Integrated Circuit Design for High-Speed Frequency Synthesis

Appendix A: A Review of Basic Control Theory

A.I Introduction

Control systems are ubiquitous in modern society. They are everywhere and part of just about everyone's life, even if only engineers bother to describe them using equations. The heating system in your house is an example of a feedback system. You request a temperature in your house, and if the temperature falls below this value, the thermostat triggers the furnace to come on and increase the temperature. This is an example of negative feedback (the system takes action to keep the system output at constant level). This system is usually stable and is a well-understood example of a feedback-control system. The stock market is another example of a feedback system. If a stock price falls, triggering more selling and causing the stock price's decline to accelerate, this is an example of positive feedback. If however, a falling stock price encourages people to buy (perhaps they feel the stock is now at a bargain price), this is an example of negative feedback as this will probably cause the stock price to stabilize or rise again. Sadly, there is no equation in this appendix that will predict the stock market, and if the authors knew of one, they would be keeping it to themselves. This system is too complex and has too many inputs to be modeled with the techniques shown here. However, many engineering systems can be modeled using some math, and system behavior can be predicted quite well with control theory.

This appendix is intended to be a...

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