## Table of Contents

(NOTE:

*Most chapters begin with a Preview and conclude with Summary, Further Reading, and Problems for the Reader.*) **I. THE ELEMENTS.**

**1. The Excitement of Control Engineering.**

Motivation for Control Engineering. Historical Periods of Control Theory. Types of Control-System Design. System Integration.

**2. Introduction to the Principles of Feedback.**

The Principal Goal of Control. A Motivating Industrial Example. Definition of the Problem. Prototype Solution to the Control Problem via Inversion. High-Gain Feedback and Inversion. From Open- to Closed-Loop Architectures. Trade-Offs Involved in Choosing the Feedback Gain. Measurements.

**3. Modeling.**

The Raison d'être for Models. Model Complexity. Building Models. Model Structures. State Space Models. Solution of Continuous-Time State Space Models. High-Order Differential and Difference-Equation Models. Modeling Errors. Linearization. Case Studies.

**4. Continuous-Time Signals and Systems.**

Linear Continuous-Time Models. Laplace Transforms. Laplace Transform. Properties and Examples. Transfer Functions. Stability of Transfer Functions. Impulse and Step Responses of Continuous-Time Linear Systems. Poles, Zeros, and Time Responses. Frequency Response. Fourier Transform. Models Frequently Encountered. Modeling Errors for Linear Systems. Bounds for Modeling Errors.

**II. SISO CONTROL ESSENTIALS.**

**5. Analysis of SISO Control Loops.**

Feedback Structures. Nominal Sensitivity Functions. Closed-Loop Stability Based on the Characteristic Polynomial. Stability and Polynomial Analysis. Root Locus (RL). Nominal Stability Using Frequency Response. Relative Stability: Stability Margins and Sensitivity Peaks. Robustness.

**6. Classical PID Control.**

PID Structure. Empirical Tuning. Ziegler-Nichols (Z-N) Oscillation Method. Reaction Curve Based Methods. Lead-Lag Compensators. Distillation Column.

**7. Synthesis of SISO Controllers.**

Polynomial Approach. PI and PID Synthesis Revisited by Using Pole Assignment. Smith Predictor.

**III. SISO CONTROL DESIGN.**

**8. Fundamental Limitations in SISO Control.**

Sensors. Actuators. Disturbances. Model-Error Limitations. Structural Limitations. An Industrial Application (Hold-Up Effect in Reversing Mill). Remedies. Design Homogeneity, Revisited.

**9. Frequency-Domain Design Limitations.**

Bode's Integral Constraints on Sensitivity. Integral Constraints on Complementary Sensitivity. Poisson Integral Constraint on Sensitivity. Poisson Integral Constraint on Complementary Sensitivity. Example of Design Trade-Offs.

**10. Architectural Issues in SISO Control.**

Models for Deterministic Disturbances and References. Internal Model Principle for Disturbances. Internal Model Principle for Reference Tracking. Feedforward. Industrial Applications of Feedforward Control. Cascade Control.

**11. Dealing with Constraints.**

Wind-Up. Anti-Wind-Up Scheme. State Saturation. Introduction to Model Predictive Control.

**IV. DIGITAL COMPUTER CONTROL.**

**12. Models for Sampled-Data Systems.**

Sampling. Signal Reconstruction. Linear Discrete-Time Models. The Shift Operator. Z-Transform. Discrete Transfer Functions. Discrete Delta-Domain Models. Discrete Delta-Transform. Discrete Transfer Functions (Delta Form). Transfer Functions and Impulse Responses. Discrete System Stability. Discrete Models for Sampled Continuous Systems. Using Continuous State Space Models. Frequency Response of Sampled-Data Systems.

**13. Digital Control.**

Discrete-Time Sensitivity Functions. Zeros of Sample-Data Systems. Is a Dedicated Digital Theory Really Necessary? Approximate Continuous Designs. At-Sample Digital Design. Internal Model Principle for Digital Control. Fundamental Performance Limitations.

**14. Hybrid Control.**

Hybrid Analysis. Models for Hybrid Control Systems. Analysis of Intersample Behavior. Repetitive Control Revisited. Poisson Summation Formula.

**V. ADVANCED SISO CONTROL.**

**15. SISO Controller Parameterizations.**

Open-Loop Inversion Revisited. Affine Parameterization: The Stable Case. PID Synthesis by Using the Affine Parameterization. Affine Parameterization for Systems Having Time Delays. Undesirable Closed-Loop Poles. Affine Parameterization: The Unstable Open-Loop Case. Discrete-Time Systems.

**16. Control Design Based on Optimization.**

Optimal Q (Affine) Synthesis. Robust Control Design with Confidence Bounds. Cheap Control Fundamental Limitations. Frequency-Domain Limitations Revisited.

