Control system

A control system is an interconnection that chooses and applies control inputs to influence a controlled plant. A controller may use a reference signal, a measured output and internal state to determine those inputs. The plant, sensing, controller and input mechanism jointly determine the resulting motion. In open-loop control, the commands are chosen without updating them from the measured result; feedback control uses that result to change the commands.

An original dimensionless model shows the distinction. Let the measured output equal the plant state $x$ and let $d$ be a constant control disturbance:The open-loop command $u=r=1$ gives equilibrium $x=1+d$. A controller using both the reference command and measured tracking error can instead setSubstitution gives $\dot{x}=-(1+k)x+(1+k)r+d$. Its equilibrium and transient areWith $k=2$ and $d=0.3$, the equilibrium is1.1 instead of the open-loop value1.3. The controller reacts to the effect of the disturbance through the measured state; it need not measure $d$ separately. With no disturbance, the explicit reference term makes the equilibrium equal to1.

The interconnection matters as much as the controller formula. Measurement error changes the quantity fed back, actuator saturation can prevent delivery of the commanded input, and unmodeled dynamics can change the transient. The assumption that the entire plant state is measured is also special to this example.

Robust control asks how such a closed loop behaves across a family of possible models, distinguishing robust stability from robust performance.^[ref] A complete control-system specification therefore identifies the plant, signals, interconnection, physical limits and response criterion, rather than naming only a controller.