Feedback control

Feedback control is the discipline in which system dynamics are studied and altered by creating feedback loops. It is applied in many different fields such as electrical engineering (circuit design), chemical engineering (process control), and mechanical and astro/aeronautical engineering (e.g. consider flight and propulsion systems, cruise control).

The block diagram for applying feedback control to a system is shown in Figure 1. This could be the block diagram for a cruise controller, where the car's velocity $x$ would be driven to a target velocity $x_{target}$. $u$ would be the rate at which gasoline were combusted, and $r$ would be how far the gas pedal were pushed down by the driver. When no control were applied (i.e. $u=r$), certain system dynamics would describe the car's velocity $x$ as a function of the gas $r$. A physical model describing this relationship could be developed and inserted into the block labeled ``System'' (see Figure 1). A simple physical model would probably assume that the road were flat, while a more accurate physical model would also take the steepness of the road into account. Either way, control theory could be used to derive appropriate contents for the ``Controller'' block in Figure 1 so that the composite, controlled system would behave in an altered, preferred manner.

Figure 1: Standard block diagram for a feedback control system.

Figure 1 could just as well describe feedback control of a vibrating string. Here the ``System'' block would describe the vibrating string dynamics, and ``Controller'' would describe the electrical circuit connected between a string vibration sensor and string actuator.