Toestandsfeedback

Toestandsfeedback, translated as state feedback in English, is a control technique in which the current state vector x of a dynamical system is measured or estimated and used to compute the control input u. The goal is to influence the system’s behavior by feedback from the state rather than from the output alone.

In a typical continuous-time linear model x_dot = Ax + Bu, y = Cx + Du, state feedback uses u = -Kx (possibly with a reference term or feedforward). Substituting gives x_dot = (A - BK)x + Br, so the closed-loop dynamics depend on K. With appropriate K, one can place the closed-loop poles to achieve desired stability and response.

Requirements and limitations: full-state feedback assumes access to the complete state vector. If not available, the state must be estimated by an observer (for example, a Luenberger observer or Kalman filter), leading to output feedback or LQG architectures. Controllability of (A,B) is needed for arbitrary pole placement; robustness to model uncertainty and actuator saturation are common concerns.

Variants and extensions: integral action, dynamic compensators, decentralized or robust state feedback. A common optimization approach is the linear-quadratic regulator (LQR), which selects K to minimize a cost function J = ∫(x^T Q x + u^T R u) dt. State feedback is widely used in robotics, aerospace, and process control to achieve fast, stable, and predictable responses.