Tilapalautekytkentä

Tilapalautekytkentä, often translated as state feedback control, is a method used in control theory to design controllers for dynamic systems. It is a cornerstone of modern control engineering, offering a systematic approach to achieving desired system behavior. The core idea of tilapalautekytkentä is to use all available state variables of a system to influence its dynamics.

In a system described by state-space representation, the state variables represent the internal configuration of the system at any given time. Tilapalautekytkentä involves designing a controller that calculates a control input based on a linear combination of these state variables. This control law is typically expressed as u = -Kx, where u is the control input, x is the state vector, and K is the state feedback gain matrix. The negative sign is conventional, indicating that the feedback opposes the current state.

The primary advantage of tilapalautekytkentä is its ability to arbitrarily place the closed-loop poles of the system. By choosing the elements of the gain matrix K appropriately, the designer can shape the system's transient response, ensuring desired characteristics such as speed of response, damping, and stability. This pole placement capability makes it a powerful tool for achieving precise control objectives.

Implementing tilapalautekytkentä requires knowledge of the system's internal states. In many practical scenarios, not all state variables are directly measurable. In such cases, an observer (or state estimator) is used to reconstruct the unmeasured states from available output measurements. The combination of a controller and an observer forms a state feedback control system with an observer.