ClosedLoopSysteme

ClosedLoopSysteme, or closed-loop systems, are control systems that regulate a process by continuously comparing the actual output with a desired reference and feeding back a portion of the output to influence the input. The use of feedback aims to reduce error, improve disturbance rejection, and maintain performance under varying conditions.

In a typical feedback loop, a plant P(s) is driven by a controller C(s). The sensor S(s) provides a measurement of the output, which is compared with the reference r(t) to produce an error e(t). The loop is often summarized by the forward path G(s) = C(s)P(s) and a feedback path H(s). The closed-loop transfer from reference to output is T(s) = G(s) / (1 + G(s)H(s)).

Common design approaches include proportional-integral-derivative (PID) controllers, lead-lag compensators, and state-space methods such as full-state feedback, linear quadratic regulation (LQR) and model predictive control (MPC). Digital implementations are widespread, enabling discrete-time control and adaptive strategies that accommodate changing plant dynamics.

Closed-loop systems appear in industrial automation (temperature, level, pressure control), automotive applications (cruise control, engine regulation), robotics, HVAC, and power electronics. They provide accuracy, stability margins, and disturbance rejection, but require careful design to avoid instability, excessive sensitivity to sensor noise, and saturation.

Historically, closed-loop control emerged from developments in control theory in the mid-20th century, with foundational work on stability and frequency response guiding practical implementations.