Feedback control a closer look

Mathematically, the error drives the action of the controller. The sign of this error is an important consideration, and requires more development than one might expect. Let us begin with the notion of positive and negative feedback. 

Positive feedback represents a controller contribution that reinforces the error therefore, it precludes stability. Consider the audio feedback that occurs when a microphone is placed too close to the speaker that amplifies the microphone s output. Sound from the miCTOphone is amplified through the speaker. If this sound re-enters the microphone, it adds to itself, and so on until the speaker saturates with a deafening tone. This is an example of positive feedback. Since positive feedback has no useful purpose for automatic control, we will consider it no further. 

Negative feedback represents a controller contribution that diminishes the error therefore, it tends to add to stability. The cruise control in our automobile example works with negative feedback. If the speed is too high, then the controller cuts back on the flow of the air-fuel mixture, thereby reducing the error. The opposite happens when the speed is too low. 

As you can see, oifly negative feedback presents a viable control loop capable of maintaining stability. However, there are many different elements in a typical control loop, each one with a potentially reinforcing or subtracting contribution. Thus, we need to understand the action of each component in the loop in order to determine whether, in the aggregate, the control loop will provide negative feedback. By action, we typically mean the sign relationship between an element s input and output. The next section will explain this. 

Let us first look at the action of the process element of the controller. Consider a fiimace that heats your home in the winter. When the energy that drives the furnace increases, the temperature in the surrounding rooms increases as well. This is known as an increase/increase (I/l) relationship, or a direct-acting element [5]. Direct action refers to a control-loop element that, for an increase in its input, also experiences an increase in its output. 

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