Chapter 3. System Dynamics

In Chapter 2 we discussed how a feedback loop can drive the output of a system to a desired value. We also described the typical challenges associated with this scheme: making sure that the overall system is stable (meaning that it does, in fact, converge to the preset value) and performs well (so that it converges quickly). However, this is not the whole story.

Lags and Delays

The aspect that we have neglected so far is that many systems do not respond immediately to a control input; instead, they respond with some form of lag or delay. In addition, many systems exhibit even more complicated behavior when stimulated. These factors need to be taken into account when designing a control loop.

Let’s consider a few examples (see Figure 3-1 and Figure 3-2).

A heated vessel:

(Basically, this describes a pot on the stove.) As the heat is turned on, the temperature in the vessel does not immediately jump to its final value; rather, it shows a gradual response. Likewise, when the external heat supply is later shut off, the temperature in the vessel does not drop immediately but instead slowly decays to the ambient temperature. The temperature in the vessel (which is the tracked quantity or “output”) follows the temperature (which is the configurable quantity or “input”), but it lags behind and shows a more “rounded” behavior. This form of rounded, partial response is called a lag.

A tank fed by a pipe:

Imagine a long hose or pipe that feeds into a storage tank. When ...

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