Chapter 17. Case Study: Cooling Fan Speed

A “classic” application of feedback principles is provided by the automatic adjustment of cooling fan speeds in order to maintain some equipment at a desirable temperature—for example, the CPU in a computer or laptop. This system was already introduced in Chapter 5. In contrast to most of the other examples discussed, in this case the governing laws are known at the outset. This shifts the focus of our investigation: rather than trying to obtain a basic, approximate description of the dynamics, we need to find numerical values for the parameters of an existing model.

The Situation

We want to control the speed of cooling fans to maintain a desired temperature of the cooled component. The control output is the temperature, the control input is the fan speed, which is adjustable continuously so that we can treat it as a floating-point number. The heat generated by the CPU depends on its “load,” which we will model as changing by fixed steps at random intervals. We will also assume that the ambient temperature may undergo slow, random drifts. Besides these two effects, the system is essentially deterministic.

As mentioned in Chapter 5, the dynamics we wish to control are the cooling dynamics—that is, the reduction in temperature as the fan speed is increased. The initial state, where the system is considered to be “off,” therefore corresponds to the situation with minimal cooling (with the fan speed reduced to the lowest possible speed that won’t ...

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