prosessifunktion

Prozessifunktion, or process function, is a mathematical representation of how a process transforms inputs into outputs. It captures the essential mapping that links external stimuli, control actions, and disturbances to the observable behavior of a system. In practice, a prosessifunktion may depend on time, internal state, and parameter values, and it can describe both static relationships and dynamic evolution.

A typical formulation distinguishes inputs, outputs, and state variables. In continuous time, a dynamic model can be written as y(t) = f(x(t), u(t), d(t), t; θ) for the output, with the internal state evolving via dx/dt = h(x(t), u(t), d(t), t; φ). In discrete time, the evolution is x[k+1] = g(x[k], u[k], d[k], k; φ), y[k] = f(x[k], u[k], d[k], k; θ). Models may be deterministic or stochastic, linear or nonlinear, and may operate at different abstraction levels from first-principles to data-driven approximations.

Transfer function and state-space representations are common ways to express a prosessifunktion in control engineering. For linear time-invariant systems, the transfer function relates inputs to outputs in the frequency domain, while state-space models provide a time-domain description that accommodates multi-input, multi-output behavior and internal dynamics.

Applications include process control design, optimization, simulation, and diagnostic testing in chemical engineering, manufacturing, energy systems, and related fields. Determination of a prosessifunktion typically involves mechanistic modeling, empirical system identification, or a combination of both, followed by validation and uncertainty assessment. See also process modeling, system identification, transfer function, and state-space representation.