Styrfunktion

Styrfunktion (control function) is a term used in control theory and engineering to describe the input function that governs the evolution of a dynamical system. Formally, a system is modeled by ẋ = f(x, u, t) in continuous time or x_{k+1} = f(x_k, u_k, k) in discrete time, where x is the state and u is the control input. The styrfunktion is the rule or function that determines u, directing how the system behaves over time.

The styrfunktion can be open-loop, determined ahead of time, or closed-loop, determined from the current state (state feedback) or time. A common distinction is between feedforward control u = g(t) and feedback control u = h(x, t). In practice, the design goal is to ensure stability, track a reference, reject disturbances, or optimize performance under constraints.

Common control laws include PID controllers, state-feedback laws derived from optimal control (for example, linear-quadratic regulator, LQR), and robust or adaptive schemes. In many problems, the solution is to minimize a cost functional J(u) subject to dynamics, leading to techniques such as solving the Hamilton-Jacobi-Bellman equation or applying dynamic programming.

Styrfunktion is central in many applications: process control in chemical plants, autonomous robotics, aerospace guidance, automotive systems, and building automation. A well-designed styrfunktion improves speed, accuracy, and energy efficiency while maintaining safety margins and respecting physical limitations.