= Control system
A \b[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>:
$$
\dot x=-x+u+d,\qquad r=1.
$$
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 set
$$
u=r+k(r-x),\qquad k\geq0.
$$
Substitution gives $\dot x=-(1+k)x+(1+k)r+d$. Its equilibrium and transient are
$$
x_{\rm eq}=r+\frac{d}{1+k},\qquad
x(t)=x_{\rm eq}+[x(0)-x_{\rm eq}]e^{-(1+k)t}.
$$
With $k=2$ 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>.<Robust Stability, Robust Performance, and Mu Analysis in MATLAB documentation>[Introduction and distinction between robust stability and performance]{ref} A complete control-system specification therefore identifies the plant, signals, interconnection, physical limits and response criterion, rather than naming only a controller.
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