Log In
Or create an account ->
Imperial Library
Home
About
News
Upload
Forum
Help
Login/SignUp
Index
Feedback Control for Computer Systems
Preface
What Is Feedback?
Why This Book?
How to Read This Book
Conventions Used in This Book
Using Code Examples
Safari® Books Online
How to Contact Us
Acknowledgments
I. Foundations
1. Why Feedback? An Invitation
A Hands-On Example
Hoping for the Best
Establishing Control
Adding It Up
Summary
Code to Play With
2. Feedback Systems
Systems and Signals
Tracking Error and Corrective Action
Stability, Performance, Accuracy
The Setpoint
Uncertainty and Change
Feedback and Feedforward
Feedback and Enterprise Systems
Code to Play With
3. System Dynamics
Lags and Delays
Forced Response and Free Response
Transient Response and Steady-State Response
Dynamics in the Physical World and in the Virtual World
Dynamics and Memory
The Importance of Lags and Delays for Feedback Loops
Avoiding Delays
Theory and Practice
Code to Play With
4. Controllers
Block Diagrams
On/Off Control
Proportional Control
Why Proportional Control Is Not Enough
Integral Control
Integral Control Changes the Dynamics
Integral Control Can Generate a Constant Offset
Derivative Control
Problems with Derivative Control
The Three-Term or PID Controller
Code to Play With
5. Identifying Input and Output Signals
Control Input and Output
Directionality of the Input/Output Relation
Examples
Thermal Control 1: Heating
Situation
Input
Output
Commentary
Item Cache
Situation
Input
Output
Commentary
Server Scaling
Situation
Input
Output
Commentary
Controlling Supply and Demand by Dynamic Pricing
Situation
Input
Output
Commentary
Thermal Control 2: Cooling
Situation
Input
Output
Commentary
Criteria for Selecting Control Signals
For Control Inputs
For Control Outputs
A Note on Multidimensional Systems
6. Review and Outlook
The Feedback Idea
Iteration
Process Knowledge
Avoiding Instability
The Setpoint
Control, Not Optimization
II. Practice
7. Theory Preview
Frequency Representation
The Transfer Function
Block-Diagram Algebra
PID Controllers
Poles of the Transfer Function
Process Models
8. Measuring the Transfer Function
Static Input/Output Relation: The Process Characteristic
Practical Considerations
Dynamic Response to a Step Input: The Process Reaction Curve
Practical Aspects
Process Models
Self-Regulating Process
Accumulating Process
Self-Regulating Process with Oscillation
Non-Minimum Phase System
Other Methods of System Identification
9. PID Tuning
Tuning Objectives
General Effect of Changes to Controller Parameters
Ziegler–Nichols Tuning
Semi-Analytical Tuning Methods
Practical Aspects
A Closer Look at Controller Tuning Formulas
10. Implementation Issues
Actuator Saturation and Integrator Windup
Preventing Integrator Windup
Setpoint Changes and Integrator Preloading
Smoothing the Derivative Term
Choosing a Sampling Interval
Variants of the PID Controller
Incremental Form
Error Feedback Versus Output Feedback
The General Linear Digital Controller
Nonlinear Controllers
Error-Square and Gap Controllers
Simulating Floating-Point Output
Categorical Output
11. Common Feedback Architectures
Changing Operating Conditions: Gain Scheduling
Gain Scheduling for Mildly Nonlinear Systems
Large Disturbances: Feedforward
Fast and Slow Dynamics: Nested or “Cascade” Control
Systems Involving Delays: The Smith Predictor
III. Case Studies
12. Exploring Control Systems Through Simulation
The Case Studies
Modeling Time
Control Time
Simulation Time
The Simulation Framework
Components
Plants and Systems
Controllers
Actuators and Filters
Convenience Functions for Standard Loops
Generating Graphical Output
13. Case Study: Cache Hit Rate
Defining Components
Cache Misses as Manufacturing Defects
Measuring System Characteristics
Controller Tuning
Simulation Code
14. Case Study: Ad Delivery
The Situation
Measuring System Characteristics
Establishing Control
Improving Performance
Variations
Cumulative Goal
Gain Scheduling
Integrator Preloading
Weekend Effects
Simulation Code
15. Case Study: Scaling Server Instances
The Situation
Measuring and Tuning
Reaching 100 Percent With a Nonstandard Controller
Dealing with Latency
Simulation Code
16. Case Study: Waiting-Queue Control
On the Nature of Queues and Buffers
The Architecture
Setup and Tuning
Derivative Control to the Rescue
Controller Alternatives
Simulation Code
17. Case Study: Cooling Fan Speed
The Situation
The Model
Tuning and Commissioning
Closed-Loop Performance
Simulation Code
18. Case Study: Controlling Memory Consumption in a Game Engine
The Situation
Problem Analysis
Architecture Alternatives
A Nontraditional Loop Arrangement
A Traditional Loop with Logarithms
Results
Simulation Code
19. Case Study Wrap-Up
Simple Controllers, Simple Loops
Measuring and Tuning
Staying in Control
Dealing with Noise
IV. Theory
20. The Transfer Function
Differential Equations
Laplace Transforms
Properties of the Laplace Transform
Using the Laplace Transform to Solve Differential Equations
A Worked Example
The Transfer Function
Worked Example: Step Response
Worked Example: Ramp Input
The Harmonic Oscillator
What If the Differential Equation Is Not Known?
21. Block-Diagram Algebra and the Feedback Equation
Composite Systems
The Feedback Equation
An Alternative Derivation of the Feedback Equation
Block-Diagram Algebra
Limitations and Importance of Transfer Function Methods
22. PID Controllers
The Transfer Function of the PID Controller
The Canonical Form of the PID Controller
The General Controller
Proportional Droop Revisited
A Worked Example
23. Poles and Zeros
Structure of a Transfer Function
Effect of Poles and Zeros
Special Cases and Additional Details
Complex conjugate poles
Multiple poles
Poles on the imaginary axis
Pole/zero cancellations
Pole Positions and Response Patterns
Dominant Poles
Pole Placement
What to Do About Delays
24. Root Locus Techniques
Construction of Root Locus Diagrams
Root Locus or “Evans” Rules
Angle and Magnitude Criteria
Practical Issues
Examples
Simple Lag with a P Controller
Simple Lag with a PI Controller
25. Frequency Response and the Bode Plot
Frequency Response
Frequency Response in the Physical World
Frequency Response for Transfer Functions
A Worked Example
The Bode Plot
A Criterion for Marginal Stability
Other Graphical Techniques
26. Topics Beyond This Book
Discrete-Time Modeling and the z-Transform
State-Space Methods
Robust Control
Optimal Control
Mathematical Control Theory
V. Appendices
A. Glossary
B. Creating Graphs with Gnuplot
Basic Plotting
Plot Ranges
Inline Transformations
Plotting Simulation Results
Summary
C. Complex Numbers
Basic Operations
Polar Coordinates
The Complex Exponential
D. Further Reading
Recommended Reading
Additional References
Mathematical Prerequisites
Index
Colophon
Copyright
← Prev
Back
Next →
← Prev
Back
Next →