Feedback control of computing systems

Title:

Publication Information:

Hoboken, NJ : John Wiley & Sons, 2004

ISBN:

9780471266372

Subject Term:

Feedback control systems

Control theory

Electronic data processing

Added Author:

Hellerstein, Joseph, 1952-

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010082180	TJ216 F43 2004	Open Access Book	Book	Searching... Unknown

This is the first practical treatment of the design and application of feedback control of computing systems. MATLAB files for the solution of problems and case studies accompany the text throughout. The book discusses information technology examples, such as maximizing the efficiency of Lotus Notes.
This book results from the authors' research into the use of control theory to model and control computing systems. This has important implications to the way engineers and researchers approach different resource management problems. This guide is well suited for professionals and researchers in information technology and computer science.

Author Notes

JOSEPH L. HELLERSTEIN, YIXIN DIAO, and SUJAY PAREKH are researchers at the IBM Thomas J. Watson Research Center in Hawthorne, New York. They are also adjunct professors at Columbia University, where they are using this book to teach a class on feedback control to computer science students.

DAWN M. TILBURY is Associate Professor of Mechanical Engineering at the University of Michigan.

Preface	p. xv
Part I Background	p. 1
1 Introduction and Overview	p. 3
1.1 The Nature of Feedback Control	p. 3
1.2 Control Objectives	p. 6
1.3 Properties of Feedback Control Systems	p. 7
1.4 Open-Loop versus Closed-Loop Control	p. 10
1.5 Summary of Applications of Control Theory to Computing Systems	p. 11
1.6 Computer Examples of Feedback Control Systems	p. 13
1.6.1 IBM Lotus Domino Server	p. 13
1.6.2 Queueing Systems	p. 15
1.6.3 Apache HTTP Server	p. 16
1.6.4 Random Early Detection of Router Overloads	p. 19
1.6.5 Load Balancing	p. 20
1.6.6 Streaming Media	p. 21
1.6.7 Caching with Differentiated Service	p. 22
1.7 Challenges in Applying Control Theory to Computing Systems	p. 24
1.8 Summary	p. 26
1.9 Exercises	p. 27
Part II System Modeling	p. 29
2 Model Construction	p. 31
2.1 Basics of Queueing Theory	p. 31
2.2 Modeling Dynamic Behavior	p. 35
2.2.1 Model Variables	p. 35
2.2.2 Signals	p. 35
2.2.3 Linear, Time-Invariant Difference Equations	p. 38
2.2.4 Nonlinearities	p. 40
2.3 First-Principles Models	p. 42
2.4 Black-Box Models	p. 44
2.4.1 Model Scope	p. 45
2.4.2 Experimental Design	p. 47
2.4.3 Parameter Estimation	p. 49
2.4.4 Model Evaluation	p. 53
2.5 Summary	p. 56
2.6 Extended Examples	p. 56
2.6.1 IBM Lotus Domino Server	p. 56
2.6.2 Apache HTTP Server	p. 57
2.6.3 M/M/1/K Comparisons	p. 58
2.7 Parameter Estimation Using MATLAB	p. 59
2.8 Exercises	p. 62
3 Z-Transforms and Transfer Functions	p. 65
3.1 Z-Transform Basics	p. 65
3.1.1 Z-Transform Definition	p. 66
3.1.2 Z-Transforms of Common Signals	p. 68
3.1.3 Properties of Z-Transforms	p. 71
3.1.4 Inverse Z-Transforms	p. 74
3.1.5 Using Z-Transforms to Solve Difference Equations	p. 75
3.2 Characteristics Inferred from Z-Transforms	p. 81
3.2.1 Review of Complex Variables	p. 81
3.2.2 Poles and Zeros of a Z-Transform	p. 83
3.2.3 Steady-State Analysis	p. 86
3.2.4 Time Domain versus Z-Domain	p. 88
3.3 Transfer Functions	p. 89
3.3.1 Stability	p. 92
