Topical Guide 610
Mark Dorset
Gadgets: Control Systems: Feedback
Where Do You Stop? Chapter 20:
I knew that Guppa even had a suitable gadget nearly ready. […] It was a device for watering the garden automatically. […] The principle was similar to—but the reverse of—the method that fills a toilet tank to a certain level. In a toilet tank (and you can confirm this in the privacy of your own home), a floating ball rises with the rising water. Through a set of rods and pivots, the ball is linked to a valve. As the ball rises, the valve closes.
Arthur L. Stevens, “Control Systems in Engineering, Nature and Society”:
A flushing toilet is a simple and widely known example of a feedback control system. After a toilet is flushed, the water tank must be refilled to a suitable level. Imagine how inconvenient it would be if we had to open a tap, wait until the correct level was reached, and then close the tap. Fortunately a simple control system using a valve controlled by a floating ball takes care of this task on our behalf.
Figure 4 is a diagram of the flushing toilet and its simplified block diagram model.
The floating ball is used to measure the water level h and turn the valve on or off. The rate of rise of the level in the tank is proportional to the flow rate and inversely proportional to the tank area A. The level is given by the integral of the rate of change of level. When the tank is empty after being flushed, the position of the float near the tank bottom causes the valve to open fully, allowing water to flow into the tank at a rate of Qv litres per second.
The difference between the desired water level c and the actual level h is large and the valve is fully open providing a large actuation signal, that is, a large flow rate. As the water level rises the error decreases, slowing down the flow of water until the error reaches zero, whereupon the valve shuts off and the flow stops (Qv=0). Thus, the negative feedback control system ensures that the actual level reaches the desired level and stays there until the next flush occurs. […]
Feedback control is a fundamental principle of nature and an enabling technology for humankind. The aim of this article has been to demonstrate the pervasiveness of this principle across such diverse fields as engineering, natural science and society.
It is reasonably certain that with the progression of time, future investigations will show that every complex dynamical system, ranging from biological evolution, psychology and stock market dynamics to the creation of stars and planets in our universe, are all feedback systems.
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