Thursday, March 18, 2010

Feedback Systems

Feedback systems are comprised of several parts. In this section we will introduce the different components of an overall feedback system and explain what each of them do:

The two main components of a feedback system are the original system and the compensator.

The original system, is also called the plant.

The central component of the control system is the compensator. This is the brain of the control system. Given a plant, our overall goal is to design a compensator, to command the plant to perform as we desire.

The reference input is the desired output we want. For example, a certain position. Sometimes the system cannot understand the reference input. Therefore, it needs to be “translated”. For example, a rover robot’s computer does not understand what a distance of 5m means. Therefore, this reference input is converted to a certain voltage, which the computer is able to understand. This “conversion” is done through an input transducer. The same is true for the output signal; the actual output sensed is “converted” to a system-readable format through an output transducer. It is important to note that the scale of conversion is not always unity; in some cases 5m means 5v. This is called unity feedback. However, in some cases we have non-unity feedback; in these cases there exists a certain scaling factor (gain) between the actual signal and the system-readable signal. It is important to note which case we have, as the analysis for each is different.

The actual output is the actual behavior of the plant.

The feedback path is the actual output signal being fed back to the system.

The summing junction subtracts the actual output (which was fed back) from the reference input (desired output).

The result is called the error.

The error is fed into the compensator. The compensator then generates and commands a control signal which is based on the error. This control signal then drives the plant.

This overall process is repeated until the plant performs our desired output.

Now that we have become familiar with a control system’s components (and reasons for having a control system) we would like to see how we can design one?! The first step in designing a control system is understanding your plant dynamics. This means you have to have mathematical models of your system’s parts. We will talk about this important first step in the next section.