Response -- 2.3.5. Undamped Natural Frequency and Damping Ratio -- 2.3.6. Rise Time, Overshoot and Settling Time -- 2.4. Higher-Order System Response -- 2.5. Stability Testing -- 2.5.1. Coefficient Tests -- 2.5.2. Routh-Hurwitz Testing -- 2.5.3. Significance of the Array Coefficients -- 2.5.4. Left-Column Zeros -- 2.5.5. Row of Zeros -- 2.5.6. Eliminating a Possible Odd Divisor -- 2.5.7. Multiple Roots -- 2.6. Parameter Shifting -- 2.6.1. Adjustable Systems -- 2.6.2. Khartinov's Theorem -- 2.7. An Insulin Delivery System -- 2.8. Analysis of an Aircraft Wing -- 2.9. Summary -- 3. Performance Specifications -- 3.1. Preview -- 3.2. Analyzing Tracking Systems -- 3.2.1. Importance of Tracking Systems -- 3.2.2. Natural Response, Relative Stability and Damping -- 3.3. Forced Response -- 3.3.1. Steady State Error -- 3.3.2. Initial and Final Values -- 3.3.3. Steady State Errors to Power-of-Time Inputs -- 3.4. Power-of-Time Error Performance -- 3.4.1. System Type Number -- 3.4.2. Achieving a Given Type Number -- 3.4.3. Unity Feedback Systems -- 3.4.4. Unity Feedback Error Coefficients -- 3.5. Performance Indices and Optimal Systems -- 3.6. System Sensitivity -- 3.6.1. Calculating the Effects of Changes in Parameters -- 3.6.2. Sensitivity Functions -- 3.6.3. Sensitivity to Disturbance Signals -- 3.7. Time Domain Design -- 3.7.1. Process Control -- 3.7.2. Ziegler-Nichols Compensation -- 3.7.3. Chien-Hrones-Reswick Compensation -- 3.8. An Electric Rail Transportation System -- 3.9. Phase-Locked Loop for a CB Receiver -- 3.10. Bionic Eye -- 3.11. Summary -- 4. Root Locus Analysis -- 4.1. Preview -- 4.2. Pole-Zero Plots -- 4.2.1. Poles and Zeros -- 4.2.2. Graphical Evaluation -- 4.3. Root Locus for Feedback Systems -- 4.3.1. Angle Criterion -- 4.3.2. High and Low Gains -- 4.3.3. Root Locus Properties -- 4.4. Root Locus Construction -- 4.5. More About Root Locus -- 4.5.1. Root Locus Calibration -- 4.5.2. Computer-Aided Root Locus -- 4.6. Root Locus for Other Systems -- 4.6.1. Systems with Other Forms -- 4.6.2. Negative Parameter Ranges -- 4.6.3. Delay Effects -- 4.7. Design Concepts (Adding Poles and Zeros) -- 4.8. A Light-Source Tracking System -- 4.9. An Artificial Limb -- 4.10. Control of a Flexible Spacecraft -- 4.11. Bionic Eye -- 4.12. Summary -- 5. Root Locus Design -- 5.1. Preview -- 5.2. Shaping a Root Locus -- 5.3. Adding and Canceling Poles and Zeros -- 5.3.1. Adding a Pole or Zero -- 5.3.2. Canceling a Pole or Zero -- 5.4. Second-Order Plant Models -- 5.5. An Uncompensated Example -- 5.6. Cascade Proportional Plus Integral (PI) Compensation -- 5.6.1. General Approach to Compensator Design -- 5.6.2. Cascade PI Compensation -- 5.7. Cascade Lag Compensation -- 5.8. Cascade Lead Compensation -- 5.9. Cascade Lag-Lead Compensation -- 5.10. Rate Feedback Compensation (PD) -- 5.11. Proportional-Integral-Derivative Compensation (PID) -- 5.12. Pole Placement -- 5.12.1. Algebraic Compensation -- 5.12.2. Selecting the Transfer Function -- 5.12.3. Incorrect Plant Transmittance -- 5.12.4. Robust Algebraic Compensation -- 5.12.5. Fixed-Structure Compensation -- 5.13. An Unstable High-Performance Aircraft -- 5.14. Control of a Flexible Space Station -- 5.15. Control of a Solar Furnace -- 5.16. Summary --

6. Frequency Response Analysis -- 6.1. Preview -- 6.2. Frequency Response -- 6.2.1. Forced Sinusoidal Response -- 6.2.2. Frequency Response Measurement -- 6.2.3. Response at Low and High Frequencies -- 6.2.4. Graphical Frequency Response Methods -- 6.3. Bode Plots -- 6.3.1. Amplitude Plots in Decibels -- 6.3.2. Real Axis Roots -- 6.3.3. Products of Transmittance Terms -- 6.3.4. Complex Roots -- 6.4. Using Experimental Data -- 6.4.1. Finding Models -- 6.4.2. Irrational Transmittances -- 6.5. Nyquist Methods -- 6.5.1. Generating the Nyquist (Polar) Plot -- 6.5.2. Interpreting the Nyquist Plot -- 6.6. Gain Margin -- 6.7. Phase Margin -- 6.8. Relation between Closed Loop and Open Loop Frequency Response -- 6.9. Frequency Response of a Flexible Spacecraft -- 6.10. Summary -- 7. Frequency Response Design -- 7.1. Preview -- 7.2. Relationship between