3.3.2 Steady-State Gain	p. 95
3.3.3 System Order	p. 96
3.3.4 Dominant Poles and Model Simplification	p. 96
3.3.5 Simulating Transfer Functions	p. 100
3.4 Summary	p. 102
3.5 Extended Examples	p. 103
3.5.1 M/M/1/K from System Identification	p. 103
3.5.2 IBM Lotus Domino Server: Sensor Delay	p. 103
3.5.3 Apache HTTP Server: Combining Control Inputs	p. 104
3.6 Z-Transforms and MATLAB	p. 105
3.7 Exercises	p. 107
4 System Modeling with Block Diagrams	p. 111
4.1 Block Diagrams Basics	p. 111
4.2 Transforming Block Diagrams	p. 115
4.2.1 Special Aggregations of Blocks	p. 115
4.3 Transfer Functions for Control Analysis	p. 116
4.4 Block Diagram Restructuring	p. 119
4.5 Summary	p. 120
4.6 Extended Examples	p. 121
4.6.1 IBM Lotus Domino Server	p. 121
4.6.2 Apache HTTP Server with Control Loops	p. 123
4.6.3 Streaming	p. 124
4.7 Composing Transfer Functions in MATLAB	p. 126
4.8 Exercises	p. 128
5 First-Order Systems	p. 129
5.1 First-Order Model	p. 129
5.2 System Response	p. 131
5.2.1 Steady-State and Transient Responses	p. 131
5.2.2 Input Signal Model	p. 133
5.2.3 Time-Domain Solution	p. 133
5.3 Initial Condition Response	p. 135
5.4 Impulse Response	p. 136
5.5 Step Response	p. 141
5.5.1 Numerical Example	p. 141
5.5.2 Time-Domain Solution	p. 141
5.5.3 Steady-State Response	p. 143
5.5.4 Transient Response	p. 144
5.6 Transient Response to Other Signals	p. 147
5.6.1 Ramp Response	p. 147
5.6.2 Frequency Response	p. 150
5.7 Effect of Stochastics	p. 152
5.8 Summary	p. 154
5.9 Extended Examples	p. 156
5.9.1 Estimating Operating Region of the Apache HTTP Server	p. 156
5.9.2 IBM Lotus Domino Server with a Disturbance	p. 157
5.9.3 Feedback Control of the IBM Lotus Domino Server	p. 159
5.10 Analyzing Transient Response with MATLAB	p. 161
5.11 Exercises	p. 162
6 Higher-Order Systems	p. 165
6.1 Motivation and Definitions	p. 165
6.2 Real Poles	p. 168
6.2.1 Initial Condition Response	p. 168
6.2.2 Impulse Response	p. 171
6.2.3 Step Response	p. 174
6.2.4 Other Signals	p. 176
6.2.5 Effect of Zeros	p. 177
6.3 Complex Poles	p. 179
6.3.1 Second-Order System	p. 179
6.3.2 Impulse Response	p. 181
6.3.3 Step Response	p. 183
6.4 Summary	p. 185
6.5 Extended Examples	p. 186
6.5.1 Apache HTTP Server with a Filter	p. 186
6.5.2 Apache HTTP Server with a Filter and Controller	p. 189
6.5.3 IBM Lotus Domino Server with a Filter and Controller	p. 191
6.5.4 M/M/1/K with a Filter and Controller	p. 192
6.6 Analyzing Transient Response with MATLAB	p. 196
6.7 Exercises	p. 197
7 State-Space Models	p. 201
7.1 State Variables	p. 201
7.2 State-Space Models	p. 204
7.3 Solving Difference Equations in State Space	p. 207
7.4 Converting Between Transfer Function Models and State-Space Models	p. 211
7.5 Analysis of State-Space Models	p. 216
7.5.1 Stability Analysis of State-Space Models	p. 216
7.5.2 Steady-State Analysis of State-Space Models	p. 218
7.5.3 Transient Analysis of State-Space Models	p. 220
7.6 Special Considerations in State-Space Models	p. 221
7.6.1 Equivalence of State Variables	p. 221
7.6.2 Controllability	p. 222
7.6.3 Observability	p. 225
7.7 Summary	p. 228
7.8 Extended Examples	p. 229
7.8.1 MIMO System Identification of the Apache HTTP Server	p. 229
7.8.2 State-Space Model of the IBM Lotus Domino Server with Sensor Delay	p. 234
7.9 Constructing State-Space Models in MATLAB	p. 237
7.10 Exercises	p. 239
Part III Control Analysis and Design	p. 243
