Feedback Control Systems

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Introduction
Your body is jammed full of feedback control systems. A few examples of things so controlled are: Blood pressure; blood volume; body temperature; circulating glucose levels (by insulin); blood partial pressures of carbon dioxide and oxygen (PCO2 , PO2 ); pH; hormone levels; thousands of proteins that keep cells alive and functioning. Without these control systems, life would not be possible. These are just a few examples. Open a physiology textbook at random and you will be reading about some part of some control system. (As a challenge, try to think of a process that is not under feedback control.)


What Good is Negative feedback?
Mother Nature discovered negative feedback millions of years ago and obviously found it to be GOOD (we discovered it in the 1930s in the labs of Ma Bell). So what's so good about it?
Let's take Fig. 1 and reduce it to its bare, universal form. Let the gains of SA, LV and R be multiplied and call the net result G. Let the feedback gain Rb/P be 1.0 for this example.


Reminder & A Little History
You have probably already learned about Laplace transforms and Bode diagrams. These tools are essential for systems analysis so we review what is relevant here, with some historical comments thrown in to show you where Laplace transforms came from.


Sine Waves
Sine waves almost never occur in biological systems but physiologists still use them experimentally. This is mostly because they wish to emulate systems engineering and use its trappings. But why do systems engineers use sine waves? They got started because the rotating machinery that generated electricity in the late 19th century produced sine waves. This is still what you get from your household outlet. This led, in the early 20th century, to methods of analyzing circuits with impedances due to resistors ( R ), capacitors ( 1/jωC ) and inductors ( jωL ) - all based on sine waves.1