Root Locus, Time Domain and Frequency Domain -- 7.3. Compensation Using Bode Plots -- 7.4. Uncompensated System -- 7.5. Cascade Proportional Plus Integral (PI) and Cascade Lag Compensation -- 7.6. Cascade Lead Compensation -- 7.7. Cascade Lag-Lead Compensation -- 7.8. Rate Feedback Compensation (PD) -- 7.9. Proportional-Integral-Derivative Compensation -- 7.10. An Automobile Driver as a Compensator -- 7.11. Summary -- 8. State Space Analysis -- 8.1. Preview -- 8.2. State Space Representation -- 8.2.1. Phase-Variable Form -- 8.2.2. Dual Phase-Variable Form -- 8.2.3. Multiple Inputs and Outputs -- 8.2.4. Physical State Variables -- 8.2.5. Transfer Functions -- 8.3. State Transformations and Diagonalization -- 8.3.1. Diagonal Forms -- 8.3.2. Diagonalization Using Partial-Fraction Expansion -- 8.3.3. Complex Conjugate Characteristic Roots -- 8.3.4. Repeated Characteristic Roots -- 8.4. Time Response From State Equations -- 8.4.1. Laplace Transform Solution -- 8.4.2. Time-Domain Response of First-Order Systems -- 8.4.3. Time-Domain Response of Higher-Order Systems -- 8.4.4. System Response Computation -- 8.5. Stability -- 8.5.1. Asymptotic Stability -- 8.5.2. BIBO Stability -- 8.5.3. Internal Stability -- 8.6. Controllability and Observability -- 8.6.1. The Controllability Matrix -- 8.6.2. The Observability Matrix -- 8.6.3. Controllability, Observability and Pole-Zero Cancellation -- 8.6.4. Causes of Uncontrollability -- 8.7. Inverted Pendulum Problems -- 8.8. Summary -- 9. State Space Design -- 9.1. Preview -- 9.2. State Feedback and Pole Placement -- 9.2.1. Stabilizability -- 9.2.2. Choosing Pole Locations -- 9.2.3. Limitations of State Feedback -- 9.3. Tracking Problems -- 9.3.1. Integral Control -- 9.4. Observer Design -- 9.4.1. Control Using Observers -- 9.4.2. Separation Property -- 9.4.3. Observer Transfer Function -- 9.5. Reduced-Order Observer Design -- 9.5.1. Separation Property -- 9.5.2. Reduced-Order Observer Transfer Function -- 9.6. A Magnetic Levitation System -- 9.7. Summary -- 10. Advanced State Space Methods -- 10.1. Preview -- 10.2. The Linear Quadratic Regulator Problem -- 10.2.1. Properties of the LQR Design -- 10.2.2. Return Difference Inequality -- 10.2.3. Optimal Root Locus -- 10.3. Optimal Observers--The Kalman Filter -- 10.4. The Linear Quadratic Gaussian (LQG) Problem -- 10.4.1. Critique of LGQ -- 10.5. Robustness -- 10.5.1. Feedback Properties -- 10.5.2. Uncertainty Modeling -- 10.5.3. Robust Stability -- 10.6. Loop Transfer Recovery (LTR) -- 10.7. H¥ -- 10.7.1. A Brief History -- 10.7.2. Some Preliminaries -- 10.7.3. H¥ -- 10.7.4. Weights in H¥ -- 10.8. Summary -- 11. Digital Control -- 11.1. Preview -- 11.2. Computer Processing -- 11.2.1. Computer History and Trends -- 11.3. A /D and D /A Conversion -- 11.3.1. Analog-to-Digital Conversion -- 11.3.2. Sample and Hold -- 11.3.3. Digital-to-Analog Conversion -- 11.4. Discrete-Time Signals -- 11.4.1. Representing Sequences -- 11.4.2. Z-Transformation and Properties -- 11.4.3. Inverse z-Transform -- 11.5. Sampling -- 11.6. Reconstruction of Signals from Samples -- 11.6.1. Representing Sampled Signals with Impulses -- 11.6.2. Relation between the z-Transform and the Laplace Transform -- 11.6.3. The Sampling Theorem -- 11.7. Discrete-Time Systems -- 11.7.1. Difference Equations Response -- 11.7.2. Z-Transfer Functions -- 11.7.3. Block Diagrams and Signal Flow Graphs -- 11.7.4. Stability and the Bilinear Transformation -- 11.7.5. Computer Software -- 11.8. State Variable Description of Discrete-Time Systems -- 11.8.1. Simulation Diagrams and Equations -- 11.8.2. Response and Stability -- 11.8.3. Controllability and Observability -- 11.9. Digitizing Control Systems -- 11.9.1. Step-Invariant Approximation -- 11.9.2. Z-Transfer Functions of Systems with Analog Measurements -- 11.9.3. A Design Example -- 11.10. Direct Digital Design -- 11.10.1. Steady State Response -- 11.10.2. Deadbeat Systems -- 11.10.3. A Design Example -- 11.11. Summary -- Appendix A. Matrix Algebra -- Appendix B. Laplace Transform.

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