Feedback Control of Computing Systems -- Contents -- PREFACE -- PART I BACKGROUND -- 1 Introduction and Overview -- 1.1 The Nature of Feedback Control -- 1.2 Control Objectives -- 1.3 Properties of Feedback Control Systems -- 1.4 Open-Loop versus Closed-Loop Control -- 1.5 Summary of Applications of Control Theory to Computing Systems -- 1.6 Computer Examples of Feedback Control Systems -- 1.6.1 IBM Lotus Domino Server -- 1.6.2 Queueing Systems -- 1.6.3 Apache HTTP Server -- 1.6.4 Random Early Detection of Router Overloads -- 1.6.5 Load Balancing -- 1.6.6 Streaming Media -- 1.6.7 Caching with Differentiated Service -- 1.7 Challenges in Applying Control Theory to Computing Systems -- 1.8 Summary -- 1.9 Exercises -- PART II SYSTEM MODELING -- 2 Model Construction -- 2.1 Basics of Queueing Theory -- 2.2 Modeling Dynamic Behavior -- 2.2.1 Model Variables -- 2.2.2 Signals -- 2.2.3 Linear, Time-Invariant Difference Equations -- 2.2.4 Nonlinearities -- 2.3 First-Principles Models -- 2.4 Black-Box Models -- 2.4.1 Model Scope -- 2.4.2 Experimental Design -- 2.4.3 Parameter Estimation -- 2.4.4 Model Evaluation -- 2.5 Summary -- 2.6 Extended Examples -- 2.6.1 IBM Lotus Domino Server -- 2.6.2 Apache HTTP Server -- 2.6.3 M/M/1/K Comparisons -- *2.7 Parameter Estimation Using MATLAB -- 2.8 Exercises -- 3 Z-Transforms and Transfer Functions -- 3.1 Z-Transform Basics -- 3.1.1 Z-Transform Definition -- 3.1.2 Z-Transforms of Common Signals -- 3.1.3 Properties of Z-Transforms -- 3.1.4 Inverse Z-Transforms -- 3.1.5 Using Z-Transforms to Solve Difference Equations -- 3.2 Characteristics Inferred from Z-Transforms -- 3.2.1 Review of Complex Variables -- 3.2.2 Poles and Zeros of a Z-Transform -- 3.2.3 Steady-State Analysis -- 3.2.4 Time Domain versus Z-Domain -- 3.3 Transfer Functions -- 3.3.1 Stability -- 3.3.2 Steady-State Gain -- 3.3.3 System Order.

3.3.4 Dominant Poles and Model Simplification -- 3.3.5 Simulating Transfer Functions -- 3.4 Summary -- 3.5 Extended Examples -- 3.5.1 M/M/1/K from System Identification -- 3.5.2 IBM Lotus Domino Server: Sensor Delay -- 3.5.3 Apache HTTP Server: Combining Control Inputs -- *3.6 Z-Transforms and MATLAB -- 3.7 Exercises -- 4 System Modeling with Block Diagrams -- 4.1 Block Diagrams Basics -- 4.2 Transforming Block Diagrams -- 4.2.1 Special Aggregations of Blocks -- 4.3 Transfer Functions for Control Analysis -- 4.4 Block Diagram Restructuring -- 4.5 Summary -- 4.6 Extended Examples -- 4.6.1 IBM Lotus Domino Server -- 4.6.2 Apache HTTP Server with Control Loops -- 4.6.3 Streaming -- *4.7 Composing Transfer Functions in MATLAB -- 4.8 Exercises -- 5 First-Order Systems -- 5.1 First-Order Model -- 5.2 System Response -- 5.2.1 Steady-State and Transient Responses -- 5.2.2 Input Signal Model -- 5.2.3 Time-Domain Solution -- 5.3 Initial Condition Response -- 5.4 Impulse Response -- 5.5 Step Response -- 5.5.1 Numerical Example -- 5.5.2 Time-Domain Solution -- 5.5.3 Steady-State Response -- 5.5.4 Transient Response -- 5.6 Transient Response to Other Signals -- 5.6.1 Ramp Response -- 5.6.2 Frequency Response -- 5.7 Effect of Stochastics -- 5.8 Summary -- 5.9 Extended Examples -- 5.9.1 Estimating Operating Region of the Apache HTTP Server -- 5.9.2 IBM Lotus Domino Server with a Disturbance -- 5.9.3 Feedback Control of the IBM Lotus Domino Server -- *5.10 Analyzing Transient Response with MATLAB -- 5.11 Exercises -- 6 Higher-Order Systems -- 6.1 Motivation and Definitions -- 6.2 Real Poles -- 6.2.1 Initial Condition Response -- 6.2.2 Impulse Response -- 6.2.3 Step Response -- 6.2.4 Other Signals -- 6.2.5 Effect of Zeros -- 6.3 Complex Poles -- 6.3.1 Second-Order System -- 6.3.2 Impulse Response -- 6.3.3 Step Response -- 6.4 Summary -- 6.5 Extended Examples.