**17. Linear State Space Models.**

Linear Continuous-Time State Space Models. Similarity Transformations. Transfer Functions Revisited. From Transfer Function to State Space Representation. Controllability and Stabilizability. Observability and Detectability. Canonical Decomposition. Pole-Zero Cancellation and System Properties.

**18. Synthesis via State Space Methods.**

Pole Assignment by State Feedback. Observers. Combining State Feedback with an Observer. Transfer-Function Interpretations. Reinterpretation of the Affine Parameterization of All Stabilizing Controllers. State Space Interpretation of Internal Model Principle. Trade-Offs in State Feedback and Observers. Dealing with Input Constraints in the Context of State-Estimate Feedback.

**19. Introduction to Nonlinear Control.**

Linear Control of a Nonlinear Plant. Switched Linear Controllers. Control of Systems with Smooth Nonlinearities. Static Input Nonlinearities. Smooth Dynamic Nonlineartiies for Stable and Stably Invertible Models. Disturbance Issues in Nonlinear Control. More General Plants with Smooth Nonlinearities. Nonsmooth Nonlinearities. Stability of Nonlinear Systems. Generalized Feedback Linearization for Nonstability-Invertible Plants.

**VI. MIMO CONTROL ESSENTIALS.**

**20. Analysis of MIMO Control Loops.**

Motivational Examples. Models for Multivariable Systems. The Basic MIMO Control Loop. Closed-Loop Stability. Steady-State Response for Step Inputs. Frequency-Domain Analysis. Robustness Issues.

**21. Exploiting SISO Techniques in MIMO Control.**

Completely Decentralized Control. Pairing of Inputs and Outputs. Robustness Issues in Decentralized Control. Feedforward Action in Decentralized Control. Converting MIMO Problems to SISO Problems. Industrial Case Study (Strip Flatness Control).

**VII. MIMO CONTROL DESIGN.**

**22. Design via Optimal Control Techniques.**

State-Estimate Feedback. Dynamic Programming and Optimal Control. The Linear Quadratic Regulator (LQR). Properties of the Linear Quadratic Optimal Regulator. Model Matching Based on Linear Quadratic Optimal Regulators. Discrete-Time Optimal Regulators. Connections to Pole Assignment. Observer Design. Linear Optimal Filters. State-Estimate Feedback. Transfer-Function Interpretation. Achieving Integral Action in LQR Synthesis. Industrial Applications.

**23. Model Predictive Control.**

Anti-Wind-Up Revisited. What Is Model Predictive Control? Stability. Linear Models with Quadratic Cost Function. State Estimation and Disturbance Prediction. Rudder Roll Stabilization of Ships.

**24. Fundamental Limitations in MIMO Control.**

Closed-Loop Transfer Function. MIMO Internal Model Principle. The Cost of the Internal Model Principle. RHP Poles and Zeros. Time-Domain Constraints. Poisson Integral Constraints on MIMO Complementary Sensitivity. Poisson Integral Constraints on MIMO Sensitivity. Interpretation. An Industrial Application: Sugar Mill. Nonsquare Systems. Discrete-Time Systems.

**VIII. ADVANCED MIMO CONTROL.**

**25. MIMO Controller Parameterizations.**

Affine Parameterization: Stable MIMO Plants. Achieved Sensitivities. Dealing with Model Relative Degree. Dealing with NMP Zeros. Affine Parameterization: Unstable MIMO Plants. State Space Implementation.

**26. Decoupling.**

Stable Systems. Pre- and PostDiagonalization. Unstable Systems. Zeros of Decoupled and Partially Decoupled Systems. Frequency-Domain Constraints for Dynamically Decouple Systems. The Cost of Decoupling. Input Saturation. MIMO Anti-Wind-Up Mechanism.

**APPENDICES.**

**Appendix A: Notation, Symbols, and Acronyms.**

**Appendix B: Smith-McMillan Forms.**

Polynomial Matrices. Smith Form for Polynomial Matrices. Smith-McMillan Form for Rational Matrices. Poles and Zeros. Matrix Fraction Descriptions (MFD).

**Appendix C: Results from Analytic Function Theory.**

Independence of Path. Simply Connected Domains. Functions of a Complex Variable. Derivatives and Differentials. Analytic Functions. Integrals Revisited. Poisson and Jensen Integral Formulas. Application of the Poisson-Jensen Formula to Certain Rational Functions. Bode's Theorems.

**Appendix D: Properties of Continuous-Time Riccati Equations.**

Solutions of the CTDRE. Solutions of the CTARE. The Stabilizing Solution of the CTARE. Convergence of Solutions of the CTARE to the Stabilizing Solution of the CTARE. Duality between Linear Quadratic Regulator and Optimal Linear Filter.

**Appendix E: MATLAB Support.**

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