Examples

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Chapter 3 - Examples

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In this chapter we present a collection of examples spanning many different fields of science and engineering. These examples will be used throughout the text and in exercises to illustrate different concepts. First time readers may wish to focus only on a few examples with which they have the most prior experience or insight to understand the concepts of state, input, output, and dynamics in a familiar setting.

Textbook Contents Examples (pdf, 28Sep12) 1. Cruise control 2. Bicycle dynamics 3. Operational amplifier 4. Computing Systems and Networks Web server control Congestion control 5. Atomic force microscope 6. Drug administration Compartment model Insulin-glucose dynamics 7. Population dynamics Predator prey Exercises

Lecture Materials Additional Exercises Supplemental Information Frequently Asked Questions Errata Additional Examples Wikipedia entries: cruise control, op amp, atomic force microscope, population dynamics Additional Information

Chapter Summary

This chapter describes a collection of examples that illustrate some of the diverse applications of feedback.

1. The cruise control system of a car is one of the most common control systems encountered in everyday life. The system attempts to keep the speed of the car constant in spite of disturbances caused by changing slope of the road and variations in the wind and road conditions. The system measures the speed of the car and adjusts the throttle.

2. The dynamics of a bicycle provide an example of how simple models can be used to give important insights into the behavior of a complex system. Using simple models, we can understand how tilting a bicycle affects its motion and stability properties.

3. The operational amplifier (op amp) is a modern implementation of Black's feedback amplifier. It is a universal component that is widely used for for instrumentation, control, and communication. It is also a key element in analog computing.

4. Web server admission control is used to help regulate the flow of requests to a web server and insure good performance even under high load. A continuous time model can be used to understand nonlinear feedback strategies for improving the performance of the system.

5. Atomic force microscople are used to provide molecular-scale imaging by moving an atomically sharp tip across a sample. Feedback is used to maintain a constant force on the sample and provide a signal that describes the height of the surface.

6. Drug administration involves maintaining the concentration of a drug in one's body by control the rate at which drugs are given. Compartment models allow analysis of the rate of diffusion of the drug in the body.

7. Population dynamics allow prediction of species populations in controlled and natural ecosystems. The models for these systems are often nonlinear in nature and include effects such as birth rates, environmental capacity limits and predators.

Frequently Asked Questions FAQ: In the predator prey example, where is the fox birth rate term? FAQ: In the two compartment model, what does q0 represent? FAQ: What are the parameters for the Whipple bicycle model? FAQ: Why do the two terms for the rate of change of the congestion control window size in equation (3.16) have different units? FAQ: Why isn't there a term for the rabbit death rate besides being killed by the foxes?

Errata Errata: A21 entry for op amp dynamics should have a negative sign No errata reported in most recent version of this chapter Full list of errata starting from first printing Submit bug report Additional Information Control tutorials for MATLAB (U. Michigan)