8 Proportional Control	p. 245
8.1 Control Laws and Controller Operation	p. 245
8.2 Desirable Properties of Controllers	p. 252
8.3 Framework for Analyzing Proportional Control	p. 254
8.3.1 Closed-Loop Transfer Functions	p. 255
8.3.2 Stability	p. 257
8.3.3 Accuracy	p. 258
8.3.4 Settling Time	p. 260
8.3.5 Maximum Overshoot	p. 260
8.4 P-Control: Robustness, Delays, and Filters	p. 261
8.4.1 First-Order Target System	p. 261
8.4.2 Measurement Delay	p. 266
8.4.3 Moving-Average Filter	p. 268
8.5 Design of Proportional Controllers	p. 271
8.6 Summary	p. 275
8.7 Extended Examples	p. 276
8.7.1 IBM Lotus Domino Server with a Moving-Average Filter	p. 276
8.7.2 Apache with Precompensation	p. 278
8.7.3 Apache with Disturbance Rejection	p. 282
8.7.4 Effect of Operating Region on M/M/1/K Control	p. 282
8.8 Designing P-Controllers in MATLAB	p. 286
8.9 Exercises	p. 289
9 PID Controllers	p. 293
9.1 Integral Control	p. 293
9.1.1 Steady-State Error with Integral Control	p. 294
9.1.2 Transient Response with Integral Control	p. 296
9.2 Proportional-Integral Control	p. 301
9.2.1 Steady-State Error with PI Control	p. 303
9.2.2 PI Control Design by Pole Placement	p. 303
9.2.3 PI Control Design Using Root Locus	p. 307
9.2.4 PI Control Design Using Empirical Methods	p. 309
9.3 Proportional-Derivative Control	p. 315
9.4 PID Control	p. 320
9.5 Summary	p. 324
9.6 Extended Examples	p. 325
9.6.1 PI Control of the Apache HTTP Server Using Empirical Methods	p. 325
9.6.2 Designing a PI Controller for the Apache HTTP Server Using Pole Placement Design	p. 327
9.6.3 IBM Lotus Domino Server with a Sensor Delay	p. 328
9.6.4 Caching with Feedback Control	p. 330
9.7 Designing PI Controllers in MATLAB	p. 332
9.8 Exercises	p. 333
10 State-Space Feedback Control	p. 337
10.1 State-Space Analysis	p. 337
10.2 State Feedback Control Systems	p. 339
10.2.1 Static State Feedback	p. 340
10.2.2 Precompensated Static State Feedback	p. 342
10.2.3 Dynamic State Feedback	p. 346
10.2.4 Comparison of Control Architectures	p. 351
10.3 Design Techniques	p. 353
10.3.1 Pole Placement Design	p. 353
10.3.2 LQR Optimal Control Design	p. 358
10.4 Summary	p. 362
10.5 Extended Examples	p. 364
10.5.1 MIMO Control of the Apache HTTP Server	p. 364
10.5.2 Effect of the LQR Design Parameters in a Dynamic State Feedback System	p. 370
10.6 Designing State-Space Controllers Using MATLAB	p. 372
10.7 Exercises	p. 373
11 Advanced Topics	p. 375
11.1 Motivating Example	p. 376
11.2 Gain Scheduling	p. 378
11.3 Self-Tuning Regulators	p. 381
11.4 Minimum-Variance Control	p. 384
11.5 Fluid Flow Analysis	p. 386
11.6 Fuzzy Control	p. 389
11.7 Summary	p. 393
11.8 Exercises	p. 395
Appendix A Mathematical Notation	p. 397
Appendix B Acronyms	p. 401
Appendix C Key Results	p. 403
C.1 Modeling	p. 403
C.1.1 Dominant Pole Approximation	p. 403
C.1.2 Closed-Loop Transfer Functions	p. 403
C.2 Analysis	p. 404
C.2.1 Stability	p. 404
C.2.2 Settling Time	p. 405
C.2.3 Maximum Overshoot	p. 405
C.2.4 Steady-State Gain	p. 405
C.3 Controller Design	p. 405
C.3.1 Control Laws	p. 405
C.3.2 Pole Placement Design	p. 406
C.3.3 LQR Design	p. 407
Appendix D Essentials of Linear Algebra	p. 409
D.1 Matrix Inverse, Singularity	p. 409
D.2 Matrix Minor, Determinant, and Adjoint	p. 409
D.3 Vector Spaces	p. 410
D.4 Matrix Rank	p. 411
D.5 Eigenvalues	p. 411

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