6.5.1 Apache HTTP Server with a Filter -- 6.5.2 Apache HTTP Server with a Filter and Controller -- 6.5.3 IBM Lotus Domino Server with a Filter and Controller -- 6.5.4 M/M/1/K with a Filter and Controller -- *6.6 Analyzing Transient Response with MATLAB -- 6.7 Exercises -- 7 State-Space Models -- 7.1 State Variables -- 7.2 State-Space Models -- 7.3 Solving Difference Equations in State Space -- 7.4 Converting Between Transfer Function Models and State-Space Models -- 7.5 Analysis of State-Space Models -- 7.5.1 Stability Analysis of State-Space Models -- 7.5.2 Steady-State Analysis of State-Space Models -- 7.5.3 Transient Analysis of State-Space Models -- 7.6 Special Considerations in State-Space Models -- 7.6.1 Equivalence of State Variables -- 7.6.2 Controllability -- 7.6.3 Observability -- 7.7 Summary -- 7.8 Extended Examples -- 7.8.1 MIMO System Identification of the Apache HTTP Server -- 7.8.2 State-Space Model of the IBM Lotus Domino Server with Sensor Delay -- *7.9 Constructing State-Space Models in MATLAB -- 7.10 Exercises -- PART III CONTROL ANALYSIS AND DESIGN -- 8 Proportional Control -- 8.1 Control Laws and Controller Operation -- 8.2 Desirable Properties of Controllers -- 8.3 Framework for Analyzing Proportional Control -- 8.3.1 Closed-Loop Transfer Functions -- 8.3.2 Stability -- 8.3.3 Accuracy -- 8.3.4 Settling Time -- 8.3.5 Maximum Overshoot -- 8.4 P-Control: Robustness, Delays, and Filters -- 8.4.1 First-Order Target System -- 8.4.2 Measurement Delay -- 8.4.3 Moving-Average Filter -- 8.5 Design of Proportional Controllers -- 8.6 Summary -- 8.7 Extended Examples -- 8.7.1 IBM Lotus Domino Server with a Moving-Average Filter -- 8.7.2 Apache with Precompensation -- 8.7.3 Apache with Disturbance Rejection -- 8.7.4 Effect of Operating Region on M/M/1/K Control -- *8.8 Designing P-Controllers in MATLAB -- 8.9 Exercises -- 9 PID Controllers.

9.1 Integral Control -- 9.1.1 Steady-State Error with Integral Control -- 9.1.2 Transient Response with Integral Control -- 9.2 Proportional-Integral Control -- 9.2.1 Steady-State Error with PI Control -- 9.2.2 PI Control Design by Pole Placement -- 9.2.3 PI Control Design Using Root Locus -- 9.2.4 PI Control Design Using Empirical Methods -- 9.3 Proportional-Derivative Control -- 9.4 PID Control -- 9.5 Summary -- 9.6 Extended Examples -- 9.6.1 PI Control of the Apache HTTP Server Using Empirical Methods -- 9.6.2 Designing a PI Controller for the Apache HTTP Server Using Pole Placement Design -- 9.6.3 IBM Lotus Domino Server with a Sensor Delay -- 9.6.4 Caching with Feedback Control -- *9.7 Designing PI Controllers in MATLAB -- 9.8 Exercises -- 10 State-Space Feedback Control -- 10.1 State-Space Analysis -- 10.2 State Feedback Control Systems -- 10.2.1 Static State Feedback -- 10.2.2 Precompensated Static State Feedback -- 10.2.3 Dynamic State Feedback -- 10.2.4 Comparison of Control Architectures -- 10.3 Design Techniques -- 10.3.1 Pole Placement Design -- 10.3.2 LQR Optimal Control Design -- 10.4 Summary -- 10.5 Extended Examples -- 10.5.1 MIMO Control of the Apache HTTP Server -- 10.5.2 Effect of the LQR Design Parameters in a Dynamic State Feedback System -- *10.6 Designing State-Space Controllers Using MATLAB -- 10.7 Exercises -- 11 Advanced Topics -- 11.1 Motivating Example -- 11.2 Gain Scheduling -- 11.3 Self-Tuning Regulators -- 11.4 Minimum-Variance Control -- 11.5 Fluid Flow Analysis -- 11.6 Fuzzy Control -- 11.7 Summary -- 11.8 Exercises -- APPENDIX A MATHEMATICAL NOTATION -- APPENDIX B ACRONYMS -- APPENDIX C KEY RESULTS -- C.1 Modeling -- C.1.1 Dominant Pole Approximation -- C.1.2 Closed-Loop Transfer Functions -- C.2 Analysis -- C.2.1 Stability -- C.2.2 Settling Time -- C.2.3 Maximum Overshoot -- C.2.4 Steady-State Gain.

C.3 Controller Design -- C.3.1 Control Laws -- C.3.2 Pole Placement Design -- C.3.3 LQR Design -- APPENDIX D ESSENTIALS OF LINEAR ALGEBRA -- D.1 Matrix Inverse, Singularity -- D.2 Matrix Minor, Determinant, and Adjoint -- D.3 Vector Spaces -- D.4 Matrix Rank -- D.5 Eigenvalues -- APPENDIX E MATLAB BASICS -- E.1 Variables and Values -- E.1.1 Vectors -- E.1.2 Matrices -- E.2 Functions -- E.3 Plotting -- E.4 M-files -- E.5 Summary of MATLAB Functions and Commands -- REFERENCES -- INDEX.